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Putting the Focus on Mathematics: Content-based Professional Development for Grade 5-12 Teachers. Steve Benson Education Development Center sbenson@edc.org. MAA Session on Professional Development Programs for K-12 Teachers, I San Antonio, TX; January 12, 2006 . Motivation
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Putting the Focus on Mathematics:Content-based Professional Development for Grade 5-12 Teachers
Steve Benson
Education Development Center
sbenson@edc.org
MAA Session on Professional Development Programs for K-12 Teachers, ISan Antonio, TX; January 12, 2006
I’m still not sure why I had to learn about rings and fields
and other such topics to be a high school math teacher.
— A veteran high school teacher
Messages from the mathematics community
Over the past 15 years, two refrains have echoed through the discourse about teachers’ knowledge of mathematics: (1) that U.S. teachers mathematical knowledge is weak(2) that the mathematical knowledge needed for teaching is different from that needed by mathematicians.
— Mathematical Proficiency for All Students: Toward a Strategic Research and Development Program in Mathematics Education (RAND, 2001)
The mathematical knowledge needed by teachers at all levels is substantial, yet quite different from that required by students pursuing other mathematics-related professions. . . . Collegecourses developing this knowledge should make connections between the mathematics being studied and mathematics prospective teachers will teach.
— The Mathematical Education of Teachers (CBMS, 2001)
Messages from the mathematics community
— Principles and Standards for School Mathematics (NCTM, 2001)
Knowledge of Mathematics for Teaching
Knowledge of Mathematics for Teaching (cont’d)
Knowledge of Mathematics for Teaching (cont’d)
Knowledge of Mathematics for Teaching (cont’d)
Responses to the call for connections
Ways to Think About Mathematics: Activities and Investigations forGrade 6-12 Teachers; Benson, Addington, Arshavsky, Cuoco, Goldenberg, Karnowski; Corwin Press, 2004.
Mathematical Connections: A Companion for Teachers and Others;Cuoco, MAA, 2005.
Mathematics for High School Teachers - An Advanced Perspective;Usiskin, Peressini, Marchisotto, Stanley; Prentice Hall, 2003.
Seeing the Connections: Promoting Profound Understanding of Secondary Mathematics; Benson, Cuoco, Graham, Greenes,
Grundmeier, Portnoy (in preparation)
Ways to Think About Mathematics: Activities and Investigations for Grade 6-12 Teachers isavailable from Corwin Press. A Facilitator’s Guide and Supplementary CD (including solutions and additional activities) are also available.
More information athttp://www2.edc.org/wttam
Ways to Think About Mathematics: Activities and Investigations for Grade 6-12 Teachers
I. What is Mathematical Investigation?
Problem solving and problem posing
You’ve got a conjecture-now what?
Do it yourself
You know the answer? Prove it.
Discerning what is; predicting what might be
II. Dissections and Area
Be a mathematical cut-up
Making assumptions, checking procedures
Thinking about area
Areas of nonpolygonal area
Transformations and area
III. Linearity and Proportional Reasoning
Mix it up
Filling in the gaps
Guess my rule
Functions of two variables
From cups to vectors
IV. Pythagoras and Cousins
What would Pythagoras do?
Puzzling out some proofs
Pythagoras’s second cousins
Pythagorean triples (and cousins)
More classroom cousins
V. Pascal's Revenge: Combinatorial Algebra
Trains of thought
Getting there
Trains and paths and triangles, oh my!
Binomial theorem connection
Supercalifragilisticgeneratingfunctionology
VI. Problems for the Classroom (+ solutions)
VII. Answers to Selected Problems
http://www2.edc.org/wttam
Seeing the Connections:Promoting Profound Understanding of Secondary Mathematics
A collaborative curriculum project from
Education Development Center
University of New Hampshire
Stony Brook University
Funded by NSF DUE-0231342
Steve Benson sbenson@edc.org Karen Graham karen.graham@unh.edu
Al Cuoco acuoco@edc.org Neil Portnoy nportnoy@math.sunysb.edu
http://www2.edc.org/connect
The Seeing the Connections materials
The Seeing the Connections materials are the “offspring” of three NSF-funded proof-of-concept projects:
Making the Connections: Higher Algebra to School Mathematics(DUE-9950722)
Carole Greenes, PI, BU
Al Cuoco, Co-PI, EDC
Carol Findell, BU
Emma Previato, BU
Making Mathematical Connections in Programs for Prospective Teachers
(DUE-9981029)
Karen Graham, PI, UNH
Neil Portnoy, CSU, Chico*
Todd Grundmeier, UNH‡
Gateways to Advanced Mathematical
Thinking (DUE-9450731)
Al Cuoco PI, EDC
Wayne Harvey, Co-PI, EDC
* Now at Stony Brook University
‡ Now at California State University San Luis Obispo
The Seeing the Connections project is producing curriculum modules for use in mathematics courses that help preservice teachers develop a knowledge ofmathematics for teaching.
Making Mathematical Connections in Programs for Prospective Teachers
Making Mathematical Connections in Programs for Prospective Teachers, developed a series of activities that provide prospective teachers with the opportunity to make connections between two mathematical areas (transformational geometry and liner algebra) and school and university mathematics.
In addition, there is a series of 3 pedagogical activities that the prospective teachers explore within the context of the developing mathematical understandings above. These activities involve the prospective teachers in the analysis of pre-college mathematical curricula and tasks, the analysis of classroom observations conducted in middle school and/or high school classrooms, and the development, implementation, and evaluation of a class activity focused on transformational geometry.
Making Mathematical Connections in Programs for Prospective Teachers
Making Mathematical Connections in Programs for Prospective Teachers
Making the Connections: Higher Algebra to School Mathematics
Making the Connections: Higher Algebra to School Mathematicswas a proof-of-concept project, funded by the National Science Foundation (DUE-9950722), which produced materials for use in courses for preservice mathematics teachers that make explicit connections between the mathematics they learn in college to the mathematics they will eventually teach.
The content focus of this project was algebra and number theory with three main themes: Modular Arithmetic, Periods of RepeatingDecimals, and The Chinese Remainder Theorem.
Making the Connections: Higher Algebra to School Mathematics
1. Algebra as Structure
2. Modular Arithmetic
3. Making it a System
4. Decimals, Fractions, and Long Division
5. The Fundamental Theorem of Arithmetic
6. Interlude
7. Units, Orders, and Periods
8. The Chinese Remainder Theorem
10. Euler, Units, and Periods of Decimals
11. Irrational Numbers: An Introduction
Gateways to Advanced Mathematical Thinking
Gateways to Advanced Mathematical Thinking was a dual curriculum development/research project funded by the National Science Foundation (DUE 9450731). The development component of the project built a model curriculum module for use with undergraduates, and particularly with preservice teachers,
which motivates appreciation for mathematics, focuses on conceptual understanding without sacrificing formal techniques, and makes explicit connections to the high school curriculum. Topics include precalculus methods for solving — and/or approximating the solution of — optimization problems.
Gateways to Advanced Mathematical Thinking
Seeing the Connectionsmaterials are available online
Making Mathematical Connections in Programs for Prospective Teachers
http://www2.edc.org/connect/mathconnlink.html
Making the Connections: Higher Algebra to School Mathematics
http://www2.edc.org/connect/connectionslink.html
Gateways to Advanced Mathematical Thinking
http://www2.edc.org/connect/gatewayslink.html
Copies of slides and handouts will be available at
http://www2.edc.org/cme/showcase.html
All files are in PDF or Powerpoint format
Questions? Problems? Send email to sbenson@edc.org
Where have these materials been used?
Master of Science for Teachers program at the University of New Hampshire (1-unit content courses and supplement to core courses)http://www.math.unh.edu/~mathadm/mst/
Focus on Mathematics Mathematics Science Partnership(3-hour seminars, weekly study group content, 1-week all-day summer content institutes for grade 5-12 mathematics teachers) http://focusonmath.org
MAA Minicourses at Mathfest and Joint Meetings (2005-2006)Next minicourse at Lexington Mathfest, August 2006.
University, district, and school-based courses and professional developmentworkshops for inservice and preservice middle and high school teachers
Interested in using any of these materials?
Send me a note: sbenson@edc.org