The purpose of this study was to investigate and describe how middle school mathematics teachers "make meaning" of proofs and the process of proving in the context of their classroom practices. A framework of "making meaning," created by the researcher, guided the data collection and analysis phases of the study. This framework…

Many mathematics classrooms use cooperative learning to support equitable learning environments for all students. Past research in the field has focused primarily on increasing achievement rather than on contexts that support equitable interactions. This year-long study in 3 secondary mathematics classes compares 2 activity structures--a group…

Technology is a natural part of education for all students across a variety of subjects, including mathematics, as educators work to prepare students for tomorrow's work force and align their curriculum and teaching with national standards such those developed by the National Council of Teachers of Mathematics (NCTM, 2000). This article reviews…

This article describes the goals of a capstone course for secondary preservice mathematics teachers and how those goals are achieved. Moreover, student reaction to the course will be examined.

Technology is available and accessible in many mathematics classrooms. Adopting technology to support teaching and learning requires teachers to change their teaching practices. This paper reports the responses of a diverse cohort of 92 secondary mathematics teachers who chose to respond to an Australian state-wide survey (Mathematics with…

This article describes a cohesive theory of classroom management, developed by the author. This "three Fs" theory, predicated upon extant empiricism and scholarship vis-a-vis classroom management, was devised and implemented over several semesters within a field-based course at the University of Texas at Austin for preservice mathematics majors…

When given opportunities to explore mathematics, make conjectures, and write about what they have discovered, students gain a deeper understanding of this fascinating subject. In this article, the author describes her successful Geometry Portfolio class. In addition to traditional student work, the author frequently added short essay questions or…

This article describes a technology-based and hands-on instructional intervention designed to advance middle school students' understandings of fractions. This problem-solving experience is based on the principles of Enhanced Anchored Instruction (EAI) and proved instructionally worthwhile and motivating to teachers and students in both inclusive …

The NCTM calls for the use of rich tasks that encourage students to apply their own reasoning to problem situations. When students work through algebraic generalization tasks, their reasoning often elicits a variety of strategies (Lannin 2003; Stacey 1989; Swafford and Langrall 2000). Challenges for teachers include facilitating student awareness…

In this experimental study, use of Computer Assisted Instruction (CAI) followed by use of an Intelligent Tutoring System (CAI+ITS) was compared to the use of CAI (CAI only) in tutoring students on the topic of Algebraic Expression. Two groups of students participated in the study. One group of 32 students studied algebraic expression in a CAI…

Pedagogical maps provide a graphic depiction of the way in which teachers exploit the presence of Computer Algebra Systems (CAS) in their classrooms. They can show differences, and can also show growth, as well as personal preferences and reactions to particular teaching assignments. They might also be used for teachers to reflect on their own…

This article allows students to apply their knowledge and experience of area and volume to find the volume of Norris Lake, a large reservoir lake in Tennessee. Students have the opportunity to demonstrate their skills in using maps and scales as well as to incorporate the use of technology in developing the solution. This project satisfied the…

"Concept study" is described in this article as a collaboration of teachers to investigate images, analogies, metaphors, exercises, and other experiences that are used to support students' understandings of concepts. The discussion is illustrated with the examples of multiplication and prime numbers. (Contains 3 figures.)

This article illustrates the kinds of mathematical discussions that should occur with students in classrooms. The authors use a sample from professional development to show discussions that focus on the relationships of events within a problem that led to each representation, the connections between the ways participants chose to represent those…

This article describes one seventh-grade teacher's classroom efforts to integrate traditional exercises from different content areas to form more robust questions that provide genuine problem-solving opportunities for students. These exercises are illustrated by connecting the Pythagorean theorem with a variety of prealgebra topics. Since the…