Abstract
Working with mathematics curriculum materials to create learning opportunities for pupils, and at the same time to develop mathematical knowledge for teaching is an important part of the work of teaching. In this study I investigate the role of curriculum materials, more precisely a task analysis schedule, as catalyst for teacher learning. I explore the different forms of feedback resulting from developing and working with a “tool” designed to analyse mathematical tasks/curriculum materials for instruction. The results are based on the work with two lower secondary school teachers in England, John and Paul, as they work together, over the period of 9 months, in a group of teachers and with a university academic, on the analysis, development and teaching of mathematics curriculum materials. It is argued that the task analysis “tool” develops, to become a “catalytic tool” to provide feedback for teacher learning. In the process it affords feedback loops and changes its character, from “tool” as artefact to “epistemic object” at the interface between task design and enactment. The results provide deeper insights into the processes of teacher learning with the help of analytic tools and the feedback these may afford.
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Acknowledgements
Particular thanks to the teachers featuring in the study; my colleague Dr Linda Haggarty who helped to develop some of the thinking behind the analysis schedule and to the NCETM who funded this project.
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Appendix
Appendix
Task analysis schedule | |||
|---|---|---|---|
Text source: | Grade/year: | ||
Content | Domain | Number | |
Algebra | |||
Geometry | |||
Measures | |||
Statistics and probability | |||
Conn. through maths | Within | ||
Across other subjects | |||
Processes | Representing | ||
Analysing – reasoning | |||
Analysing – procedural | |||
Interpreting | |||
Oral communication – implicit/none | |||
Oral communication – explicit | |||
Proced. fluency | 1 Step to be carried out | ||
2 Steps to be carried out | |||
3 Steps to be carried out | |||
Task type | Familiarity | Typically met in programme | |
Some novel aspects | |||
Situation not met before | |||
Context | Pure | ||
Artificial/contrived | |||
Authentic | |||
Conceptual understanding | Implicit | ||
Explicit | |||
Subordinated | |||
Cognitive demand | Knowledge (write, list, name) | ||
Comprehension (describe, summarise) | |||
Application (use, solve, apply) | |||
Analysis (compare/contrast, analyse) | |||
Synthesis (design, invent, develop) | |||
Evaluation (critique, justify) | |||
Mathematical repres. | Analogy | ||
Pictorial (e.g. charts) | |||
Symbolic | |||
Numerical | |||
Tools | Calculator | ||
Computer | |||
Geometric tools (compass, protractor) | |||
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Pepin, B. (2011). Task Analysis as “Catalytic Tool” for Feedback and Teacher Learning: Working with Teachers on Mathematics Curriculum Materials. In: Gueudet, G., Pepin, B., Trouche, L. (eds) From Text to 'Lived' Resources. Mathematics Teacher Education, vol 7. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1966-8_7
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