From Arithmetic to Algebra: Variables, Word Problems, Fractions and the Rules

CONTENTS OF CURRICULUM UNIT 17.05.03

  1. Unit Guide
  1. Introduction and Rationale
  2. Polya’s Method
  3. A Brief History of Singapore Math
  4. Model Method
  5. Whole Group Discussion
  6. Taxonomy of Word Problems
  7. Activities
  8. Sample Collection of Problems 
  9. Bibliography
  10. Additional Resources for Teachers and Students
  11. Appendix A: Implementing District and National Standards
  12. Common Core Standards
  13. Endnotes

Understanding Problems: Using Bar Models with Common Core Taxonomies

Valerie J. Schwarz

Published September 2017

Tools for this Unit:

Bibliography

Bokhorst-Heng, W.D., M.D. Osborne, K. Lee, J. Albright, B. Comber, J. Dornbrack, H. K. Fai, A. Firkins, N.S. Fong, G. Forey, P.J. Gilmer, M. Hanrahan, C. Hart, J.G. Hedberg, M. Hoechsmann, S.L. Hoon, M. Ismail, B. Kamler, F. Khng, D. Kwek, K. Lee, L.M. Ling, T.A. Ling, L.T. Lioe, J. Ng, M.D. Osborne, K.D. Purohit, D. Sankey, L. Soong, A. Vongalis-Macrow, C.S. Walsh, J. Wolf, S. Wright, E.H. Wuan, A.S. Yin, W.K. Yong, and K.P. Yuk. Redesigning pedagogy: reflections on theory and praxis. Rotterdam The Netherlands: Sense Publishers, 2006.

The Model method: obstacle or bridge to learning symbolic algebra pages 227-242 was referenced in the Looi & Lim article and this is where the referenced study originated.

Cheong, Yan Kow. "The Model Method in Singapore." The Mathematics Educator, 2002nd ser., 6, no. 2 (2002): 47-64. Accessed June 09, 2017. JSTOR.

This article speaks to the power of the model method as a technique to teach problem solving.

Englard, Lisa. "Raise the Bar on Problem Solving." Teaching Children Mathematics17, no. 3 (October 2010): 156-63. Accessed May 14, 2017. JSTOR.

This article is easy to read and reveals the results of teaching bar models to students.

Fan, Lianghuo, and Yan Zhu. "Representation of problem-solving procedures: A comparative look at China, Singapore, and US mathematics textbooks." Educational Studies in Mathematics66, no. 1 (2007): 61-75. Accessed June 09, 2017. doi:10.1007/s10649-006-9069-6.

This article compared problem solving in text books from three countries. It was not very helpful, but provided a little insight.

Fong, Ng Swee, and Kerry Lee. "Model Method: A Visual Tool to Support Algebra Word Problem Solving at the Primary Level." Series on Mathematics Education Mathematics Education, 2009, 169-203. Accessed June 09, 2017. doi:10.1142/9789812833761_0008.

This article focuses on using the model method to solve algebra word problems. It addresses some strengths, but also some shortfalls.

Kaur, Berinderjeet. "Evolution of Singapore's school mathematics curriculum." MERGA, July 2014, 24-36. Accessed June 9, 2017. JSTOR.

This report describes how the education in Singapore has evolved. The report was insightful.

Kaur, Berinderjeet. "The model method: A tool for representing and visualising relationships." Conference Proceedings of ICMI Study 23: Primary mathematics study on whole numbers, June 3-7, 2015, 448-55. Accessed June 09, 2017. JSTOR.

This article provides an overview of the model method for primary students.

Looi, C.-K.,-S. Lim. “From bar diagrams to letter-symbolic algebra: a technology-enabled bridging.” Journal of Computer Assisted Learning 25.4 (2009): 358-74. Web. 5 June 2017. JSTOR. This article addresses the difficulty students in Singapore have moving from bar diagrams to algebra. The ALGEBAR computer technology helps to bridge the gap.

Melvin, George W. “Polya’s Problem Solving Techniques.” https://math.berkeley.edu/~gmelvin/polya.pdf., N.p. n.d. Web. 6 July 2017. This site provides a brief overview of Polya’s steps.

Ng, Swee Fong, and Kerry Lee. "The Model Method: Singapore Children's Tool for Representing and Solving Algebraic Word Problems." Journal for Research in Mathematics Education 40, no. 3 (May 2009): 282-313. Accessed June 09, 2017. JSTOR.

This article examines the model method and emphasizes aspects to look for when teaching students the method.

Xin, Yan Ping, and Dake Zhang. "Exploring a Conceptual Model-Based Approach to Teaching Situated Word Problems." The Journal of Educational Research102, no. 6 (2009): 427-42. Accessed June 09, 2017. doi:10.3200/joer.102.6.427-442.

This article supports the use of the model method to teach students in grades 3 through 5.

Comments:

Grace Laz

March 29, 2021 at 6:40 am

Can bar method be applied to complex word problems?

Hi. I am an educator to my 11 year old daughter. We has been using Singaporean math books for her year 5 and came across this bar method. Do you think the bar method can be applied to complex word problems? Thank you.

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