Individual differences in students’ knowing and learning about fractions: Evidence from an in-depth qualitative study

Abstract

We present the results of an in-depth qualitative study that examined ninth graders’ conceptual and procedural knowledge of fractions as well as their approach to mathematics learning, in particular fraction learning. We traced individual differences, even extreme, in the way that students combine the two kinds of knowledge. We also provide preliminary evidence indicating that students with strong conceptual fraction knowledge adopt a deep approach to mathematics learning (associated with the intention to understand), whereas students with poor conceptual fraction knowledge adopt a superficial approach (associated with the intention to reproduce). These findings suggest that students differ in the way they reason and learn about fractions in systematic ways and could be used to inform future quantitative studies.

Keywords

• fractions
• conceptual/procedural knowledge
• individual differences
• learning approach