By using ill-structured problems and examining problem- solving processes, this study was conducted to explore the nature of solving complex, multistep problems, focusing on how prior knowledge, problem-solving process utilization, and analogical problem solving are related to success. Twenty-four college students qualified to participate by…

This paper describes the implications of constructivism both for what to teach and for how to teach. The first part discusses three approaches on what to teach: (1) relating mathematical knowledge to other knowledge; (2) checking for self-consistency; and (3) putting thinking before facts. The second part is on how to teach based on…

Teaching students to think mathematically or to apply mathematics to the solution of real-world problems has become a national priority. This paper explores a method of developing the basic problem-solving skills in a remedial mathematics course at the college freshman level. The first part of this paper describes some basic problem-solving skills…