Fraction mapping and fraction comparison skills among grade 4 Chinese students: An error analysis

Background

Mapping fraction symbols to magnitudes is easier for students to master than comparing fraction magnitudes. Fraction mapping assesses students’ understanding of part-whole interpretations of fractions; fractions represent the parts of an object or set of objects. Fraction comparison assesses students’ understanding of measurement interpretations of fractions; a fraction is a single numerical quantity, not a combination of two whole numbers.

Aim

To examine and compare the types of errors made by emergent fraction learners on fraction mapping and comparison tasks.

Sample

Grade 4 Chinese students (N = 1036; 577 boys; Mage = 9.9 years).

Method

We examined performance and identified errors on fraction mapping and comparison tasks. For mapping, students converted pictorial representations into fraction notation. For comparison, they chose the larger of two symbolic fractions.

Results

Consistent with curriculum expectations, most students successfully mapped pictorial representations to fraction notation. In contrast, few students were able to accurately compare fraction magnitudes. Within each task, students’ errors were consistent across trials, suggesting that they applied systematic but incorrect procedures. However, errors were not consistent between tasks and the correlation between mapping and comparison performance was weak.

Conclusion

Emergent fraction learners can acquire part-whole knowledge of fractions without acquiring measurement interpretations of fractions. Moreover, misconceptions about different interpretations of fractions need not overlap. Awareness of the types of errors that students make can assist educators in identifying misconceptions early so that students do not build their fraction knowledge on erroneous beliefs.