What is it about?

Fractions, decimals, and percentages are an important but difficult topic for many children and adults. This paper examines how college students perform on comparing rational numbers. Some of the problems involved within-notation comparisons (e.g., which is larger: 2/5 or 1/4?). Some of the problems involved cross-notation comparisons (e.g., which is larger: 2/5 or 0.25?). When analyzing within- and cross-notation comparison, we found that cross-notation skills play a more important part explaining SAT/ACT scores and other math skills. Further, in cross-notation comparisons, undergraduate students showed that they did not perceive equivalent fractions, decimals, and percentages as being equivalent; many students perceived percentages as larger. Students who had this percentages-are-larger bias performed substantially worse on all measures.

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Why is it important?

Our research suggests that many undergraduate students have not internalized the idea that fractions, decimals, and percentages represent the same numbers, expressed in different formats. Undergraduates who have an integrated understanding of these numbers have better math outcomes, including reporting higher SAT/ACT scores. However, current educational approaches do not emphasize connections among notations. Further, in both education and research, we tend to focus separately on individuals' understanding of fractions, decimals, and percentages, with little emphasis on individuals' understanding about how these notations are related. Our findings show that cross-notation understanding of rational numbers is critical to math success. Thus, we may need to think more carefully about how we teach and assess rational numbers in school.

Perspectives

As a former 6th grade math teacher, I saw first-hand how difficult math could be for students who did not understand how fractions, decimals, and percentages were related. As a daily classroom activity, I used to have my students translate among the notations and place these values on number lines. I thought understanding of the relations among rational numbers was important but I didn't know to what extent. Here, we found that college students who were better at cross-notation comparisons (e.g., what is larger: 2/5 or 25%?) had higher SAT/ACT scores! It isn't enough to just understand the notations in a vacuum (e.g., what is larger: 2/5 or 1/4?). To fully understand rational numbers (and perhaps all of K-12 mathematics), it is important to understand the rational number notations in relation to one another.

Lauren Schiller
Kean University

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This page is a summary of: Lack of integrated number sense among college students: Evidence from rational number cross-notation comparison., Journal of Experimental Psychology Human Perception & Performance, January 2025, American Psychological Association (APA),
DOI: 10.1037/xhp0001268.
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