The Odd Shape Out task was an open-ended problem that engaged students in comparing shapes based on their properties. Four teachers submitted the work of 116 students from across the country. This article compares various student's responses to the task. The problem allowed for differentiation, as shown by the many different ways that students…

The objective of this paper is to present two preservice secondary mathematics teachers' beliefs about teaching Geometric Transformations (GTs) using Geometer?s Sketchpad (GSP). The study comprised of series of five task-based interviews with each of two participants, who were senior undergraduate preservice teachers, at a medium-sized public…

"Cognitive Tutor"® is a secondary mathematics curriculum developed by Carnegie Learning that focuses on how students think about and learn mathematics. Teachers facilitate student learning as students acquire and apply new information and discuss their work. The curriculum can be implemented using a textbook, adaptive software, or…

This article analyses students' thinking as they interacted with a dynamic geometric sketch designed to explore eigenvectors and eigenvalues. We draw on the theory of instrumental genesis and, in particular, attend to the different dragging modalities used by the students throughout their explorations. Given the kinaesthetic and dynamic…

This study explores interactions with diagrams that are involved in geometrical reasoning; more specifically, how students publicly make and justify conjectures through multimodal representations of diagrams. We describe how students interact with diagrams using both gestural and verbal modalities, and examine how such multimodal interactions with…

Given a parabola in the standard form y[superscript 2] = 4ax, corresponding to three points on the parabola, such that the normals at these three points P, Q, R concur at a point M = (h, k), the equation of the circumscribing circle through the three points P, Q, and R provides a tremendous opportunity to illustrate "The Art of Algebraic…

Here is a way to show a sound wave travelling through air in real time. The method employs a set of low-cost microphone--LED units and demonstrates the movement of a pulse of sound as it lights up LEDs along a long (100-200 m) distance across a field. (Contains 4 figures.)

We produce a continuum of curves all of the same length, beginning with an ellipse and ending with a cosine graph. The curves in the continuum are made by cutting and unrolling circular cones whose section is the ellipse; the initial cone is degenerate (it is the plane of the ellipse); the final cone is a circular cylinder. The curves of the…

Calculation of moments of inertia is often challenging for introductory-level physics students due to the use of integration, especially in non-Cartesian coordinates. Methods that do not employ calculus have been described for finding the rotational inertia of thin rods and other simple bodies. In this paper we use the parallel axis theorem and…

People need the idea of transformation geometry in order to understand the nature and environment they live in. The teachers should provide learning environments towards perceptual understanding in symmetry training and development practice skills of the students. In order to make up such a learning environment, teachers should have information…

This study examined the effectiveness of an integrated context approach to the instruction of basic compass-and-straightedge construction. The formulation of a perpendicular bisector of a segment was used as a knowledge module to guide students from the pre-attention level to the elaboration level of information processing. The students were…

Studies of the impact of various types of computer use on the results of learning and student motivation have indicated that the use of computers can increase learning motivation, and that computers can have a positive effect, a negative effect, or no effect at all on learning outcomes. Some results indicate that it is not computer use itself that…

We conducted an intervention-based study in secondary classrooms to explore whether the use of geometric transformations can help improve students' ability in constructing auxiliary lines to solve geometric proof problems, especially high-level cognitive problems. A pre- and post-test quasi-experimental design was employed. The participants were…

The central roles that modelling plays in the processes of scientific enquiry and that models play as the outcomes of that enquiry are well established (Gilbert & Boulter, 1998). Besides, there are considerable similarities between the processes and outcomes of science and technology (Cinar, 2016). In this study, we discuss how the use of…

The purpose of this qualitative study was to understand the perceptions of high school mathematics teachers regarding the support provided through professional development (PD) as they engage in the implementation of the Common Core State Standards (CCSS). By means of a qualitative instrumental case study, eight high school mathematics teachers…