Preservice mathematics teachers are entrusted with developing their future students' interest in and ability to do mathematics effectively. Various policy documents place an importance on being able to reason about and prove mathematical claims. However, it is not enough for these preservice teachers, and their future students, to have a narrow focus on only one type of proof (demonstration proof), as opposed to other forms of proof, such as generic example proofs or pictorial proofs. This article examines the effectiveness of a course on reasoning and proving on preservice teachers' awareness of and abilities to recognize and construct generic example proofs. The findings support assertions that such a course can and does change preservice teachers' capability with generic example proofs.
Shiv Karunakaran, Ben Freeburn, Nursen Konuk and Fran Arbaugh
Jonathan F. Lawes
Graphing the polar function on a rectangular plane simplifies graphing, increases student understanding, and reinforces connections.
This article presents a method for approximating π using similar triangles that was inspired by the author's work with middle school teachers. The method relies on a repeated application of a geometric construction that allows us to inscribe regular polygons inside a unit circle with arbitrarily large number of sides.
Nancy K. Mack
Exploring number systems of other cultures helps students deepen mental computation fluency, knowledge of place value, and equivalent representations for numbers.
Applying known facts to derive unknown facts results in efficiency, flexibility, and an understanding of number combinations for young students.