Mathematical knowledgeforteaching
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This document discusses the differences between mathematical knowledge for teaching and other specialized knowledge. It begins by asking critical questions about what mathematics is important for teaching and how it differs from mathematics used in other fields. It then defines mathematical knowledge for teaching as having two components: common mathematical knowledge that all should know, and specialized knowledge for teaching mathematics, such as representing ideas, providing explanations, and appraising unusual student solutions. The document provides examples of these different types of knowledge and knowledge used in pedagogical situations versus pure content knowledge. It concludes by introducing a diagram that further categorizes the specialized knowledge needed for teaching mathematics.
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Mathematics: skills, understanding or both?
Presentation for researchED maths and science on June 11th 2016. References at the end (might be some extra references from slides that were removed later on, this interesting :-)
Interested in discussing, contact me at C.Bokhove@soton.ac.uk or on Twitter @cbokhove
I of course tried to reference all I could. If you have objections to the inclusion of materials, please let me know.
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Mathematical knowledgeforteaching
- 1. Selecting, Designing & Using Mathematical Tasks in the K-5 Classroom
- 2. Critical Question… o What mathematics matters for What teaching? Distinguishes o Is it different from mathematics Mathematical knowledge as known and used by mathematicians, engineers, biologists, Knowledge candy sellers? If so, how can we From The characterize what makes it different? Specialized o What of that mathematics is “content,” Knowledge and what is more properly called by other names such as “practices,” Needed For “sensibilities,” or “orientations”? Teaching Mathematics? o What is the difference between “pure” content knowledge and knowledge used in pedagogical situations?
- 3. Mathematical Knowledge for Teaching Common mathematical knowledge Number halfway between 1.1 and 1.2 Specialized knowledge for teaching mathematics Representing mathematical ideas and operations Providing explanations for mathematical ideas and procedures Appraising unusual student methods, claims, or solutions
- 5. Appraising Unusual Student Solutions Student A 35 x 25 125 +750 _ 875 Student B 35 x 25 175 +700 _ 875 Student C 35 x 25 25 150 100 +600 875 Which of these students is using a method that could be used to multiply any two whole numbers?
- 6. Reflect and Discuss o What did you do to solve the original problem of 25 x 35? o What did you do to solve the task concerning the varied student solutions? o What was different in the way you thought mathematically about each task, and what you needed to know?
- 7. Subject Matter Knowledge Common Content Knowledg e (CCK) Knowledge at the mathematica l horizon Pedagogical Content Knowledge Specialize d Content Knowledg e (SCK) Knowledge of Content and Students (KCS) Knowledge of Content and Teaching (KCT) Knowledg e of Curriculu m Diagram created by Deborah Ball & colleagues, University of Michigan