A Problem-Posing Approach to Specializing, Generalizing, and Extending Problems with Interactive Geometry Software

Mathematicians and mathematics educators (e.g., Brown and Walter [1990]; Freudenthal [1973]; Halmos [1980]; Kilpatrick [1987]; Moses, Bjork, and Goldenberg [1990]; Pólya [1954]; and Silver [1994]) consider problem posing to be an important mathematical activity and therefore believe that students should have experiences posing problems. For instance, Kilpatrick argues that the experience of “creating one's own mathematics problems ought to be part of every student's education” (1987, p. 123). In the same vein, reform documents of the National Council of Teachers of Mathematics strongly support the inclusion of problem posing both as a curricular activity and as a means of instruction (NCTM 1989, 1991, 2000). For example, Principles and Standards for School Mathematics states that teachers should “regularly ask students to formulate interesting problems based on a wide variety of situations, both within and outside mathematics” (NCTM 2000, p. 258).