The purpose of this article is to present and discuss two recommended sequences of learning the areas of polygons, starting from the area of a rectangle. Exploring the algebraic derivations of the two sequences reveals that both are valid teaching progressions for introducing the area formula for various polygons. Further, it is suggested that…

Mairead Hourigan and Aisling Leavy describe a range of teaching and learning activities focusing on the identification and classification of 2-dimensional shapes. The activities described are useful in highlighting students' misconceptions regarding non-traditioanl and non-prototypical shapes.

"That was the day I decided I was bad at math." Countless times, preservice and in-service teachers make statements such as this after sharing vivid memories of learning multiplication facts. Timed tests; public competitive games, such as Around the World; and visible displays of who has and has not mastered groups of facts still…

Using a constructionist framework in music, specifically through an emphasis on composition, is revolutionizing the field of music and education by bridging the gap between the novice and professional. Much of the research has been spearheaded by Jeanne Bamberger and others, who noted the computer's potential to highlight what it means to be a…

The premise underlying this article is that identifying and using the "five practices model" can make discussions of cognitively challenging tasks more manageable for teachers. By giving teachers a roadmap that they can follow before and during whole-class discussions, these practices have the potential for helping teachers more effectively…