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

Background

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.

Aims

We investigated whether an increased ability to reason about fraction magnitude can improve students’ accuracy and reduce the natural number bias when comparing fractions.

Sample

Participants were 225 sixth-grade students from German academic-track secondary schools.

Methods

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.

Results

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).

Conclusions

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.