One possible way of evaluating set curricula is to examine the consistency of study programmes with students' psycho-cognitive development. Three theories were used to evaluate matching between developmental theories and content proposed in the mathematics programmes (geometry section) for primary and the beginning of secondary education. These…

Opportunities for teacher candidates to investigate and enact the work of teaching in settings of reduced complexity--what are called "approximations of practice"--offer a promising path toward preparing more ambitious and equitable mathematics teachers. However, these approaches face the risk of not preparing individuals to continue…

Students often find geometrical concepts abstract and difficult to understand. This results in poor performance, which contributes in the declining interest in geometry. The aim of this study was to examine the impact of using the free educational software program, "GeoGebra" on 9th grade student's mathematics achievement in learning…

This study examined the effects of a dynamic geometry software (DGS) program, GeoGebra, on student engagement and student achievement on students in four geometry classes at a secondary school in Belize. Two teachers and 139 students in ninth grade were part of this study for three weeks during a geometry unit. There was a control group that was…

The Isoperimetric Quotient, or IQ, introduced by G. Polya, characterizes the degree of sphericity of a convex solid. This paper obtains closed form expressions for the surface area and volume of any Archimedean polyhedron in terms of the integers specifying the type and number of regular polygons occurring around each vertex. Similar results are…

The intersection of a plane and a cone is a conic section and rotating the plane leads to a family of conics. What happens to the foci of these conics as the plane rotates? A classical result gives the locus of the foci as an oblique strophoid when the plane rotates about a tangent to the cone. The analogous curve when the plane intersects a…

The geometrical shapes in Fig. 1 recently came into the Greenslade Collection. The semi-triangular pieces of wood looked like slices from a pie, each 22.5 degrees in angular width. They were tied together with a thin leather band tacked around their curved surfaces. What is this apparatus?

Following Husserl's speculations on how geometry originated, we suggest that spatial perception is "seduced" by language as a result of human attempts to capture, signify and share its concepts. And this language traps geometry and humans themselves in to the forms that have guided and regulated past practices, thereby obscuring possibilities for…

The international debate about experimental approaches to the teaching and learning mathematics is very current. While number theory lends itself naturally to such approaches, elementary geometry can also provide interesting starting points for creative work in class. This article shows how simple considerations about right triangles and the…

We will first recall useful formulas in integration that simplify the calculation of certain definite integrals with the quadratic function. A main formula relies only on the coefficients of the function. We will then explore a geometric proof of one of these formulas. Finally, we will extend the formulas to more general cases. (Contains 3…

In this article, a simple exercise for finding groups isomorphic to the symmetry group of the real line is presented. A mechanism for producing metrics on the real line is used to construct the group elements, and these transformations, by construction, are isometries with respect to the generating metric.

In Joe Crawford's last two articles, he examined the process of building standards-based curriculum documents to drive instruction in the K-8 environment. Continuing with this theme, this article explores "closing the loop" and following this work into the high school experience. There is one huge difference in the Common Core State…

This research examined a potential mechanism underlying gender differences in math performance by testing a mediation model in which women's higher anxiety taxes their working memory resources, leading to underperformance on a mathematics test. Participants for the 2 studies were college students (N = 87, N = 118) who completed an anxiety measure,…

This study compared conversations among groups of teachers of high school geometry that had been elicited by a representation of instruction (either a video or an animation) and facilitated with an open-ended agenda. All artifacts used represented instruction scenarios that departed from what, according to prior work, had been hypothesized as…

Access to advanced study in mathematics, in general, and to calculus, in particular, depends in part on the conceptual architecture of these knowledge domains. In this paper, we outline an alternative conceptual architecture for elementary calculus. Our general strategy is to separate basic concepts from the particular advanced techniques used in…