Keeping the Meaning in Mathematics: The Craft of Word Problems

CONTENTS OF CURRICULUM UNIT 07.06.05

  1. Unit Guide
  1. Introduction
  2. Rationale
  3. Objectives
  4. Addition and Subtraction Categories
  5. Multiplication and Division Categories
  6. Multi-step
  7. Strategies for Teaching Students to Use the Singapore Bar Models
  8. Activity 1
  9. Activity 2
  10. Activity 3
  11. Appendix A: Collection of Problems
  12. Appendix B: Resources for Classroom Use
  13. Appendix C: Annotated Bibliography
  14. Appendix D: Implementing District Standards:

Dr. Word Problem - Solving Word Problems with the Four Operations Using Singapore Bar Models

Valerie J. Schwarz

Published September 2007

Tools for this Unit:

Appendix C: Annotated Bibliography

Carpenter, T., Fennema, E., Franke, M., Levi, L., & Empson, S. (1999). Children's

mathematics: Cognitively guided instruction. Portsmouth, NH: Heinemann. This was a great book that clearly identifies different types of word problems.

Carpenter, T., Franke, M., & Levi, L. (2003) Thinking mathematically: Integrating

arithmetic & algebra in elementary school. Portsmouth, NH: Heinemann. This was not very useful for this unit, but is important for developing algebra concepts early.

Leinwand, Steven, (2005). New AIR study compares the quality of U.S. math instruction

with Singapore recognized world leader U.S. trails, but both nations could learn from

each other. 2/7/05 http://www.air.org/news/documents/ Singapore.htm. This website shares the results of a study that ranks Singapore the world leader in math achievement.

Ma, Liping. (1999). Knowing and teaching elementary mathematics. Mahwah, NJ:

Lawrence Erlbaum Associates, Publishers. This book compares Chinese teachers to American teachers and reveals some striking differences.

Singapore primary math texts, U.S. Edition Curriculum Planning and Development Division, Ministry of Education, Singapore: Federal Publications. These textbooks and workbooks have a more simplistic appearance, but are more challenging than the corresponding U.S. grade level. These books show bar models and present place value in a slightly different way.

Sowder, Larry, (1995). Addressing the story-problem problem. In J. Sowder & B.

Schappelle (Eds.), Providing a foundation for teaching mathematics in the middle

grades (123-131). New York: State University of New York Press. An interesting article that looks at limited and desired strategies for problem solving.

Thinking Blocks, (2006) http://www.thinkingblocks.com. Date last accessed 7/3/07. This is a great website and offers many uses for teachers and students.

Comments:

Kathryn Patrice Freeman

November 9, 2010 at 11:52 pm

Dr. Word Problem - Solving Word Problems with the Four Operations Using Singapore Bar Models by Valerie Schwarz

This unit gave me exactly the information I needed to confidently discuss word problems with our home-schooled daughter. We've done extensive work with bar modeling while using Singapore's curriculum over the last 5 years, but I still never felt completely versed in the method. We take an 'everyone around the table' approach to math, more so than any other subject, so that my daughter can benefit from seeing the very different ways I work problems as compared to her father, and although we can all three wiggle out the answers to word problems, none of us are really confident enough in our method to adequately explain it. This was incredibly helpful to me, and to my daughter. Thank you! Kathryn Freeman

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