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Schemas and cognitive load: Challenges for mathematics teachers and teaching

Schemas and cognitive load: Challenges for mathematics teachers and teaching. Mohan Chinnappan mohan@uow.edu.au. Cognitive Load and Schema. Schemas as organised knowledge Problem solving. Issues. Mathematics teachers need substantive mathematical knowledge

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Schemas and cognitive load: Challenges for mathematics teachers and teaching

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  1. Schemas and cognitive load: Challenges for mathematics teachers and teaching Mohan Chinnappan mohan@uow.edu.au

  2. Cognitive Load and Schema • Schemas as organised knowledge • Problem solving

  3. Issues • Mathematics teachers need substantive mathematical knowledge • Teacher knowledge is significant in driving student learning outcomes • Link between teacher’s schema and students’ schema

  4. What have we done? • Provide a hypothetical model/schema for teacher knowledge in specific mathematics domain • Empirical data on the qualitative aspects of teacher content knowledge

  5. Future lines in inquiry • Develop schemas for pedagogical content knowledge • Examine links between CK, PCK and student schemas • Link between PCK and Learning Tasks • Going from CK to PCK - Cognitive Loads

  6. Transfer from Content knowledge (CK) to Pedagogical Content Knowledge (PCK) CK PCK Half Part/whole Numerator/Denominator Why is 1/2 difficult What are the different ways kids think about 1/2 Given 1/2, a kid says top number is one and bottom number is 2. How would you help this child grasp the idea of half? What are some of misconceptions involving simple fractions?

  7. PCK - Representations Symbolic Linguistic Tabular Graphical

  8. Teacher Schemas • Schema structure • Expert Teacher Schema • Novice Teacher Schema

  9. Components of teacher’s lesson/schema

  10. Impact of WEs in the transfer of CK to PCK? • Define CK is discrete manner • Describe PCK in terms of representations • WEs that show the translation of CK to PCK

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