How to Teach Fractions

When I look back on my education in mathematics, there is one concept that stands out to me as being the most difficult. From the time I was in first grade until I was a senior in AP Statistics, I could never wrap my brain around fractions! This semester, my peers and I are specifically learning how to teach math to middle level students. As we practiced problem solving with fractions, I realized that I am not alone in my struggle. Fractions seem to be a leading cause of stress among the majority of math learners. For this blog post, I wanted to get to the heart of the issue. Why are fractions so daunting? How can educators successfully mold the conceptual understanding of rational numbers (fractions, decimals, and percentages) in students?

In, “Developing Children’s Understanding of the Rational Numbers: A New Model and and Experimental Curriculum,” Joanne Moss and Robbie Case discuss the issue with how rational numbers are taught. They say, “although most students eventually learn the specific algorithms that they are taught, their general conceptual knowledge often remains remarkably deficient (Moss and Case 1999). Just because students may understand the steps to solving a problem, does not mean that they have a true grasp of the conceptual meaning. This leads to an inability to problem solve in new situations. When students are confronted with tasks that require conceptual understanding of rational numbers, they can’t solve them, because they have been relying on memorization. Moss and Case developed a program for combatting misconceptions with rational numbers and promoting true understanding. The four features that make up this program are listed below (Moss and Case 1999).

1. A greater emphasis on meaning rather than procedures when manipulating rational numbers
2. A greater emphasis on the proportional nature of rational numbers
3. A greater emphasis on children’s natural way of viewing problems
4. The use of alternative forms of visual representations

I believe that my courses this semester are following this approach to instruction. This gives me hope that students are currently learning math differently than I did in my elementary and middle school years. Moss and Case’s study was developed in 1999, which was a few years before I entered kindergarten. I think in the past ten years, with a recent emphasis on STEM, students are taught math in a drastically different way than I was. For example, growing up, I was always taught fractions through the use of pie charts. Moss and Case argue that continually using the same form of visual representation will not help students develop conceptual understanding of fractions. In my courses this semester, we are learning how to use paper folding to teach students. I find this very beneficial because it allows students to actually manipulate the paper. They can physically see the fractions they are working with. Rational numbers are not impossible for students to understand, however the way in which they have been taught has set students up for failure. It is our job as teachers to instill in students a deep conceptual understanding of rational numbers so that they can face any problem and work through it. Students should no longer be relying on the memorization of procedures to solve a problem. I am excited to be a part of this approach to instruction!

Moss, J., & Case, R. (1999). Developing children’s understanding of the rational numbers: A new model and an experimental curriculum. Journal for Research in Mathematics Education, 30, 122-147.