What is it about?
Division is an important math skill but is often challenging for students to perform and understand. In this study, we taught 4th-5th grade students in the US one of two division algorithms: long division or partial quotients. When solving problems, students were comparably accurate with either algorithm, but they were faster on large problems when using long division. For incorrect answers, the students using partial quotients were closer to the correct solution. In guided interviews, students demonstrated a much deeper understanding of how the partial quotients method works, with students showing almost no understanding of the rationale behind long division.
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Why is it important?
Even students who can successfully solve division problems often struggle with the how and why behind what they are doing. Our findings suggest that incorporating the partial quotients method into classroom division instruction may improve students' understanding of division without sacrificing problem-solving performance. This is important because strong division skills lead to better math outcomes.
Perspectives
Procedural skills and conceptual understanding are often focused on separately, with more conceptually-transparent procedures framed as inefficient but important tools for promoting deeper understanding. This study shows that procedural efficiency and conceptual understanding do not need to be mutually exclusive--rather, it is possible to teach strategies that are understandable as well as efficient. I hope this article encourages people to explore and study other transparent "alternative" procedures for things that may traditionally be deemed too complicated for students to conceptually understand.
Alexa Mogan
Vanderbilt University
Read the Original
This page is a summary of: Bridging the divide: Comparing the efficiency and transparency of two division algorithms., Journal of Educational Psychology, June 2026, American Psychological Association (APA),
DOI: 10.1037/edu0001046.
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