“Fractions. Ugh! I’ve never been good with fractions.”
I can’t count how many times I’ve heard this statement. Every teacher knows that working with fractions is an area where many kids struggle. As a middle school teacher, I saw these struggles and how they can lead to further struggles in math. In fact, mastery of fractions has been found to be a predictor of students’ later success with algebra and other higher-level mathematics (Robert Siegler et.al, 2012). Operations with fractions are taught and re-taught year after year to many children. Even with all the time, planning, and energy put into lessons, fractions continue to cause frustration for children, teachers, and parents. However, there are several new types of activities being developed to address this issue.
Fair sharing is one such type of activity. Being used increasingly in classrooms, it’s aim is developing fractional understanding. The Coordinating Units team here at AIMS, in its investigation of fractions, is using sharing tasks with second and third graders. My teammates have written recently about their experiences during these sessions. You can read those blog posts here [Brook Lewis March 6 and Elin Anderson March 20].
We ask the children we are working with to share a “candy bar” among a number of people. Their responses have shown a wide variety of understanding. When asked to share a candy bar we have seen students cut off small pieces of equal size but not using the whole bar. Others students may use the entire bar but might not create pieces of equal size. We have also seen students who manage to create equal size pieces while using the entire bar and yet they still see several, unique pieces, rather than recognizing the pieces as possible copies of one another.
An interesting development, noticeable through our work, is that a child’s understanding of number is giving us a basis for understanding their work with fractional concepts. When I began at the AIMS Center a year and a half ago, I was introduced to Dr. Les Steffe’s research on how children come to know number. The relationship that emerges between number development and fractional development is one area we are exploring. Dr. Steffe describes the relationship between whole number and fractions in his reorganization hypothesis. Contrary to some who believe that working with whole numbers interferes with the development of fractional operations, his stages in the development of number are giving us a foundation for understanding how and why students behave in the ways they do during these sharing situations. We are also exploring activities to promote children’s increasingly sophisticated fractional knowledge and operations through the use of sharing tasks. This may allow teachers an avenue to develop operations with fractions in ways that are meaningful and make sense for children.
If fractions are a key predictor of future success in high school mathematics, then understanding a child’s development of number is necessary for promoting fractional knowledge. Keep reading as our team continues to work and write about fractions.