In this paper, we analyze and compare two didactical designs for introducing primary school pupils to proportional reasoning in the context of plane polygons. One of them is well-documented in the literature; the other one is based on our own data and is accordingly presented and discussed in more detail in this paper. The two designs come from…

Two experiments investigated whether the spatial reference directions that are used to specify objects' locations in memory can be solely determined by layout geometry. Participants studied a layout of objects from a single viewpoint while their eye movements were recorded. Subsequently, participants used memory to make judgments of relative…

We investigate experienced high school geometry teachers' perspectives on "authentic mathematics" and the much-criticized two-column proof form. A videotaped episode was shown to 26 teachers gathered in five focus groups. In the episode, a teacher allows a student doing a proof to assume a statement is true without immediately justifying it,…

Current reforms in undergraduate mathematics education devoted to proof and counterexample highlight its importance in teaching and learning mathematics. While undergraduate students who have taken a number of upper-level mathematics courses are expected to have mastered the skills required to verify statements as well as to read and write proofs…

This study investigated the relationship between middle school math teacher pedagogical content knowledge as gathered from a teacher assessment and student Standards of Learning scores. Nine middle-school math teachers at two rural schools were assessed for their pedagogical content knowledge in geometry and measurement in the specific area of…

In this study, the effect of Cabri 2D software on drawings of height, perpendicular bisector in triangles and diagonal in polygons was explored. Case study method was used in the study. Diagnostic questions and computer assisted worksheets related to height, perpendicular bisector and diagonal concepts were developed as data collecting tools.…

"Scratch" is a media-rich digital environment that utilises a building block command structure to manipulate graphic, audio, and video aspects. It incorporates elements of Logo including "tinkerability" in the programming process. In "Scratch" students use geometric and measurement concepts such as coordinates, angle,…

This article presents an activity that allows students to use mathematics and critical-thinking skills to emulate processes used by the ancient Egyptians to prepare the site for the Pyramids of Giza. To accomplish this, they use three different methods. First, they create a square using only simple technological tools that were available to the…

This paper proposes a taxonomy of the pedagogical opportunities that are offered by mathematics analysis software such as computer algebra systems, graphics calculators, dynamic geometry or statistical packages. Mathematics analysis software is software for purposes such as calculating, drawing graphs and making accurate diagrams. However, its…

Open-ended tasks focused on content specific features are regarded as an effective way to promote particular concept development and to elicit higher-order thinking. Such tasks may vary widely in their focus and approach and they can be formulated without unnecessary complexity. When mathematics tasks are designed in an open-ended fashion they can…

Early in development, there is a transition in spatial working memory (SWM). When remembering a location in a homogeneous space (e.g., in a sandbox), young children are biased toward the midline symmetry axis of the space. Over development, a transition occurs that leads to older children being biased away from midline. The dynamic field theory…

This Annual Measurable Objective (AMO) is designed to keep Florida moving forward toward national and international competitiveness. Florida will compare its National Assessment of Educational Progress (NAEP) scores to those of the top five states and its Trends in International Mathematics and Science Study (TIMSS), Progress in International…

Discussed are implications and derivations from vux" triangles (triangles having one angle the integral multiple of another). (JG)

In this note we show the existence of a surprising analogy between quadrilaterals and tetrahedra, determining some properties that hold for both families of figures. This analogy suggests some new properties of quadrilaterals. (Contains 11 figures,)

In this experiment, physical science students measured the mass of several soda cans, measured the mass and volume of water displaced when these cans were placed in water, and determined whether these cans sank or floated in water. Then, the students plotted graphs of the mass of displaced water versus the volume of displaced water, the mass of…