Most mathematical problems can be solved using different methods. We tested the effectiveness of presenting more than one solution method by means of worked-out examples. In Experiment 1, a 2x3-factorial design was implemented ("multiple solutions": multiple/uniform; "instructional support": none/self-explanations/instructional explanations).…

In this article, the author describes a 200-year-old ladder problem that can carry learners to high levels of mathematical thinking and activity. This problem requires learners to go from a word problem to an equation to a graph and from there to a solution. As this problem of specifics is turned into a problem using variables, technology,…

In this article we present a structured set of Design Patterns (DPs) that deals with tracking students while they solve problem in specific domains such as programming or mathematics. Our collection of 17 DPs yields a three step approach: First step: to collect and analyze information on each student for each exercise; Second step: to build a…

The general background of this study is an interest in how digital tools contribute to structuring learning activities. The specific interest is to explore how such tools co-determine students' reasoning when solving word problems in mathematics, and what kind of learning that follows. Theoretically the research takes its point of departure in a…

Presents the opinion that the learning environment of recitation classes can be vastly improved if instructors pay attention to some basic learning principles. Summarizes these learning principles and presents a specific example of their application. (GS)

Problem solving is presented as a resource for creating curriculum through reflections on intuition such as: exploring available intuitions, making explicit the intuitions used, and using intuition to generalize. (MP)

A situation is presented that is intended to lead to open-ended mathematical discussions that allow students to conjecture, discover, and prove mathematical statements. (MP)

A general method is given for determining an efficient problem-solving process for a given type problem. An application of the method is then described in an experiment involving teaching indefinite integration. (MP)

Tells about an assignment in a technical writing course, in which students are presented with a hypothetical problem faced by a business corporation; they then work in groups to write memos detailing possible solutions to the problem. (GW)

"Solve a simpler problem" is the strategy illustrated, with suggestions on other strategies included. (MNS)

The problem-solving strategy of using a drawing is highlighted, with two problems discussed. Tips on classroom climate and other teaching ideas are also given. (MNS)

Empty food containers can be used to have students devise mathematical problems. Sample questions that might be asked about two food boxes are included. (MNS)

Participation in the National History Day program (involving student papers, presentations, projects, and performances) provides many opportunities for eliciting the gifted behavior of sixth- through twelfth-grade students. The program, which emphasizes student involvement in real problems, can be used in the resource room, mainstreamed, advanced…

Using open-ended problems with more than one answer is disucssed, with examples. Other tips on open-ended problem solving are included. (MNS)

The four-step method of problem solving is described: read the problem, represent or diagram, set up the calculations and compute, and write the answer. Other problem-solving tips are also included. (MNS)