1. Mara AlagicSITE 20021 Teachers’ Learning of Mathematics in the Presence of Technology: Participatory Cognitive Apprenticeship Mara Alagic Wichita State University

2. Mara AlagicSITE 20022 Paradigm shift: Changes in the teaching/learning of the (school) mathematics introduced by current school reform for standards- based teaching that supports integration of technology (NCTM, 2000) development of the IC technologies information from cognitive sciences about the nature of human learning

3. Mara AlagicSITE 20023 Designing Mathematics Learning Environments address the needs of an increasingly complex student body recognize need for standards-based teaching/learning “balance” availability and the development of the IC technologies understand the nature and development of long term memory

4. Mara AlagicSITE 20024 Teachers’ beliefs Teachers’ beliefs about teaching and learning of mathematics & integration of technology shape... Using ongoing assessment of student readiness, interests, and learning profile teachers (can) differentiate content, process, products, and/or environment (Tomlinson, 1999)

5. Mara AlagicSITE 20025 Goal Interventions

6. Mara AlagicSITE 20026 What to differentiate?

7. Mara AlagicSITE 20027 Classroom Environment Classrooms - promote understanding Reflective teachers - applying reflective decision-making processes A standards-based curriculum & the teacher’s understanding of it Students - variety of experiences, capabilities, learning profiles, social contexts, and confidences in their ability to learn

8. Mara AlagicSITE 20028 What does technology bring in?

9. Mara AlagicSITE 20029 Technology Supporting Learners’ Meaning Making of MATHS Tool - knowledge construction Information vehicles - exploring knowledge Context - learning by doing, representing and simulating real-world problems and contexts Social medium - learning through conversation An intellectual partner - learning-by-reflecting... (Wenglinsky, 1998)

10. Mara AlagicSITE 200210 Impact of Technology on Student Learning...... depends on how the technology is used and therefore implies the need for different instructional processes and better preparation of teachers (Jonassen, Peck, & Wilson, 1999)

11. Mara AlagicSITE 200211 “Mathematics teachers need to do mathematics in environments supported by diverse technologies” Link to the core lessons & and to the skills the student is working to acquire Model best practices by using technology Empower teachers & students to learn by doing, communicate and exchange ideas locally/globally through the use of technologies

12. Mara AlagicSITE 200212 Successful Apprenticeship Programs (Berryman,1989) Focus on application of the knowledge & skills Weave together specific knowledge with the development of general basic skills and problem-solving strategies Stimulate questions - learner = s original ideas + staged discrepant or confirming experiences Emphasize learning in context

13. Mara AlagicSITE 200213 The cognitive apprenticeship framework (Berryman, 1989, 1993) êContent êPedagogical methods êScaffolding êContext

14. Mara AlagicSITE 200214 PCASTLE model exemplified in engages supported by have context mimic USING reflects demonstrates learn through derived from involves focuses on based on emphasis Anchored instruction cognitive apprenticeships Situated learning learner activities Participatory cognitive apprenticeship community of learners coaching modeling scaffolding classroom learning apprenticeships alternative assesment computer tools inquiry modeling cognitive skills thinking process Conversation & Action community of practitioners Legitimate peripheral participation Central participation social constructivism

15. Mara AlagicSITE 200215 PCASTLE framework oContent: oMATH content and “tricks of the trade” ocognitive management strategies olearning strategies oPedagogical methods oScaffolding oContext

16. Mara AlagicSITE 200216 PCASTLE framework oContent  Pedagogical methods - employed to encourage and support this learning environment: both students = group and independent work oScaffolding oContext

17. Mara AlagicSITE 200217 PCASTLE framework oContent oPedagogical methods oScaffolding: Sequencing of learning activities by classroom “experts” so that learners tasks are increasingly complex oContext

18. Mara AlagicSITE 200218 PCASTLE framework oContent oPedagogical methods oScaffolding oContext: The sociology of learning environment providing some motivational characteristics resembling real-world situations

19. Mara AlagicSITE 200219 “Technology in the Mathematics Classroom K-12” All four grade bands were represented 19 teachers Motivation Previous experiences The computer lab - state-of-the-art Technical support

20. Mara AlagicSITE 200220 The content of the course “Current changes” in the teaching of the school mathematics (NCTM 2000, NRC 2000) »standards-based »learning for understanding »differentiating instruction »integrating technology Variety of computer programs for learning and doing mathematics Web resources for developing of mathematics teaching and learning Portfolio - performance assessment

21. Mara AlagicSITE 200221 Integrating Technology: Differentiating Instruction conceptual understanding of integration of IC technologies differentiating instruction through the use of technology On which motives these teachers base their decision concerning to what extent, if at all, they are willing to differentiate instruction through the use of PCASTLE model in their own classroom?

22. Mara AlagicSITE 200222 Activities: Three Levels Learner’s Level Challenging goal in the context Network Level Broadening interactions Local Level “Lectures” and group-work

23. Mara AlagicSITE 200223 Confidence Question How would you rate your confidence and abilities at using appropriate technology as you teach mathematics in your own classroom? On a scale of 1 to 10 with 10 as high.

24. Mara AlagicSITE 200224

25. Mara AlagicSITE 200225 Participants –primary - 2 –elementary - 5 –middle - 6 –high - 5 –college - 1 ICT use –11 NO - classroom –8 YES - classroom –8no + 2yes - Lab available –16 - personal use Projects (required) –2 LOGO –4 CAS –2 Maple –5 on dynamic geometry –6 on spread sheets Everyone was exposed to all of the above + Concept Maps + variety of software on CDs and exploration through the Internet + …

26. Mara AlagicSITE 200226 Question 1: Obstacles If in the fall you had everything you wanted in IC technology to enhance teaching of mathematics, what other obstacles would you need to overcome, if any?

27. Mara AlagicSITE 200227

28. Mara AlagicSITE 200228 Question 2 How are you planning to differentiate instruction in your classroom as a result of experiences in this class?

29. Mara AlagicSITE 200229 Guide on the Side or... ICT= source for DI (2 teachers) already “differentiating” - ICT just an additional opportunity (4 teachers) training “How to...?” before they can even think of DI (4 teachers) need for appropriate curriculum materials & training (5 teachers)

30. Mara AlagicSITE 200230 … or Sage on the Stage? Maize: centers with 4-6 computers - shared some ideas for DI (3 teachers) 2 other teachers that have already been using GCs very actively expressed an enthusiasm in preparing their materials for DI; reporting some positive results

31. Mara AlagicSITE 200231 Learning Cycle (Bybee’s 5Es) ENGAGE EXPLORE EXPLAIN - TERM INTRODUCTION EXPAND EVALUATE

32. Mara AlagicSITE 200232 ENGAGE EXPLORE PCASTLE PC AST LEEXPLAIN - TERM INTRODUCTION: PCASTLE - Participatory Cognitive Apprenticeship Situated in the Technology- based Learning Environment EXPAND EVALUATE

33. Mara AlagicSITE 200233 EXPAND/EVALUATE: Next steps This summer - new group of teachers Both quantitative and qualitative data is being gathered Online discussion group established Research questions for classrooms action research to determine changes that these teachers are taking into their classrooms effects on student learning

34. Mara AlagicSITE 200234 Future: Searching for Reasonable Research Questions and Appropriate Methods What types of teacher knowledge are needed in order to provide successful use of technological tools in their mathematics classroom? Are there particular stages in the development of such knowledge? What influences this development? What kind of impact is this experience going to have on students learning in their classroom?

35. Mara AlagicSITE 200235 IF TIME,... http://education.twsu.edu/faculty/mara_alagic.html

36. Mara AlagicSITE 200236 What Did Teachers Say: Support and Impediments Paradigm shift - What students can DO? Changing learning environment Teachers’ involvement Inadequate technological resources Absence of appropriate curriculum materials Limited time/saving time

37. Mara AlagicSITE 200237 Class-initiated Discussions skills for utilizing IC technologies conceptual understanding of mathematical representations differentiating instruction - obstacles have been noted explicit plans for implementation small steps a teacher as “all knowing” - pupils “more comfortable around technology than we are” high school teachers - graphing calculators the issue of “memorizing multiplication table” was not missed, as usual :)

38. Mara AlagicSITE 200238 The Whole Picture

39. Mara AlagicSITE 200239 Situated Learning