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 amongst learners taught by expert teachers. Existing research also lacks sufficient attention towards latent classes and reasoning processes amongst primary learners at scale. The current study thus looks into the learning of the topics amongst 2,642 fifth and sixth graders taught by master mathematics teachers in China. Utilising items identified as top-level tasks in previous research, the paper captures performance patterns, latent classes and reasoning processes of the learners, from a cross-sectional perspective. data are analysed with Rasch, mixture Rasch model (MRM) and complementary statistical methods. Variation between grades and gender is scrutinised 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. Micro-level analyses show that different characteristics of reasoning lead to different performance of members affiliated to different latent classes.

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ORCID for Christian Bokhove: orcid.org/0000-0002-4860-8723

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