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…

Describes basic problem-solving skills and presents a protocol of a student solving a problem. Discusses some of the difficulties in obtaining a correct solution. Lists basic prompts for problem solving. (YP)

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…

Peer tutoring sessions involving two eighth-grade girls were recorded and analyzed through a Vygotskian lens. A "microgenetic analysis" of particular protocol excerpts from the tutoring sessions was conducted. When a lapse of intersubjectivity existed, participants frequently launched into narrative as a mediating device to negotiate a…

Recent research has focused on how prospective teachers formulate beliefs related to teaching and learning mathematics and science. This paper examines the use of videotaped mathematics and science lesson segments to aid in the description or identification of initial belief structures of prospective elementary school teachers. Using a…