This paper presents the findings of a convergent parallel mixed methods research that was carried out to explore the views of student-teachers on how geometry was taught and the confidence of those student-teachers in teaching geometry to secondary school learners when they will become professionally qualified. Respondents were randomly selected…

Valid proofs need not be in the traditional two-column format. This classroom activity allows students to explore, discuss, and use specialized facts to create a general statement of truth.

This paper details an exploratory study of ten elementary preservice teachers (PSTs) involvement in the problem-solving process in a mathematics methods course. The dynamic, messy and nonlinear nature of this process was demonstrated by discussing PSTs' solution process of an open box construction problem. Effective approaches to solve this…

In this article, we describe one possible way to modify volume tasks in textbooks to promote conceptual understanding of the volume formula: length × width × height. From the results of previous studies regarding students' understanding of volume measurement, we identified three conceptual ideas key to understanding volume: filling…

Functional dependency is a term coming out of mathematical software terminology. It shows the dependency of one representation (either diagrammatic or algebraic) to one another in the form of a formula, a conceptual relation or an algorithm. In mathematics, it is important since it shows students' understanding of those conceptual relationships if…

The concept of angles is important for future geometric knowledge (Arslan et al., 2016; Moore, 2013; Yigit, 2014). However, although Piaget (1948) suggests angles lead to the discovery of lines, angles are typically taught later in schools, after points, lines, and planes (Charles, 2011). Therefore, the way in which angles are taught can affect…

The study presented here utilized a cross case comparison of three different professional development programs to examine the contextual factors associated with uptake related to what teachers learned related to content, pedagogy and the resources used in their professional development (PD) workshops. From a theoretical perspective this study…

Proof, though central to mathematical practice, is rarely explored through the lens of embodiment because of the centrality of abstraction and generalization. We use the case of a high school geometry student to investigate two research questions: (1) How do embodied processes facilitate mathematical learning? (2) How can generalized mathematical…

The observational and interview study explored how two middle school teachers, Ms. Watson and Mr. Garry, from two different public schools in a small college town in a midwestern state in the United States, used talk moves to establish mathematical discussions during both small group and whole class discussions. The study also examined their…

This article discusses GeoGebra's geometry capabilities to assist the teaching issues and learning of geometry and measurement content in grades 5-9. Within this geometry context, the authors focus on using learning goals to select applets from a large public database. Also mentioned are some common pitfalls to avoid, such as error-prone applets.

We look at the problem of the minimum speed of projectiles in a constant gravitational field. In the absence of resistance, the problem may be studied in the frame of a high school curriculum. One needs only Newton's laws and a minimum amount of analytic geometry to compute the orbit, which turns out to be parabolic. Furthermore, in case the…

This is a descriptive study which attempts to answer how well 8th grade students define a rectangle. The subjects for this study were 93 of 8 th grade students. The students were administered a written open ended test on the definition of a rectangle which was adapted from Ahuja (1996). Responses of the students were coded by each researcher…

The introduction of auxiliary elements as a method of solving problems in high-school geometry is considered here from two perspectives: first, to elicit recalling some known result or concretizing a definition and, second, as a means of shifting the focus and structure of the students' attention. We present and compare various examples of how…

In this paper, we demonstrate how atypical visual representations of a triangle, square or a parallelogram may hinder students' understanding of a median and altitude. We analyze responses and reasoning given by 16 preservice middle school teachers in a Geometry Connection class. Particularly, the data were garnered from three specific questions…

This article explores three processes involved in attending to evidence of students' thinking, one of the Mathematics Teaching Practices found in "Principles to Actions: Ensuring Mathematical Success for All." These processes, explored during a classroom activity on proportional relationships, are discussed in this article, another…