Fractions are among the most problematic concepts that children encounter in their primary school years because of the many different conceptions of fractions. Textbook analyses have tried to provide insights into how fractions are introduced, focusing on the different concepts and representations of fractions. In this paper, we contribute to…

The ethnomathematics field plays a crucial role in understanding how students can comprehend, express, manipulate, and apply mathematical concepts. However, it is acknowledged as a complex concept, particularly in Asian countries like Indonesia and Thailand, requiring a comprehensive understanding. This study aims to bridge this gap by exploring…

Developing mathematical connections for pupils continues to be at the forefront of educational policies worldwide. One strategy suggested to support the connections pupils make is the idea of developing "coherence". Research regarding coherence has increased within mathematics education, however, the term is used widely. It therefore…

Educational technologies in mathematics typically focus on fostering either procedural knowledge by means of structured tasks or, less often, conceptual knowledge by means of exploratory tasks. However, both types of knowledge are needed for complete domain knowledge that persists over time and supports subsequent learning. We investigated in two…

It has become increasingly clear that the early use of decomposition for addition is associated with later mathematical achievement. This study examined how younger children execute a base-10 decomposition strategy to solve complex arithmetic (e.g. two-digit addition). 24 addition problems in two modalities (WA: Written Arithmetic; OA: Oral…

Cross-cultural research covering multiple languages and cultures involves negotiating conceptual and linguistic challenges. This paper focuses on how researchers working across cultural and linguistic boundaries navigate the research process and negotiate a common understanding of the constructs under study. Working towards intersubjectivity…

This study compared area lessons from Korean textbooks and US standard-based textbooks to understand differences and similarities among these textbooks, as well as how these textbooks address known learning challenges in area measurement. Several well-known challenges have been identified in previous studies, such as covering, array structure, and…

This study examines how sampled Chinese and U.S. third and fourth grade students (N[subscript China] = 167, N[subscript US] = 97) understand the commutative, associative, and distributive properties. These students took both pre- and post-tests conducted at the beginning and end of a school year. Comparisons between students' pre- and post-tests…

This article describes a study of how Chinese preservice teachers unpacked a learning goal pertaining to adding fractions and understanding the concepts underlying the operation. Based on work in the USA by Morris, Hiebert, and Spizter ("Journal for Research in Mathematics Education," 40(5), 491-529, 2009), 50 Chinese preservice teachers…

This study compares English- and Korean-speaking university students' colloquial and mathematical discourses on the notion and practice of limit. There exists a lexical discontinuity in Korean with the word limit, since the mathematical word for limit is not commonly used as a colloquial word in Korean, unlike its use in English. This study…

With the aid of longitudinal country-level data from five IEA TIMSS assessments (1995--2011), the current study addresses the issue of the globalisation of curricula and achievement. To explore the hypothesis of global convergence, we study performance in four subdomains of mathematics. Using regression with fixed effects for countries, we…

In an experiment, secondary students from Australia and Malaysia (n = 130) were randomly assigned to one of three approaches (equation, unitary, unitary-pictorial) to learn how to solve challenging percentage-change problems. In line with the differential types of cognitive load associated with the three approaches, the unitary-approach group…

International comparisons of languages have shown how mathematical concepts can be expressed and conceptualised in different languages. For multilingual students, these findings raise the question of how the interplay of languages and conceptualisations shape multilingual learning processes. This paper presents an investigation of case studies of…

This study investigates how students in England and Shanghai understand linear function. Understanding is defined theoretically in terms of five hierarchical levels: Dependent Relationship; Connecting Representations; Property Noticing; Object Analysis; and Inventising. A pilot study instrument presented a set of problems to both cohorts, showing…

This essay reflects on the challenges of thinking about scale--of making sense of phenomena such as continuous professional development (CPD) at the system level, while holding on to detail at the finer grain size(s) of implementation. The stimuli for my reflections are three diverse studies of attempts at scale--an attempt to use ideas related to…