# Produce Basket: The Development of PB module for improving fraction learning

## Keywords:

Fractions, Representation, Problem Solving## Abstract

Formal notation of fractions is a critical stumbling block for students, impeding their progress to acquire flexible number sense beyond integers and greatly impacting their success in algebra. Conflicting and vague definitions of fractions are a major cause of confusion and frustration among students and their teachers. Although several authors have identified this lack of clarity and have attempted to help teachers understand fractions better, a successful curriculum unit has not appeared that teachers and students can both use to make the meaning of fractions mathematically precise. To address this lack, a team consisting of a veteran fourth-grade teacher, a professional development leader/university instructor, a math educator, and a mathematician developed an experiential learning module called Produce Basket (PB) for elementary grades fraction learning. The module is a graduated set of games and activities around the metaphor of a basket (standing for "whole") that enables teachers to scaffold the precise definition of a fraction. The aim of this article is to describe the PB learning module with its roots in Bob Moses and the Algebra Project. Additionally, this article will discuss the theory of action that underpins the design of the module.

## References

CBC Radio “How failing at fractions saved the Quarter Pounder” CBC Radio. https://www.cbc.ca/radio/undertheinfluence/how-failing-at-fractions-saved-the-quarter-pounder-1.5979468#:~:text=And%20it%20became%20a%20McDonald's,of%20just%20a%20quarter%20pound.

Davis, F. E. & West, M. M. (2000). The Impact of the Algebra Project on Mathematics Achievement. Cambridge, MA: Program Evaluation & Research Group, Lesley University.

Kieren, T. (1976). On the mathematical, cognitive, and instructional foundations of rational numbers. In R. A. Lesh (Ed.), Number and measurement (pp. 101). Columbus, Ohio: ERIC/SMEAC.

Kieren, T. (Ed.). (1980). The rational number construct-Its elements and mechanisms. Columbus, Ohio: ERIC/SMEAC.

Kieren, T. (1983). Axioms and intuition in mathematical knowledge building. Proceedings of the fifth annual meeting of the North American chapter of the International Group for the Psychology of Mathematics Education, Columbus, Ohio. 67.

Kieren, T. (1988). Personal knowledge of rational numbers: Its intuitive and formal development. Number Concepts and Operations in Middle Grades, 162.

Kieren, T. (1993). Rational and fractional numbers: From quotient fields to recursive understanding. In T.P. Carpenter, E. Fennema, T.A. Romberg (Ed.), Rational Numbers: An integration of research (pp. 49). Hillsdale, NJ: Erlbaum.

Kolb, D. A. (1984). Experiential learning: Experience as the source of learning and development (Vol. 1). Englewood Cliffs, NJ: Prentice-Hall.

Lamon, S. (1993). Ratio and Proportion Connecting Content and Children's Thinking. Journal for Research in Mathematics Education, 24(1), 41.

Lamon, S. J. (1996). The development of unitizing: Its role in children's partitioning strategies. Journal for Research in Mathematics Education, 27(2), 170.

Lamon, S. J. (2007). Rational Numbers and Proportional Reasoning. Second Handbook of Research on Mathematics Teaching and Learning, 1, 629.

Lamon, S. (2006). Teaching Fractions and Ratios for Understanding. Mahwah, NJ: Lawrence Erlbaum Associates.

Moses, R. and Cobb C. (2001) Radical Equations, Beacon Press.

Wu, H. (1999) Some Remarks on the Teaching of Fractions in Elementary School. Available at: http://math.berkeley.edu/~wu/fractions2.pdf.

Wu, H. H. (2011) Understanding Numbers in Elementary School Mathematics. American Mathematical

Society.

## Downloads

## Published

## How to Cite

*Ohio Journal of School Mathematics*,

*92*(1), 32–41. Retrieved from https://ohiomathjournal.org/index.php/OJSM/article/view/9080