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Mathematical Knowledge for Teaching at the Secondary Level Examples from the Situations Project

Mathematical Knowledge for Teaching at the Secondary Level Examples from the Situations Project. Mathematics Education Research Colloquium November 16, 2007 Mid Atlantic Center for Mathematics Teaching and Learning Center for Proficiency in Teaching Mathematics. Jeremy Kilpatrick Jim Wilson

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Mathematical Knowledge for Teaching at the Secondary Level Examples from the Situations Project

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  1. Mathematical Knowledge for Teaching at the Secondary LevelExamples from the Situations Project • Mathematics Education Research Colloquium • November 16, 2007 • Mid Atlantic Center for Mathematics Teaching and Learning • Center for Proficiency in Teaching Mathematics

  2. Jeremy Kilpatrick Jim Wilson Pat Wilson Glen Blume M. Kathleen Heid Rose Mary Zbiek Bob Allen Sarah Donaldson Kelly Edenfield Ryan Fox Brian Gleason Eric Gold Sharon O’Kelley Heather Godine Shiv Karunakaran Situations Research Group

  3. Situations Project • Mathematical knowledge for teaching at the secondary level (MKTS) • Recommendations for preparing mathematics teachers • Strategy for investigating MKT • Examples of situations • Future directions

  4. Mathematical Knowledge for Teaching Mathematics at the Secondary Level • Why is MKT difficult to define? • What is the difference between • MKT and mathematical knowledge? • MKT and pedagogical content knowledge? • Is MKT at the secondary level distinct from MKT at the elementary level?

  5. Recommendations on Formal Mathematics Background for Secondary Teachers • 1911 ICTM: “dealing critically with the field of elementary mathematics from the higher standpoint” • 1935 MAA: “calculus, Euclidean geometry, theory of equations, and a history of mathematics course” • 1959 NCTM: 24 semester hours of mathematics courses

  6. Recommendations on Formal Mathematics Background for Secondary Teachers • 1991 MAA’s Committee on the Mathematical Education of Teachers (COMET): “the equivalent of a major in mathematics, but one quite different from that currently in place at most institutions” • 2000 NCATE: “know the content of their field (a major or the substantial equivalent of a major)” Compiled in Ferrini-Mundy and Findell

  7. MET Report Recommendations • Knowledge of the mathematical understandings and skills of elementary and middle school students • Knowledge of the post-secondary mathematics (collegiate, vocational or work). • Ability to continue growth of mathematical knowledge and its teaching.

  8. MET Report Recommendations • Understanding of the properties of the natural, integer, rational, real, and complex number systems. • Understanding of the ways that basic ideas of number theory and algebraic structures underlie rules for operations on expressions, equations, and inequalities. • Understanding and skill in using algebra to model and reason about real-world situations. • Ability to use algebraic reasoning effectively for problem solving and proof in number theory, geometry, discrete mathematics, and statistics. • Understanding of ways to use graphing calculators, computer algebra systems, and spreadsheets to explore algebraic ideas and algebraic representations of information, and in solving problems.

  9. Strategy for Learning aboutMathematical Knowledge for Teaching at the Secondary Level • Begin with practice • Identify mathematical ideas and ways of thinking about mathematics that could be useful to secondary mathematics teachers • Use what we learn to build a way to think about Mathematical Knowledge for Teaching at the Secondary level

  10. Begin with Practice • We draw from events that have been witnessed in practice. • Practice includes but is not limited to classroom work with students. • Events were in high schools or universities. • Events were related to secondary level mathematics. • We write brief prompts that describe mathematical events from practice.

  11. Identify Mathematical Ideas and Ways of Thinking about Mathematics • Given an event from practice (Prompt), • We describe the mathematical ideas that could be useful to a teacher in that situation • We are not trying to decide what a teacher should do! • We write a Situation which includes the practice-based Prompt and a set of Foci and Commentary.

  12. Then we… • Argue and rewrite • Debate and rewrite • Defend and rewrite • Rethink and rewrite . . .

  13. Create Situations Mathematics Classroom Mathematics Knowledge for Teaching Mathematical Knowledge Mathematical Work of Teaching ? Mathematical Knowledge for Teaching at the Secondary Level

  14. Website of Situations Situations project webpage

  15. Teacher preparation Methods courses Shadow courses Capstone courses Professional development Reflection on practice Situation study Theory building Research Projects Dissertations Assessment Where are we going?

  16. This presentation is based upon work supported by the Center for Proficiency in Teaching Mathematics and the National Science Foundation under Grant No. ESI 0227586. and the Mid-Atlantic Center for Mathematics Teaching and Learning under Grant Nos. 0083429 and 0426253 . Any opinions, findings, and conclusions or recommendations expressed in this presentation are those of the presenter(s) and do not necessarily reflect the views of the National Science Foundation.

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