Understanding part-whole relations is crucial in early mathematics education. However, both analogue and digital learning environments often lack systematic approaches to foster part-whole understanding. With the rising popularity of educational apps, it is essential to evaluate how they implement learning of part-whole relations. Accordingly,…

The conception of functions, defined as the relationship between magnitudes or sets of ordered pairs, varies among students depending on the contextualization of the concept within the curriculum, notably in school textbooks. This investigation endeavors to scrutinize the approach taken by Indonesian textbooks in introducing the function concept…

On the basis of a substantial, robust, and well-replicated cognitive science research literature, interleaving has been recommended across a range of professional pedagogical works as an evidence-based strategy for mathematics teachers. This report first notes the conflation of interleaving and spacing effects underpinning those recommendations…

This study aims to clarify the role of generating questions in mathematical modeling and construct principles for teaching and learning mathematical modeling with an emphasis on generating questions. To achieve this purpose, the role of generating questions was determined by solving a sprinkler problem and considering the investigation process.…

The algorithm for fraction multiplication is relatively easy to memorize and implement with accuracy. The simplicity of the algorithm masks the conceptual complexity involved in making sense of what fraction multiplication means in quantitative situations. One important interpretation of fraction multiplication involves fraction composition,…

In STEM education, the engineering design process serves as a pedagogical strategy to connect science and mathematics concepts. While STEM approaches are increasingly favored in science courses, the role of mathematics in integrated STEM activities is often overlooked, despite its foundational importance across STEM disciplines. This manuscript…

Through instructional tasks, teachers can present content in ways that require students to apply critical thinking, problem-solving, and other cognitive skills. The purpose of this mixed methods collective case study was to determine how teacher-assigned instructional tasks in mathematics impact students' learning of mathematical concepts. In this…

The aim of this study is to explore the possibility of introducing the general notions of function and inverse function through a mathematical activity on linear functions, focusing on the quantitative meaning associated to the connection between a relation and its inverse. We present a genetic decomposition, that is, a viable cognitive path for…

The study examined the impact of concept-based instruction on the teaching and learning of mathematics. Functions is the topic that was implemented in order to identify the improvements in learners' understanding. A total of 35 Grade 11 learners from a South African township school in Limpopo province participated in this study. Data were…

We examined widely used popular calculus textbooks to explore opportunities to learn the limit concept. Definitions, worked problems, and exercise problems were coded to examine if these tasks allow students to use informal thinking to coordinate domain and range processes to understand the infinite process of limit. Results revealed many exercise…

Learning progressions have become increasingly prevalent in mathematics education as they offer a fine-grain map of possible learning pathways a child may take within a particular domain. However, there is an opportunity to build upon this research in ways that consider learning from multiple perspectives. Many current forms of learning…

Tangent lines are often first introduced to students in geometry during the study of circles. The topic may be repeatedly reintroduced to students in different contexts throughout their schooling, and often each reintroduction is accompanied by a new, nonequivalent definition of tangent lines. In calculus, tangent lines are again reintroduced to…

In the last two decades, studying the possible relations between the history of mathematics and mathematics education has revealed the importance of certain foundational issues concerning the nature, relevance and validity of historical knowledge vis-à-vis problems of teaching and learning, which call for deeper exploration. Reviewing aspects of…

Vectors have important applications both within and outside mathematics, but the concept of vectors is often taught to students in a less-than-engaging way, leading to students feeling inadequate and frustrated. This article describes the use of a mathematical microworld, "Driving with Vectors," to explore vectors using equitable…

The primary school mathematics syllabuses in Singapore as of the year 2020 reinforces that Big ideas are central to the learning of mathematics. In support of the push to teach for big ideas, a research study is presently underway. A part of it is on the professional development (PD) of primary school mathematics teachers. As part of the PD…