Extending the Conception of Mathematics Teaching
It is well known that the predominant practice of teaching mathematics has been to "show the children what to do and then give them practice in it" (Meserve & Suydam, 1992, p. 16). It is also recognized that these long-standing teaching procedures are considered most appropriate in learning that consists of the mastery of facts or procedural skills that can be taught in a step-by-step manner. However, these practices are thought to be least applicable for teaching involving learning that includes problem solving, higher order thinking, and reasoning, which are the goals for reforming mathematics education (National Council of Teachers of Mathematics [NCTM], 1989, 2000). Hence, it is widely accepted that the change in the practice of teaching mathematics will require more than simply minor adjustments in current ways of teaching (NCTM, 1991).