Prospective Elementary Teachers’ Knowledge of Fraction Division

Dec. 01, 2012

Source: Journal of Mathematics Teacher Education, Vol. 15, No. 6, p. 481–500, December 2012.

(Reviewed by the Portal Team)

This article investigates the fraction knowledge of prospective elementary teachers in Taiwan.
Specifically, the authors sought to answer the following two research questions:

1. How secure was the common fraction division knowledge of Taiwanese prospective elementary teachers who are not mathematics and science education majors?
What types of strategies did they use to solve fraction division word problems?

2. How secure was the specialized fraction division knowledge of Taiwanese prospective elementary teachers who are not mathematics and science education majors?
What types of multiplication and division structures as well as everyday context did they use to create their word problems?
What types of models did they use to represent their word problems?

Methods and Participants
Data were collected through an interview, and a written questionnaire.
Participants of this study comprised 45 prospective elementary teachers from a traditional teacher education university in Taiwan.
The participants in this study included 28 special education majors, 7 art education majors, and 10 counseling education majors.
The data for this study were collected at the beginning of the required mathematics methods course.


The findings suggest that Taiwanese prospective elementary teachers’ common fraction knowledge is quite secure.
Many of them have developed multiple strategies for solving fraction division word problems and showed flexibility in utilizing them.

All three of the major strategies prospective teachers used to solve the number line problem and the jogging problem are built upon multiple pieces of the knowledge package described by Ma (1999).
These prospective teachers have a secure understanding of the concept of unitizing and part-whole relationship.
The findings of this study also indicated that prospective elementary teachers are not as secure on some aspects of Specialized content knowledge (SCK) for fraction division.
They preferred to use measurement division within a measurement context to create their word problems, and they preferred linear and area models equally over the other models.


The findings suggest that many Taiwanese prospective elementary and middle school teachers enter the teaching profession with many components of mathematical knowledge for teaching already developed.
Since the prospective elementary teachers in this study received no additional mathematics instruction as part of their teacher education program, the findings suggest that narrowing the gap requires both an improvement in K-12 mathematics teaching and learning, and quality mathematics courses for prospective teachers that support the development of mathematical knowledge for teaching.

Taiwanese prospective elementary teachers possess a secure understanding of the concepts of unitizing and part-whole relationship and can move flexibly between algebraic and arithmetic reasoning.
They appear to be more comfortable with a measurement division problem than a partition division problem when the divisor is less than 1 and prefer a continuous model such as linear or area diagrams than a discrete model.

The authors recommend a concerted effort to help prospective elementary teachers develop a level of proficiency on fraction division comparable to their Taiwanese counterparts at the conclusion of their required mathematics courses.

Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates.

Updated: Jun. 18, 2014