A story problem about borrowing money, presented in this article, may be represented with positive or negative numbers and thought about in different ways. The authors describe ideas related to integers (both positive and negative) and how students used them in relation to a story problem, and how they related these ideas to equations.

Fostering algebraic thinking is an important goal for middle-grades mathematics teachers. Developing mathematical reasoning requires that teachers cultivate students' habits of mind. Teachers develop students' understanding of algebra by engaging them in tasks that involve modeling and representation. This study was designed to investigate how…

This article presents two statistical tasks, one on comparing data sets, another on repeated sampling, both of which have powerful connections to proportional reasoning. Students' work and reasoning on these tasks are included, as well as suggestions for ways to use these tasks with middle school students to connect statistical thinking to…

During the preliminary stages of classroom-based research, this author conducted a sequence of interviews with six seventh graders regarding their understanding of fractions, decimals, ratios, and proportions. The students represented a variety of ability levels and were all in their first semester of prealgebra. The interviews began with notions…