A discussion of the use of mathematics problems containing erroneous statements and the use of mutual consultation by students on the solution of mathematics problems. Critical questioning ability of students is enhanced through the utilization of both these procedures, according to the author. (JG)

This paper considers the aspect of heuristic teaching in which theorems are introduced in the form of problems and the proofs of these theorems as solutions to problems. The traditional treatment along with an illustration of a heuristic approach is discussed for each of several well-known theorems. (MN)

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)

Two experiments on the translation of verbal expressions into mathematical expressions are described. The author concludes that the usual way of training students to solve arithmetic word problems is inadequate. (SD)

The iconographic means of illustrating mathematical facts is discussed along with several examples of graphical solutions to descriptive mathematics problems proposed by pupils. (MN)

The nature of insight is discussed as it relates to mathematical models. Intuition and the intuitively obvious are argued to have no necessary connection with models. (MP)

An analysis of methods of teaching children to solve verbal arithmetic problems is presented together with transcriptions of interviews in which children solve problems by reference to problem types. (SD)

Outlines a guided discovery activity for ascertaining the conditions which allow for the correct tracing of networks. (JP)

Experiments by Russian educators on teaching algebra in elementary grades are summarized by the author. The algebra taught consisted of generalized solutions to concrete problems that are usually presented with fixed numerical values. (JP)

A case is presented for the importance of focusing on: (1) average ability students; (2) substantive mathematical content; (3) real problems; and (4) realistic settings and solution procedures for research in problem solving. Suggestions for ways to modify existing applied problem solving materials are given. (MP)