Empirical studies of angle, angle measure, and radian angle measure have primarily focused on documenting students' and teachers' conceptions. Representations of angle measure have the potential to inform and build on these conceptions. To gain insight into the concept of radian angle measure from a curricular perspective, I investigated the…

The purpose of this research is to promote the construction of mathematical proof from argumentation at the primary level. To show this is a viable instructional strategy at the primary level, we use a teaching experiment methodology and a task related to geometric proof in this research study. To model and analyze the collective argumentation…

Body-based activities have the potential to support mathematics learning, but we know little about the impact they have in the classroom. This study compares high school geometry students learning through either body-based or analogous non-body-based activities over the course of a two-week unit on similarity. Pre- and post-tests revealed that…

Metaphors are regularly used by mathematics teachers to relate difficult or complex concepts in classrooms. A complex topic of concern in mathematics education, and most STEM-based education classes, is problem solving. This study identified how students and teachers contextualize mathematical problem solving through their choice of metaphors.…

Use of mathematics-related literature can engage students' interest and increase their understanding of mathematical concepts. A quasi-experimental study of two second-grade classrooms assessed whether daily inclusion of geometry-related literature in the classroom improved attitudes toward geometry and achievement in geometry. Consistent with the…

Presents a qualitative and global method of graphing functions that involves transformations of the graph of a known function in the cartesian coordinate system referred to as graphic operators. Explains how the method has been taught to students and some comments about the results obtained. (MDH)

Develops the Pythagorean Theorem in the context of the Van Hiele levels by presenting activities appropriate for each level. Activities point to preparatory development (level 0), give 3 different versions of Euclid's proof (levels 1, 2, and 3), give some generalizations of the theorem (level 3), and explore the Pythagorean relationship in other…

Pascal's triangle can be used as early as grades five and six to teach children to recognize mathematical patterns. Children can be guided to discover patterns or sequences of numbers if they begin with pictures or physical objects which they can manipulate and count. (Author/BB)

Describes a study to determine the relative effects of formal deductive presentations versus informal inductive presentations and the effect of the number of exercises completed with each learning set on seventh grade students. No reliable difference between the modes of instruction was shown; the number of exercises per set made no significant…

Providing for original and creative thinking by geometry students is discussed. Techniques for discovering theorems are suggested, and examples of places in geometry where these methods can be used are given. (DT)

This model is useful in identifying specific learning problems and in providing techniques for the teacher to motivate and teach students at all levels. What it is and how it can be used are discussed, illustrated by specific strategies for geometry and science. (MNS)

Introduces The Square Thing, a lesson that engages and invites student development of problem solving and reasoning skills, understanding through connections within the content, and mathematics voice. Describes components for successful pedagogy and benefits for students experiencing this and similar mathematics pedagogies. (Author/MM)

Mathematical solutions to simple atomic structure problems involving (a) simple cubic, (b) body-centered cubic, and (c) face-centered cubic models are presented. (CP)

Geometry and a hand-held calculator are used to find a value of pi accurate to five decimal places. (CP)

Presents a short study of proper values of two-by-two matrices with real entries. Gives examples of symmetric matrices and applications to systems of linear equations of perpendicular lines intersecting at the origin and central conics rotated about the origin to eliminate the xy term from its equation. (MDH)