Visualization and argumentation are central processes in the learning of geometry, giving rise to specific lines of research in mathematics education. However, it is worth asking whether they should be developed independently or if it is possible and in what way an articulation between them can be promoted. The objective of this paper is to search…

The goal of this note is to obtain the area enclosed between a parabola and two tangent lines using visual arguments. The first step that we have to follow, in order to do that, is noticing that the area between a parabola and a tangent line only depends on the leading coefficient of the quadratic function of the parabola. Finally, the…

The main difficulty in studying molecular symmetry is the mental manipulation of molecules when searching for symmetry. Numerous methods of teaching molecular symmetry require students to identify symmetry elements of objects or molecules. As an alternative, we propose activity that identifies symmetry using elements outside the objects, together…

Several articles deal with tilings with squares and dominoes on 2-dimensional boards, but only a few on boards in 3-dimensional space. We examine a tiling problem with coloured cubes and bricks on a (2 × 2 × "n")-board in three dimensions. After a short introduction and the definition of breakability we show a way to get the number of…

In this article, we examine spatial inscriptions marked in real or rendered spaces, rather than on two-dimensional surfaces, conceptualize spatial inscriptions from an inclusive materialist perspective and consider realizations of spatial inscriptions that are possible with emerging technologies (e.g. 3D pens, immersive virtual reality). We then…

Two of the Standards for Mathematical Practice (SMP) in the Common Core State Standards for Mathematics (CCSSM; NGA Center and CCSSO 2010), "Look for and use structure" (SMP 7) and "Look for and express regularity in repeated reasoning" (SMP 8), are particularly abstract and sometimes clear only in the mind. For a given…

In the context of rapid technological changes and modernization of society, the issue of ensuring adequacy of content in secondary education based on the use of advanced information technologies (ICT) is being updated. The necessity of an appropriate level of primary intellectual activity development in a person in terms of the current trends in…

In this work we examined the content of approximately 950 mathematics questions used in measuring achievement among 4th, 5th and 6th graders in the US in an attempt to determine how the current standardized examinations, which were developed to reflect new national curricular mandates, compared to the old measures used for the same purpose. Using…

The representation of figures in mongean projection (double system planned orthographic projection used in the studies of Descriptive Geometry), specially when placed in a particular situation in relation to the projection plans, possesses the quality that, through them, the actual dimensions of represented spatial objects can be found directly…

We examined geometric calculation with number tasks used within a unit of geometry instruction in a Taiwanese classroom, identifying the source of each task used in classroom instruction and analyzing the cognitive complexity of each task with respect to 2 distinct features: diagram complexity and problem-solving complexity. We found that…

Diagram describing texts are integral part of science and engineering subjects including geometry, physics, engineering drawing, etc. In order to understand such text, one, at first, tries to draw or perceive the underlying diagram. For perception of the blind students such diagrams need to be drawn in some non-visual accessible form like tactile…

This paper describes the development of an instrument to assess teachers' views on their geometry instruction and their classroom learning environments in six government high schools in southwest Sydney. The sample consisted of 18 Years 9/10 ESL teachers from participating schools. The study involved completion of a survey form using a modified…

This paper discusses an investigative approach to problems concerned with approximations. Two problems are analysed in detail and both are inspired by their historical origins. The first examines an ancient Chinese formula for calculating the area of a segment. The second looks at Durer's construction for the trisection of an angle. It is argued…

The present study examines how changes in the amount of on-screen text will influence student learning from a multimedia instructional unit on basic concepts of coordinate geometry. The relative effectiveness of two different versions (short-text and whole-text) of the instructional unit was examined for students who differed in terms of their…

When students take General Chemistry there are substantially fewer molecular images than they will encounter in Organic Chemistry. The molecular images Organic Chemistry students see in their textbooks are ones that use dashes and wedges to represent 2D and semi 3D views, ball and spoke, ball and wire, and structural formulas, to name just a few.…