In this design experiment study, we investigated the problem: What conditions might foster students' discernment of a critical aspect--variation in unidirectional change (e.g., discerning a "decreasing" increase)? At a public middle school in a large US city, we led a sequence of three days of whole class lessons, followed by task-based,…

Perceiving a 3-dimensional (3D) diagram on a 2-dimensional (2D) surface or plane can be a challenging endeavor for students at the elementary or primary grade levels. Adding to this challenge are the intricacies present in understanding the processes involved in geometric problems of such a nature. To ease the comprehension of these processes,…

As three-dimensional (3D) printing technology is fast becoming more affordable and accessible, calculus instructors can now consider using 3D printing and 3D printed models to actively engage students in core concepts relating to objects in R[superscript 3]. This article describes three lessons for a multivariable calculus class in which students…

Mathematics textbooks play a very important role in mathematics education and textbook tasks are used by students for practice to a large extent. Since the nature of the tasks may influence the way students think it is important that the textbooks provide a balance of a variety of tasks. The analyses of the requirements in textbook tasks contain…

In our research, we focused on the design of assessment instruments for measuring teachers' mathematical knowledge for teaching geometry. Since 1987 when Lee Shulman conceptualized pedagogical content knowledge, different research groups have expanded on this construct and developed their own measurement instruments. The strengths and limitations…

The foundation of geometric knowledge and understanding starts in primary school, and in contemporary mathematics education there is an emphasis on identifying learning progressions and trajectories as a way of moving students forward. The van Hiele (1986) theory is well-documented and provides insights into the progression and differences of…

In this study we analyze and contrast approaches that future high school math teachers show when solving word problems with the use of pencil and paper and later, with the use of a Dynamic Geometry System (DGS). The resources, representations, strategies and forms of mathematical reasoning that the participants exhibit when they use GeoGebra in…

This study reports on the development, validation, and reliability of a geometry disposition scale (GDS) to measure pre-service teachers' (PSTs') attitudes to geometry learning. PSTs from two Colleges of Education (CoEs) in Ghana volunteered to participate in the study (N = 153). A principal component analysis (PCA) extracted four factors: deep…

The study investigated the effects of a technology-integrated guided inquiry-based approach on pre-service mathematics teachers' conceptual understanding of geometry when compared to a guided inquiry approach and a traditional teacher-centered approach. A non-equivalent pretest-posttest control group quasi-experimental design was used. A…

This study investigated the cognitive and social processes through which high school students acquire the differential concepts through communication in a dynamic geometry environment through some cases. Additionally, we observed how a dynamic geometry environment affects these processes. To achieve this objective, eight students were recruited by…

Advancement of self-regulation during complex problem solving and the development of strategical reasoning are among the central educational goals linked to 21st century skills. In this paper we introduce the notion of "Stepped Tasks", which are specially designed in Top-Down structure to achieve these goals in mathematics instruction.…

The purpose of this study was to examine the effects of using GeoGebra software in a computer-supported collaborative learning (CSCL) environment on seventh grade students' geometry achievement, retention of learning, and attitudes toward geometry. The study was designed using a quasi-experimental research method with pretest, post-test and…

In our pursuit to broaden and deepen understandings of what it means to engage in an assessment activity, we explored the designing and implementing of a geometry performance task as an instantiation of authentic assessment to assess elementary school students' mathematics learning. Using participatory action research, we incorporated a…

This contribution belongs to a larger empirical study that focuses on issues related to the implementation of inquiry-based learning and formative assessment in science and mathematics education, while it also refers to the issue of STEM education. Here, we discuss the two topics from the perspective of professional preparation of primary school…

The capacity to recognise, represent, and reason about relationships between different quantities, that is, to think multiplicatively, has long been recognised as critical to success in school mathematics in the middle years and beyond. Building on recent research that found a strong link between multiplicative thinking and algebraic, geometrical,…