In this article, the author presents five problems that are representative of some of the "movie problems" that he has used on tests in various courses, including reactor design, heat transfer, mass transfer, engineering economics, and fluid mechanics. These problems tend to be open-ended. They can be challenging and can often be worked a variety…

The importance of teaching mathematics as a body of strategies and methods of inquiry is stressed; examples of situations which emphasize skills in classification, generalization, using symbols, and proof are given. (DT)

BECAUSE OF THE EVER INCREASING EXPANSION OF KNOWLEDGE AND CULTURAL CHANGES, TEACHING CHILDREN TO DISCOVER (DEFINED HERE AS THE ACQUISITION OF AN ABILITY TO FORMULATE AND SOLVE PROBLEMS) SHOULD BE GIVEN CONSIDERABLE SIGNIFICANCE AS AN EDUCATIONAL GOAL. THE PURPOSE OF THIS REPORT IS (1) TO CLARIFY CERTAIN ASPECTS OF TEACHING CHILDREN TO DISCOVER,…

Describes a combinatorics problem involving pizza toppings. Includes three activity sheets. (Author/NB)

The author presents ideas for allowing LD students to discover ways to improve their problem-solving skills. Activities touch upon the influence of the environment, the need for patience and planning, factors in sequencing and organization, and the importance of thoroughness and revision. (CL)

Describes a study of university students that examined the ability of people to learn a computer system by exploration and discusses the role of thinking aloud and reflection to obtain information about the goals of the user. Considers display-based, exploratory learning in relation to planning and problem solving. (Author/LRW)

Many important human activities involve accomplishing goals without a script. There is no formula for true problem-solving. Heuristic, cognitive "rules of thumb" are the problem-solver's best guide. Learners should understand heuristic tools such as means-end analysis, working backwards, successive approximation, and external representation. Since…

Inquiry-based instruction teaching helps students to think independently and scientifically, which in turn enables problem solving ability in them. Different approaches to encourage inquiry-based instructions like verification approach, and discovery approach are discussed by matching the background knowledge and reasoning skills among the…

The author's thesis is that there is sufficient research evidence to make any reasonable person skeptical about the benefits of discovery learning--practiced under the guise of cognitive constructivism or social constructivism--as a preferred instructional method. The author reviews research on discovery of problem-solving rules culminating in the…

In many mathematics classes, students are asked to learn via the discovery method, in the hope that the intrinsic beauty of mathematics becomes more accessible and that making conjectures, forming hypotheses, and analyzing patterns will help them compute fluently and solve problems creatively and resourcefully (NCTM 2000). The activity discussed…

"Principles and Standards for School Mathematics" (NCTM 2000) proposes that mathematics instruction provide opportunities for students to engage in mathematical inquiry and in meaning-making through discourse. Mathematics teachers are encouraged to build on student discoveries in designing subsequent instruction. In this article, the author…

A series of studies conducted to identify the factors that block and unblock problem solving is described. Through the construction of an isomorph of the classic "water jar" problems developed by A. S. Luchins (1942) as a dynamic graphic micro-world, several factors involved in producing blocked states were identified. Subjects included…