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…

This study aims to examine the types of mathematical connections that pre-service mathematics teachers use in their instructions and their opinions on the mathematical connection. For this purpose, a total of 60 pre-service mathematics teachers made lesson plans related to a learning objective from the Turkish middle school mathematics curriculum.…

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…

This theoretical article explores the affordances and challenges of Euler diagrams as tools for supporting undergraduate introduction-to-proof students to make sense of, and reason about, logical implications. To theoretically frame students' meaning making with Euler diagrams, we introduce the notion of logico-spatial linked structuring (or…

In this theoretical article, we explore the possibility that instead of a mathematical connection arising "in-between" two (or more) pre-existing ideas or objects, which have presumably been known or understood, that connection is itself the motor of understanding. The standard view of connection, in which two existing ideas or concepts…

This study investigated the effects of working memory load (WML) and automaticity on mental addition through an examination of both task and individual characteristics within the framework of cognitive load theory. Results from 73 fourth graders showed that WML, automaticity, and their interaction had significant effects on mental addition.…

Math educators must engage students in deep learning and talk spanning shorter, medium, and longer time frames to offer both the structures and language so that secondary English learners can participate fully alongside their classmates. In this article, the authors present: (1) "structure and language" to facilitate full participation…

This research developed academic achievements to attain a pass rate of 70% and assessed student motivation in studying mathematics. The target group consisted of 40 Grade 10 students during the second term of the 2023 academic year at Sarakham Pittayakhom School under the Mahasarakham Secondary Educational Service Area Office. The tools used in…

Children with autism spectrum disorder often demonstrate self-regulation challenges and academic difficulties. Although self-regulation has been well documented as an important factor for academic achievement in neurotypical children, little is known about how it is related to academic learning in autistic children, especially during preschool, a…

This study explored pre-service teachers' perceptions of a 3D printing integrated science, technology, engineering, and mathematics (STEM) module within a college-level mathematics content course. Data from surveys and reflections collected from nineteen participants were analyzed. Results indicated that the pre-service teachers perceived…

The study reported in this paper contributes to the literature on prospective teachers' decision making, specifically regarding how they analyze and make informed decisions about the use of their textbooks. We designed a training intervention with 28 future Costa Rican teachers, in which they had to identify and manage semiotic conflicts that can…

When learning physics, students need more than just an understanding of mathematical and physical concepts. Integrating the two fields is crucial, as research indicates that students often struggle even when they have a strong grasp of both. In this paper, we use the heat equation as an example from higher education. Given the importance of the…

Enhancing understanding is crucial for "all" students. Instructional approaches have been developed to achieve this goal, yet little is known about the kind of support that teachers need for their effective implementation. We compare two support conditions designed to enable teachers to enhance students' understanding of the mathematical…

Achieving meaningful educational outcomes requires scalable strategies for mastering mathematical concepts and skills, with student engagement at the core. This paper examines the use of comprehensive, technology-enhanced activities designed to promote active learning and deeper conceptual understanding. Specifically, it focuses on the integration…

This article describes how the authors developed the activity Speaqual to enable their students to "speak" about the "equal" sign and foster communication of their reasoning. The article explains how to play Speaqual and how the students were thoroughly engaged in a friendly competition, centralizing algebraic concepts and…