Learning the concept of fractions is among the most challenging topics in school mathematics. One of the main sources of difficulties in learning fractions is related to "natural number bias" (Van Hoof, Verschaffel & Van Dooren, 2015). Applying properties of the natural numbers incorrectly in situations involving rational numbers can…

In this note we introduce an infinite series which represents an interesting challenge for students with the relevant background.

Fraction knowledge is an essential building block for successful completion of advanced mathematics courses and linked to the development of algebraic understanding. Many students, especially those with disabilities, experience significant difficulties developing fraction knowledge. Intensive fraction interventions have been shown to be effective…

Many studies have used fraction magnitude comparison tasks to assess people's abilities to quickly assess fraction magnitudes. However, since there are multiple ways to compare fractions, it is not clear whether people actually reason about the holistic magnitudes of the fractions in this task and whether they use multiple strategies in a flexible…

This study contributes to efforts to characterize teaching that is responsive to children's mathematical ideas and linguistic repertoire. Building on translanguaging, defined in this article as a pedagogical practice that facilitates students' expression of their understanding using their own language practices, and on the literature surrounding…

A multidisciplinary origami activity that could be used in middle school mathematics and science lessons was designed and implemented. Mathematical purpose of the origami activity is to support students' conceptual understanding and procedural skills related to the concept of fraction. Regarding science, the activity aims to visualize Solar system…

Imbalances in problem distributions in math textbooks have been hypothesized to influence students' performance. This hypothesis, however, rests on the assumption that textbook problems are representative of the problems that students encounter in classroom assignments. This assumption might not be true, because teachers do not present all…

In November 2022, ChatGPT, an Artificial Intelligence (AI) large language model (LLM) capable of generating human-like responses, was launched. ChatGPT has a variety of promising applications in education, such as using it as thought-partner in generating curricular resources. However, scholars also recognize that the use of ChatGPT raises…

A one-on-one dialogue-based mathematics intelligent tutoring system (ITS) for learning multiplication and division of fractions was developed and evaluated in this study. This system could identify students' error types and misconceptions in real-time by using a block-based matching method. The adaptive dialogue-based instruction was supported by…

As digital technology use increases in K-12 education, greater numbers of strategies become available to support students in mathematics. One technology that provides students diverse representations of mathematical concepts is virtual manipulatives. Although instruction featuring representations with physical manipulatives possesses a large body…

Although the teaching of vocabulary in mathematics lessons is requested in content- and language-integrated lesson designs, the clarification of the specific lexical language demands is still an open question for many mathematical topics. In a content- and language-integrated lesson design towards understanding the concept of equivalent fractions,…

Understanding fraction magnitudes is especially important in daily life, but fraction reasoning is quite difficult. To accurately reason about fraction magnitudes, adults need to monitor what they know and what they do not know. However, little is known about which cues adults use to monitor fraction performance. Across two studies, we examined…

The objective of this research is to understand how a learning trajectory supports pre-service primary teachers in their noticing of students' mathematical understanding. A total of 95 pre-service primary school teachers used a learning trajectory related to the part-whole meaning of the fraction concept to interpret students' understanding and…

Understanding fraction magnitudes is especially important in daily life, but fraction reasoning is quite difficult. To accurately reason about fraction magnitudes, adults need to monitor what they know and what they do not know. However, little is known about which cues adults use to monitor fraction performance. Across two studies, we examined…

The notion or expectation of simplifying final mathematical results remains problematic in that it is ill-defined, tied more closely to algorithmic versus conceptual understanding, and decontextualized from the content, purpose, and application of the mathematics in question. In this article, the authors advocate for a tool-focused view of…