The Tower of Hanoi is an old, popular, and engaging puzzle. It is an exceptional puzzle too considering how effective it can be in engendering multiple valuable outcomes when used as a tool for learning. One of the fundamental goals of mathematics teacher preparation is to enable the prospective teacher to develop mathematical habits of mind and…

Online teaching allows students to discuss their work and learn from varied media, gain nonhomogenous perspectives through global collaboration, and tackle challenging, relevant, real-world problems. In this article, the author describes ways that real-world applications encourage student exploration, how nonhomogenous perspectives challenge the…

In the authors' attempts to incorporate problem solving into their mathematics courses, they have found that student ambition and creativity are often hampered by feelings of risk, as many students are conditioned to value a produced solution over the actual process of building one. Eliminating risk is neither possible nor desired. The challenge,…

Research has found that students, particularly those in middle school and high school, believe that their participation in mathematics classrooms includes listening to teachers explaining, working in textbooks, and solving exercise problems quickly (Franke, Kazemi, and Battey 2007). In this article, the authors describe a classroom vignette and…

A WebQuest is an inquiry-based lesson plan that uses the Internet. This article explains what a WebQuest is, shows how to create one, and provides an example. When engaged in a WebQuest, students use technology to experience cooperative learning and discovery learning while honing their research, writing, and presentation skills. It has been found…

This article describes the use of microteaching lesson study as an approach to promoting collaboration and learning among teachers, particularly those in prospective-teacher education programs, through a repeated cyclic process of developing, implementing, analyzing, and revising mathematics lessons and reporting their experience. (Contains 3…

Discusses cooperative learning and describes a method of implementing a cooperative-learning setting called Exchange of Knowledge. Contains 28 references. (ASK)

Argues that assessment is not consistent with curricular or pedagogical reforms. Presents an assessment format and several variations that incorporate both individual and group work. Outlines a testing format that promotes the alignment of the assessment of student mathematical achievement and skills with some of the curricular reforms occurring…

Discusses the mathematics education philosophy of J. W. A. Young and how it compares to the principles in the National Council of Teachers of Mathematic's "Curriculum and Evaluation Standards for School Mathematics." Elaborates on Young's views concerning rote learning, establishing connections between mathematics and other disciplines,…

Shares students' experiences with working geometrical proofs in cooperative groups. Presents an example of week-long group take-home test. (ASK)

Describes desktop teaching which involves giving students individual topics and having them prepare lessons on those topics to share with the class. Presents the structure of desktop teaching including how to prepare, introduce, set up, implement, and evaluate it. Emphasizes that desktop teaching helps students engage in discussing and learning…

In order for teachers to use cooperative-learning strategies effectively, they must become sensitized to the many complexities of the technique. Explains how a mathematics teacher-education class can engage pre-service and in-service teachers in a cooperative-learning activity that can be used both as a model and as a subject for reflection and…

Describes how a researcher used student cooperative-learning teams to contribute test items. Discusses the questions generated by students and concludes that teachers have the flexibility to encourage students to generate and solve their own problems. Also concludes that students have the opportunity to be creative and formulate and pose questions…

Presents activities involving multiple embedded figures beginning with the problem of counting the number of squares on a checkerboard. Offers several extensions and assessment suggestions. Includes student worksheets. (MKR)

Introduces a technique for developing tasks suitable for group investigation where students work from sets of numerical examples toward making generalizations. (ASK)