Learning progressions (LPs) describe the development of domain-specific knowledge, skills, and understanding. Each level of an LP characterizes a phase of student thinking en route to a target performance. The rationale behind LP development is to provide road maps that can be used to guide student thinking from one level to the next. The validity…

We analyze the interaction of 3 students working on mathematics problems over several days in a virtual math team. Our analysis traces out how successful collaboration in a later session is contingent upon the work of prior sessions and shows how the development of representational practices is an important aspect of these participants' problem…

The present study investigated (a) whether the perceived cognitive load was different when geometry problems with various levels of configuration comprehension were solved and (b) whether eye movements in comprehending geometry problems showed sources of cognitive loads. In the first investigation, three characteristics of geometry configurations…

Initial exposure to algebraic thinking involves the critical leap from working with numbers to thinking with variables. The transition to thinking mathematically using variables has many layers, and for all students an abstraction that is clear in one setting may be opaque in another. Geometric counting and the resulting algebraic patterns provide…

A geoboard-related extremal problem dealing with both concave and convex polygons is discussed and a proof is given of the solution. (MP)

Designs and arrangements of pentominoes are examined. (SD)

Relationships between the linear dimensions, surface area, and volume of parallelepipeds are examined. (SD)

Using the overhead projector, or overlays on an original pattern, a variety of tessellations can be generated. Several illustrations are included. (SD)

Activities involving estimation of the number of objects in a configuration can motivate students to consider parametric models. (SD)

This pamphlet introduces the student to the basic ideas and procedures of transformational geometry through a series of worksheets. After developing intuitively the idea of rigid motion, vector diagrams are introduced, and translations are discussed in some detail. (SD)

Students, using the materials provided, can determine the number of diagonals, number of triangles formed by the diagonals, and degree measures of interior and exterior angles of regular polygons. The activity is designed to lead them to general formulae for polygons with n sides. (SD)

Geometric concepts and theorems can be discovered by high school students using the materials described. Among the topics explored are Platonic solids and Euler's formula. (SD)