What's Your Angle on Angles?

The word angle may conjure up several thoughts—a corner, two rays and a vertex, or a degree measure. But what about the idea of a turn (a rotation around a fixed point) or of the space between two rays, and what exactly is a degree? Many upper-elementary students have such limited notions of angle that they struggle to provide an appropriate mathematical definition for the term and, instead, describe what we are measuring when we measure an angle. Yet, according to NCTM (2000), students in grades 6–8 must be able to “carefully examine the features of shapes in order to precisely define and describe fundamental shapes” (p. 233). Angle is certainly a prominent feature of shape, so, beginning in the elementary grades, providing students with opportunities to carefully explore the idea of angle is critical for the development of their understanding of geometry. Doing so, however, requires us as teachers to first realize the complexity of the concept of angle. As one sixth-grade student put it, “An angle is a lot more than just degrees.”

Debriefing Strategies in Adventure Based Counselling

This paper describes an Adventure Based Counselling (ABC) program that aimed to improve sixth grade student behaviour in the classroom. In particular, this paper focuses on the ABC debriefing strategy, as summarised in the “What?” “So What?” and “Now What?” format. This debriefing process was employed with both students and ABC program facilitators. While there is extensive literature concerned with the application of the ABC debrief with the target group, an ABC debrief with the facilitators of the program is lacking in the applied literature. The strategies and sample questions employed in the ABC format, as applied to both groups, are described in detail. The procedure was highly effective for both behavioural intervention with students and for maximising learning of the ABC facilitators.

A Physical Model for Operations with Integers

Several models for operations with integers are shown. The model for the product of two negatives was discovered by a sixth-grade student.