Technological mediums such as dynamic environments with drag-and-drop features have been considered promising agents in helping students explore and generate conjectures about mathematical concepts. This study investigated the dragging modalities sixth and seventh-grade students use in solving proportional problems in a dynamic geometry…

This study investigated how problem-solving videos can be used in video-mediated professional learning to support secondary preservice mathematics teachers (PMTs) in developing teacher knowledge for noticing student thinking in the context of the derivative concept in calculus. A model of the trajectory of PMTs' noticing was constructed as six…

Feedback in exploratory learning systems has been depicted as an important contributor to encourage exploration. However, few studies have explored learners' interaction patterns associated with feedback and the use of external representations in exploratory learning environments. This study used Fractions Lab, an exploratory learning environment…

Understanding a graph in pairs, in a productive way, improves the comprehension of a concept. In this research, we had 2 objectives: 1) to delve deep into the behavior of 15 pairs of remedial physics students when solving a problem with a graph of velocity, 2) to understand the interchange of personal meanings during their interactions. We posed…

This paper examines whether using "From Here to There!" (FH2T:E), a dynamic game-based mathematics learning technology relates to improved early algebraic understanding. We use student log files within FH2T to explore the possible benefits of student behaviors and gamification on learning gains. Using in app measures of student…

In this article, I use the Vygotskian concept of the Zone of Proximal Development (ZPD) to examine the learning experience of two grade seven pupils as they attempted to solve an addition of fractions problem using fraction strips. The aim is to highlight how tools can facilitate the enactment of a ZPD, within which the tool provides the guidance.…

That mathematics education has been one of the central concerns of educational systems worldwide is no secret. It is also an established consensus that as far back as eighty years ago, Russian psychologists such as Vygotsky, Luria, Meshcheryakov, and Davydov have pioneered work that contributed to the understanding of teaching and learning and…

This paper examines whether using "From Here to There!" ("FH2T:E"), a dynamic game-based mathematics learning technology relates to improved early algebraic understanding. We use student log files within FH2T to explore the possible benefits of student behaviors and gamification on learning gains. Using in app measures of…

Mathematics classrooms have reflected little change over the past century, consisting of the learning of inert, disjoint procedures with few connections between mathematics concepts and students' everyday experiences. However, problem posing, that is, the reformatting of existing problems and the generation of new ones, has been promoted by the…

Background: Students, parents, teachers, and theorists often advocate for direct instruction on both concepts and procedures, but some theorists suggest that including instruction on procedures in combination with concepts may limit learning opportunities and student understanding. Aims: This study evaluated the effect of instruction on a math…

We report a qualitative analysis of elementary school students engaged in collaborative problem solving involving mathematical equivalence tasks. We build on previous research showing that students often use strategies based on either operational or relational understandings of the equal sign. We closely analyze three cases and identify nuanced…

Field placements serve as the traditional "clinical" experience for prospective mathematics teachers to immerse themselves in the mathematical challenges of students. This article reports data from a different type of learning experience, that of a clinical simulation with a standardized individual. We begin with a brief background on…

Mathematical engagement is a complex process of interaction between the person and the world. This interaction is strongly influenced by the concepts and structure of the mathematical field, by the practical and symbolic tools of mathematics and by the focus of investigation in the world. This paper reports on research that involves a detailed…

This study designed a learning system to facilitate elementary school students' fraction learning. An experiment was carried out to investigate how the system, which runs on multi-touch tabletop versus tablet PC, affects fraction learning. Two groups, a control and experimental, were assigned. Control students have learned fraction by using tablet…

This study analysed the different types of arithmetic knowledge that young children utilise when solving a multiple-step addition task. The focus of the research was on the procedural and conceptual changes that occur as children develop their overall problem solving approach. Combining qualitative case study with a micro-genetic approach,…