Many students find proofs frustrating, and teachers struggle with how to help students write proofs. In fact, it is well documented that most students who have studied proofs in high school geometry courses do not master them and do not understand their function (Battista 2007; Harel and Sowder 2007). And yet, according to NCTM's Principles and Standards for School Mathematics(2000), “By the end of secondary school, students should be able to understand and produce mathematical proofs … and should appreciate the value of such arguments” (p. 56).
Anne Larson Quinn
Anne Quinn and Karen Larson
The free Web-based app Census at School allows random sampling of survey data for students' use in projects and statistical analysis.
Cynthia Barb and Anne Larson Quinn
What role does problem solving play in the mathematics classroom today? What methods should be used to help students become better problem solvers?
Anne Larson Quinn and Karen R. Larson
The relationship between algebra and arithmetic is not at all obvious to many students (Kieran 1992; Lee and Wheeler 1987; Vergnaud 1987). To help students make the connection between algebra and arithmetic, many researchers suggest that students should be exposed to multiple methods of representing problems, including pictures, models, tables, and graphs (Dufour-Janvier, Bednarz, and Belanger 1987; Vergnaud 1987). The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989, 129–31) advocates that all students can and should learn algebra; however, some students will be capable of more abstraction than others. Encouraging multiple representations of problems is a way of accommodating students working at all levels of abstraction.
Anne Larson Quinn, Robert M. Koca Jr. and Frederick Weening
The game of Set has proved to be a very popular game at our college mathematics club meetings. Since we started playing, the membership has grown every month. In fact, one of our members brought her sixyear- old son to a meeting, and he now looks forward to playing Set with us. As a result of playing the game in our club and thinking about the results, we created and solved a variety of mathematical questions. For example, we wondered about possible strategies for winning and conjectured about phenomena that happened when playing. These questions involve a wide variety of traditional mathematical topics, including the multiplication principle, combinations and permutations, divisibility, modular arithmetic, and mathematical proof.
Anne Larson Quinn
Edited by Charles Vonder Embse and Arne Engebretsen
I have always used concrete marupulatives, such as marshmallows and toothpicks, to create models for my geometry and discrete-mathematics courses. These models have come in handy when discussing volume, introducing the 4-cube, or illustrating isomorphic or bipartite graphs. However, after discovering what a dynamic geometry–software package could do for geometry teaching, which has been well documented by research (e.g., Battista and Clements ), I realized that this type of technology also had much to offer for teaching graph theory in my discrete-mathematics course. Although this article discusses The Geometer's Sketchpad 3 (Jackiw 1995), any software that can draw, label, and drag figures can be substituted for Sketchpad.
Anne Larson Quinn, Cynthia A. Barb and Pameia R. Lasher
A light fare to whet your mathematical appetite.