Math Education for STEM disciplines in the EU

Math education for STEM disciplines in EU

Seppo Pohjolainen Tampere University of

Technology (TUT)

TEMPUS MetaMath Kazan 8-10.12.2014

Contents


•  Importance of mathematics •  Pisa and Timms and consequences •  From content to competence •  Reform in math education •  Role of technology

Mathematics

•  “The remarkable development of the natural sciences and engineering since the

Renaissance is a consequence of the fact that all nature’s known laws can be expressed as

mathematical equations.”

•  (OECD 2008)


•  “Mathematics offers business a formula for success.“

–  (Financial Times, February 2006)


•  Know-how on mathematical and natural sciences must be emphasised more strongly as

a part of common cultivation and their valuation must be improved in the society

•  (Finnish Association of Graduate Engineers 2009)


Quality of school math education

•  The Programme for International Student Assessment

(PISA) is an internationally standardized assessment for15-year-olds in schools. PISA aims at testing literacy in three competence fields: reading, mathematics, science.

•  TIMSS (Trends in International Mathematics and Science Study) collects educational achievement data at the 4th and 8th grades to provide information quantity, quality, and content of instruction.


Targets of TIMSS and PISA •  The PISA mathematics test asks students to apply their

mathematical knowledge to solve problems set in various real-world contexts.

•  TIMSS, on the other hand, continues to measure more traditional classroom content such as an understanding of fractions and decimals and the relationship between them.

http://www.edinformatics.com/timss/TIMSS_PISA_test.htm TEMPUS MetaMath Kazan 8-10.12.2014

http://www.theguardian.com/news/datablog/2013/dec/03/pisa-results-country-best-reading-maths-science

Quatar

Luxembourg

Singapore

China (Shanghai)

Peru

Europe

USA

Pisa 2012

Vietnam


http://www.theguardian.com/news/datablog/2013/dec/03/pisa-results-country-best-reading-maths-science

Pisa 2012: Results


Education versus economical growth

Hanushek, Wößmann:The Role of Education Quality in Economic Growth World Bank Policy Research Working Paper 4122, February 2007

•  “The existing research provides strong reasons to believe that quality of education is causally related to economic outcomes.

•  To be sure, quality may come from formal schools, from

parents, or from other influences on students. •  But, a more skilled population – almost certainly

including both a broadly educated population and a cadre of top performers – results in stronger economic performance for nations.”


OECD REPORT: Added-variable Plots of Growth and Education

Hanushek, Wößmann:The Role of Education Quality in Economic Growth TEMPUS MetaMath Kazan 8-10.12.2014

PISA and TIMMS

•  Asian countries are doing well: criticized for teacher centered education, large amounts of homework, rote learning etc..

•  European countries are doing well, but lagging behind. Pedagogical and instructional reforms.

•  Developing countries at the bottom.


University engineering mathematics

•  Facing the same problems as in schools

•  The problems from school will transfer to university level

•  We need to educate all engineering students to a sufficient level.

•  We can not escape the problems by concentrating only on good students


Evolution of Student Interest in Science and Technology Studies, Global Science Forum, OECD, May 2006.


AUSTRALIA •  Period 1997-2005 has experienced a 52% growth

in employment demand for the mathematical sciences. The number of students taking a mathematics subject has decreased by 34 %.

•  Henderson,Broadbridge:Engineering Mathematics Education in Australia, (2009)


Australia


Europe

•  At the 1998 meeting of the SEFI Mathematics Working Group the decline in entry competencies of students was a common theme, from across Europe and beyond.

•  In 1997 only 54% of A-level UK students tested at the start of their university studies, could correctly identify the graph of the cosine function. In 1991 all comparably qualified students could do this.

•  SEFI “Report on “Mathematics for the European Engineer - a Curriculum for the twenty-first Century”(2003)

•  SEFI= European Society for Engineering Education


SEFI (Report 2003)

•  Universities taken measures to handle the problem:

•  1. Reducing syllabus content, replacing some of the harder material with more revision (or, for some students, vision) of lower level work,

•  2. Developing additional units of study, •  3. Establishing mathematics support centres, •  4. Doing nothing.


Finland •  Despite PISA results teachers at Finnish

universities are worried about degrading mathematical skills of incoming students.

•  In PISA survey (2003) Finland showed highest mathematical literacy performance in OECD and second highest among all 41 countries.

•  In PISA (2012) Finland dropped 12 th in mathematics.


Changes in Finnish comprehensive school (1980-2000)

Näveri (2009)

numerical, math structural, evaluation, application


Aamulehti (2014) News on PISA 2012 :Every Finn has 500 competitors in mathematics from China and India


A student’s comments in the Aamulehti newspaper

•  I have studied mathematics at TUT and my opinion is that current math teaching does not improve one’s problem solving skills. •  It is more about rote learning of mathematical procedures and routine calculations. •  Student motivation is lost somewhere when they are asked to solve assignments that have nothing to do with their future. Only 1% of students need this kind of mathematics in their future life. •  Others will forget math as unnecessary stuff after graduation. The idea that problem solving skills are dependent on mathematics is absurd. •  One can learn logical thinking with but also without mathematics.


TUT Teacher’s opinions

•  Manipulation skills are weak – some students do not know even how to handle fractions

•  Weakest students do not know basic rules of algebra: sin(a+b)=sin(a)+sin(b)

•  Too much work with formula books and calculator •  No idea about mathematical proof. •  If asked to prove A implies B they assume B is true and try to

show that A is true.


Pedagogical reform

•  Engineering education similar to schools: we have to

teach for all kind of students •  We cannot drop out the weakest students

•  From content to competencies •  What do students learn ?

•  Motivate students to do their job ? •  Use ICT a tool



Reports on school reform in science for EU

EURYDICE: Mathematics Education in Europe: Common Challenges and

National Policies 2011


Recommendations on how to increase motivation to learn mathematics and encourage the take-up of mathematics-related careers. Many European countries are confronted with declining numbers of students of mathematics, science and technology, and face a poor gender balance in these disciplines.

•  The mathematics curriculum (contents->competences, math in everyday life)

•  Teaching approaches and methods (PBL, Inquiry based mehods, contextualization....)

•  Addressing low achievement •  Improving student motivation(extra curricular activities,

companies, gender issues)

•  Education and professional development of mathematics teachers

•  Promoting evidence-based policies (collection and evidence on best practices)

Mathematics in Europe:Common Challenges and National Policies (EURYDICE 2011)


SEFI (2013): Pedagogical reform

•  The main message is that although contents are still

important, they should be embedded in a broader view of mathematical competencies that the mathematical education of engineers strives to achieve.


SEFI: A Framework for Mathematics Curricula in Engineering Education 2013


Mathematical Competence for Engineers

”the ability to understand, judge, do, and use mathematics in a variety of intra- and extra-mathematical contexts and situations in which mathematics plays or could play a role” SEFI (2013): ”A Framework for Mathematics Curricula in Engineering Education”

General Mathematical Competencies for Engineers

–  Competencies

•  thinking mathematically •  reasoning mathematically •  posing and solving mathematical problems •  modelling mathematically •  representing mathematical entities •  handling mathematical symbols and formalism •  communicating in with and about mathematics •  making use of aids and tools

–  Dimensions (of extent) –  Clusters (reproduction, connections, reflection)



•  Symbolic calculators •  Learning platforms (Moodle,...)

–  distribution of material –  collaboration and feedback –  motivation (links to applications and

other sources) •  Mathematical Software (Matlab, R-,

Octave, Maple, Mathematics, Wolfram Alpha...) –  application of mathematics to ”real”

world problems –  visualization of results

•  Course delivery & cognitive support (MatBridge,...)

The role of ICT

The Role of ICT •  The design of a computer-based instructional system

should be based on content specific research of learning and comprehension and pedagogical model of the learner and the learning process.

•  In designing computer-based teaching and learning environments real didactic tasks should be considered. One should think thoroughly what to teach and how to teach.

•  Reusser, K.: “From Cognitive Modeling to the Design of Pedagogical Tools”; (1995).


Teacher’s role •  Teacher’s role may change, but they can not be replaced by peer/

independent learning or technology.

•  In Norway curriculum for compulsory school 1997, emphasized that students should be independent, proactive and 'learn by doing'.

•  Analysis of declining results revealed that students were sometimes left alone to construct their knowledge from a multitude of experience and the teacher's role was being reduced to facilitator.


Conclusion

•  Importance of mathematics is well understood.

•  Deterioration in the students’ skills is recognized.

•  Pedagogical and school reforms are the way EU is going.

•  Technology can play a important role here.



•  Thanks !