Transitions in the Conception of Number: From Whole Numbers to Rational Numbers to Algebra

CONTENTS OF CURRICULUM UNIT 23.03.04

  1. Unit Guide
  1. Introduction
  2. Rationale
  3. Background Content Knowledge
  4. National Council of Teachers of Mathematics Process Standards
  5. Framework for Mathematical Discourse and Schema Building
  6. Strategies
  7. Activities
  8. Appendix on Implementing District Standards 
  9. Bibliography
  10. Notes

A Framework for Problem Solving: Schema Development and Discourse

Valerie Schwarz

Published September 2023

Tools for this Unit:

Notes

1 Schoenfield, Alan. “Making MathematicsWork for All Children: Issues of Standards, Testing, and Equity.” Educational Researcher, 13.

2 National Research Council. Everybody counts: A report to the nation on the future of mathematics education, 7.

3 https://schoolquality.virginia.gov/divisions/richmond-city-public-schools#desktopTabs-4

4 https://learning.ccsso.org/wp-content/uploads/2022/11/Math_Standards1.pdf p.88-89.

5 https://teachers.yale.edu/curriculum/viewer/initiative_17.05.03_u

6 Bednarz, Nadine and Janvier, Bernadette. “Emergence and Development of Algebra as a Problem-Solving Tool: Continuities and Discontinuities with Arithmetic.” Approaches to Algebra, 115–36.

7 Xin, Yan Ping. “Word Problem Solving Tasks in Textbooks and Their Relation to Student Performance.” The Journal of Educational Researcher, 347.

8 IBID, 357.

9 Xin, 528.

10 Fuchs et al. “Explicitly Teaching for Transfer: Effects on Third-Grade Students’ Mathematical Problem Solving.” Journal of Educational Psychology, 294.

11 Fuchs et al., “Expanding Schema-Based Transfer Instruction to Help Third Graders Solve Real-Life Mathematical Problems.” American Educational Research Journal, 438

12 Chen, Zhe. “Schema Induction in Children’s Analogical Problem Solving.” Journal of Educational Psychology, 713.

13 Fuchs et al “Expanding Schema-Based Transfer Instruction to Help Third Graders Solve Real-Life Mathematical Problems.” American Educational Research Journal, 420.

14 Hiebert, J. & Carpenter, T.P. “Learning and teaching with understanding. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning, 69.

15 Xin, 530.

16 Fuchs et al. “Explicitly Teaching for Transfer: Effects on Third-Grade Students’ Mathematical Problem Solving.” Journal of Educational Psychology, 293.

17 Fuchs et al “Explicitly Teaching for Transfer: Effects on Third-Grade Students’ Mathematical Problem Solving.” Journal of Educational Psychology, 438.

18 Xin, 528

19 Polya, George. How to Solve It; a new aspect of mathematical method.

20 Fuchs et al “Explicitly Teaching for Transfer: Effects on Third-Grade Students’ Mathematical Problem Solving.” Journal of Educational Psychology, 294.

21 https://www.nctm.org/flipbooks/standards/pssm/html5/index.html, 29.

Comments:

Be the first to comment on this unit!

Add a Comment

Characters Left: 500

Unit Survey
Feedback