Work

Magnitude-based reasoning can reduce the natural number bias when comparing fractions: An intervention study

Year: 2025

Type: article

Study designs: Randomized Controlled Trial, Clinical Trial

Abstract: When comparing fractions, students often focus on the natural number components rather than on the fractions’ numerical values (e.g., they reason that 2/4 > 1/2 because 2 > 1 and 4 > 2). This phenomenon is known as natural number bias . To date, there has been little research on ways to reduce this bias. We investigated whether an increased ability to reason about fraction magnitude can improve students’ accuracy and reduce the natural number bias when comparing fractions. Participants were 225 sixth-grade students from German academic-track secondary schools. We used a three-arm randomized pretest-posttest intervention design. For six weeks (18 sessions), the intervention group received computer-based training linking visual representations to symbolic fractions to activate fraction magnitude. One control group used a different tool for fraction learning that did not focus on fraction magnitude, while the other control group received no training. On average, students in the intervention group improved their fraction comparison accuracy by 15% (control groups: 3% and 6%, respectively). Pretest and posttest results revealed interindividual differences in accuracy for fraction pairs congruent or incongruent with naïve natural number-based reasoning. In the intervention group, 74% of students who showed a typical natural number bias at pretest no longer showed it at posttest, a higher percentage than for both control groups (15% and 22%, respectively). Students’ increased ability to reason about fraction magnitude reduced the natural number bias, challenging previous research that the bias is persistent. The findings contribute to discussions about effective ways to reduce biased reasoning in mathematics. • Students often struggle to compare fractions due to natural number-based reasoning. • Students were trained to connect symbolic fractions and visual representations. • The intervention group outperformed two control groups in fraction comparison. • Magnitude-based reasoning is causally related to reduced natural number bias. • The natural number bias may be less resistant to change than previously assumed.

Source: Learning and Instruction

DOI: 10.1016/j.learninstruc.2025.102109

Authors: Michael D’Erchie, Johannes Rosenkranz, Sabrina Schwarzmeier, Thomas Dresler, Andreas Obersteiner

Institutions: Technical University of Munich, University of Education Freiburg, Deutsches Zentrum für Psychische Gesundheit, University of Tübingen

Language: English

Topic: Cognitive and developmental aspects of mathematical skills

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

SDG: Quality education

Open Access status: hybrid

Estimated APC paid: $4,580