Grade 8 students were given a task that had pairs of shapes that had been transformed (i.e., preimages and images). Students were to identify which of the three rigid transformations--reflections, rotations, or translations--were used to map the preimage to the image. Students were also asked to give a justification for their choice of…

Continuing our critique of the classical derivation of the formula for the area of a disk, we focus on the limiting processes in geometry. Evidence suggests that intuitive approaches in arguing about infinity, when geometric configurations are involved, are inadequate, and could easily lead to erroneous conclusions. We expose weaknesses and…

This article offers a particular analytic method from systemic functional linguistics, "thematic analysis," which reveals the mathematical meaning potentials construed in discourse. Addressing concerns that discourse analysis is too often content-free, thematic analysis provides a way to represent semantic structures of mathematical content,…

An online interactive geometry item was developed to explore students' abilities to create prototypical and "tilted" rectangles out of line segments. The item was administered to 1,002 students. The responses to the item were hand-coded as correct, incorrect, or incorrect with possible evidence of a misconception. A variation of the nearest…

The present study is concerned with assessing Logo programming experiences among seventh grade students. A formal multiple-choice test and five performance tasks were used to collect data. The results provided that students' performance was better than the expected score by the probabilistic laws, and a very low correlation between their Logo…