Rational numbers and proportional reasoning in Chinese primary schools: Patterns, latent classes, and reasoning processes

Abstract

Rational numbers and proportional reasoning are challenging topics in school mathematics. Though much research has been conducted, the learning of these topics is rarely explored among learners taught by expert teachers. Existing research also lacks sufficient attention toward latent classes and reasoning processes among primary learners at scale. The current study thus looks into the learning of the topics among 2,642 fifth and sixth graders taught by master mathematics teachers in China. Utilizing items identified as top level tasks in previous research, the article captures performance patterns, latent classes and reasoning processes of the learners, from a cross-sectional perspective. Data are analyzed with Rasch, mixture Rasch model (MRM), and complementary statistical methods. Variation between grades and gender is scrutinized where possible. The results show that, at the macro level, students have an average success rate of 78%, 78%, and 52% in decimals, fractions, and proportional reasoning, respectively; sixth graders outperform fifth graders; gender gap exists in the majority of Grade 5 but closes in Grade 6. At the meso level, two to three latent classes emerge in each grade with differential performance. Microlevel analyses show that different characteristics of reasoning lead to different performance of members affiliated to different latent classes.