Since Albrecht Durer studied the trochoid curves in a 1525 treatise on geometry called "The Art of Measurement with Compass and Straightedge," it is natural to wonder whether he used them in his artwork. We therefore consider several pieces on which we overlay hypocycloids, limacons, and epicycloids so as to check for good matches in a fun…

This paper describes students' interactions with dynamic diagrams in the context of an American geometry class. Students used the dragging tool and the measuring tool in Cabri Geometry to make mathematical conjectures. The analysis, using the cK[cent sign] model of conceptions, suggests that incorporating technology in mathematics classrooms…

This study tested a dynamic field theory (DFT) of spatial working memory and an associated spatial precision hypothesis (SPH). Between 3 and 6 years of age, there is a qualitative shift in how children use reference axes to remember locations: 3-year-olds' spatial recall responses are biased toward reference axes after short memory delays, whereas…

The first goal of this article to show the profound difference between how equality and similarity are understood in Greek geometry and how they are presented in modern mathematics classes. It highlights that the formula "equal-and-similar" reflects the distinct character of "equal" and "similar" as signs in Greek…

This study examined the influence of sex, social dominance, and context on motion-tracked head movements during dyadic conversations. Windowed cross-correlation analyses found high peak correlation between conversants' head movements over short ([approximately equal to]2-s) intervals and a high degree of nonstationarity. Nonstationarity in head…

Students often find the difference in the electromagnetic and the acoustic Doppler formulae somewhat puzzling. As is shown below, geometrical diagrams and the concept of "event"--a point in spacetime having coordinates (x,y,z,t)--can be a useful and simple way to explain the physical background behind the fundamental differences between the two…

When studying correlations, how do the three bivariate correlation coefficients between three variables relate? After transforming Pearson's correlation coefficient r into a Euclidean distance, undergraduate students can tackle this problem using their secondary school knowledge of geometry (Pythagoras' theorem and similarity of triangles).…

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,…

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…

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,…