This article describes an exciting exploration-based activity in which students develop an alternative definition of factor that can help them solve problems like the one presented above. Students work in groups to collect data, analyze the data to make conjectures, and then spend a significant amount of time debating and justifying their…

This article describes how teachers address issues and tensions that students meet in learning division of fractions. First, students must make sense of division of fractions on their own by working individually and in small groups, using concrete or pictorial representations, inventing their own processes, and presenting and justifying their…

Describes the use of the principles of challenging work, student autonomy, and student collaboration to involve students in constructing mathematical meaning as part of the regular curriculum. Challenge is created by the material and by the classroom environment to encourage student interest and thinking. Autonomy is encouraged by leading students…