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

CONTENTS OF CURRICULUM UNIT 23.03.06

  1. Unit Guide
  1. Introduction
  2. Rationale
  3. Content Objectives
  4. Teaching Strategies
  5. Teaching Implementation
  6. Lessons
  7. Classroom Activities
  8. Resources
  9. Appendix
  10. Implementing District Standards
  11. Works Cited

Division of Fractions in Algebra, from real-life applications to abstract equations

J. Ulises Reveles

Published September 2023

Tools for this Unit:

Works Cited

Chabe, A. M. 1963. Rationalizing “inverting and multiplying.” The Arithmetic Teacher, 10(5), 272–273.

Elashhab, G. A. 1978. A division of fractions-Discovery and verification. School Science and Mathematics. 78(2), 159–162.

Heid, M. K., Blume, G. W., and Clarin, M. V., eds. 2005. Research on Technology and the Teaching and Learning of Mathematics: Research Syntheses. Information Age Publishing.

(This collection of research syntheses may include studies supporting the role of division of fractions in preparing students for advanced mathematical concepts).

Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K. C., Wearne, D., Murray, H., and Human, P. 1997. Making Sense: Teaching and Learning Mathematics with Understanding. Portsmouth, NH: Heinemann.

(This book delves into the importance of understanding mathematical concepts, including division of fractions, to support later learning in advanced mathematics).

Koichu, Boris, Guershon Harel, and Alfred Manaster. "Ways of thinking associated with mathematics teachers’ problem posing in the context of division of fractions." Instructional Science 41 (2013): 681–698.

Li, Yeping. "What do students need to learn about the division of fractions?" Mathematics teaching in the middle school 13, no. 9 (2008): 546–552.

Ma, L. 1999. Knowing and teaching elementary mathematics. Mahwah, NJ: Erlbaum.

Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education, National Research Council; Jeremy Kilpatrick, Jane Swafford, and Bradford Findell, editors. Adding It Up: Helping Children Learn Mathematics. Washington, DC: National Academy Press, 2001.

Sharp, J.; Adams, B. “Children's constructions of knowledge for fraction division after solving realistic problems” Journal of Educational Research.  95(6): (2002): 333-347.

Silvia, E. M. (1983). A look at division with fractions. The Arithmetic Teacher; 30(5), 3841.

Singapore Ministry of Education. Primary Mathematics 6B. Singapore: Times Media Private Limited, 2003.

Streefland, L. (1991). Fractions in realistic mathematics education. Dordrecht l Boston l London: Kluwer.

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