Much of physics involves the construction and interpretation of equations. Research on physics students' understanding and application of mathematics has employed Sherin's symbolic forms or Fauconnier and Turner's conceptual blending as analytical frameworks. However, previous symbolic forms analyses have commonly treated students' in-context…

Play allows young children to acquire and practice mathematics skills and concepts while engaging in meaningful and enjoyable activities (Bobis, 2010; Reed & Young, 2018). In particular, open-ended play provides children opportunities to discover materials, explore concepts, and solve problems (Rosli & Lin, 2018) and in the process,…

Beginning a mathematics lesson involving a challenging task with a carefully chosen preliminary experience is an effective means of activating student cognition. In this article, the authors highlight a variety of preliminary experiences, each with a different structure and form, all designed to support students to more successfully engage with…

This article explores the conceptual challenges that engineering students encounter with double integrals in a vector calculus course. Drawing on previous literature and utilising APOS (Activity- Process- Objects- Schema) as a theoretical framework, this study investigates the difficulties that students face in understanding and applying double…

This paper discusses findings from an ongoing study investigating mental mechanisms involved in the conceptualisation of linear transformations from the perspective of Action (A), Process (P), Object (O), and Schema (S) (APOS) theory. Data reported in this paper came from 44 first-year linear algebra students' responses on a task regarding the…

In this theoretical paper, I use an empirically based example to illustrate particular design features of the Learning Through Activity (LTA) design framework and examine the impact of particular design principles. The LTA design framework is based on our elaboration of Piaget's construct of reflective abstraction. The example discussed here,…

At the school level statistics begins with exploratory data analysis, or EDA. Statistical learning goes on to include statistical inference, which will be discussed in the second part of this article. In this article, the author will talk about EDA and CODAP. EDA can be thought of as looking for patterns in data using graphs and simple statistics…

Although there is much research exploring students' covariational reasoning, there is less research exploring the ways students can leverage such reasoning to coordinate more than two quantities. In this paper, we describe a system of covariational relationships as a comprehensive image of how two varying quantities, having the same attribute…

Understanding the intricate quantifier relations in the formal definitions of both convergence and continuity is highly relevant for students to use these definitions for mathematical reasoning. However, there has been limited research about how students relearn previous school mathematics for understanding multiply quantified statements. This…

Previous research in mathematics education has explored teachers' conceptions of mathematics and its teaching and learning, and how their instructional tendencies (e.g., "traditional", "technological", "spontaneous" and "investigative") relate to these conceptions. However, empirical evidence on this topic…

Students entering sixth grade operate with three different multiplicative concepts that influence their reasoning in many domains important for middle school. For example, students who are operating with the second multiplicative concept (MC2 students) can begin to construct fractions as lengths but do not construct improper fractions as numbers.…

Children with Down Syndrome (DS) can experience a number of difficulties in mathematics but one relatively unexplored area is that of being able to discriminate between quantities; an important foundational skill for later learning. This study examines whether children with DS can make judgements about relative quantity in the context of a card…

The purpose of this study was to investigate university students' conceptions of the definite integral in the process of finding the volume of a solid of revolution. The participants were four students enrolled in a university calculus course in Turkey. Data were obtained by task-based interviews, in which the participants had to work on a problem…

We are all fascinated by loops and their formation in space. When a line cuts itself, it forms an intersection point and creates a space. This is an experimental study done by analyzing several loops, forming a concrete formulation by visualizing the patterns observed, and then proving the formulations proposed using the known standard…

Problems involving the composition of mixtures are common in chemical practice and are thus part of introductory Chemistry courses at the early undergraduate level. However, they are often perceived by students as a rather obscure matter, which may be due to poor familiarity with algebraic manipulations. Furthermore, to increase the distaste of…