Helpful Review

Summary

This paper presents teaching ideas derived from recent research on three aspects of the learning of fractions: partitioning, ordering fractions, and informal knowledge of fractions. The author discusses some of the difficulties related to partitioning that children experience and presents some ways that teachers could address those difficulties. Next, the author discusses issues related to ordering fractions and discusses strategies that are used by children but that are seldom taught directly. In the section on informal knowledge, the author discusses some of the problems arising when children interpret fraction notation using their whole number experience.

Strengths

The article focuses on three aspects of the learning of fractions that are important in a first approach to the learning and teaching of fractions.

Teachers will find a wealth of sound teaching ideas and activities that are directly supported by research findings. For each section, the author provides detailed guidance on how this knowledge can be used to improve students' learning of fractions. In the section related to partitioning, the author gives examples of paper folding, partitioning shapes, and dissection motion operations.

The description of the concepts involved is done in a clear language. The author avoids, for the most part, the technical terms used in research reports.

Weaknesses

The article is too long for this journal. It is almost twice as long as the suggested length in the guidelines. More clarity is needed in the discussion of why children's ways of referring to fractions (for example, "one pizza is cut into three parts" on p. 12), which are per se correct, may nevertheless lead to problems later if students' conceptions are not extended beyond their initial approach.

Recommendations to the Editorial Panel

Although the paper contains many valuable ideas and suggestions, it is too long in its present form. The paper could be separated into two sequenced and, to some degree, independent articles; the first dealing with partitioning and ordering fractions and the second with students' informal knowledge. The author should be encouraged to revise and resubmit the article.

Comments and Suggestions to the Author

All comments above can be shared with the author.

It would be helpful to distinguish "informal knowledge" from "limited conceptions" or "misconceptions." As the examples in the article show, children's informal knowledge is generally sound, and they are usually successful in solving problems in a context with appropriate concrete tools; it is when they deal with an unfamiliar notation that most problems arise. On the other hand, students do indeed often form misconceptions that need to be explicitly addressed by the teacher.