Enhancing the Teaching and Learning of Early Statistical

Reasoning in Europeans SchoolsCyprus Consortium Meeting

Pilot Course Development, Testing and Delivery

Grupo de Investigación:Desarrollo profesional del Docente

Design of the pilot course

Teachers Schedule Aims

Methodology ConsortiumTeachersRole

Course Management,Testing andDelivery

Teachers (pp. 22)

• Elementary and middle school mathematics teachers• Pilot tested with a group of around 10-12 teachers (2-3 teachers from each partner country)

Proposal:• Select at least:

- a novice teacher- an expert teacher

• Novice teachers tends be less unwilling to innovation.• Expert teachers tends to reflect about practice easily. • The purpose is not to contrast both.• Selected by us, in order to anticipate teachers expectations about the pilot course, or by an initial questionnaire.• We must prepare a letter of application for the “Principal of the School” where they are going to apply the course in their own pupils. And also a letter for the parents of the pupils (because they are under legal age, and we are going to video taping, and getting information about them).• It is necessary to make any kind of compromise with the teachers?

Schedule (pp. 40)

Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep2005/06

Development of statistics education pedagogical frameworks and instructional content

Strategy Development Evaluation. Initial external evaluation

Technical design of knowledge base infrastructure and services

Schedule (pp. 40)

Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep2006/07

Development of statistics education pedagogical frameworks and instructional content

Implementation of knowledge base infrastructure and services

Initial external evaluation.

Design and development of eLerning infrastructure and services

Schedule (pp. 40)

Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep2007/08

Training base infrastructure

and services

Enrichment and projects outputs integration of infrastructure and services

Pilot delivery of professional development course and follow-up classroom experiment

Main external evaluation of information obtained of the pilot course delivery.

Schedule (pp. 40, 22)

Pilot delivery of professional development course and follow-up classroom experiment

Oct 1 Content + design •Learning situation

•Technologies

•Curricula

•Epistemology

•Hand on

•Computer based practice and experimentation

•Use of simulation and visualization

•Contrast and reflection with theoretical documents

Oct 8

Oct 15

Oct 22

Schedule (pp. 40, 22)

Pilot delivery of professional development course and follow-up classroom experiment

Oct 29 Children’s learning + design

•Computer-supported teaching

•Curriculum issues

•Statistics education research

•Educational software

•Role of statistics

•Statistical reasoning on children

•misconceptions

Nov 5

Nov 12

Nov 19

Nov 26 Teaching experiment

•Customize and expand materials

•Apply them

•Write up experiences

•Provide samples

Dic 3

Dic 10

Dic 17 Reflection and evaluation

•Power point

•PortfolioJan 7

Aims

• Content to:- Analyze the nature of the statistical knowledge:

* history* organization* meanings

- Analyze and reflection about bedrock concepts in probability and statistics:

* hands on and computer based technologies* intensive use of simulations

- Analyze didactical and historical problems (phenomelogical)- Analyze and contrast of curricula:

* Cyprus, Greece, Norway and Spain curricula* Other international curricula (NCTM)

- Design of the pupils knowledge selection and organization, and selection of tools to use pupils.

Aims

• Cognition to:- Analyze how the pupils learn statistics and probability.- Analyze and reflection about the investigation literature:

* Statistics Education* Difficulties, Obstacles and Misconceptions.* Emotive nature

- Analyze about of the paper of technological tools in the pupil learning.- Design of how to organize the process teaching and learning:

* Strategies.* Activities* Tools* Organization and management of pupils’ classroom.

Aims

• Teaching experiment to:- Customize and expand materials.- Apply the materials and design developed before- Regulate the process of teaching and learning:

* observation* value* change

- Develop a classroom paper (Write up their experiences)

Aims

• Reflect and evaluate to:• Analyze of:

• difficulties during the process• strategies, activities and tools used in the process• teacher interventions• pupils interventions and interactions• pupils’ learning

• Report on their experiences to the other teachers.• Provide samples of their students’ work for group reflection and evaluation.• Reflect about how to further improve their practice and to increase students achievement.• Inform consortium teachers about (auto assess):

• Statistics education pedagogical frameworks and instructional content.• Technical design of knowledge base infrastructure and services.• e-learning infrastructure.• Pilot course delivery.

Methodology

Pilot course framework Innovation Course structure

Activities Resources Evaluation tools

Underlying didactical model of the teacher

Explicit didactical model of the teacher

Knowledgeof and aboutmathematics

KnowledgeTeaching/learning

Practicalknowledge

EpistemologicalFramework

CognitiveFramework

Teachingframework

Explicit didactical model of the teacher

Underlying didactical model of the teacher

Teacher

Tea cher

Consort ium

teacherC

onsortium tea cher

Innovation

PROFESSIONAL KNOWLEDGE

PROCESS OF CONTINUOUS REORGANIZATION OF THE PROFESSIONAL KNOWLEDGE

DEPARTURELEVEL

Traditional didactical

model

INTERMEDIALLEVEL

InnovativeDidactical models

(technologicalspontaneous)

DESIRABLEPROFESSIONALKNOWLEDGE

InvestigativeDidactical

models

Superación de obstáculos

Models Traditional Technological Spontaneous Investigative

Aims Deduce calculus strategies

Induce strategies to calculate

Explore properties

Construct

Notions

Contents Random experiments, outcome, Laplace rule

Random experiments, outcome, Laplace rule, frequencies stability

Hazard, Randomness, Probability

Methodology Lineal explanations/ pen and paper activities

Closed series Unsystematic organization/exploration

Problem solving overcoming obstacles

Context Random games Games, computer simulators

Natural, Social phenomena

Example of the hypotheses of progression in probability

Course structure

Knowledge aboutteaching /learning

1 2 3

Content Cognition Teacher

experiment

Kownledge of and aboutStatistics

Practical knowledge

4Reflectionevaluation

Activities torecognize, identify

y formulate practical problemsto invest

Activities toMovilize the conceptions,

experiences andObstacles asociated

to the practicalproblems

Activities ofCurricular

experimentation

Activities toFacilitate the structuration ymetareflection

Activities toPromote theContrast ofConceptions andExperiences ofTeachers

Activities

TEACHER WORK

DISCUSSION

TEACHERWORK

REFLECTION

CIC

LE

SE

CE

UN

CE

EXPOSITIONTEACHER WORK

DISCUSSION

Recognize, identifyy formulate

Contrastconceptionsexperiences

Conceptionsexperiences obstacles

Structurationmetareflection

Curricularexperimentation

Resources

•Textual documents:• Investigation papers.• Theoretical papers.• Instructional materials• Cyprus, Greece, Norway and Spain curricula• Case studies about teaching and learning statistics

• Outlines to read and reflect about:•Textual documents•Practice

•Links to statistics education resources available on the Internet•Illustrations, animations, audio/video•Technology-rich interactive problems.

PortfolioPortfolio

Tool for reflection and evaluation

Pilot course activities

Pilot course activities

Designexperiment

Designexperiment

Experiences report, power point

Experiences report, power point

Classroompaper

Classroompaper

Pupils productions

Pupils productions

PupilsVideo tapes

PupilsVideo tapes

Consortium teachers role

Before pilot course delivery:• Development of statistics education pedagogical frameworks, and instructional content.• Design and development of knowledge base infrastructure and services.• Design and development of eLerning infrastructure and services

During pilot course delivery:• AUTH, UCA, CC:

• delivery the pilot course.• assist teachers during the classroom intervention

• UHT: • Monitor and maintain the knowledge base• Collaboration tools

• HIST:• Distance learning infrastructure• Distribute audio/video communications

Course Management, Testing and Delivery

• How many hours is supposed that must work a teacher during cycle 1 and 2?at least 12 per week.

• When we are going to delivery the information?• at the beginning of the course• along the course• on demand• on necessity

• Are we going to adapt the course in function of teacher demand or necessity?• Are we going to fix a final period were every activity must be ended?

• no, then during conferencing and forums discussion they are going to argue from a traditional manner or with the first idea.• yes, in order to use the chat, conferencing and forums discussion as a a place to reflect, collaborate and construct professional knowledge.

• Which initial information is needed to give to the teachers in order to enrol them?• Are we going to ask them to improve an activity, if we need it is necessary, after a chat or a forum?• It is necessary to fix previously a timetable and schedule for the forums?