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Teachers’ Learning of Mathematics in the Presence of Technology: Participatory Cognitive Apprenticeship. Mara Alagic Wichita State University. current school reform for standards-based teaching that supports integration of technology (NCTM, 2000) development of the IC technologies

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Teachers’ Learning of Mathematics in the Presence of Technology: Participatory Cognitive Apprenticeship


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    1. Teachers’ Learning of Mathematics in the Presence of Technology:Participatory Cognitive Apprenticeship Mara Alagic Wichita State University SITE 2002

    2. 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 Paradigm shift: Changes in the teaching/learning of the (school) mathematics introduced by SITE 2002

    3. 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 Designing Mathematics Learning Environments SITE 2002

    4. 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) Teachers’ beliefs SITE 2002

    5. Goal Interventions SITE 2002

    6. What to differentiate? SITE 2002

    7. 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 Classroom Environment SITE 2002

    8. What does technology bring in? SITE 2002

    9. 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) Technology Supporting Learners’ Meaning Makingof MATHS SITE 2002

    10. . . . 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) Impact of Technology on Student Learning . . . SITE 2002

    11. 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 “Mathematics teachers need to do mathematics in environments supported by diverse technologies” SITE 2002

    12. 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 Successful Apprenticeship Programs (Berryman,1989) SITE 2002

    13. Content Pedagogical methods Scaffolding Context The cognitive apprenticeship framework(Berryman, 1989, 1993) SITE 2002

    14. PCASTLE model social Situated based on constructivism learning focuses on learner emphasis activities exemplified in apprenticeships Anchored Conversation instruction & Action mimic Participatory cognitive learn through apprenticeships cognitive engages community have context apprenticeship of learners classroom learning derived from supported by coaching community of computer scaffolding practitioners tools USING alternative involves assesment modeling modeling Central cognitive Legitimate inquiry skills peripheral participation demonstrates reflects participation process thinking process SITE 2002

    15. Content: MATH content and “tricks of the trade” cognitive management strategies learning strategies Pedagogical methods Scaffolding Context PCASTLE framework SITE 2002

    16. Content Pedagogical methods - employed to encourage and support this learning environment: both students= group and independent work Scaffolding Context PCASTLE framework SITE 2002

    17. Content Pedagogical methods Scaffolding: Sequencing of learning activities by classroom “experts” so that learners tasks are increasingly complex Context PCASTLE framework SITE 2002

    18. Content Pedagogical methods Scaffolding Context: The sociology of learning environment providing some motivational characteristics resembling real-world situations PCASTLE framework SITE 2002

    19. All four grade bands were represented 19 teachers Motivation Previous experiences The computer lab - state-of-the-art Technical support “Technology in the Mathematics Classroom K-12” SITE 2002

    20. “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 The content of the course SITE 2002

    21. 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? Integrating Technology: Differentiating Instruction SITE 2002

    22. Learner’s Level Challenging goal in the context Network Level Broadening interactions Local Level “Lectures” and group-work Activities: Three Levels SITE 2002

    23. 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. Confidence Question SITE 2002

    24. SITE 2002

    25. 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 + … SITE 2002

    26. 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? SITE 2002

    27. SITE 2002

    28. How are you planning to differentiate instruction in your classroom as a result of experiences in this class? Question 2 SITE 2002

    29. 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) Guide on the Side or... SITE 2002

    30. 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 … or Sage on the Stage? SITE 2002

    31. ENGAGE EXPLORE EXPLAIN - TERM INTRODUCTION EXPAND EVALUATE Learning Cycle(Bybee’s 5Es) SITE 2002

    32. ENGAGE EXPLORE EXPLAIN - TERM INTRODUCTION: PCASTLE - Participatory Cognitive Apprenticeship Situated in the Technology-based Learning Environment EXPAND EVALUATE Learning Cycle PCASTLE SITE 2002

    33. 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 EXPAND/EVALUATE:Next steps SITE 2002

    34. 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? Future: Searching for Reasonable Research Questions and Appropriate Methods SITE 2002

    35. IF TIME, ... http://education.twsu.edu/faculty/mara_alagic.html SITE 2002

    36. Paradigm shift - What students can DO? Changing learning environment Teachers’ involvement Inadequate technological resources Absence of appropriate curriculum materials Limited time/saving time What Did Teachers Say: Support and Impediments SITE 2002

    37. 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 :) Class-initiated Discussions SITE 2002

    38. The Whole Picture SITE 2002

    39. Situated Learning SITE 2002