Enhancing the Teaching and Learning of Early Statistical Reasoning in Europeans Schools Cyprus Consortium Meeting Pilot Course Development, Testing and Delivery Grupo de Investigación: Desarrollo profesional del Docente

Design of the pilot course TeachersSchedule Aims Methodology Consortium Teachers Role Course Management, Testing and Delivery

Teachers (pp. 22) Elementary and middle school mathematics teachers Pilot tested with a group of around 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) OctNovDecJanFebMarAprMayJunJulAugSep 2005 /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) OctNovDecJanFebMarAprMayJunJulAugSep 2006/ 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) OctNovDecJanFebMarAprMayJunJulAugSep 2007/ 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 1Content + designLearning 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 29Children’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 26Teaching experiment Customize and expand materials Apply them Write up experiences Provide samples Dic 3 Dic 10 Dic 17Reflection and evaluation Power point Portfolio Jan 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 frameworkInnovation Course structure Activities Resources Evaluation tools

Underlying didactical model of the teacher Explicit didactical model of the teacher Knowledge of and about mathematics Knowledge Teaching/ learning Practical knowledge Epistemological Framework Cognitive Framework Teaching framework Explicit didactical model of the teacher Underlying didactical model of the teacher Teacher Consortium teacher

Innovation PROFESSIONAL KNOWLEDGE PROCESS OF CONTINUOUS REORGANIZATION OF THE PROFESSIONAL KNOWLEDGE DEPARTURE LEVEL Traditional didactical model INTERMEDIAL LEVEL Innovative Didactical models (technological spontaneous) DESIRABLE PROFESSIONAL KNOWLEDGE Investigative Didactical models Superación de obstáculos

ModelsTraditionalTechnologicalSpontaneousInvestigative AimsDeduce calculus strategies Induce strategies to calculate Explore properties Construct Notions ContentsRandom experiments, outcome, Laplace rule Random experiments, outcome, Laplace rule, frequencies stability Hazard, Randomness, Probability MethodologyLineal explanations/ pen and paper activities Closed seriesUnsystematic organization/ex ploration Problem solving overcoming obstacles ContextRandom gamesGames, computer simulators Natural, Social phenomena Example of the hypotheses of progression in probability

Course structure Knowledge about teaching /learning 12 3 ContentCognition Teacher experiment Kownledge of and about Statistics Practical knowledge 4 Reflection evaluation

Activities to recognize, identify y formulate practical problems to invest Activities to Movilize the conceptions, experiences and Obstacles asociated to the practical problems Activities of Curricular experimentation Activities to Facilitate the structuration y metareflection Activities to Promote the Contrast of Conceptions and Experiences of Teachers Activities

TEACHER WORK DISCUSSION TEACHER WORK REFLECTION CICLE SECEUNCE EXPOSITION TEACHER WORK DISCUSSION Recognize, identify y formulate Contrast conceptions experiences Conceptions experiences obstacles Structuration metareflection Curricular experimentation

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.

Portfolio Tool for reflection and evaluation Pilot course activities Design experiment Design experiment Experiences report, power point Classroom paper Classroom paper Pupils productions Pupils Video tapes Pupils Video 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?