Improving Maths Education in Rural Honduras
A research study on maths teaching and learning in the Sistema de Aprendizaje Tutorial (SAT)
Sarah Richards, Consultant
August 2010
2
This report is dedicated to the Baha’i youth of Iran.
They have been denied access to higher education for decades,
and are beacons of hope, compassion and fortitude.
3
Contents Acknowledgements .......................................................................................................................................................... 5
Executive Summary ....................................................................................................................................................... 6
Background ...................................................................................................................................................................... 11
Objectives .......................................................................................................................................................................... 13
Methodology .................................................................................................................................................................... 13
Limitations of the study .............................................................................................................................................. 13
Creating an atmosphere of consultation .............................................................................................................. 15
In the classroom ........................................................................................................................................................ 15
Improving the educational value of classroom talk ................................................................................... 17
General Training and consultation skills ........................................................................................................ 19
The use of questions and answers .......................................................................................................................... 20
Allowing time for reflection ................................................................................................................................. 20
Questions: increasing participation .................................................................................................................. 20
Questioning: a formative assessment tool ..................................................................................................... 21
Tutor/student questions ....................................................................................................................................... 22
Three ways of working ................................................................................................................................................ 22
The use of tutor/student presentations of work ......................................................................................... 23
Working in small groups........................................................................................................................................ 25
Peer teaching and ‘social loafing’ .................................................................................................................. 25
A forgotten method? .......................................................................................................................................... 26
Individual work: the third force ......................................................................................................................... 27
Thinking time ........................................................................................................................................................ 27
Formative Assessment: fine tuning acompanimiento ..................................................................................... 28
Taking responsibility for learning .......................................................................................................................... 28
Unsupervised working ........................................................................................................................................... 29
Homework ................................................................................................................................................................... 29
Formative assessment helps students take responsibility for learning ............................................ 29
Tools and Representations ........................................................................................................................................ 30
The importance of the texts.................................................................................................................................. 30
Multiple representations ....................................................................................................................................... 31
Updating and revision of texts ............................................................................................................................ 33
Guías de Aprendizaje y Evaluación (Ciclo Común) ..................................................................................... 35
Practical application of maths ............................................................................................................................. 37
4
Statistics ....................................................................................................................................................................... 37
Linking SAT and community maths .................................................................................................................. 38
Evaluation ......................................................................................................................................................................... 38
Community Evaluation ........................................................................................................................................... 39
Evaluation – testing and retesting..................................................................................................................... 40
Maths: a problematic part of the program ..................................................................................................... 40
Percentages of retakes for 2008 ......................................................................................................................... 40
Comparing SAT performance with the government system .................................................................. 41
Tutors and mathematics: knowledge, attitudes and beliefs about teaching and learning ..................... 42
Tutor attitudes to maths: the positive results of training ........................................................................ 42
Building on an apprenticeship of observation.............................................................................................. 44
Theory- based practice ........................................................................................................................................... 45
Maintaining positivity: getting unstuck ........................................................................................................... 45
Tutor knowledge ....................................................................................................................................................... 46
Basic mathematical operations ......................................................................................................................... 47
The transition to Bachillerato ......................................................................................................................... 48
Preparing for training .................................................................................................................................................. 50
To study or not to study texts .............................................................................................................................. 50
Maintaining the quality of maths training ........................................................................................................... 50
The Training................................................................................................................................................................ 50
Supporting tutors’ development of practice in the field........................................................................... 51
The role of the field assessor .................................................................................................................................. 51
Institutional links .......................................................................................................................................................... 52
Conclusions ....................................................................................................................................................................... 55
References ........................................................................................................................................................................ 60
Appendix 1: Observations: maths trainings .................................................................................................. 62
Appendix 2 – Summary of the field assessors’ session observations ................................................. 63
Appendix 3: Summary of field assessors comments on classroom observations (not monthly
reports) ......................................................................................................................................................................... 66
Appendix 4: Questionnaire Survey .................................................................................................................... 69
Appendix 5: Additional comments of the tutors on the questionnaire .............................................. 77
5
Acknowledgements
This report was made possible through grant number 1070-0932 from the Ford Foundation.
I would also like to acknowledge the assistance of all those currently involved in the
implementation of SAT-Honduras who gave their time and professional assistance during
this investigation, including the Executive Director of Bayan Association, Ing Soheil Dooki,
for his sustained encouragement; the mathematics coordinator, Ing Ruhollah Sayyáh, for his
fine example and patient, good humoured support; and the many other people, tutors, field
assistants, coordinators and administrative staff who all gave generously of their time,
inspired me by their dedication, and treated me with great kindness. This report would have
been impossible without them and I am very grateful. In addition, I am very grateful to Dr
Chris Martin (ex Ford Foundation) and Prof Diana Coben for helping identify the need for
this research, and for their useful ideas on how to undertake it, to Prof Malcolm Swan for
his valuable comments, to my colleagues at Abingdon & Witney College for their warm
support and the granting of extended leave and finally, a very heartfelt thank you to Dr
Michael Richards for his editing and wise advice.
The views and opinions expressed in the report, as well as any errors, are those of the
consultant1 and do not necessarily represent those of the Asociación Bayán or the Ford
Foundation.
1 Consultant qualifications include: BSc in Psychology (Open University, UK), Post Graduate Certificate in Education (Oxford University), MA in Education (Oxford Brookes University) and SAT Tutor (Impulsor level). Experience in education includes 20 years teaching and teacher training/mentoring in England, Malawi, Ghana, Mexico and Honduras. The consultant has delivered workshops/papers at various international conferences/training events in England, Ireland, Scotland, USA and Mexico. In 2002, she was on the final evaluation team of the UK Department for International Development (DFID) project to establish SAT on the north coast of Honduras (1997-2002). [email protected]
6
Executive Summary
The Sistema de Aprendizaje Tutorial (SAT) is an interdisciplinary secondary school program
designed to provide a high quality and appropriate education in rural areas. The quality of
the Honduran SAT program has been nationally and internationally acknowledged. In
Honduras, SAT is implemented in a partnership of the Ministry of Education and four NGOs.
Asociación Bayán’s responsibilities include: philosophical guidance; the adaption and
updating of educational materials; implementation of the curriculum; all training; and
monitoring and evaluation of the educational processes.
Asociación Bayán and the Ford Foundation commissioned this report to:
Investigate tutor training for maths and the impact that this has on the mathematical
understanding and pedagogy of the tutors.
Assess other aspects of SAT affecting the development of the students’
mathematical capacity in the classroom.
Make recommendation to improve the effectiveness of the maths component in
SAT, with particular reference to tutor training.
It is further stated that the results of the study will be made available to the educational
community so that they can be of use to other educational programs, both national and
international.
It would be difficult and counterproductive to attempt to completely separate the maths
component, especially as regards the pedagogic aspects, from the overall SAT program,
in view of some of the generic pedagogic challenges faced. Therefore some more
general analysis of the learning process and challenges in SAT is in order.
In a little over a decade SAT has expanded dramatically from about a hundred students
to nearly eight thousand. This rapid expansion is a remarkable achievement made
possible by the energy and sacrifice of a dedicated team of people, and has involved the
formidable challenge of training about 700 tutors (there is a high turnover rate) and 80
field advisors and coordinators. One of the key challenges to maintaining the quality of
SAT is that it is based on several assumptions that are notoriously difficult to change,
about the purpose of education and learning processes which underpin the whole SAT
methodology, but which the trainees, despite a rigorous selection process, often do not
initially share. The most critical assumptions are that:
tutors and students are co-workers committed to individually and collaboratively
developing their spiritual, practical and intellectual capacities and service-orientated
attitudes;
7
the learning process is most effective when it is active, participatory and applied to
solve real life problems;
the role of the tutor is to guide and accompany students on their developmental
journey - this is very different from the role of a traditional ‘transmission’ orientated
teacher.
A new type of educator is required, ‘con una amplia visión, no solo de los aspectos
educativos, sino también de lo relacionado a la gestión comunitaria y desarrollo
social.’2
The tutors, who are often without a sound maths education themselves3, face the daunting
task of enabling poorly prepared students4 to access, and succeed with, a curriculum that is
much more conceptually challenging (and necessarily so) than they have themselves
experienced. It is therefore unsurprising that maths has been the most problematic area of
SAT since the beginning of the program5.
It is an indication of the
fundamentally sound nature
of the training that almost all
the questioned tutors
reported that their own
maths had benefitted
significantly, and that they
had a more positive attitude
towards maths as a result of
their training with SAT. The
vast majority of the tutors
reported enjoying teaching
maths, and felt they
understood the material well enough to explain it to their students. A major contributing
factor to this success is the inclusive and collaborative learning environment created in most
of the trainings, and, very significantly, field reports and observations indicate this is almost
always replicated in the SAT classrooms.
The strong emphasis on the practical applications of maths, conceptual understanding and the integrated nature of the curriculum appears to be profoundly motivating for both tutors
2 ‘A broad vision of not only of education but also of the promotion of social and community development’
(taken from the introduction to Aprender Enseñando, the SAT teacher training text). . 3 Honduras was reported to have the worst maths education in Central America in the Informe de Progreso
Educativo de Honduras. (2005). Programa de Promoción de la Reforma Educativa en América Latina y Caribe (PREAL). Washington, DC/Chile: Inter-American Dialogue/Corporación de Investigación y Desarrollo 4 Rural schools are more likely to have several grades in one classroom and experience much more frequent
teacher absences than urban schools. 5 If students score less than 60% in an end of module test they have to retake it. In 2009, the percentage
retaking maths was 45% compared to a 16% average for the other four areas of SAT.
8
and students, but during observations of trainings it was apparent that some key aspects of the SAT methodology are not being implemented, or are only being partially implemented. These are the aspects of the methodology that are most associated with effective maths pedagogy according to international research.
The neglected activities include ones that are strongly associated with conceptual development, increasing classroom participation, taking ownership of the learning process, and assisting teachers in assessing and responding to student learning. For example, activities explicitly recommended in the SAT texts, but not seen in 195 hours of training/classroom observations, are:
Individual work followed by small group work, in which each student in turn should explain/justify their method of resolving a problem or explaining a concept to the other members of the group
Use of the SAT Learning and Evaluation Guides
The SAT texts are innovative,
engaging and generally very
supportive to the learner, but they
sometimes assume a knowledge
and understanding of maths, and
its associated pedagogy, which
tutors have not yet developed. It
may be that many tutors are
satisfied with their delivery of the
curriculum because they are
unaware of the more challenging
aspects of the SAT methodology,
and the concomitant need for
greater conceptual understanding.
Many key teaching staff have therefore identified as an urgent need the development of
additional materials and activities which can enable the tutors and students to overcome
the deficiencies of their previous education. There is a strong commitment by SAT
coordinators to do this. A more complete utilisation of the SAT methodology may reduce
the need for additional materials, although some important (according to recent research
and international good practice for effective maths teaching) tools/activities should be
considered in terms of their potential to significantly enhance the learning process in SAT.
Teaching staff are very aware of the need to focus more on conceptual development and
pedagogy, but find that this is very difficult due to the severe time constraints of the current
training schedules. The more careful planning of training could help with this, but there is
also a need to increase (carefully selected) field support staff capacity to deliver more
specialist maths training in small, local trainings, and to mentor tutors. The process of
training maths specialists has begun and two trainings have taken place.
9
Interviews revealed that most tutors are also studying for undergraduate degrees, and are
taking classes on education. But no linking of university studies and SAT, and very limited
reference to SAT educational theory, was observed during the trainings, apart from during
the initial training. A greater understanding of the theoretical underpinnings of the SAT
methodology, its relationship to wider educational theory, and how these relate to their
own beliefs and practices would significantly help tutors to more fully implement the SAT
methodology, and to become more reflective and effective practitioners (this finding is
supported by educational research literature).
The rapid expansion of SAT has placed Asociación Bayán under considerable stress, and all
the interviewed coordinators expressed serious concerns about maintaining quality.
Inconsistencies in data collection on field activities (although there are plans to produce a
manual), serious archiving problems,6 and the lack of effective fora for discussing concerns,
are (in the consultant’s view) are impacting Asociación Bayán’s capacity to address these
issues. It is vital that such constraints are urgently addressed.
It is clear that the quality of the tutors as effective teachers is the key to the success of the
SAT program. The high turnover rate of tutors7 means that the SAT trainings have to be very
effective. It is vital that tutors experience the full SAT methodology while in training,
understand the reasons for it, and are supported in their adoption of participatory teaching
practices. Therefore the most important recommendations of this consultancy report are
that:
Activities which are a part of the SAT methodology, but which have only partially
been adopted, or have not been adopted, are fully implemented, unless
consultation with FUNDAEC identifies them as being no longer appropriate.
Priority is given to building the capacity of:
o trainers to use the SAT methodology fully;
o the field assessors to be able to ‘accompany’ the tutors in the development
of their general pedagogic skills;
o carefully selected maths field support staff to be able to effectively support
the tutors in the development of their maths pedagogy/knowledge.
Effective fora for the consultation of pedagogical and other educational issues are
established.
Tutors are mentored in order to help develop their capacities to reflect on their
practice, and to be able to systematically experiment with small changes (action
research).
Relevant insights, techniques and tools originating outside SAT, particularly those
associated with increased classroom participation, conceptual development and
‘formative assessment’, are identified and considered for adoption and adaptation,
6 See Limitations: page 13/14
7 See Background: paragraph 5
10
since (according to the consultant’s experience and relevant research literature)
these have the potential to significantly enhance key aspects of the SAT
pedagogy/curriculum.
The collection and analysis of field data and feedback is systematised and
standardised (where appropriate), and archiving systems are improved.
11
Introduction
Background
The Sistema de Aprendizaje Tutorial (SAT) was developed in Colombia in the 1970s to
provide a good quality and appropriate secondary education in rural areas. The curriculum
is interdisciplinary and focused on developing students’ spiritual, moral, practical and
intellectual potential in order that they can, along with other community members, take
charge of their own autonomous and sustainable development (Box 1). The quality of SAT
has been nationally and internationally
acknowledged8.
In Honduras, SAT is implemented in a partnership
of the Ministry of Education and four NGOs,
including Asociación Bayán. Asociación Bayán,
among other services, provides: philosophical and
pedagogical guidance, including curriculum
development; all the training; monitoring and
evaluation; and adapts or updates SAT texts in
consultation with the founding NGO of SAT, the
Foundation for the Application and Teaching of
Sciences (FUNDAEC), Colombia.
SAT’s dramatic expansion from about a hundred
students to about eight thousand in a little over a
decade has presented the formidable challenge of
inducting and training over 700 new tutors, as
well as about 80 field advisors and coordinators.
The SAT philosophy and pedagogy is a new and
challenging paradigm for the majority, because
most Hondurans, especially those from poorer
backgrounds, have mainly experienced the
‘transmission’ or ‘empty container’ method of
teaching (UNDP, 2009a). It is widely recognised
that teachers tend to adopt the style of teaching
8 A 2005 Ministry of Education report on education in Honduras noted that: "SAT .... through the
development of contents relevant to the aspirations and real needs of the rural population, has shown
itself to be adapted to the special conditions of rural people." In 2002, SAT-Colombia received a Club of
Budapest “Change the World – Best Practice Award”; and in 2008 Asociación Bayán was invited to
present SAT-Honduras as a ‘best practice’ sustainable development case study at the UN Commission for
Sustainable Development (CSD-16) meeting.
Box 1
The search for a valid rural
education implies changes in
the relationships between
many of the elements of the
educational system - time,
space, students, teachers,
school, and the community.
For example, the relationship
between the students and the
professors in the programs of
FUNDAEC is one of co-workers
embarked on an enterprise of
great importance - the search
for the path of development
of their people. The student is
not considered an empty
container to be filled drop by
drop but a mine of hidden
talents and potential that
need to be discovered,
perfected, and directed
toward the service of others.
Source: Arbab el al (1988)
12
that they have experienced as students (Schwille & Dembele, 2007).
However SAT has been able to achieve some significant positive changes in teaching style.
This is probably because of its strong philosophical base, and the fact that the training
already has some elements known to increase active teaching methods, such as systematic
training over a long period and support by peers in the field (Wiliam, 2006).
On the other hand SAT and Asociación Bayán have also faced the challenge of a high
turnover rate of tutors, which is to be expected in a rapidly expanding program. From 2000
to 2008 just over 500 tutors were trained, and about 20% left after an average 2.4 years.
The high turnover rate is partly due to the understandable tendency for tutors,
most of whom are undergraduates, to look for a secure job after completing their degree.
Those still in SAT average about 2 years of service9. This is problematic in that research
shows that experience is a key factor in improved teacher performance (Chingos &
Peterson, 2010; Wiliam, 2007); the short average length of tutor service also increases the
pressure on tutor training to be particularly effective.
The SAT methodology (Box 2) is largely inspired by
the Baha’i Writings, in which consultation is
conceptualised as the collaborative search for truth
and the process by which decisions are made for
community action. The criteria for consultation are
demanding and include (italicised phrases are from
the Bahá’í writings10): ‘purity of motive‘; an
atmosphere of ‘love and harmony’; objectivity or
detachment; ‘courtesy’; ‘absolute freedom’ of
expression; and the responsibility of all to give an
opinion supported by logical arguments rather than
personal emotions.
In SAT there is great emphasis on the quality of the textbooks and tutors. The textbooks are
fundamental to the methodology, and are designed to be worked through systematically by
the students, accompanied and helped, where necessary, by their tutor. This is very
different to normal Honduran practice in which the teacher stands at the front and teaches,
and the students listen. The SAT texts, through a series of thought provoking questions,
explanations and graded activities, develop key concepts, skills (intellectual and practical)
and attitudes so that students can become independent and rigorous mathematical
thinkers, and accurate, efficient practitioners.
9 Tutor data was only available up to 2008 so average length of service could have changed.
10 For example, ‘Should any one oppose, he must on no account feel hurt for not until matters are fully
discussed can the right way be revealed. The shining spark of truth cometh forth only after the clash of differing opinions.’ (Abdu’l Baha, cited in Shoghi Effendi, 1922).
Box 2
The method of teaching,
reflected in the design of
textbooks, is one of raising
questions and trying to find
answers in an atmosphere of
consultation between
teachers and students.
Source: Arbab et al (1988)
13
There is substantial research evidence that teachers have a major influence on student
achievement; students with the best teachers learn at twice the rate of those with average
teachers (Rivkin, 2005). Asociación Bayán, in consultation with the Ford Foundation, has
identified or hypothesised that improving the level of maths teaching would have a
substantial impact both on overall academic progress and the running of small businesses,
agricultural and community projects. For these reasons Asociación Bayán and The Ford
Foundation commissioned this study and report.
Objectives
To investigate tutor training for maths, and the impact that this has on the
mathematical understanding and pedagogy of the tutors.
To report on other aspects of SAT affecting development of the students’
mathematical capacity in the classroom.
To make recommendations to improve the effectiveness of the maths component in
SAT, with particular reference to tutor training.
Methodology
Semi-structured interviews with coordinators, field advisors and tutors (Appendix 1)
Observations of maths and general training (156 hours), SAT lessons (15 attended in
the Departments of Atlantida, Colon and Santa Barbara) and a range of meetings,
including coordinator meetings (Appendix 1)
Participatory observation, including that derived from conducting tutor training in
maths11 and English, and providing support to other trainers/coordinators
Questionnaire surveys, focusing on tutor experience and attitudes to maths learning
and teaching (applied to 190 tutors of whom 133 responded (70%), adapted from
proven questionnaires by Swan (2006) and a seminal study by Fennema & Sherman
(1976) as translated by Ignacio et al (2006) (Appendix 4)
Review of documents: SAT Texts; Tutors’ worked Texts; Field Assessor Observation
Reports and Monthly Reports; Asociación Bayán Nacional Profiles; data on tutor
length of service; one Asociación Bayán internal report; and reports to donors (see
below).
Limitations of the study
The paucity of reports: after repeated requests for any report which contained
references of any sort to education, I was advised that due to hard disc failures and
archiving problems only the following reports were available: 2010 January Informe
de Actividades; the Perfiles Nacionales for 2010 (Block 1), 2008 (Blocks 2 & 3) and
11 Maths: 4 hours, English: 12 hours
14
2009 (incomplete due to the coup); and three reports to donors12, two for 2007 (Jan
– June and July – Dec) and one for 2004-2006.13
SAT students were not consulted in this study, partly since the three year Hewlett
study by the Universities of Berkely, New York, Wellesley College (USA) and the
National Pedagogic University (Honduras) will contain an in-depth impact analysis of
student achievement and experience for the first two years of study14.
I decided that it was beyond the scope of this report to analyse the interactions
between mathematics and other curriculum areas, economic activities and
community development (in SAT these process are all integrated). It is however
hoped that this report will contribute to a holistic reflection on the SAT program.
The Asociación Bayán plans to review working conditions and practices and
therefore these are not addressed in this report.
12 Reports:
Scaling up the System of Tutorial Learning (SAT) as an alternative education program tackling rural poverty and gender inequity in Honduras:01:07:04-30:06:06 (No:1045-0688)
Building Sustainable Livelihoods through Agriculture 01.01.07:31.07.07 (CIDA)
Fortaleciendo la Candidación del Programa Educativa Rural SAT en Intibucá, La Paz y Comayagua. Junior 07 – Dec 07 (IBIS)
13
There is very little documentation of SAT’s development in Honduras; this, combined with the loss of many key reports means that the opportunity for Association Bayán to reflect on its experience and for other organisations to benefit from them is seriously diminished. When the innovative nature and success of the program is taken into account this is a significant loss. 14
2007 (Draft proposal) 4 mains goals were: 1) To develop and apply appropriate measures of secondary school quality; 2) To evaluate the impact of SAT on treated communities, particularly student participants; 3) To explain the impact (or lack thereof) of the SAT program; 4) To extract lessons for the scaling-up of SAT in Latin America and expansion to new countries.
15
Findings
SAT is implemented by a dedicated team that
believes strongly in its value and is committed to its
sustainable development. Although many senior
staff said that SAT’s rapid expansion has made it
difficult to maintain the high standard of training
achieved in earlier years, the vast majority of tutors
report that the maths training has had a significant
positive impact on them (Box 3) and that it
prepares them well for teaching. This report finds
that the maths tutor training is basically sound, but
that senior staff concerns are valid and there is an
urgent need to address them for quality to be
maintained and improved.
Creating an atmosphere of consultation
In the classroom
In the major recent Human Development report of Honduras by UNDP (2009a), which
focused on youth issues and contains a major survey of Honduran youth attitudes (UNDP,
2009b), Honduran youth responded that, after poverty, their greatest problem was
violence, principally feuds and fights. The SAT centres are located in communities where
family feuds are common and therefore can be a
difficult environment in which to develop an
‘atmosphere of consultation’.
In interviews with first year tutors and other tutors
recalling their first year, frequent mention was
made of the difficulties and sustained effort
required to establish and maintain classroom
norms of respect and collaboration. The majority
appear to achieve it; in the Field Assessor reports,
the boxes for: ‘Se observa un ambiente alegre y de
motivación en el grupo’15 and ‘Se observa respeto
hacia las opiniones de los compañeros’16 were
ticked 96% of the time (Appendix 2). This is a
15 ‘A happy and motivated atmosphere was observed.’ 16 ‘Students were respectful of one another’s opinions.’
Box 4
The class worked in small interacting
groups for two hours and then, during
the recess, most of the centre’s
seventy students played football
together with vigour and good
humour. The tutors were unable to
explain how the students formed their
teams - age, sex and community did
not appear to be factors.
Observation: March 2010
Box 3
En SAT la experiencia en matemática
es fascinante porque aprendes a
desarrollar tu propio concepto y te
pones a utilizar tu lógica matemática
que a veces esta muy dormida en
problemas de la vida diaria y te llevas
a resolver esos problemas de la vida
diaria.
Source: SAT tutor comment on
questionnaire
16
Box 5
When a student in one group was
undergoing chemotherapy and not
robust enough to leave the house so
his SAT group met in his home during
his treatment and convalescence. Two
years later he is studying Bachillerato
with the same group.
A first year tutor realised at the
beginning of the year that the low
literacy levels of some of his students
would impede their progress so he
gave extra classes every Saturday for
the first block.
A tutor accompanied a group of his
students on the two hour walk to their
community and stayed for the night in
order to get to know their families and
experience their daily journey.
Parents, students and tutor worked
together, bringing sand from the river
so that they could build a new
classroom.
Source: observation Oct 2008 & April
2010, coordinator interview May 2010
tutor interview with video evidence May
2010.
yes/no Box, but judging by additional comments
(Appendix 4), they appear to be using fairly
similar indicators17 and, in most of the sixteen
classes observed, there was a collaborative,
purposeful and cheerful atmosphere (Box 4).
Tutors remain with the same students for up to
six years, and are responsible for academic
progress and pastoral support. It seems, from
interviews and conversations with tutors and co-
ordinators that most tutors demonstrate
commitment to, and develop strong bonds of
affection for, their students (Box 5). The fact that
they often go to considerable trouble to get to
know their home circumstances, provide extra
help and are active with their students in
community projects (Appendix 3) also contributes
to the generally united classroom atmosphere.
It was noticeable that although some assessor
monthly reports were fuller and franker than
others, most contained observations about the
learning environment that could usefully be
reflected on.
It is recommended that:
1. Asociación Bayán continues to build
on these good foundations by
continuing to reflect and
experiment with ways of further
developing ‘an atmosphere of consultation.’
17 Example of monthly reports were received from 8 out of 12 regions and observation reports on 36 tutors completed by 8 assessors. This represents less than 1% of the tutors it and cannot be considered representative.
17
Improving the educational value of classroom
talk
Asking probing questions in order to consult on
them is at the heart of SAT methodology (Box 6).
This approach is supported by wide body of
research showing the value of discussion in the
learning process (Anthony & Walshaw, 2009).
Given the constant talking observed in SAT
classrooms, and the vital role that tutors
think this plays in learning,18 it is essential
to note that the evidence indicates that
some types of discussion are much more
productive than others (Box 7).
The concept of ‘consultation’ is far more
complex than that of ‘exploratory talk’
(Box 7), but they share common
characteristics, and developing
tutor/student capacity for ‘exploratory
talk’ can be considered as contributing to
the creation of ‘an atmosphere of
consultation’.
The whole-group discussions observed in
the trainings and classes were almost
exclusively of the ‘cumulative talk’ type.
The better trainers sometimes tried to
facilitate ‘exploratory’ discussions, with
some success, but generally it seemed as
though the trainers needed further
guidance in how to promote ‘exploratory
talk.’19 For example, it was observed that
in the tutor trainings, tutors rarely built on previous contributions by themselves or others
and this was never observed in a classroom.
18
86% of tutors reported (in the questionnaire survey) that their students usually learnt through discussion. 19
It may be that assessors (and tutors) have different conceptions of what it means to take part in a discussion. For example in the Informes de Visita (Appendix 2) in response to ‘Durante su estadia en el aula cuantos participantes vio opinar’ the reported percentage of students ranged from 100% to 6%. It was noticeable that assessors tended to give a similar estimate for all their observations. It may be that some assessors count giving an answer as ‘opinar’ while others require justification or elaboration as well.
Box 6
Un proceso en el cual se tiene como
referencia el método científico: el
grupo explora, identifica problemas,
formula interrogantes e hipótesis,
consigue información, experimenta,
descubre, crea modelos, aplica,
explica y plantea nuevas preguntas …
Source: Valcarcel & Correa (1995)
Box 7
Mercer (1995,2000) has described in some
depth the types of interaction that promote
effective and ineffective learning. In particular
he demonstrates the superiority of exploratory
talk over disputational and cumulative talk.
Exploratory talk consists of critical and
constructive exchanges, where challenges are
justified and alternative ideas are offered.
Disputational talk consists of disagreement
and individualised decision making. This is
characterised by short exchanges consisting of
assertions and counter-assertions. In
cumulative talk speakers build positively but
uncritically on what each of the others has
said. This is most typically characterised by
repetitions, confirmations and elaborations. In
short the most helpful talk appears to be that
where the participants work on and elaborate
each other’s reasoning in a collaborative rather
than a competitive atmosphere. Exploratory
talk enables reasoning to become audible and
knowledge becomes publicly accountable. -my
italics-
Source: Swan (2006:87)
18
Box 9
Entonces en general SAT tiene un desafío y es
justamente ayudar a sus participantes a pensar
más. Este es el problema. El Doctor Gustavo
Correa decía si tan solo logramos a ayudar a
los jóvenes pensar es un gran logro (¿). Porque
están acostumbrados que le profesor les digan
todo y ellos toman notas y cuando toman
examen es muy literal y entonces en SAT les
ponen difícil porque les está preguntando a
cado rato ‘¿Y Usted que piense y porque es
falso, y porque es verdadero, cual es la
justificación?’
Source: coordinator interview Abril 2010
The texts offer many opportunities for activities
associated with conceptual development, but most
tutors seemed unaware of them. This is indicated by
the fact that, although discussions which involved
sustained reasoning (photograph) were rarely
observed.20 96% of tutors reported that usually ‘mis
estudiantes realizan todos los ejercicios del texto de
matematicas’.21 Most exercises are diligently done,
but it was also observed that opportunities to probe
and extend conceptual understanding and analytical
capacity are lost (Box 8). Developing student
conceptual
understandin
g and capacity to think analytically is internationally
acknowledged to be challenging. Trainers are
aware of the difficulties (Box 9) and keen to
develop this key aspect of SAT methodology.
It is recommended that:
2. Tutors are explicitly taught the
characteristics of ‘exploratory talk’, provided
opportunities to develop these skills, and
mentored in facilitating appropriate kinds of
‘exploratory talk’ in the classroom.
3. Topics where tutors regularly experience difficulties are identified before training so that
questions, reflection, activities and discussion can be carefully planned.
4. Opportunities for developing mathematical thinking are clearly identified during training,
and appropriate activities are clearly demonstrated.
20 Trainers frequently asked students a question in order to probe understanding but discussions based around these answers were very rare. 21 ‘My students do all the exercises in the maths’ textbook’.
Box 8
It was clearly explained how to record
a quantity in different bases. The
tutors then constructed tables to
show how quantities were
represented in bases 2 – 10 (some
used beans to model the bases).
Students worked in small groups and,
with the help of the trainer, nearly all
had completed the table by the end of
the session. No time was given at the
end of the session for observations,
questions and the forming
generalisations related to the activity
Source: Observation May 2010
19
5. Tutors should have a written record (e.g., training handouts) to support classroom practice
and/or training in the taking of pedagogical notes, since inspection of many tutor texts
revealed that tutors very rarely take pedagogical notes22.
General Training and consultation skills
The process of developing an ‘atmosphere of consultation’ (Arbab, 1988) clearly transcends
subject areas; it is the foundation of the SAT methodology. The thrice yearly, two week
trainings are seen by coordinators as the key to raising tutor awareness of the qualities and
attitudes necessary to create a transformative learning environment.
Five different trainers were observed delivering Aprender Enseñando. It is clearly desirable
that trainers contribute creatively to the course content and method of delivery, but the
style of facilitation and content of the orientation varied to such a degree that tutors cannot
be considered to have received the same training. In some of the trainings there was an
open and accepting atmosphere, and tutors appeared to speak freely, but in others there
was little opportunity for the tutors to express their thoughts, and on one occasion an
opinion (valid in my view) was dismissed as incorrect. It is important that tutors have
substantial and varied experience of an ‘atmosphere of consultation’, particularly during
their early training; otherwise it is harder for them to develop such an atmosphere, in far
more challenging circumstances, in their own classes.
It is recommended that:
6. Aprender Enseñando is used to develop consultation skills and its delivery is
collaboratively planned so that tutors have a comparable experience.
22
A quick inspection of approximately 60 tutor texts revealed that some tutors never take pedagogical notes, even when it is recommended that they do. For example on one occasion after a very clear analogy and diagram was used by a trainer to clarify a concept it was suggested that a note was made of this. Subsequent inspection of the books revealed that only 15/21 tutors had done this and that the notes, when taken, were often very brief. When note taking is not suggested pedagogical notes are very rare. On one occasion tutors were provided with paper to make additional notes and glue to stick this into their books. This increased the quantity and legibility of notes.
20
The use of questions and answers
Allowing time for reflection
The questions in the texts have many purposes,
among them bringing to the student’s attention
something that s/he may not have considered
before (Box 10). The student may not be
expected to say or write anything immediately
after this reflection, but the act of doing it aids
learning, encourages independent thinking, and
enriches subsequent discussion. There is
evidence that a slight pause between asking a
question, even the simplest one, and a
student/tutor being required to answer, increases
participation (Hodgen & Wiliam, 2006). It was
observed that some trainers allowed time for reflection while others did not.
It is recommended that:
7. Trainers allow time between questions
and responses, and discuss the reasons for
doing this with the tutors.
Questions: increasing participation
It was observed that a large number of
questions are asked by the trainers/tutors.
Almost always, in both training and classes,
either a particular person is nominated to
answer (sometimes before the question is
asked) or it is addressed to the whole group,
and someone shouts out the answer. This
means that, although most tutors/students
contribute in most sessions, a vocal minority
tends to dominate.
It is recommended that:
8. Trainers/tutors are taught a range of techniques for increasing tutor/student
participation when answering questions.
Box 10
No se trata de entregar conceptos
totalmente elaborados, sino de
plantear preguntas y situaciones que
ayudan al estudiante a precisar ideas
en las cuales posiblemente no se
había detenido a pensar. ¿Cómo se
llego a nociones como punto, recta,
plano? ¿ Qué relaciones hay entre
ellas?
¿Para qué sirven esas ideas?
Source: Bosquejo General: El Espacio y Sus
Elementos.
21
Box 11
Practice in classrooms is formative to
the extent that evidence about
student achievement is elicited,
interpreted and used by teachers,
learners or their peers to make
decisions about the next steps in
instruction that are likely to be better,
or better founded, than decisions
made in the absence of the evidence
that was elicited.
Source: Black & Wiliam (2009)
Questioning: a formative assessment tool
There is strong research evidence that improving
formative assessment (Box 11) is the most
effective way of raising student performance
(Hattie & Timberley, 2007). Questioning can be a
good formative assessment tool if the teacher
asks appropriate questions, listens to the
answers, and builds on the information gained.
Student answers sometimes require probing and
reflecting on in order to understand what is
meant and to expose underlying assumptions
which may be impeding progress. This can take
time, but is essential for building up clear
communication. It was observed that some
trainers are much more skilled than others in this
process.
The SAT tutors seemed unaware of the power of
using student errors to explore and develop
conceptual understanding, as is shown by the fact
that 90% of the tutors in the questionnaire
reported that they tried to teach so that the
students did not make mistakes. Many of the
questions in the SAT texts are designed to
develop understanding; exploring mathematical
ideas, making mistakes and subsequently
analysing and rectifying them is an important part
of this process (Box 12).
It is recommended that:
9. Tutors are supported and mentored in the didactic use of questions and ‘error
analysis’ as a formative assessment tool; this includes being informed of the utility
of this approach;, experiencing it in training; knowing where it is most appropriate;
and being mentored in developing these skills by field assessor accompanimiento.
10. Students are encouraged to experiment, take risks, make mistakes, identify and
correct them. This would facilitate exploratory talk.
Box 12
Es necesario tener lápiz, papel y
borrador en mano, no para copiar,
sino para resolver personalmente
todos y cada uno de los ejercicios,
corriendo el riesgo de cometer
errores, de tomar caminos esquivados
y asumiendo también la
responsabilidad de revisar, corregir y
de proponer soluciones originales y
creativas.
Source: Bosquejo General: Manejo de
Variables, Unidad 1
22
Tutor/student questions
Developing student capacity to form probing questions is an important part of the SAT
methodology23. There are two ways this happens:
Firstly, students are specifically asked to make up a problem for other students to solve.
92% of the tutors reported that ‘aprendo mucho inventando nuevos problemas’24. Creating
problems or questions often requires more complex processing of the concepts than
responding to a readymade question. This type of activity assists in the internalisation and
development of concepts (Swan, 2006); the form and content of a student-made question
gives insights into understanding, and so can be used for formative assessment. Also being
able to create mathematical problems is a useful skill for tutors to acquire so that they can
provide students with additional examples, and support them in forming their own
problems.
Secondly, there are questions that originate from the students’ own engagement with the
topic and/or development processes. In the trainings for maths specialists25 it was observed
that participants asked questions about mathematical reasoning and representations, but in
the normal trainings and classes almost all the questions made by tutors/students referred
to algorithmic procedures as opposed to more substantial conceptual or community
development issues.
It is recommended that:
11. Activities where question formation is explicitly asked for or which lend
themselves to this are clearly identified in the trainings to help tutors more fully
utilise the texts.
12. Trainers experiment with using small group work as a way of encouraging the
formation of more reflective student questions, and encourage tutors to do the
same.
Three ways of working
The tutor guide Aprender Enseñando (Dooki & Arias, 2007) is studied by tutors in their first
training. It is a basic introduction that divides SAT pedagogy into three parts: Lectura
comentada; Estudio en pequeños grupos; y Estudio individual.26 In the field assessor report
form (Appendix 3) it is made explicit that lessons are expected to be a combination of these
23 El estudiante aprenda a plantearse el mismo los problemas, buscar los datos y encontrar las respuestas
(Bosquejo General, Suma y Resta)
24 I learn a lot inventing new problems
25 The maths coordinator is building up a team of maths specialist who will support other tutors, run the micro
centres (local, short trainings given when the need arises) and the best will deliver training. So far about 24 have attended a training, eight either have a maths degree or are near completing one 26
‘Reading and discussion’, ‘Small group work’ and ‘Individual work’
23
three groups: ‘Usa tanto la lectura comentada como trabajo en grupo y lectura individual?’27
is one of the criteria of a good class. All except one of the tutors (out of 29)28 were reported
by field assessors to be doing this. The three methods are explained quite generally in the
tutor guide, so that it is likely that each assessor/tutor/trainer has a different understanding
of what these terms mean.
In interviews and meetings it was clearly demonstrated that the SAT coordinators are deeply
committed to improving the pedagogy of SAT, and would like to have more time to reflect
on experience and initiate change. Each of the three methods above has an important
contribution to make towards creating an atmosphere of consultation but it is possible that,
as they are only described very generally, that staff members have very different
conceptualisations as to their principal characteristics. So it would be fruitful if assessors,
coordinators and tutors were given time to discuss what each one of the methods means to
them and a richer conceptualisation is attained. If this does not happen it could be
damaging, particularly in the case of trainers, if individual assumptions about the methods
cause a departure from the core SAT methodology.
It is recommended that:
13. Sufficient time is allowed for this at coordinator meetings for consultation on
pedagogy.
The use of tutor/student presentations of work
In about a third of the observed
classes, one or two students were
invited to the board to
demonstrate their calculations.
The student would, usually
silently, write up the procedure
and answer. The tutor or another
student would comment if there
was a mistake in the working out
and/or the final answer.
Use of the board followed a similar
pattern in the trainings. Some trainers had more tutor demonstrations than others, but the
main purpose of the activity was almost always to check the correct use of an algorithm. In
smaller groups the whole group would, sometimes animatedly, join in with the calculation,
but with larger groups there was less participation. Quite often it would become an
27 ‘Equal amounts of whole group reading and commenting on text (combined doing related activities), small group work and individual work.’ 28
6 observations received no comment for this category
24
exchange between the trainer and tutor (both with their backs to the group), the trainer
trying to plug a hole in the tutor’s understanding or of the algorithm.
Checking algorithms in this
way is time consuming.
Also 23% of tutors
reported finding it
stressful. This might not be
too concerning as long as it
is not humiliating, which it
appeared to be
sometimes.
Tutor whiteboard
presentations should be
used as a stimulus for discussion when a variety of responses are valid, and these can also
be compared and evaluated. Presentations, such as
that illustrated in the photograph (a tutor is telling
colleagues how he explains factorisation), can help
weaker members of the group because peers often
use more accessible language than the teacher. But in
order to be effective, the tutor presentations need to
be clearly delivered and allow sufficient time to
develop discussions and follow-up questions. It would
also be better to have fewer presentations, but for
them to be well thought out and closely analysed. The
aim should be to move towards analysing
mathematical methods and approaches and their
practical applications rather than practising
algorithms (Box 13).
It is recommended that:
14. More efficient methods to check answers and
correct procedures (e.g., use of small
individual white boards, peer checking, etc.)
be used in the trainings and classes instead of
whole class presentations by individual students/tutors.
15. Student/tutor presentations of work are used as the basis for discussions.
16. Appropriate activities are identified beforehand and adequate time allocated for
them.
Box 13
Effective teachers encourage their
students to explain and justify their
solutions. They ask them to take
and defend positions against the
contrary mathematical claims of
other students. They scaffold
student attempts to examine
conjectures, disagreements and
counterargument ... as attention
shifts from procedural rules to
making sense of maths ... students
become less preoccupied with
finding the answers and more with
the thinking that leads to the
answers.
Source: Anthony & Walshaw (2009):19
25
Working in small groups
Peer teaching and ‘social
loafing’
Peer teaching is
encouraged in SAT, for
example, 78%29 of tutors
reported other tutors
asking them for help with
maths. There is strong
research evidence to support peer teaching. In an internationally acclaimed meta-study
(Hattie, 1999) it was found to have an above average impact on student achievement, and
to be more effective than homework in improving student performance. With a peer, as
opposed to a teacher, people often feel more relaxed, more able to ask questions, request
clarification, try out something new and risk making mistakes. This complements the SAT
philosophy that the whole group should move forward together, and no one should be left
behind.
In small groups those who are more advanced gain by explaining and supporting their peers
as this helps them consolidate their
own knowledge. This contrasts with
whole group work when those who are
already proficient can be bored by
trainers/tutors revisiting material, as
was seen during the whole class
checking of algorithms. It was observed
that in the trainings the tutors almost
always work in unchanging friendship
groups of two to four people, and on
almost every occasion the exercises are
done collaboratively. However it was
also observed that occasionally more
‘social loafing’ than peer teaching or
collaborative group work took place. It is also well known that constant group work can
encourage passivity and dependency.
Another observed problem of constant collaboration was that struggling tutors were not
always identified and given the help they needed. For example, in the training for El
Sistema de Numeracion Decimal, a tutor was observed after the lesson copying out a table
29 First year tutors (who had not yet taught maths/completed training) were asked not to respond to this question. Of the other tutors 28% failed to respond.
26
of numbers made with different bases. When asked about the table, she could not express
any of the given numbers using a binary or any other base. Her textbook was correct, but it
is probable that her teaching of this section would have been unsatisfactory (appropriate
support, was of course, given to the tutor).
The observed small group working was usually informal and unstructured; on only a few
occasions was a group given a task that they were expected to provide feedback on as a
group. Therefore the focus of the group/pair activity tended to be on each person filling in
their textbook, sometimes with one member of the group playing the role of a transmission-
based teacher, and occasionally with the weaker tutors just copying out the answers.
It is recommended that:
17. Tutors are given clear criteria of how to assess their own and others’ work, and
guidelines are written on how to peer teach/accompany a tutor/student without
creating dependency (perhaps using the Guias de Aprendizaje y Evaluaciόn)
18. Tutors/students are encouraged to work in different groups.
19. Tutors/students capacity to work in groups is developed by using different types of
group work and providing opportunities for analysis of the effectiveness and
inclusivity of the group work.
20. Tutors experience and reflect on a range of techniques for improving group work
(see below)
21. Tutors are made more accountable for their progress in the trainings (e.g., a test at
the beginning and end) and/or tutors’ texts are formally reviewed before the end
of the training (this was a goal in the October 2008 Perfíl Nacional but not
observed in the maths trainings).
A forgotten method?
The following explicit instruction appears in the text Fracciones y Porcentajes (6.4): ‘para
revisar los ejercicios, formen grupos de 4 estudiantes y cado uno explique a los compañeros
de grupo como resolvió uno de los ejercicios’30.
Similar instructions appear in many other places in
this and various other texts. The instruction implies
that the students have done the exercise on their
own, have had time to reflect on it, and then that
each student should verbalise their understanding
of the exercise and explain it in a small group. It
appears to be vital part of the methodology (Box
14) and the effectiveness of this technique is also
strongly recognised in the literature, for example:
30 “Revise your answers in groups of four, each person explaining how s/he did one of the exercises.”
Box 14
‘los momentos más importantes de
cada lesión son los dedicados a
explicar a los compañeros la forma
cada uno resolvió los ejercicios’
Source Destrezas Algebraicas
En la Vida Rural:303
27
‘In small supportive groups students learn how to make conjectures and engage in
mathematical argumentation and validation’ (Anthony & Walshaw, 2009).
In spite of the explicit guidance to use it, this method was never observed. In the Teacher’s
Guide for this text there is no mention of a different review method having being
introduced, and therefore it can be assumed that it remains a key SAT method as developed
by FUNDAEC but it appears not to have been adopted in SAT-Honduras.
It is recommended that:
22. SAT Text instructions, and specifically this one, are implemented, unless
consultation with FUNDAEC reveals a method is no longer regarded as appropriate.
23. Recommended activities/methods, if not explicit in the text, are clearly explained
to the tutors.
Individual work: the third force
Thinking time
The SAT texts are full of questions. Some of the questions are to draw the students’
attention to a concept or aspect of a concept of which he/she might be unaware and which
is about to be developed in the text. The student is expected to reflect (briefly) on the
question before reading on. Students are also sometimes explicitly told to work through an
exercise independently. Independent working is an essential part of learning, as explained
in a recent overview of international research on effective maths pedagogy: ‘Teachers
should ensure that all students are given opportunities to think and work quietly by
themselves when they are not required to process the varied and sometimes conflicting
perspectives of others’ (Anthony & Walshaw, 2009).
28
In the tutor questionnaire, 88%31 reported that ‘mis estudiantes realizan los ejercicios por sí
mismo y consultan a sus compañeros de vez en cuando’. It was observed that there were
short periods of spontaneous independent working (2–5 minutes) in most SAT classes, but
that this rarely happened in the trainings. The limited time for training was given as the
reason. This is however a false economy since (according to research) it impedes learning,
creativity and independent thinking, as well as making it harder to assess tutor progress.
Not using this method in training gives tutors the impression that independent working is of
less value than group work.
It is recommended that:
24. Sufficient time should be allocated for ‘independent working’ in the trainings.
25. The reasons why independent working is important should be presented and
discussed in the trainings.
Formative Assessment: fine tuning acompanimiento32
In most trainings and classrooms there is a clearly visible interest and concern about the
progress of each tutor/student, and teaching is adapted in response to this. Interviews with
tutors resulted in many examples of the considerable effort expended in acompanimiento,
or accompanying each student on their developmental journey.
Improving formative assessment skills would greatly assist trainers/tutors in their
acompanimiento because the systematic use of a wider range of techniques would improve
the quality of the information obtained about teaching/learning, and thus make more
attuned adjustments possible. Many of these techniques are suggested in the texts but are
not, as yet, being fully used.
It is recommended that:
26. A range of formative assessment techniques is used; those in the texts are
identified and, where necessary, additional ones are introduced and
trainers/tutors/students are supported in developing their capacity to use them.
Taking responsibility for learning
It is expected that SAT students will ‘dejan de ser observadores pasivos de hechos y
circunstancias para convertirse en personas activas en la exploración de caminos de
mejoramiento personal y comunitario’33(Valcarcel & Lizcano, 1995:6). This is achieved
slowly by the acquisition of new habits and attitudes. One of the key attitudes/habits that 31
99% responded to question 32
An analogy that is used for both the tutors’ and assessors’ role is that of a person who ‘accompanies’ another on their educational journey. 33
Stop being passive observers of events and become active in the search for new ways of changing oneself and the community for the better.
29
Box 15
Yo prefería que hagamos las tareas en
el aula porque así yo los miro que
trabajan realmente. Si les doy un
trabajo y se encuentra a un amigo que
ya está en secundo y lo ayuda? Hacen
la mayoría del trabajo dentro del aula.
Yo les doy cosas para hacer en la casa
que yo se que pueden hacer.
Source: Interview with first year tutor
whose group had no retakes in first
module. May 2010
need to be developed in order to achieve this paradigm shift is taking responsibility for
one’s own learning. Tutors identified this as their second most important priority when
working with the students34 (Appendix 3).
Unsupervised working
During the tutor training periods SAT groups are often left unsupervised. Twelve tutors
were asked what their students were doing during this two week period. Only one replied
that they were not doing a SAT related activity. The others either had special tasks (e.g.
reading a book together and doing a report) or were working on the group agricultural plot.
No independent maths work was reported, apart from revising for tests. The tutors were
confident that the unsupervised work would be done.
On two occasions35 the tutor was absent and the class was observed working collaboratively
with their maths textbooks. And just as impressively, in
all the maths classes observed student discussions
focused on the maths. Once or twice a tutor urged
students to work faster, but it was never necessary to
ask a student to return to the task.
Homework
Coordinators and assessors reported that in some
groups the assigned homework was not done or if it
was done, copying was widespread, while in other
groups homework was well done and appeared to be
having an impact on learning. The texts emphasise the
importance of fluency, speed and accuracy when
calculating as well as conceptual understanding.
Homework can be very useful in developing the later (Box 15)
It is recommended that:
27. Tutors are given opportunities to share good practice on homework (and other
aspects of practice) e.g., trainings, micro-centres, tutor meetings, bulletin, website.
Formative assessment helps students take responsibility for learning
It is easier for students to be responsible for their own learning when they know what they
are supposed to be learning and the criteria for success, and when they are given clear
guidance on what they have to do to improve their performance. It is suggested in
Aprender Enseñando that the Guías de Aprendizaje y Evaluación should be studied closely by
34
When asked to allocate 100% between six possible priorities (appendix 4) the two highest scoring ones were: ‘Motivarse y tomar responsabilidad sobre su propio aprendizaje’ (mean: 24%) and ‘Utilizar la matemática para explorar y describir el mundo y resolver problemas de su vida cotidiana’ (mean: 32%). 35
Observations made during a previous visit, October 2008
30
Box 16
Effective teachers draw on a range of
representations to support their
students’ mathematical development.
These include the number system
itself, algebraic symbolism, graphs,
diagrams, models, equations,
notations, images, analogies,
metaphors, stories, textbooks and
technology. Such tools provide
vehicles for representation,
communication, reflection and
argumentation. They are most
effective when they cease to be
external aids, instead becoming
integral parts of students’
mathematical reasoning. As tools
become increasingly invested with
meaning, they become increasingly
useful for furthering learning.
Source: Summary of research findings
Anthony & Walshaw (2009)
tutors and students together as a way of
evaluating learning, but at no time was this
observed in either the trainings or classes.
It is recommended that:
28. The use of the Guias de Apprendizaje y
Evaluación as a formative assessment
tool is investigated, or students are given
other means to help them monitor their
progress.
Tools and Representations
If the metaphor for the learner is a ‘mine rich in
gems to be discovered and polished’ rather than
‘an empty pot to be filled’, then appropriate
‘tools’ (Box 16) are needed.
The importance of the texts
In her seminal study Ma (1999) found that the
most effective Chinese primary school teachers
developed a ‘profound understanding of
fundamental mathematics’ (PUFM) after
becoming teachers, and that this understanding
continued to develop throughout their careers (in contrast to US teachers who usually do
not develop PUFM). When interviewed, the teachers with PUFM attributed this to: teaching
more than one grade and intensive study of the teaching materials both independently and
with colleagues (Ma, 1999). This is good news for SAT in that tutors teach different grades,
and the texts are studied as part of the training and so there is a good basis on which to
build.
31
Box 18
On turning to page 232 El Espacio y sus Elementos at a micro centro
with four students. There was a murmur of recognition when
Pythagorus was mentioned. With a little prompting of one another
they recited, in unison: ‘the square of the hypotenuse is equal to ..’
When asked what that meant, someone said: ‘a squared plus b
squared ..’
And when asked what that meant, no one could offer an explanation.
The trainer drew a diagram drawn on the whiteboard showing the
sides squared and demonstrated how the squares of the two sides
were equal to the square on the hypotenuse. The tutors expressed
pleasure at the insight that this diagram gave them and said that now
they could understand the diagram in the text.
Source: Observation March 2010
Multiple representations
It is international good practice, as in SAT, to view
the learner as an active participant in the learning
process. It is widely agreed that each person
constructs his/her own understanding by
interpreting and internalising new information and
experiences. An implication of this is that the
more complex and varied is the experience of a
concept, the more ‘concrete’ or real it is to the
learner (Box 17).
Some of the texts have rich and varied
representations of concepts (e.g., El Sistema
Decimal), while others (e.g. Manejo de Variables
Unidad 1) assume a familiarity or ‘internalisation’
of algebraic symbolism which tutors appear not to
have developed (as shown by the errors made).
The better trainers use analogies, examples and
sometimes objects (e.g., a pair of scales when
explaining equations), but it is likely that many of
the tutors do not subsequently use these as very
few take notes about pedagogy.
In other texts, there are several situations in which
tutor/student
knowledge or
understanding is
assumed which they
do not yet have (Box
18). The act of
constructing a
representation and
experimenting with it
makes a concept
more ‘concrete’.
These sorts of
activities are
recommended in the
text but were rarely
observed in the
Box 17
I now offer a new perspective from which to expand our understanding of the concrete. The more connections
we make between an object and other objects the more concrete it becomes
for us. The richer the set of representations of the object, the more ways we have of interacting
with it, the more concrete it is for us. Concreteness, then, is that property which measures the degree of our
relatedness to the object, (the richness of our representations,
interactions, connections with the object), how close we are to it, or, if
you will, the quality of our relationship with the object.
Concreteness is not a property of an object but rather a property of a
person’s relationship to an object. Concepts that were hopelessly
abstract at one time can become concrete for us if we get into the ‘right
relationship’ with them.
Source: Wilensky (1991)
32
trainings. The reason given for this was lack of time.
Perhaps some of these issues stem from the fact that the texts were written for Columbia
where the standard of maths education is higher. In Honduras is it necessary to provide
varied representations at secondary level to make up for educational deficiencies at the
primary level (in the photograph students are doing an exercise on multiples
representations with algebra36) Many coordinators and tutors identified extra materials as
an urgent necessity.
It is recommended that:
29. Tutors are informed of the
utility/theory of multiple
representations and related
activities in the text are clearly
identified.
30. The texts are analysed with
tutors to identify where extra
representations and tools are
needed, and these developed in
collaboration with the tutors. (The
Maths Coordinator has for many years wanted to address this concern and in June
2010 Asociación Bayán submitted a proposal to Irish Aid for funding).
31. When the representations are physical they should, as far as possible be made
with locally available and sustainable/recycled materials (e.g. photographs:
representing the difference between (3 + 2 )2 and 32 + 22 using bottle tops and
seeds to represent the decimal system)
36
Activity taken from The Standard Units developed by Malcolm Swan, Susan Wall & others
33
Updating and revision of texts
The texts are innovative and engaging. The maths
is integrated with the other core SAT areas,
communication, technology, science and most
importantly, service to the community. The
constant application of the maths to worthwhile
practical applications is motivating. This is
demonstrated by the vast majority of tutors37
reporting that studying with SAT had made them
feel much more positively about maths and
generally giving the practical nature of the texts as
one of the reasons. However there are some
concerns:
Most coordinators interviewed
spontaneously complained about the
number of errors in the texts because they
undermine tutor/student confidence in the
texts38. Some of the information is out of
date, and therefore now incorrect. For
example, in Matematicas 1 Conjuntos y Numeros, (revised by Asociación Bayán in
2008), the number of species is given as about a million. Current estimates are
between two and one hundred million (an interesting fact in itself) and no mention is
made of the rate at which species are judged to be disappearing.
Other opportunities to engage tutors and students with current issues are missed.
Examples of this are: the balance between using animals for economic gain and
humane treatment, and the limitations of double entry book keeping e.g. it does not
record the social or environmental cost/benefits. In Para Salvar las Barreras it is
suggested that additional material is introduced where appropriate but this was
rarely observed.
The study and practice of maths offers many opportunities for the development of a
range of attitudes/qualities/skills, for example patience, perseverance, courage,
attention to detail, etc. Trainers/tutors rarely referred to this. These are sometimes
mentioned in the Guides to Learning and Evaluation and in the introductions to the
texts, as in Box 19. This example is from the second year of Bachillerato but it would
be beneficial to give more emphasis to attitudinal development from the first
text/guide.
37
Percentage 38
For example in Manejo de Variables: Unidad 2 (adapted and contextualised by Asociación Bayán 2004) there are at least 14 typographic errors, while some are minor (e.g. omission of question marks) six could impede understanding (e.g. incorrect answer)
Box 19
Lo mismo que las otras unidades hay
un énfasis en el desarrollo de
actitudes positivas, como las
siguientes: compromiso personal en el
aprendizaje proprio y del grupo;
satisfacción por enfrentar y vencer
retos; reconocimiento del valor de lo
que se aprende para la formación
personal y para la solución de
problemas; honestidad en la
búsqueda de soluciones, convicción
en las respuestas; reconocimiento de
los propios errores y interés por
corregirlos Source: Bosquejo General, Manejo de
Variables, Unidad 4
34
It is regrettable that the standard of illustration is not higher, for example, many of
the drawings of animals in Conjuntos y Numeros look as though they have been
rather carelessly traced. In one instance the illustrations cause confusion and need
additional material or redrawing.39
It was reported by the maths coordinator that some of the longer exercises
consistently fail to engage the students (e.g., the final exercise for the community
water supply and study of house plans). The exercises were developed in Columbia
where the original students were older than the majority of the present ones in
Honduras, perhaps this is the reason why they are less successful in Honduras than
Columbia.
It is desirable that the students are fully conversant with the metric system but
Honduras still mainly uses the Imperial system and more opportunities should be
given for them to become competent in both systems and conversions.
The texts produced in Honduras do not always follow FUNDAEC referencing
conventions (and international good practice). In Aprender Enseñando there is
reference in the introduction to material from the Ruhi Institute being used but it is
not clear where. Substantial passages40 from Para Salvar Las Barreras (FUNDAEC,
1995) have been used without identifying the source.
It is recommended that:
32. Errors be corrected (the most urgent task), new illustrations commissioned in order
increase the utility of some representations (e.g. Suma y Resta), and the general
attractiveness of the texts improved.
33. The texts are analysed to identify where exercises need to be modified/changed to
make them more engaging to Honduran students and where extra information or
discussion topics could be introduced. This could be put the Teaching and
Evaluation Guides.
34. Activities are developed to enable students to become competent with metric and
imperial systems.
35. Texts follow referencing conventions with regard to acknowledging the origin of
material taken from other sources.
39 The tutors in the Maths Specialist Course reported that students find the diagrams confusing in the first exercises in Suma and Resta, La Union de Conjuntos:1. Tutors said that that these exercises are demoralising since addition is one of the few aspects of maths that students feel confident about, and they get very dispirited when they find they cannot do the first exercises in the book. The Maths Specialists suggested developing a range of activities such as stories the students could act out in order to clarify the concept of combining sets with identical elements. It might be clearer to use intersecting Venn diagrams to represent this concept rather than the current diagrams. 40
e.g. pages 40 -44 in Aprender Enseñando are very similar to pages 28 – 32 in Para Salvar Las Barreras but not referenced
35
Guías de Aprendizaje y Evaluación (Ciclo
Común)41
Informing learners of the content, purpose and
criteria for success of the curriculum is a key
factor in enabling students to become
independent learners (Anthony & Walshaw,
2009); this is emphasised in Varcarcel and Correa
(1995) and they identify the important role of the
Guias de Aprendizaje y Evaluaciόn42 (GAE) in this.
The GAE are booklets of 4 to 10 pages that
accompany each text. They contain an outline of
the curriculum, indicators for assessing student
progress, and two to five short paragraphs of
‘observaciones’ or guidance. This guidance tends
to be fairly general.43
The role of the GAEs in evaluation is discussed in the
Evaluation section below but evaluation is not the key
purpose of the GAE, as is explained in Box 20. The GAEs
are designed to help tutors and students become
active, analytical and collaborative participants in the
learning process by informing them of the curriculum.
Asociación Bayán’s vision (Box 21) has ‘transparency’ as
a key value. One of the ways this is demonstrated in an
educational institution is by making the curriculum and
evaluation criteria clear to the teachers. Therefore for
both philosophical and practical reasons it is important
that tutors are trained to use the GAEs.
Unfortunately this does not appear to be
happening: in 186 hours of observation,
the GAEs were never used or referred to.
The GAE for Book 4 (multiplication and
division) was not usable because it had not
been updated for the revised text. Tutors
cannot use the GAEs without training
because they assume a knowledge and
41
The Bachillerato GEA were not made available until 08/07/10 and so are not included in this report. 42 Learning and Evaluation Guides 43 ag., ‘representar fracciones en la recta numérica implica comprender muy bien los conceptos que se están manejando’ and ‘insistimos en la necesidad de seguir muy cerca el trabajo de cada estudiante para verificar el desarrollo de las capacidades …’
Box 20
En realidad, más que guías de la
evaluación, son guías de estudio para
ser analizadas por el tutor y los
estudiantes antes de iniciar cada
unidad. Se buscar con esto promover
una verdadero participación de
tutores y estudiantes en el proceso de
evaluación, mayor conciencia sobre
los propósitos que se pretenden y
hacer realidad la evaluación
permanente y participativa
Source: Aprender Enseñando:41
Box 21
Ser una organización comprometida con el bienestar
individual y colectivo, la excelencia, la innovación y la transparencia; con una sólida base ética, moral y espiritual, coherente en su accionar; con
una actitud y práctica de aprendizaje.
Source: Bayán website
Source: Asociación Asociación Bayán website
Box 22
The secret of what anything means to us
depends on how we've connected it to all the
other things we know. That's why it's almost
always wrong to seek the "real meaning" of
anything. A thing with just one meaning has
scarcely any meaning at all
Source: Minsky, 1987 p. 64
36
methodology which the tutors do not necessarily
have.
Another important role that the GAEs could play
is in enabling tutors and students to create links
between concepts and topics. The formation of
links is believed to be important in the process of
building up rich conceptualisations (Box 22). The
GAEs, with their brief, clear descriptions of
concepts, skills and attitudes could help tutors
and students do this.
When the tutors are in the communities they
often have very limited access to support. The
field assessors may visit a SAT centre once every
two weeks but they, and other tutor colleagues,
often do not have the knowledge to help (it is
anyway unrealistic to expect field assessors to
know the specifics of 70 texts). Almost every
coordinator and tutor interviewed spontaneously
requested additional materials so that (often
isolated) tutors could have something to refer to
for guidance and extra information.
Ma (1999) in an internationally acclaimed study
found that having guidance such as that in Box 23
played an important role in developing teacher
capacity. The GAEs, Aprender Enseñando and
texts44 comprise the tutors’ written orientation/instructions on mathematics and pedagogy.
These contain a wealth of guidance on different topics but it is often difficult to locate it
because there are no indexes and tables of contents (if present) tend to be very general.
There is a need to identify what support the tutors need and, if present in the texts, make it
easier to locate and, where necessary, develop new materials. This would assist with micro
centro45 trainings as well as individual study.
It is recommended that:
36. The Guias de Aprendizaje y Evaluación are studied in the training and tutors are
mentored in their use in the communities.
37. There is increased reflection and use of the introductions to the texts.
44 The introductions to the texts are an under-utilised resource. They are read through at the beginning of a training and were not observed to be referred to subsequently. 45
Short training organised locally for a small group of tutors to address a specific training need.
Box 23
Teachers’ manuals provide the
background for the maths in the
corresponding textbook and
suggestions of how to teach it. The
introduction of a typical teacher’s
manual gives an overview of the
textbook, its main topics, the rationale
for the text book’s organisation, the
relationship between the topics in the
textbook and the topics of the
preceding and succeeding volumes.
The main body is a section by section
discussion of each topic and subtopic
of the textbook. The discussion of
each topic focuses on these questions:
What is the concept connected with
the topic
What are the difficult points of
teaching the topic
What are the important points of
teaching the topic
What are the errors and confusions
that students tend to have when
learning this topic.
Source: Ma (1999)
37
38. Appropriate additional materials, are developed in collaboration with tutors, to
support the tutors in their mathematical development and teaching practice (Irish
Aid funding has been requested for this). The Guias de Aprendizaje y Evaluación
are adapted if necessary, studied in the trainings and tutors are mentored in their
use in the communities.
39. Appropriate additional materials, are developed in collaboration with tutors, to
support the tutors in their mathematical development and teaching practice (Irish
Aid funding has been requested for this).
Practical application of maths
Linking the maths being learnt in the classroom to real life applications is widely
acknowledged to be motivating and conceptually enriching. The tutors expressed great
enthusiasm for the practical nature of SAT maths in interviews and questionnaire responses.
Interestingly, assisting with their own university studies was the most common example
given of how studying maths had benefitted them46 (Box 23). 78%47 said that they usually
related the maths they taught in class to maths in daily life, and 96%48 said that maths was
useful in community development projects.
When asked for examples of how students used
their maths in the community, the most
frequently mentioned activities were ‘shopping’,
‘measuring out land’ and ‘planting’. Surprisingly
there was no mention of statistics.
Statistics
Coordinators report that statistical projects (for
example, on chicken production, community
health, etc.) are sometimes done in a perfunctory
way because these projects are not as
important as the end of module tests in
determining if a student passes the
module.
The data in the texts is often out of
date (e.g., in El Estado de Salud de La
Comunidad the data is for 1997), and
46
There were many references to ‘daily life’ but ‘university studies’ was the only specific example. 47
98% of respondents answered this question 48
95% of respondents answered this question
Box 24
Quien trabaja por el mejoramiento de
las condiciones de vida en el campo
debe ser capaz de analizar indicadores
sociales, entender como se
construyen, aplicarlos para
poblaciones especificas, determinar su
utilidad y también sus limitaciones e
incluso hacer propuestas para mejorar
los indicadores existentes.
Source: Bosquejo General: Destrezas
Algebraicas en la Vida Rural
38
sometimes statistical concepts are introduced but not elaborated sufficiently in the text
(e.g., the concept of the mean in the text Aritmética en la Investigación Científica). In the
training for Destrezas Algebraicas en la Vida Real very little discussion or analysis of social
indicators was observed which was surprising as it is a fundamental tool in community
development (Box 24)
Linking SAT and community maths
53% of tutors reported that ‘mis alumnus comparten en la clase los métodos matematicas
que sus padres utilizan en su vida cotidiana’. When asked for examples, after some head
scratching, tutors gave examples of simple agricultural situations, e.g., spacing between
plants. The educative process should generate ‘una armoniosa fusión de saberes, del saber
tradicional con el conocimiento moderno (Valcarcel & Correa, 1995). It appears that this
process and potential is under-developed in Honduras-SAT as yet.
It is recommended that:
40. More up to date data is used in the trainings.
41. Tutors are given copies of this data to use in the communities.
42. Statistical concepts
inadequately explained in the
texts should be identified, and
extra exercises developed.
43. Trainings are carefully planned
so that key statistical concepts
are adequately developed
44. Ways of increasing the value
that students place on
statistical projects are
investigated (and the copying
of previous years’ assignments
stopped).
45. Ways of integrating traditional
representations and methods
(estimation, measurement, etc.) are investigated.
Evaluation
In SAT, evaluation is more concerned with continuous reflection on the process rather than
making judgements on a final result (Box 25). Effective evaluation requires acting and
observing simultaneously; this is a power of the mind which has to be developed (Box 26).
Box 25
En SAT pretendemos evaluar procesos, más
que resultados. No se trata de registrar si el
estudiante adquiero tal concepto o
desarrollo tal capacidad o actitud, sino de
analizar sus progresos en caso de que sean
mínimos, tratar de detectar las causas y
encontrar la manera de superar esa
situación; lo mismo en casa de buenos
avances, promover el ir más allá en la
búsqueda de aplicaciones o de ampliaciones.
Source: Aprender Enseñando:40
39
The main purpose of evaluation in SAT, as stated
in Aprender Enseñando, is ‘assessment for
learning’. Aprender Enseñando states that the
GEA should be used to capture the learning
process; and make adjustments based on the
information. It is difficult to see how tutors can
use the GEAs to do this because the GEAs are
mainly lists of the concepts, capacities and
information that students should develop or
acquire, (and their related indicators), but there is
no mention of how the process should be
captured. It is assumed that the tutor will be able
to interpret the GEAs, but as they have not
studied them in the trainings this is not possible.
At the moment they are more a guide for
‘summative’ or end of course assessment than for
‘assessment for learning’.
It is recommended that:
46. Tutors are systematically supported in
the use of GEAs for assessment for learning and, if necessary the GEAs are adapted
or additional material provided.
Community Evaluation
All of the parent groups are expected to be active in the evaluation of learning and
identification of goals. Some groups are very active (Box 27).
Box 27
En algunas comunidades de X además de la sociedad de Padres y Madres de familia existe un
asociación a la que se le llama la Junta del Colegio. Esta junta está conformada por 5 a
7 miembros, electos en una reunión donde todos los habitantes de la comunidad participan
(tengan o no hijos estudiando en el centro educativo). Esta junta vela por el desarrollo de
actividad para todo el centro ... Su labor es apoyar al máximo el bienestar de la comunidad
educativa y se encargan de las actividades macro, es decir actividades en las cuales toda la
comunidad debe estar involucrada. Es importante mencionar que muchos de los miembros de
la junta son jóvenes, que tiene niños pequeños que no van ni al Kínder o están en la escuela y
algunos no tienen hijo.
Source: coordinator email junio 2010
Box 26
The image of two birds, one eating
and the other watching pervades
Eastern and Western art. There are
multiple interpretations ... an
educational interpretation is that the
two birds are forms of attention ... the
eater is the part of us that gets caught
up in doing while the watcher is the
internal monitor-witness that
observes without judging. The
watcher has been likened to
conscience which needs to be
awakened and developed...When
applied to teaching it means it means
having a part of you separately
witnessing the lesson, able to observe
and suggest alternative actions
Mason & Johnston-Wilder (2004)
40
Evaluation – testing and retesting
Maths: a problematic part of the
program
Of the five SAT curriculum areas,
students generally have least success
with the maths’ tests. Data on test
performances are available from 2008,
and shows that maths has almost
invariably been the area with the
highest number of test retakes (Figure
1). It was reported orally that maths has been
problematic since the beginning of the program. This can be
largely explained by the fact that tutors come from a low
quality educational system (Box 28) and that the tutors’
literacy levels affects maths understanding (Box 29). It is
widely believed by tutors that the maths in the SAT
curriculum is at a higher level than
other Honduran Bachilleratos; one reason for this could be that it demands more
conceptual understanding and for this to be articulated. It is therefore unsurprising that
there are significant problems.
Percentages of retakes for 2008
Students take a test at the end of each module and if they score less that 60% they are
required to retake it. Data on retake rates for different regions was available for 2008
(Block 2 & 3). 2008. 2008, Block2, Impulsor 2 was selected as an example because it was the
most complete. The wide range is remarkable and sometimes difficult to explain. The two
regions with the highest retake rates border on the region with the lowest rate (I, M & K).
The tutors would have attended the same training and the student population was similar.
01020304050
Percentage of students retaking test by area
2008
2009
2010
0
20
40
60
80
100
A B C D E F G H I J K K L M Npe
rce
nta
ge
of
stu
de
nts
re
tak
ing
te
st
Region
2008 Block 2: Impulsor II
Photograph:Ruth Moulton
Figure 1
41
Some centres had lower retake rates at each level. It has been suggested that one reason
for this could be that different criteria are used to define a retake. In 2008 a student could
retake the test various times, and some centres might have counted each attempt as a
retake while others only counted the student once. Also, it was reported to the consultant,
some centres allow students to redo a couple of answers in a test if they only are a few
marks short of 60, and do not count this as a retake, while other centres do not allow this.
It is also possible that good practice is affecting retake rates. If so, this should be identified
and widely shared. A standardised system of data collection and analysis is necessary to be
able to make any judgement.
Data on summative assessment (if valid and reliable) can be valuable in the evaluation
process. Currently the test data are of limited value as the retake rate is a blunt instrument
for measuring performance. All students gaining 0-59 marks have to retake. There is no
way of knowing if a student scored 59 or 0, and whether those passing scored 60 or 100.
Data on maths performance is held in the Institutes to which each SAT centre is affiliated,
but is difficult to obtain. It would greatly assist Asociación Bayán in identifying trends and
assessing the effectiveness of educational interventions, as well as to monitor the progress
of individual students, if data on test scores were collected.
It is recommended that:
47. Criteria for defining a ‘retake’ are standardised (Asociación Bayán is developing a
data entry system to improve accuracy of entry and calculations, and there are
plans to produce a data collection manual for staff) and reports are archived.
48. Data on student and tutor test scores are collated and analysed.
Comparing SAT performance with the government system
The Universidad Pedagogica Nacional Francisco Morazan is in the process of carrying out a
study for the Secretaria de Educación Pública (SEP) comparing the ‘rendimiento academico y
factores asociados’49 of SAT over 2008-2010 with a control. The control is the Secondary
School or Centro de Referencia (CER) that the SAT group is associated with for administrative
purposes. There are 53 SAT Centres (853 students) and 25 CERs (1,234 students) in the
study.
There was not a statistically significant difference between the two groups but as the
questions are based on the CER and not the SAT curriculum, the validity of the comparison is
questionable50. It was interesting to note that the SAT students who had not been taught
49
Academic achievement and associated factors. 50
However, due to frequent teacher strikes/absences, the CER students may not have been taught the material that the test was based on either!
42
statistics, probability and geometry did about as well as the CER students, who supposedly
had been taught these subjects! The Hewlett study, which has a more rigorously defined
comparison group, plans to apply questions which have been designed for an international
comparison study.
Tutors and mathematics: knowledge, attitudes and beliefs about teaching and learning51
It is widely recognised that obtaining information on attitudes and beliefs is problematic,
and the results should therefore be treated with caution. However, as SAT is concerned
with the development of attitudes and beliefs and the impact they have on action, it is
something that must be attempted. Based on empirical evidence, it is essential to ‘start
where the learner is’ and this requires knowing something of the underpinning premises
that the learner is using to construct his/her understanding of mathematics.
Tutor attitudes to maths: the positive results of training
The tutors reported generally
positive attitudes towards maths
in the questionnaire survey
(Appendix 3). Almost all the
tutors said that being good at
maths was something that was
accessible to all, not just the
‘brainy’. They appeared to enjoy
learning maths, and feel ‘un gran
satisfación con exíto con un
problema matematico’52. All53 SAT tutors thought ‘las matematicas son utiles y necessarias
en todos los ambitos de la vida’54. But, interestingly, only 76% thought that maths was
necessary for understanding the sciences. There is a tendency in attitudinal questionnaires
to report what is considered to be the ‘correct’ attitude, and so the answers may be
aspirational or compliant, but, even taking this into account, there is a pleasing positivity
about maths.
A remarkable 98% of tutors55 reported feeling more positive about maths after studying the
SAT texts, and 66%56 of tutors felt they were ‘capáz y hábil’ at maths. 83% reported that
51
A rigorous selection process, interviews and two week initial training, assist Asociación Bayán in selecting tutors who appear to have an attitude of learning and are orientated towards service to the community. Co coordinators expressed the expectation that as the number of SAT graduates working as tutors increases, the training process will become easier because they will already be familiar with the texts and core values/assumptions. 52
‘Very satisfied with when a maths’ problem is solved’. 53
Over 99% of respondents replied to this question/statement 54
‘Maths is useful and necessary for all aspects of life’. 55
All tutors who had studied with SAT for more than a year reported improved attitude to maths 56
95% of respondents replied to this question/statement
43
after training they felt they understood all the material and could do all the exercises. This is
supported by interviews and casual conversations in which tutors often spontaneously said
how much they had learnt with SAT. It is an outstanding achievement to have enabled the
vast majority of tutors to feel more positive about maths (Box 28).
Tutors particularly mentioned the
practical application of maths, the
emphasis on ‘porque?’57, and how
easy it was to ask questions in SAT
trainings. However there appears
to be a minority who struggle in
each training and, are either left
behind or slow the progress of the
whole group. If the standard of
maths in SAT is to be raised it is
vital that these tutors are
identified and systematically
supported.
It is recommended that:
49. Tutors who find maths difficult are identified at the beginning of their training so
that they can be given extra support
57
‘why?’
Box 28
A mí me encanta las matemáticas y yo siento que lo que
he aprendido en SAT me ha ayudado mucho en mis
estudios universitarios y en mi vida diaria.
Siempre me he sentido que me gusta las matemáticas
pero desde que estoy en la sistema he descubierto que
se resuelven muchos problemas de la vida con mejor
facilitad.
Estudiar los textos de SAT y es muy importante ya que
ayudan en gran manera en nuestra vida como
profesional también para tener alguna destreza
conocimiento al momento de usar el estudio superior
en la universidad.
Source: comments on tutor questionnaires
44
Building on an apprenticeship of observation
Almost all tutors have had a long apprenticeship of
observation in the transmission approach during their
twelve or so years of schooling and the questionnaire
survey indicated that many hold beliefs consistent with
this approach (Appendix 3). Research shows that this
deep identification with often respected teachers58 and
their mode of delivery means that ‘superficial attempts’
to change teachers to a more active style will either be
‘neglected’ or ‘ignored’ (Schwille & Dembélé, 2007:30).
The skills that tutors have acquired in the transmission
method (e.g., clear explanations, see photograph)
should be recognised and developed and their beliefs
about teaching and learning explored (Box 29). One
coordinator said that he noticed that tutors who were
less good at maths tended to have more participatory
lessons, and that the most knowledgeable ones tended to take over and teach in a more
formal way. This implies that tutors may have a tendency to adopt more transmission style
if their knowledge increases and trainers should be aware of this.
Changes in beliefs59 and practice are complex but it is possible that changes in practice
precede changes in belief (Swan, 2008). It is
therefore important to use participatory and active
methods when training to demonstrate alternative
methods and tutors should be given specific and
supported opportunities to develop their practice
towards active methods which have been shown to
be effective. It is very probable that most tutors are
disposed towards doing this as they reported
developing student capacity for independent
learning as a priority (Appendix 3). Research with
teachers indicates that sustainable changes in
practice are achieved by making a few, small
changes in consultation and collaboration with other
teachers (Hodgen & Wiliam, 2006). Field assessors
could play a very important role in facilitating this.
58
Surprisingly (considering reports of the standard of maths teaching in Honduras) 79% of tutors thought that they had had good teachers at school (questionnaire). This is at variance to a discussion on previous maths’ experiences in the maths specialist training when several tutors said how ‘traumatised’ they had been. 59
For example, a change from seeing the student as ‘a mine rich in gems’ rather than ‘an empty pot’.
Box 29
Any attempt to encourage teachers
to modify their beliefs about
teaching and learning must
therefore entail the explicit
recognition of existing beliefs and
their situated nature, attend to the
constraints and difficulties under
which teachers work and allow
teachers time to reflect on the
contradictions between ‘good
practice’ and ‘existing practice’. Source: Swan, 2006:173
45
Theory- based practice
Research indicates that the ability to relate practice to theory is an important tool in the
process of reflecting on experience. Most tutors are studying at the university and it would
be enriching for them to form links between the educational theory that they are learning
there and SAT theory and practice. It is possible that the failure to fully implement the SAT
methodology is due to a lack of understanding of the reasons for some of the practices. The
importance in SAT of relating conceptual understanding to the practical application of
knowledge was mentioned during trainings, but few other instances of linking practice to
other aspects of the SAT theoretical framework or wider educational theory were observed.
Also developing tutors’ theoretical knowledge would assist tutors to modify their practice in
a systematic way as they could research and modify their practice using a theory of change
model. 60
It is recommended that:
50. The tutors’ pedagogic/theoretical learning in SAT is linked to the educational
theory and pedagogy studied in the university.
51. Tutors are systematically informed about SAT methodology and theory.
52. Tutors form groups to conduct simple collaborative action research on SMALL
changes in practice based on a theory of change model.
53. Assessors are trained to support tutors in developing more participatory practices
and to promote and support action research.
Maintaining positivity: getting unstuck
‘Being stuck is an honourable state’ (Mason
& Johnston Wilder, 2004:287). Being stuck
helps learners develop powers of
reflection, perseverance and courage. It is
often a necessary stage when studying and
applying maths and learners should realise
this. The most stressful thing for tutors
(25% of responses61) was ‘cuando me
atasco o bloqueo en la resolución de un
problema’. When asked how they
overcame ‘maths blockages’, tutors did not
have any defined strategies apart from ‘not
giving up’.
60
a cost effective and perhaps most efficient way of conducting educational research. 61 The second most stressful thing was being unexpectedly asked to do a presentation at the whiteboard (19%).
46
Box 31
El sistema educativo de Honduras presenta un retraso de 100 años respecto a las
naciones vecinas de Costa Rica y Panamá, según un informe divulgado este lunes por la Organización de Naciones Unidas para la Ciencia, la Cultura y la Educación (UNESCO) y el Banco Centroamericano de Integración
Económica (BCIE). En materias como matemáticas o lenguaje el porcentaje de
aprobados es inferior al 47 por ciento, una tasa muy lejana al 70 por ciento exigido en
los Objetivos de Desarrollo del Milenio (ODM) establecidos en 2000 por Naciones
Unidas. A pesar de que la tasa de alfabetización de Honduras ascendió del 68
al 80 por ciento en la década de los noventa, el documento de UNESCO señala la necesidad urgente de mejorar el sistema
educativo hondureño.
'Estamos 100 años atrás de lo que están Panamá y Costa Rica, sin compararnos con
países como Canadá, Estados Unidos o Japón, sino a nuestros vecinos más
cercanos', señaló el coordinador de la Red de Educación de Honduras, Elmer Villeda,
durante la publicación del informe.
En los últimos tres años apenas se han impartido un cincuenta por ciento de las
clases establecidas en el calendario escolar hondureño, según otro informe publicado
por la Federación Iberoamericana del Ombudsman (FIO), una red que sirve de
apoyo a todas las defensorías del pueblo de América Latina, informó el diario 'El
Heraldo'.
Source: 20 de abril http://noticias.terra.es
Box 30
The knowledge gap between the US and
Chinese teachers parallels the learning gap
between Chinese and US students ......the
quality of teacher subject matter knowledge
directly affects student learning – and it can
be immediately addressed
Source: Ma (1999)
It is recommended that:
54. Tutors are taught techniques for
overcoming ‘bloqueos’, and that this
is normal and even useful for the
learning process.
Tutor knowledge
Tutors are not expected to be ‘teachers’.
They guide their students through each of
the five components of the program and it
would be unrealistic to expect all tutors to
have the knowledge of a specialist maths
teacher but a sound basic knowledge is
necessary (Box 30). All coordinators
interviewed expressed concern about the
level of tutors’ mathematical knowledge
although 66% of the tutors reported
themselves as ‘capáz y hábil’. It should be
remembered that judgements about one’s
own performance are made via comparisons
within a reference group.62 Many of the
tutors may feel that they are relatively good
at maths63, but this does not necessarily
mean their maths is good enough to fully
62
Students at the university report knowing more maths in their peers and on at least one occasion being asked to assist the lecturer in teaching the other students (email correspondence with coordinator) 63
Tutors often reported how studying maths with SAT had meant they were one of the better students on their university maths courses.
47
access the SAT curriculum (Box 31 and Box
32). 64
The students entering SAT come from rural
primary schools. Frequent teacher absence
and small schools, in which five grades are
sometimes taught together, means that
the students have usually received a
woefully inadequate primary education.
Teaching quality is important for all
students, but it has most impact on the
weakest (Hodgen & Wiliam, 2006). This
increases the pressure on SAT tutors to be
good at their job.
Basic mathematical operations
Tutors sometimes had difficulties with the vocabulary (Box 33), underlying concepts and
procedures for basic mathematical operations.
For example, long division. In Book 5, Aritmetica
en la Investigación Científica, it was observed that
many tutors had problems with the long division
algorithm, and none used the recommended
vocabulary at the beginning of the session. One
tutor who came to the board could not even begin
to do the calculation, and two admitted not
knowing what to do with the decimal point. The
Trainer however was excellent at probing and
checking tutor understanding, and by the end of
the session all the tutors appeared to be
proficient. It often seemed that the tutors did not
64
Tutors take the end of module test at the same time as their students and this information is used by
coordinators to identify where more training is needed. This information does not appear to be collected
centrally.
Box 32
Hay un ejercicio que hacemos con ellos por ejemplo. ¿4 x 6 es lo mismo de 6 x 4? y la mejoría, el
99% dice que sí, es el mismo. Pero si se presentan situaciones de la vida cuando no es la misma
… claro tiene razón, porque ellos han aprendido las tablas aritmética y allá no más. No han
aprendido a relacionarlo con algo cuando les viene a SAT les cuesta.
Source: coordinator interview, May, 2010
Box 33
Una cosa curiosa también es que nos hemos
encontrado que los tutores tienen muchos
dificultades en la parte de comunicación, de
leer, de escribir, comprehension de lectura.
Tienen muchísima dificultad en
matemáticas. ... el lenguaje que se utiliza en
los textos supone que la persona, en la parte
de comunicación, comprende lo que está
pidiendo. Por ejemplo dice agrégale el doble
del producto de tal cosa por tal cosa…y allí
nos detenemos. Source: coordinator interview March 2010
Box 34
When doing an exercise requiring the
calculation of the average of food
consumed and weight of 25 chickens
six tutors came to the board to
demonstrate how they did this. Each
one painstakingly used the standard
long division algorithm even when
the number to be divided was 75000.
No one questioned this or suggested
an alternative.
Source: Observation February, 2010
48
have a sense of the numbers that they were dealing with; increasing the use of estimation
would help develop this. It was very rare to see different methods of working out a problem
discussed (Box 34) although it is a part of the SAT methodology.
It is recommended that:
55. Estimation techniques are taught and
practised.
56. Different procedures for working out a
calculation are compared (when appropriate)
particularly in respect to their efficiency.
The transition to Bachillerato
Just as students have difficulties adapting to
the SAT system when they enter Ciclo Comun
so to the transition to Bachillerato is
problematic and these difficulties often stem
from inadequately understood concepts in
Ciclo Comun.
There is rightly a strong emphasis on developing algebraic competency in SAT (Box 35).
Tutors and coordinators identified algebra
generally, and in particular the expression of
everyday problems algebraically, as the most
problematic and disliked topic. Difficulties are
apparent from the beginning. For example, at a
course for maths specialists sustained help was
needed to define the elements in the set ‘people
attending this course’. Other basic ideas from the
first maths module, such as ‘an element can
belong to both a set and a subset’ had to be
clarified. If the most competent tutors were
unsure, it is to be expected that the average tutor
will struggle, and the average assessor will be
unable to offer much support in the classroom.
In Bachillerato, weaknesses present in Ciclo
Comun become more apparent, e.g., in all six
classes observed of Polynomios II, tutors taught a
mechanical method for expanding quadratic equations. Understanding of this method was
not probed, and a substantial number of student errors went uncorrected. Twenty
Box 35
Nobody has ever been able to reach the
concrete. The concrete is so abstract
that nobody can reach it. We can only
function because of abstraction.
Abstraction makes life easy, makes it
possible ...The essential point is this
algebra is an attribute, a fundamental
power of the mind. Not of mathematics
only.
Source: Gattegno, 1970, cited in Mason &
Johnston-Wilder, 2004
Box 36
Micro centro de polinomios con
tutores de II Bach, A & B. El micro
centro se realizo con el objetivo de
reforzar tutores ya que durante la
visita pedagógica realizada al grupo
se observo debilidades en el manejo
de contenido, se reforzaron conceptos
como los siguientes, propiedades de la
multiplicación, terminos semejantes,
productos notables, propiedades de la
potenciación, grado de un polinomio.
Source: assessor monthly report, March
2010
49
Bachillerato tutors were asked if they could suggest an alternative way of representing a
quadratic equation in order to make it more meaningful to students (e.g., a diagram, graph
or real life example). Only one tutor was able to do this, relating it to an area of land. In
three SAT classes, students were asked if they could make a diagram of what they were
doing. None could at the beginning of the lesson, but following an example, most students
were able to do this and expressed relief at having gained a new level of understanding (as
did the tutors). It appears from monthly reports that
some assessors are very effective at identifying when
support is required and providing it (Box 36)
Finally it was noted that opportunities for developing
algebraic skills in the Ciclo Comun are sometimes not
used. For example, in a lively and practical lesson on
triangles and parallelograms, insufficient time was
allowed for students to explore and develop their
own formulae.
With the help of a skilled trainer many tutors make
substantial progress but limited time in training
means that additional support is needed by some
tutors (Box 37 and photograph).
It is recommended that:
57. Activities in the texts that are particularly suitable for developing algebraic skills
in the Ciclo Comun texts should be identified before training and carefully planned.
58. Work with algebra should include multiple representations.
Box 37
Destrezas Algebraicas:327: A
water supply problem
26 tutors in the group working in
friendship groups of two to four.
The text book gives 9 variables (no
of inhabitants, average number of
animals per family etc) to make
into a formula for calculating the
daily water requirement.
All groups were flummoxed and
unable to start task. Many
requested trainer’s assistance.
Two groups, with trainer help,
developed formulas which they
explained coherently at the board,
correcting errors after trainer
input. Most groups began to make
inroads into the task after
significant assistance from trainer
and other tutors, but one group of
three was unable to make any
independent progress on the task.
After lunch, in the next session a
new topic was started.
Source: Observation May 2010
50
Preparing for training
To study or not to study texts
Tutors do not usually work through the texts before trainings although they are requested
to do this65. When interviewed a tutor who had done the exercises reported finding the
training boring as it mainly consisted in redoing the exercises. If all tutors were expected to
read the texts, but not actually do the exercises, before the training and note where they
had questions or comments it would assist trainers in allocating training time efficiently.
It is recommended that:
59. Tutors read the texts before training and note where they have difficulties. At the
end of the training review, this list of difficulties can be reviewed, progress
assessed and further support needs identified.
60. Tutors read texts before training and note down ideas for additional teaching
materials, activities etc. so that these can be shared at the training.
Maintaining the quality of maths training
The Training
Some coordinators are seriously concerned that the rapid expansion of SAT and loss of some
key personnel has diminished the quality of training, not only from a technical point of view
but, more vitally, there has been a loss of ‘la mística del trabajo’ or ethos.
In the great majority of maths trainings there was a purposeful and collaborative
atmosphere and the most tutors appeared to make good progress. It was noticeable that
the trainer’s style had a large impact on the learning environment; in some observed
sessions there was a rather subdued atmosphere, questions were rarely asked by tutors,
and a mainly ‘transmission’ teaching style was used. It also appeared that some sessions
were not carefully planned. This resulted in key concepts/skills/attitudes not being clearly
identified and developed. This probably significantly affected tutor progress and their
capacity to adequately accompany their students.
Although most tutors engaged wholeheartedly with the training process, there was a
(sometimes sizeable) minority in some sessions that did not. Concern was also expressed
that the incidence of unprofessional conduct during trainings was increasing. Some tutors
also complained about feeling pressured by other members of the group not to ask
questions or discuss issues so that the text could be completed quickly. It was reported by
coordinators that, worryingly, it tended to be tutors who have been longer in SAT who were
less motivated during the trainings.
65
There is evidence that a few tutors (perhaps ones with the weakest maths) copy out other tutor’s answers if asked to fill in the texts before the trainings
51
It is recommended that:
61. The training of trainers is made a priority.
62. All training sessions are planned.
63. Maths trainers have relevant teaching
experience.
64. The most capable and enthusiastic tutors
who are studying, or have studied, maths
and pedagogy at the university are trained
as trainers (this is already happening)
Supporting tutors’ development of practice in
the field
The importance of providing teaching manuals,
additional teaching tools and videos are mentioned
in other sections of this report.
In some areas the provision of micro centros is well
developed and plays an important role in
supporting tutors. In other areas micro centros
cannot be as responsive to the tutor needs because
of a lack of trained staff. The maths specialists
could play an important role in the provision of
micro-centros but it is necessary to train them. This
is happening, in the past seven months 24
tutors/assessors received a five day maths
specialist training.
The role of the field assessor
The field assessors are another set of SAT heroes;
on motorbikes, buses or foot they travel on bad
roads or paths to visit remote communities. It was
not unusual to meet an assessor (or coordinator) in
bandages from a recent motorbike accident (Box
38) or, as happened recently, shocked by an assault
in which his motorbike was stolen and he was tied
up and thrown down a hillside.
According to the coordinators, because of lack of
training, some assessors have a limited
understanding of the SAT methodology, and this
affects the quality of the acompanimiento they
provide the tutors. Field assessors, although they sometimes attend general trainings,
Box 38
Two hours from home and an hour
away from Comayagua an assessor
collided with a motorbike that was
going the wrong way up a one way
street, both motorbikes lost balance
and fell and both riders were taken to
see the community nurse; the
assessor was bandaged up and given
something for the pain. He carried on
his journey to the Institute in order to
hand in paperwork so his tutors would
be paid. When he arrived at the
Institute the director was shocked by
his injuries and took him to the
hospital. He was bandaged up again
and given an injection for the pain. A
mechanic mended and adapted his
motor bike so he could ride it with
injured leg. He arrived in Comayagua
about an hour later, soon after
7.00pm. He went to the SAT centre to
collect text books. It was a wet, cold
and windy night. The coordinator,
who had just got home after a 12 hour
day travelling to the communities,
returned to the centre to hand over
the texts, check that he could get to
his sister’s house in Comayagua and
that he would attend properly to his
injuries. When he arrived at his
sister’s house he had to be helped off
the bike and carried in. Three months
later he is ’90%’ recovered.
Observation and tutor interview
March and August 2010
52
appear to receive very little specialist training; the one assessor training organised (to the
consultant’s knowledge) during the first half of 2010 was cancelled. Field assessors who
have not been SAT tutors often do not know the texts well.
It would of course be difficult for any field assessor to become an expert in all 70 texts, but
they could specialise in one area (as with the maths specialists) as well as general pedagogy.
It is recommended that:
65. Field assessors’ training needs are reviewed and met.
Institutional links
In the Final Report to the donor 1045-0688 (1 July 2004 – 30 June 2006) it says that one of
the lessons learned was: ‘La participación de los actores como las universidades en el
desarrollo del programa incrementa la credibilidad del programa, facilita la consecución de
becas de estudio para los estudiantes, y reduce
los costos relacionados a consultorías y
asesoramientos’.66 This was surprising to read
given that, while Asociación Bayán has excellent
links with various government departments,
there was no contact related to pedagogy or
educational theory with a Honduran university
or other educational establishment in the first
half of 2010 as far as the consultant was aware.
Bayan has had an agreement with the
Universidad Autonomia de Honduras (UNAH)
since 2001 which states that they will work
together to ‘mejorar la calidad professional de
los docentes y superar la calidad de vida de los
pobladores de la Mosquitia67 (this was later
extended to all regions in which SAT was
working). However despite many attempts and
considerable effort on Bayan’s part (Box 40) this
relationship has not developed.
66 The participation of universities in the program’s development has raised the status of the program, helped obtain scholarships for students and reduced consultancy and evaluation costs. 67 Improve teaching quality and the quality of life for the inhabitants of the Mosquitia.
Box 40
Tenemos un Convenio Marco con
UNAH,
Don X los contactó a Curla de la Ceiba
tambien, para otro convenio, no
prosperó
La universidad pedagogica ha dado algo de cursos, como "Preparación de Instrumentos de Evaluación" para Bayan, donde participaron varios coordinadores La universidad pedagogica fue abordado en multiples ocaciones para un reconocimiento oficial a las capacitaciones de Bayan, no aceptaron, etc.
Source: email from Executive Director,
August 2010
53
This is a loss for UNAH because Asociación Bayán, with 14 years of experience implementing
SAT, has much to contribute to Honduran educational discourse.
This relative isolation, national and international,
means that Asociación Bayán is not, in the view of
the consultant, doing enough to draw on recent
research findings around international best
practice in maths teaching, and to see if it
contains elements that are appropriate for
adoption and adaption.
Although the quote in Box 39 is referring to
community development it could be argued that it
is these activities which maintain the vigour and
development of any process. Some coordinators
have expressed the concern that the SAT-
Honduras risks stagnating if it does not become
part of a wider dialogue, more closely linked with
the Honduran educational system68, and to
rigorous national and international educational
debate. Therefore, even though there are huge
time pressures on key staff, time should be found for this.
The comparative evaluations being undertaken by the Universidad Pedagógica Nacional Francisco Morazan, and the Hewlett study have not, as yet, contributed to any developments in practice or theoretical understanding. To date there has been no substantive progress report of the research being undertaken under the Hewlett study but it is expected that it will make a substantial contribution to understanding the taught and learned69 SAT curriculum and its impact on students.
Finally, it is surprising to the consultant that there are not closer links with FUNDAEC. Networking or developing a forum with other SAT Programs for informal discussion of methodological/pedagogic/ philosophical questions would be invaluable for Asociación Bayán, and FUNDAEC might also benefit from such a link (for example, when the Ciclo Comun texts were revised, it could have been useful to have sought Asociación Bayán’s reflections on its considerable experience with SAT).
68 Recent changes in the Honduran curriculum may require adjustments in the SAT curriculum e.g., the teaching of the division algorithm, 69
The ‘official’ curriculum is what tutors are expected to teach, as set out in the GEA and texts but what is ‘taught’ curriculum (what actually happens) will depend on tutor knowledge, interests, and skills. Students also affect the curriculum by their previous knowledge, attitudes towards learning etc.
Box 39
It could be claimed that a people
were in charge of their own
development only if they were
learning systematically about the
changes that occurred in their society,
and were consciously incorporating in
their continuous learning process
appropriate elements from the
universe of knowledge: their own, the
modern knowledge system, as well as
the experiences of other people and
groups in the world who are facing
similar challenges.
Source: Arbab et al, 1988
54
It is recommended that:
66. Asociación Bayán’s teaching staff form links, both formal and informal with other
educational institutions, and engage more actively with national and international
discourses on education.
67. An inter SAT Program learning network be created.
55
Conclusion
The maths component of the tutor training program has achieved many notable successes:
The training and supporting in the communities of about 700 tutors over the last
decade.
The vast majority of tutors questioned reported that: SAT had made them feel
more positively about maths; after the trainings they could do the exercises in
the text book; they felt confident explaining the exercises and enjoyed teaching
maths; those studying maths at the university said that SAT had significantly
helped them with their studies, that they understood more and were able to use
maths more in practical applications.
It was observed that the inclusive and relaxed, but purposeful, atmosphere of
the trainings is usually replicated in the SAT classrooms.
There is therefore a sound foundation to build on. The rapid expansion of SAT has
however put the training process under considerable strain; all interviewed coordinators
expressed concerns about maintaining the quality of SAT. It was also found that some
key elements of the SAT methodology were not being fully implemented, and that there
were other factors which, if addressed, could significantly improve the program.
The most important recommendations of this report are therefore that:
Asociación Bayán continues to build on these good foundations by continuing to
reflect and experiment with ways of further developing ‘an atmosphere of
consultation’. Activities which are a part of the SAT methodology, but which have
only partially been adopted, or not been adopted by Asociación Bayán, are fully
implemented, unless consultation with FUNDAEC identifies them as being no
longer appropriate.
Priority is given to building the capacity of:
o trainers to use the SAT methodology fully rather than partially
o the field assessors to ‘accompany’ the tutors in the development of their
general pedagogic skills;
o carefully selected maths field support staff to effectively support the
tutors develop their (more specific) maths pedagogy/knowledge.
Relevant insights, techniques and tools originating outside SAT, particularly those
associated with increased classroom participation, conceptual development and
‘formative assessment’, are identified and considered for adoption and
adaptation, since (according to the consultant’s experience and relevant research
literature) these have the potential to significantly enhance some key aspect of
the SAT pedagogy/curriculum.
56
Effective fora for the consultation of pedagogic and other educational issues are
established.
The collection and analysis of field data and feedback is systematised and
standardised (where appropriate) and archiving systems are improved.
Other recommendations are that:
Aprender Enseñando is used to develop consultation skills, and its delivery is
collaboratively planned so that all tutors have a comparable experience.
Tutors are explicitly taught the characteristics of ‘exploratory talk’, provided
opportunities to develop these skills, and mentored in facilitating appropriate
kinds of ‘exploratory talk’ in the classroom.
Training sessions are planned for developing a wide range of pedagogic skills,
particularly those associated with assessment for learning, conceptual
development, and increased participation.
Recommended activities/methods, if not explicit in the text, are clearly explained
to the tutors.
Topics in which tutors regularly experience difficulties are identified before
training so that sufficient time can be allocated to them, and related questions,
reflection, activities and discussion adequately planned.
Sufficient time is allocated for ‘independent working’ in the trainings.
Tutors have a written record (e.g., training handouts) to support classroom
practice and/or training in the taking of pedagogic notes, since inspection of
many tutor texts revealed that tutors rarely take pedagogical notes.
Trainers allow time between questions and responses, and discuss the reasons
for doing this with the tutors.
Activities in which question formation is explicitly requested, or which lend
themselves to this, are clearly identified in the trainings in order to help tutors
more effectively utilise the texts.
Trainers experiment with small group work as a way of encouraging the
formation of more reflective student questions, and encourage the tutors to do
the same.
Tutors are supported and mentored in the didactic use of questions and ‘error
analysis’ as a ‘formative assessment’ tool; this includes being informed of the
utility of this approach; experiencing it in their training; highlighting appropriate
SAT text examples; being made aware of the key relationship between errors and
‘misconceptions’; and being mentored in developing their own questions in field
assessor accompaniment.
Trainers/tutors are taught a range of techniques for increasing tutor/student
participation when answering questions.
57
Trainings are planned so that key statistical concepts are developed and
understood.
More up to date data is used in the trainings, and tutors are given copies of these
data to use in the communities.
The reasons why independent working is important are presented and discussed
in the trainings.
Maths trainers have relevant experience.
The most capable and enthusiastic tutors who are studying, or have studied,
maths and pedagogy at the university are trained as trainers (this is already
happening to some extent).
Field assessors’ training needs, as regards supporting tutors’ pedagogic
development, are reviewed and met.
Statistical concepts inadequately explained in the texts are identified, and
additional exercises developed.
Ways of increasing the value that students place on statistical projects are
investigated (and the copying of previous annual assignments is stopped).
Ways of integrating traditional representations and methods (estimation,
measurement, etc.) are investigated.
Tutors are systematically supported in the use of the Learning and Assessment
Guides for assessment for learning and, if necessary, additional materials are
provided.
More efficient methods to check answers and correct procedures (e.g., use of
small individual white boards, peer checking, etc.) are used in the trainings and
classes instead of whole class presentations by individual students/tutors.
Student/tutor presentations of work are used as the basis for discussions.
Tutors/students experience and reflect on a range of techniques for improving
group work
A range of formative assessment techniques is used; those in the texts are
identified and, where necessary, additional ones are introduced; and
trainers/tutors/students are supported in developing their capacity to use them.
The use of the Guias de Apprendizaje y Evaluación as a formative assessment tool
is investigated, or students are given other means to help them monitor their
own progress.
Tutors/students are given clear criteria of how to assess their own and others’
work, and guidelines are written on how to peer teach/accompany a
tutor/student without creating dependency (perhaps using the Guias de
Aprendizaje y Evaluaciόn).
The texts are analysed to identify which exercises need to be modified/changed
to make them more engaging to Honduran students, and where additional
58
information or discussion topics need to be introduced (these could be put into
the Teaching and Evaluation Guides).
Errors in the texts are amended and new illustrations are commissioned where
the current ones are unclear (e.g. Suma y Resta) or unattractive (e.g., Conjuntos y
Numeros)
When the representations are physical, they are made, as far as possible, with
locally available and sustainable/recycled materials.
Texts produced in Honduras follow FUNDAEC (and normal practice) referencing
conventions with regard to identification of the origin of material taken from
other sources.
Activities are developed to enable students to become competent in both metric
and imperial systems.
Tutors are taught techniques for overcoming ‘bloqueos’, and that the process of
meeting and overcoming maths learning blockages is perceived as normal and
often key to the learning process.
Estimation techniques are taught and practised.
Work with algebra includes multiple representations.
Tutors read the texts before training and note where they have difficulties. At
the end of the training review, this list of difficulties can be reviewed, progress
assessed, and further support needs identified.
Tutors who find maths difficult are identified at the beginning of their training so
that they can be given extra support.
Sufficient time is allowed at coordinator meetings for consultation on pedagogy,
particularly with respect to the development of an enriched and common
understanding of the SAT methodology.
Asociación Bayán’s teaching staff form links, both formal and informal, with
other educational institutions, and engage more actively with national and
international discourses on education.
An inter SAT/PSA Program learning network is created.
The tutors’ pedagogic/theoretical learning in SAT is linked more closely to the
educational theory and pedagogy studied in the university.
Tutors are given opportunities to share good practice e.g., via intranet, trainings,
micro-centres, tutor meetings, the SAT Bulletin, etc.
Tutors read texts before training and note down ideas for additional teaching
materials, activities, etc., so that these can be shared at the training.
Tutors/students are given opportunities to work in different groups during
training.
Tutor/student capacity to work in groups is developed by using different types of
group work, and by providing opportunities for analysis of the effectiveness and
inclusivity of the group work.
59
Tutors form groups to conduct simple collaborative action research on small
changes in practice based on a ‘theory of change’ model, and field assessors are
trained to promote and support this action research.
Criteria for defining ‘retake’, ‘opinar’ and other terms on the feedback forms that
are subject to very different interpretations are standardised (it can be noted
that Asociación Bayán is developing a data entry system to improve accuracy of
entry and calculations, and there are plans to produce a data collection manual
for staff).
The indicators and procedures used in the Hewlett study for classroom
observations are investigated for adoption/adaptation.
Data on student and tutor test scores are collated and analysed.
Reports are archived so that reflection on, and documentation of, processes are
facilitated.
60
References
Abdu’l Baha. Cited in a letter dated 5 March 1922 written by Shoghi Effendi to the Bahá'ís of
the United States and Canada, published in "Bahá'í Administration: Selected Messages 1922-
1932", pp. 21-22
Anthony, G. & Walshaw, M. (2007) Effective Pedagogy in Mathematics. Educational
Practices Series – 19. Geneva. International Bureau of Education. FUNDAEC: its principles
and its activities
Arbab, F. Correa, G. & de Valcarcel, F. (1988). FUNDAEC: its principles and its activities. Cali:
CELATER
Atherton, J S (2010) Learning and Teaching; What works and what doesn't [On-line] UK:
Available: http://www.learningandteaching.info/teaching/what_works.htm
Chingos, M. & Peterson, P. (2010) May:draft. Predicting Teacher Effectiveness by college
selectivity, experience etc. Paper prepared for conference on: Merit Pay: Will it work? Is it
Politically Viable? Sponsored by the Harvard Program on Educational Policy and
Governance.
Hattie, J. (1999) Influences on Student Learning: Inaugural Lecture, Professor of Education,
University of Auckland.
Hattie, J., Timperley, H. (2007) The Power of Feedback. Review of Educational Research. Vol
77 (1): 81-112
Hodgen, J. & Wiliam, D. (2006) Mathematics inside the Black Box: Assessment for learning in
the mathematics classroom. London: inferNelson
Ignacio, G. I., Barona, E. G., & Nieto, L. B. (2006) El Dominio Afectivo en el Aprendizaje de las
matemáticas. Revista Electronica de Investigacion Psicoeducativa 8, Vol 4 (1): 44-72
www.investigacion-psicopedagogica.org/revista/
Informe de Progreso Educativo de Honduras. (2005). Programa de Promoción de la Reforma
Educativa en America Latina y Caribe (PREAL). Washington, DC/Chile: Inter-American
Dialogue/Corporación de Investigación y Desarollo
Ma, L. (1999, 2010ed). Knowing and Teaching Elementary Mathematics. New York:
Routledge.
Mason, J. & Johnston-Wilder, S. (Eds) (2004) Fundamental Constructs in Mathematics
Education. Abingdon:Routledge
61
República de Honduras. (2010). Visión de País 2010-2038 y Plan de Nación 2010-2022.
Tegucigalpa. www.visiondepais2010-2038.com
Rivkin, S. G., Hanushek, E. & Kain, J.F. (2005) Teachers, Schools and Achievement,
Econometrica 73(2): 417-458
Schwille, J. & Dembele, M. (2007). Global perspectives on teacher learning: improving policy
and practice. Paris:UNESCO
Swan. M. (2006). Collaborative Learning in Mathematics: a challenge to our beliefs and
practices. London/Leicester. NRDC/NIACE
Wilensky, U. (1991). Abstract Meditations on the Concrete and Concrete Implications for
Mathematics Education in in I. Harel & S. Papert (Eds.) Constructionism. Norwood N.J.:
Ablex Publishing Corp.
UNDP. (2009ª). Informe Sobre Desarrollo Desarrollo Humano. Honduras 2008/2008. De la
exclusión social a la ciudadania juvenil. Programa de las Naciones Unidas para el Desarrollo
(PNUD). Tegucigalpa, Honduras
UNDP. (2009b). Encuesta Nacional de Percepción sobre Desarrollo Humano 2008: Juventud,
Desarrollo Humano y Ciudadanía. Programa de las Naciones Unidas para el Desarrollo
(PNUD). Tegucigalpa, Honduras
Wiliam, D. (2006). Assessment: learning communities can use it to engineer a bridge
connecting teaching and learning. Journal of Staff Development Vol 27(1), 16-20
William, D. (2007). Assessment for Learning: why, what and how? Professorial lecture,
Institute of Education, University of London, 24th April.
Reports to donors:
Scaling up the System of Tutorial Learning (SAT) as an alternative education program tackling rural poverty and gender inequity in Honduras: 01:07:04 to 30:06:06 (No:1045-0688)
Building Sustainable Livelihoods through Agriculture 01.01.07 to31.07.07 (CIDA)
Fortaleciendo la Consolidación del Programa Educativa Rural SAT en Intibucá, La Paz y Comayagua. 06.07 to 12.07 (IBIS)
Internal Reports:
2010 January Informe de Actividades;
Perfil Nacional for 2010 (Block 1)
Perfil Nacional 2009 (incomplete due to the coup)
Perfil Nacional 2008 (Blocks 2 & 3)
62
Appendix 1: Observations: maths trainings70
Date Area Text Hours 25.01-29.01 1 Impulsor texts – maths specialists 45 8.02-9.02 2 Matematics 5 8 18.03 3 Micro capacitación – Polinomios II 4 26.03 3 Micro capacitación – Medidas del Espacio 4 26.04 1 Matematicas 1 & 6 7 27.04 4 Matematicas 1 & 6 4 28.04 1 Matematicas 3 & 1 7 29.04 1 Matematicas 3 4 30.04 1 Matematicas 3 2 6.05 4 Matematicas 6 2 13.05 1 Polinomios 1 7 14.05 1 Polinomios 1 7 17.05 1 Destrezas Algebraicas 4 18.05 1 Destrezas Algebraicas 7 19.05 1 Destrezas Algebraicas 4 25.05 5 Matematicas 3 3 26.05 5 Matematicas 3 & Matematicas 6 4 27.05 5 Matematicas 3 2
Observaciones: maths lessons
fecha Región Textos horas 22.02 6 Matematicas 5, Matematicas 5, Matematicas 4 3 1.03 6 Matematicas 5 1 2.03 6 Manejo de Variables, Polinomios II, Matematicas 5 4 17.03 7 Manejo de Variables, Polinomios II, El Espacio y Sus
Elementos 4
22.03 8 Matematicas 5, Polinomios II, Polinomios II, 3
Observaciones: reuniones
fecha Lugar grupo horas 2.03 6 Asesores 2 8.03-9.03 3 Coordinaros 12 31.05 9 Asesores 2
Summary of Interviews (semi-structured)
grupo no duración (approx)
Notes
coordinaros 9 0.5 – 3.0 horas
5 coordinators were interviewed on more than one occasion.
Assessors del campo
7 0.3 – 0.5
Tutores 25 0.3 – 0.5 During visits to centres and during breaks in training sessions a
70 31 hours of general training were observed: Aspirantes: Filosofía de SAT, Aprender Enseñando,
Tecnología 1, Second Year: 1 Descripciones,Third Year: Alfabetización, Lecturas 5
63
hours large number of conversations were held with tutors; these gave valuable insights and informed the framing of interview questions.
Appendix 2 – Summary of the field assessors’ session observations71
Si No na ¿El tutor utiliza metodología del enfoque analítico y participativo (no magistral)?
30 86% 0 0% 5 14%
¿Los estudiantes se sientan en circulo? 26 74% 4 11% 5 14% ¿El tutor formula preguntas adicionales a las que hay en el texto?
27 77% 3 9% 5 14%
¿Las preguntas del tutor son simples, precisas, entendibles y necesarias?
26 74% 3 9% 6 17%
¿Antes de avanzar en otro tema existe una conclusión del punto anterior?
25 74% 5 14% 5 14%
¿Se estimula la participación de todos? 25 74% 2 6% 8 23% ¿Durante su estadía en el aula cuantos participantes vio opinar
© 8/11, 10/16,18/21,14/15 12/12,6/9,20/23, 22/24, 13/17, 8/12,10/15,11/11, 13/17 (Y) 4/23, 8/16, 6/18, 7/17,3/19, 6/24, 4/12, 9/20 27/27 20/20 23/23
10
¿Usa tanto la lectura comentada como trabajo en grupo y lectura individual?
28
80%
1 3% 6 17%
¿Asegura que los participantes utilicen las puntuaciones de lectura correctamente?
26
74%
2 6% 8 23%
¿Da la oportunidad de lectura a todos los participantes?
30 86% 0 0% 5 14%
¿Hay investigación del conocimiento local (tradicional) suficientemente?
24 69% 1 3% 10 29%
¿Se asegura la comprensión del grupo antes de pasar a otros temas?
25 71% 3 9% 7 20%
¿Verifica los textos para asegurar la precisión de las respuestas escritas allí?
20 57% 7 20% 8 23%
¿Verifica la ortografía y gramática de los participantes en sus textos
19 54% 7 20% 9 26%
¿Avance del contenido está de acuerdo al tiempo transcurrido y previsto?
24 69% 4 11% 7 20%
¿Estima que el grupo podrá finalizar los textos hasta la fecha de evaluaciones?
25 71% 3 9% 7 20%
71 3 assesores (Area 5) (18 tutors) C1- 8, C2- 8, C3 – 2, 2- 6 hours, Oct 09, June 09, April 09, 3 assessors (Area 10) (11 tutors) C1 -4, C2 -4, C3-1, B2-2, 2 – 5 hours, (abril 2010) 1 assessor (Area 11) (3 tutors) C1, B1, B1 + 3 tutors
64
¿La asistencia diaria esta al día? 29 83% 1 3% 5 14% ¿Comienza puntualmente las sesiones (incluyendo luego de los recreos)?
27 77% 2 6% 6 17%
¿Se observa un ambiente limpio y organizado?
30
86%
1
3%
4
11%
¿Se observa un ambiente ordenado y disciplinado en general?
28 80% 3 9% 4 11%
¿Los participantes cumplen con las responsabilidades asignadas y son obedientes?
30 86% 1 3% 4 11%
¿Se observa respeto hacia las opiniones de los compañeros?
29 83% 2 6% 5 14%
¿Se observa respeto hacia el tutor/a? 30 86% 0 0% 5 14%
¿La practicas agropecuarias y de Servicio cuentan con un plan de fechas
8 23% 2 6% 25 71%
¿Todos los estudiantes participan en las actividades
8 23% 0 0% 27 77%
¿Los recursos para las practicas están disponibles
10 29% 0 0% 25 71%
¿La comunidad participa en la ejecución de las practicas y proyectos
8 23% 1 3% 26 74%
¿Se busca la participación de organizaciones para los proyectos
5 14% 0 0% 30 86%
¿El/la tutor/a monitorea el avance de las practicas con la frecuencia requerido
9 26% 0 0% 26 74%
¿El registro de las experiencias y practicas se lleva con el rigor debido
8 23% 3 9% 24 69%
¿Se lleva asistencia en cuanto a las practicas
8 23% 1 3% 26 74%
¿Las practicas se llevan en forma paralelas al avance de contenidos
8 23% 0 0% 27 77%
¿Se observa proyecto de servicio a la comunidad (si es positivo descríbalo)
4 11% 5 14% 26 74%
¿Se implementan los experimentos en el aula durante la lección?
2 6% 0 0% 33 94%
¿Tienen disponible los instrumentos e insumos oportunamente
2 6% 0 0% 33 94%
¿Demuestra seguridad en la realización de las experiencias?
2 6% 0 0% 33 94%
¿Hubo algún experimento durante la visita? (si si explique cuál)
2 6% 3 9% 30 94%
¿Hubo algún experimento se concluyo con éxito? (si no explicar las causas)
2 6% 0 0% 33 94%
¿Elabora su plan de clase y lo utiliza para el mejor desarrollo de su clase?
22 63% 6 17% 7 20%
¿Están al día sus informes administrativos para la Dirección Departamental
27 77% 3 9% 5 14%
¿Es muy puntual y es un ejemplo positivo en cuanto a su conducta
31 89% 0 0% 4 11%
65
¿Planea actividades académicas pertinentes para mejor comprehension del grupo?
27 77% 1 3% 8 23%
¿Promueve actividades de recaudación de fondos con sus estudiantes
28 80% 2 6% 5 14%
¿Decora apropiadamente su aula para apoyar la educación del grupo
24 69% 3 86% 8 23%
¿Se observa un ambiente alegre y de motivación en el grupo
30 86% 0 0% 5 14%
66
Appendix 3: Summary of field assessors comments on classroom observations72
(not monthly reports)
M E T O L O G I A
Se sientan en grupos ya que el mobiliario ahorita no da para que estén en circulo también la cantidad de alumnos Recomendación: elaborar preguntas para repaso de la lección y verificar los textos de los estudiantes Durante esta visita los estudiantes hicieron exposición No están en circulo por que el espacio es reducido están sentado en forma de U Que pregunta a los estudiantes que expliquen lo que entienden de la que ¿ Explore a los estudiantes ¿ qué va a estudiar antes de entrar al contenido de texto Cuando use ‘b’ no dijo ‘b’ grande o ‘v’ pequeña dijo a los estudiantes ‘b’ labial o ‘v’ dental. Fue una jornada muy interesante Se recomienda que pregunta a cada estudiante que lee lo que entiende do lo que leyó x Se debe realizar preguntas …cada párrafo Se debe enfocar a las temas Bien participativos (2) Esta cumpliendo con la metodología (3) Constructivista y participativa (2) Expositiva, analítica, Constructivista, dinámica y participativa Material didáctico (3) Material didáctico bonito
E V A L U A C I O N P R O C E S S O
siempre ratifique la ortografía de las palabras que utilizan los estudiantes al escribir las respuestas a las preguntas del texto No estaban dentro del aula de clases Hacer un repaso del tema anterior antes de seguir otro Se dieron algunas sugerencias a la tutora para prepares(¿) Cada vez que termine una lección revise las respuestas escritos por los estudiantes y rectifique la ortografía x (y no solamente verbal) (2) Revisar los textos para verificar se esten trabajando Avanzar con las (¿) para poder (¿) con el plan de evaluación En el texto de la matamatica no hay revisión de las respuestas Algunas estudiantes presentaron debilidad al escribir algunas palabres El en texto de conjuntos y números en el lección ……no lo hay …… respuestas Hasta cierta tematico si hay pero en mayoría no le hay. No en todos los textos esta revisado toda la temática (2)
D I S
Debe d ser puntual en la hora de entrada Ensenar a los estudiantes a respetar las ideas de los demás En conjuntos de 5 estudiantes una exposición
72 Number of comments per tutor 1 – 15.
67
C I P L I N A
Les (¿) fuera del aula porque la maestra de primeria tenían reunión a pesar de esto estaban bien organizados bajo la sombra de un árbol Algunos alumnos no trabajan en los textos inspectados por lo menos dos. Plan for ‘un archivo del la conducta de cada estudiante’ Cumplen con sus obligaciones asignadas (5) Trabajan bien en sus textos Bien aplicados Cumplen con sus normas Todas se integran al trabajo Bien disciplinados Son educados Portan uniformes completos Plan for ‘un archivo del la conducta de cada estudiante’ Buena cooperación entre alumnos Respeto entre compañeros Trabajan mutualmente Estudiantes respetosos al tutor Buena relación (5) Excelente relación Muy respetosas Muy buena entrega y compromiso ante el grupo Excelente relaciones con las personas de la comunidad (4)
P R A C T I C A S
En este bloque no llevan prácticas agrícolas x Hacer un cronograma de actividades antes de empezar el proyectos entre todos los padres de familia ¿ en terreno. En las practicas apoyan los padres de familia El día de hoy no estuvo en el aula, estaban trabajando en el campo con las prácticas de tecnología. Se sugiere elaborar un plan para las practicas agropecuarias
- proyectos de la comunidad (2) Estimule a los estudiantes a realizar proyectos de servicio a la comunidad Hay un proyecto planificado pero aun no ha sido ejecutado Cría de pollos campaña de alfabetización no lo hubo x campaña de limpieza en la comunidad (2) Agua caliente, – Parcela bien cultivada
E X P E R I
No presencia ningún experimento (11) Insectario se concluye con éxito muy presentable Experimento sobre la temperatura Agua caliente, tibia y fría
68
M E N T O S T U T O R
Tiene que hacer su horario de clase y pegarlo en un lugar visible dentro de aula. (3) No presento el plan de clase por olvido No andaba su plan de clases y que estaban trabajando en el campo Se sugirió laborar puntualmente el plan de clase y ¿ del mismo ¿ evitar (¿) y (¿) mejor su clase Cada día que se imparta las clases debe tener sus planes de clase para cada capacidad Tratar de mantener el entusiasmo en los estudiantes No decora el aula porque es aula prestada y los (¿) de la escuela no les gusta que peguen cosas en las paredes No tienen paredes están recibiendo clases en el galpón (porque no hay nada puesto en los paredes) No existe material (¿) en el aula de clase. So se observo algunos aspectos .. que la visita fue en la parcela … mayor tiempo Planificación esta al día
69
Appendix 4: Questionnaire Survey
The percentages on the left hand side are the percentage of students responding to each
question.73 The numbers on the left are the percentage of responses in each category.
(Questionnaire on following page)
73 If a question does not have a percentage it is because there appeared to be confusion amongst the first year students as to whether or not they should answer the question. Taking this into account the response rate was about 95% for all questions.
70
El objetivo de este cuestionario es recolectar información que nos ayude a mejorar la
capacitación y el apoyo que le damos. Esperamos que los resultados de estos puedan ser
compartidos y utilizados por capacitadores de otras partes del mundo.
No estamos colectando información que revele su identidad, por lo que sus respuestas
permanecerán como anónimas. Utilizaremos esta información para conocer su opinión sobre las
matemáticas y el proceso de enseñanza de las mismas.
Por favor, responda a las preguntas en cuanto las lea – nos gustaría conocer su primera opción,
y siendo éste un cuestionario anónimo, siéntase libre de responder de la manera más honesta
posible.
Este cuestionario ha sido elaborado para conocer su valiosa opinión COMO TUTOR/A de
matemáticas.
Para contestar el cuestionario, marque con una X la respuesta que considere más oportuna. Las
escalas de valores son las siguientes:
Casi siempre, Generalmente, 50% del tiempo, Rara vez, Muy rara vez.
Casi siempre
General-mente
50% el tiempo
Rara vez
Muy rara vez
1 93%
Mis estudiantes realizan todos los ejercicios del texto de matemáticas.
45 51 3 1 0
2 97%
Mis estudiantes resuelven los ejercicios por sí mismos y consultan a sus compañeros de vez en cuando.
33 36 21 7 2
3 98%
En la resolución de ejercicios matemáticos, mis estudiantes solo utilizan los métodos que yo les enseño.
35 36 21 6 2
4 96%
Al resolver los ejercicios matemáticos, mis estudiantes comienzan con los más “fáciles” y dejan para el final los “difíciles”.
40 29 7 16 7
5 97%
Yo motivo a mis estudiantes para que terminen los ejercicios lo más rápido posible.
32 29 11 14 14
6 95%
Mis estudiantes comparan diferentes métodos de resolución de problemas matemáticos.
25 35 17 18 6
7 98%
Cuando doy una explicación, lo hago a toda la clase de una vez.
30 35 9 14 13
8 96%
Relaciono las matemáticas que mis estudiantes han aprendido en textos anteriores con lo que enseño en el texto actual.
46 46 2 5 1
9 94%
Mis estudiantes me sorprenden con respuestas, comentarios o preguntas que encuentro originales.
20 31 22 23 3
71
10 96%
Evito que mis estudiantes cometan errores razón por lo cual explico las cosas con cuidado desde el principio.
36 46 10 5 3
Casi siempre
General-mente
50% el tiempo
Rara vez
Muy rara vez
11 95%
Todos los ejercicios que mis estudiantes trabajan en clases pueden ser resueltos con explicaciones que se encuentran en el texto.
37 42 12 6 3
12 97%
Mis estudiantes aprenden discutiendo sus ideas.
40 46 7 6 1
13 98%
Mis estudiantes aprenden trabajando en pares o en grupos pequeños.
46 35 12 6 2
14 95%
Mis estudiantes inventan sus propios métodos para resolver ejercicios matemáticos.
9 10 17 48 17
15 94%
Yo les indico a mis estudiantes cuales ejercicios deben resolver.
18 36 8 18 21
16 96%
Yo disfruto enseñando matemáticas.
50 43 6 1 0
17 95%
Mis estudiantes aplican en su vida cotidiana lo aprendido en mis clases.
36 42 14 6 2
18 95%
Yo relaciono lo avanzado en mis clases de matemáticas con lo que mis estudiantes aprenden en los otros textos.
41 44 12 2 2
19 95%
Mis estudiantes justifican sus respuestas en los ejercicios de Verdadero/Falso.
40 34 10 11 4
20 96%
Yo motivo a mis estudiantes a que razonen la resolución de los ejercicios matemáticos, aunque les tome más tiempo.
49 45 3 1 2
21 97%
Yo relaciono lo avanzado en matemáticas con la afirmación de valores espirituales.
33 45 12 6 4
22 95%
Las matemáticas son útiles en los proyectos de servicio a la comunidad.
50 46 3 1 0
23 95%
Me siento segura/o cuando explico a mis estudiantes cómo realizar los ejercicios matemáticos.
46 53 1 0 0
24 98%
Me siento segura/o cuando ayudo a mis estudiantes a entender cómo funcionan las operaciones y formulas matemáticas.
41 49 1 0 0
25 96%
Mis alumnos comparten en la clase los métodos matemáticos que sus padres utilizan en su vida cotidiana.
24 29 11 29 7
26 95%
Tomo tiempo de mis clases para contextualizar lo aprendido en la realidad de la comunidad en la que trabajo.
36 39 14 9 2
72
Los temas de matemáticas que encuentro más fáciles de enseñar son:
Los temas de matemáticas que encuentro más complicados de enseñar son:
Cada sección presentada a continuación, excepto la última, cuenta con 4
afirmaciones. Lea cada una y valórelas de modo que el total sume 100%. Estas
valoraciones deben reflejar su opinión con respecto a ellas.
Si lo desea, puede escribir comentarios personales.
Las Matemáticas son:
Un conjunto de verdades universales, reglas y procedimientos estandarizados que deben ser enseñados a los estudiantes
32
Una materia creativa en la que cada individuo crea sus propios conceptos y métodos.
20
Una de las herramientas fundamentales para el avance del desarrollo autosustentable de la comunidad.
28
Un conjunto interactivo de ideas creado en forma colectiva a través del intercambio de perspectivas e interpretaciones.
19
Si considera que no hemos presentado una definición que es importante, por favor compártala con nosotros en este espacio. Asegúrese de que este concepto sea parte de la suma del 100%
Aprender es:
Un proceso individual basado en observar, escuchar y hacer ejercicios similares hasta que la nueva conducta se afiance.
20
Un proceso individual basado en la exploración y la reflexión. 21
Un proceso interactivo en el que los estudiantes son desafiados a desarrollar su entendimiento a través de actividades desarrolladas y analizadas en grupos.
31
Un proceso motivado por el deseo de contribuir a la sociedad y en el que cada persona desarrolla sus potenciales.
28
Si considera que no hemos presentado una definición que es importante, por favor compártala con nosotros en este espacio. Asegúrese de que este concepto sea parte de la suma del 100%.
73
Enseñar es:
Introducir el aprendizaje con conceptos sencillos, yendo paso a paso hacia conceptos más difíciles. Dar instrucciones verbales y verificar, a través de ejercicios, que éstas hayan sido comprendidas, para corregir vacios de comprensión a través de los errores.
34
Facilitar discusiones en las que el estudiante conjuntamente con su tutor profundice el conocimiento de las matemáticas y exploren la interconexión e interdependencia de lo aprendido para el desarrollo personal y social.
28
Saber reconocer cuándo un estudiante está listo para aprender; proveer un ambiente estimulante que facilite la exploración y que, a través de experiencias cuidadosamente estructuradas, evite aprendizajes errados.
19
Establecer una serie de diálogos no estructurados y estimulantes entre el tutor y los estudiantes, en los que los conceptos y su interrelación son explorados verbalmente. Si se generan conceptos errados, estos son expuestos para su análisis y corrección.
19
Si considera que no hemos presentado una definición que es importante, por favor compártala con nosotros en este espacio. Asegúrese de que este concepto sea parte de la suma del 100%.
Cuando enseño, mis prioridades son dirigidas a que mis estudiantes logren:
Motivarse y tomar responsabilidad sobre su propio aprendizaje.
24
Utilizar la matemática para explorar y describir el mundo y resolver problemas de su vida cotidiana.
32
Completar los textos y estar preparados para los exámenes.
9
Explicar los conceptos y formulas matemáticos.
11
Comportarse correctamente, participar en actividades y ser solidarios con sus pares.
12
Reconocer la calidad de su trabajo y la de otros y saber qué hacer para mejorar. 11
Si considera que no hemos presentado una definición que es importante, por favor compártala con nosotros en este espacio. Asegúrese de que este concepto sea parte de la suma del 100%.
74
Este cuestionario ha sido elaborado para conocer su valiosa opinión COMO ESTUDIANTE de las
matemáticas.
Para contestar el cuestionario, marque con una X la respuesta que considere más oportuna. Las escalas de valores son las siguientes:
Muy de acuerdo, De acuerdo, No he decido, En desacuerdo, Muy en desacuerdo
Muy de acuerdo
De acuerdo
No he decido
En des acuerdo
Muy en des acuerdo
1 98%
Las matemáticas son útiles y necesarias en todos los ámbitos de la vida.
83 17 0 0 0
2 96%
Las matemáticas son difíciles, aburridas y alejadas de la realidad.
1 1 5 38 56
3 93%
En matemáticas es fundamental aprenderse de memoria los conceptos, formulas y reglas.
9 30 8 43 11
4 97%
Las únicas matemáticas que me interesan son las que tengo que enseñar, porque las tengo que conocer.
2 4 2 47 45
6 98%
Las destrezas o habilidades que utilizo en clase para resolver problemas no tienen nada que ver con las que utilizo para resolver problemas en la vida cotidiana.
2 2 2 56 37
7 98%
Busco distintas maneras y métodos para resolver un problema.
57 40 1 2 0
8 99%
Aprendo mucho inventando nuevos problemas.
56 36 4 3 2
9 98%
Si no comprendo las matemáticas difícilmente podré asimilar y dominar otras asignaturas relacionadas con ella (como física, química etc.)
43 33 9 9 6
10 98%
Mi rendimiento en matemáticas depende en gran medida de la actitud del/a capacitador/a hacia mí.
20 34 9 28 9
11 99%
Cuando dedico más tiempo de estudio a las matemáticas, obtengo mejores resultados en la resolución de problemas
78 22 0 0 0
12 95%
Cuando resuelvo un problema, suelo dudar de si el resultado es correcto.
4 20 14 50 13
13 94%
Me considero muy capaz y hábil en las matemáticas.
15 51 24 10 1
14 95%
Estoy calmado/a y tranquilo cuando resuelvo problemas de matemáticas.
30 62 2 6 1
15 99%
Los/as buenos/as profesores/as que explican con bastante claridad y entusiasmo
30 1 2 0
75
y son agradables hacen que gusten las matemáticas.
67
Muy de acuerdo
De acuerdo
No he decido
En des acuerdo
Muy en des acuerdo
16 96%
Cuando estaba en la escuela y en el colegio tuve bueno/as maestro/as de matemáticas.
36 42 6 13 2
17 96%
La gente a la que le gustan las matemáticas suele ser un poco rara.
4 10 7 46 32
18 96%
Las matemáticas son para cabezas inteligentes y creativas.
6 10 3 41 39
19 95%
La gente que es buena en matemáticas no tiene que gastar tiempo pensando cómo resolver un problema.
9 16 7 49 19
20 95%
Las clases de matemáticas se me hacen eternas, son muy pesadas, no estoy a gusto y siento deseos de salir corriendo.
2 5 6 44 44
21 96%
Ante un problema complicado suelo darme por vencido/a fácilmente.
3 2 2 58 36
22 93%
Cuando me enfrento a un problema, experimento mucha curiosidad por conocer la solución.
49 49 2 0 0
23 95%
Me provoca gran satisfacción resolver con éxito un problema matemático.
72 27 1 0 0
24 94%
Si no encuentro la solución de un problema, tengo la sensación de haber fracasado y de haber perdido el tiempo.
5 6 7 63 20
25 95%
En mis estudios matemáticos muestro perseverancia y paciencia.
46 52 0 1 1
Si tiene más de un año trabajando con SAT, por favor conteste el siguiente grupo de preguntas:
26 Mi percepción de las matemáticas es más positiva desde que recibo las capitaciones de SAT.
85 13 2 0 0
27 Otros tutores me buscan para ayudarles con las matemáticas.
17 61 5 17 1
28 Después de una capacitación siento que no entiendo toda la materia y que no puedo resolver todos los ejercicios.
3 6 8 51 32
Si está estudiando o ha estudiado matemáticas en la universidad o en la Pedagógica, por favor conteste la siguiente pregunta:
29 Mis estudios de matemáticas con SAT me han ayudado con mis estudios de matemáticas en otras instituciones.
70 28 0 0 2
76
Lea las afirmaciones sugeridas a continuación y marque con una X el número que mejor
represente cómo se siente usted cuando realiza cada una.
La escala es de 1 a 5, siendo 1 – calmado y totalmente sin estrés, y 5- muy nervioso y/o muy estresado.
Si tiene algún comentario sobre su experiencia estudiando matemáticas con SAT, o si desea hacer
alguna sugerencia, por favor compártala con nosotros en este espacio.
1 Muy
calmado/a
2 3 4 5 Muy
Estresado/a
1 Revisando el texto de matemáticas. 66
21 7 2 2
2 Planeando la clase que voy a enseñar al día siguiente.
62 23 9 4 2
3 Viendo el capacitador explicar álgebra en el pizarrón.
52 26 12 3 7
4 Empezando a estudiar el texto antes de ir a la capacitación.
51 24 9 12 3
5 Interpretando gráficos matemáticos.
40 33 20 5 3
6 Llegando a la capacitación y pensando en la capacitación de matimáticas.
61 19 10 6 4
7 Cuando voy a trabajar en el pizarrón durante la capacitación.
39 22 20 9 10
8 Cuando el/la capacitador/a me propone ‘por sorpresa’ que resuelva un problema.
33 29 13 13 12
9 Cuando me atasco o bloqueo en la resolución de un problema.
31 15 19 17 17
10
Si hay otra acitividad matemática que le de estrés anótela aquí:
77
Appendix 5: Additional comments of the tutors on the questionnaire
1. 2. Pues, bueno yo he aprendido mucho de las matemáticas en SAT estoy bien agradecido
por las capacitaciones. Y le ayuda a la preparación tanto persona como ensenar al
alumnos unos no la ha ¿a la clase y preparándolo. Se siente con confianza y eso le ¿ a
alumno.
2. 7. Las matemáticas vista en SAT han despertados interés en mi persona yo ya no tengo
miedo a matemáticas porque he aprendido como poder a desarrollo a cómo enfrentarle.
También he aprendido comprender situaciones de la vida porque (¿) miedo de la
matemáticas.
3. 10. A mí me encanta las matemáticas y yo siento que lo que he aprendido en SAT me ha
ayudado mucho en mis estudios universitarios y en mi vida diaria.
4. 12. Hay textos de mi matemática que se hacen fácil desarrollarlo de igual manera que
hay textos que se debe dar más tiempo para desarrollarlos ya que tiene un nivel de
complejidad y se vuelven un poco más difícil su realización en los textos de Bachillerato
se le debe dar mas ¿??? en estos textos en las capacitaciones. Ya que se necesita ir con
los conceptos darlos a impartirlos a los estudiantes.
5. 15. SAT nos ayuda mucho en las clases de matemáticas porque debemos contenidos muy
amplios y bien definidos
6. 18. En mi comentario lo que les puedo decir es que en SAT es donde yo he aprendido
mucho de matemática muy bonito la moralidad. Se aprende mucho en capacitaciones ya
que los capacitadores son personas muy preparados.
7. 19. Mi experiencia como tutora de SAT ha sido muy importante porque aprendemos la
clave las operaciones de matemática de diferentes maneras y las comprábamos con
situaciones de la vida diaria.
8. 20. Las matemáticas estudiados con SAT me ha servido mucho en mis estudios
universitario también a encontrado el porqué de los ejercicios.
9. 24 Los textos de matemáticas son muy interesantes pero se le debe dar más tiempo ya
que esto texto de matemática necesita más practica que los de lectura (Matemática 3)
10. 27 Siempre me he sentido que me gusta las matemáticas pero desde que estoy en la
sistema he descubierto que se resuelven muchos problemas de la vida con mejor
facilitad.
11. 31. todo lo que he aprendido hasta hoy en las matemáticas de SAT me parece muy
interesante porque el alumno y yo comprendemos lo que hacemos.
12. 34. Por los momentos pues tengo un mes de trabajo y me siento bien al saber que tengo
la capacidad de ayuda a la comunidad y a su persona y se obtiene diferentes expresiones
a vivir en otro parte y compartir unos conocimientos diferentes.
13. 37. Soy ingresada de SAT 100% y para mí las matemáticas aprendidas en SAT ya que el
tutor se detiene y se explica detalladamente tratando dar la explicación más clara y dar
un mejor resultado en la evaluaciones
14. 39. En SAT los experiencias en matemáticas es fascínate porque aprende a desarrollar su
propia concepto y te pone a utilizar tu lógica que ha a veces esta muy dormida y puedes
aplicar esta lógica matemáticas en problemas de la vida diaria y te lleva resolver estos
problemas de la vida diaria.
78
15. 43. Todavía no tengo un ano pero siento que ya me ha ayudado bastante las
capacitaciones de matemática
16. 44. Desde del momento que comencé a trabajar siento que he aprendido muchas
conceptos que en el colegio no aprende.
17. Sugerencias que el capacitador nos trate con paciencia y confianza
18. 45. Es un proceso muy bonito y importante porque son ejercicios mucho mas
explicativos que un educación de nuestro mismo nivel y estos ejercicios los podemos
utilizar para resolver ejercicios de la vida cotidiana
19. 52. Las matemáticas de SAT me ha ayudado a ser mas analítico y a ponerlo en práctica
en la vida real
20. 59 Es la primero vez que recibo una capacitación de SAT de matemáticas y fue muy
productivo. Me fue muy bien y creo con dedicación estaré preparado a dar esto texto
con el ayuda de Dios
21. 65. Mi experiencia es que encuentro mucho más fáciles los textos. Creo que es una forma
muy efectiva de enseñanza
22. 75. Pienso que para las matemáticas es necesario usar diferentes materiales el tutor o
capacitador tiene que tener paciencia para que los estudiantes le comprended y captan
mejor
23. 76. Soy egresado de SAT y me siento totalmente satisfecho porque educación que he
recibido soy tutor del mismo programa y me siento feliz de poder compartir mis
conocimientos a mis alumnos y a otras personas, Gracias. He tenido la fortuna de ser
una persona humilde y agradable ante la sociedad en SAT aprende muchas cosas que me
ha gustado en la vida. Agradezco a la Asociación Bayan y a SAT por el gran apoyo que
me ha brindado. Espero seguir adelante, seguir adelante y siempre resaltado al nombre
de SAT donde quiero que yo vaya
24. 77. Hasta el momento los textos estudiados con SAT me ha gustado mucho los mejores
capacitadores de matemáticas que he tenido son X y Z
25. 78. Estudiar los textos de SAT y es muy importante ya que ayudan en gran manera en
nuestra vida como profesional también para tener alguna destreza conocimiento al
momento de usar el estudio superior en la universidad. Sugerencia que los textos de
SAT tenga suficiente espacio como para desarrollar ejercicios con mejor orden también
que haya una secuencia en algunos temas que están muy similares.
26. 83. La experiencia de trabajo con SAT es muy bueno ya que he mejorado en el área de
matemáticas porque durante estuve en la escuela y en el colegio no había aprendida
mucho sobre la materia. En SAT encontramos con una matemática bien desarrollada
donde retomarnos la matemática estudiado anteriormente y cosas de nuestra vida
diaria
27. 92 Estudiando matemáticas en SAT me ha mejorando miro la matemática en manera
diferente, y me gusta más y me siento más confianza y miro que la matemática no es
como de niño pensé que era. Que SAT ha desarrollado en me el interés para seguir
aprendiendo mucho más sobre matemáticas.
28. 99. Hay algunos temas que son más complicados que otros por eso sugiera que para
algunos textos siempre haya micro centros aun que hayamos terminado el texto erg
expresiones y ¿ Algebraicas
29. 101. Mas que un comentario tengo un profunda agradecimiento ya que todos las
capacitaciones de matemáticas que he recibido me ha ayudado mucho porque antes me
forma parte de SAT les tenía miedo a las matemáticas y ahora es una de las clases que
79
más me gusta y lo más importante que a mis estudiantes les gusta y disfrutan las clases
de matemáticas.
30. 105. Experiencia la manera de ver las matemáticas con la metodología me ha ayudado
sobre la manera y he aprendido a razonar mejor los problemas presentados. Sugerencia
la capacitación de matemáticas debería ser al principio de la primera semana
31. 106. Respeto al texto que sea siempre de ver en los primeros días porque uno tiene más
relajado en cambio cuando los dan al final de la semana uno se desespera o se estresa
mas por el cansancio o porque nos desesperamos por unos que no ponen atención.
32. 121. En SAT se obtiene la herramienta necesaria para poder entrar diferentes ejercicios
y poder resolverlos
33. 123. En SAT la matemática se explique de una manera muy intangible porque se aplica a
la realidad y se explica con modelos sencillos pero muy importantes.
34. 128. Hacer preguntas, contestar respuestas breves que el alumno afirmaciones se
presentan para analizarlos en sentido positivo y negativo
35. 132 Las matemáticas así como el trabajo de SAT no ha sido solo una fuente de empleo
sino que ha cambiado positivamente mi vida. Gracias a Dios por el SAT.
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