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Two distinct strategies for teaching the solution to verbal problems were compared. Programs of instruction were prepared that reflected the Polya Method (read and understand the problem, plan for a solution, carry out the plan, and check the result) and the Dahmus Method (translate the verbal statements into mathematical symbols prior to solving the problem and checking the solution). A form of individualized instruction was used to present these programs to 53 ninth-grade algebra students classified into three ability levels based upon Algebra Prognosis Test scores. Following seven days of instruction, data were gathered on an investigator-constructed posttest and retention test which were scored on an equation criterion and a problem solution criterion. Results showed that Polya Method students scored higher than Dahmus Method students on the equation criterion but there was no difference between the two groups on the problem solving criterion, that scores on both criteria are highly resistant to forgetting, and that ability level differences occurred. (Author/DT)

A smooth program is defined to be one which is "go to"-free in the sense that it can be represented by a flowchart consisting only of concatenation, alternation, and interation elements. Three methods of eliminating the "go to" statement from a program have been proposed: (1) the introduction of additional Boolean variables or the equivalent recomputation of certain quantities in the program, (2) the use of recursive procedure calls, and (3) replacement of the "go to" statement by a restricted form of the "go to" such as the "exit" or "leave" statement. We show that only the first of these is capable of transforming a non-smooth program into a smooth one, since strict application of the recursive procedure method requires the use of a so-called "null procedure" which is in fact also a restricted form of the "go to." (Author)

Three studies attempted to assess the relative effects of two methods of instruction: (1) teaching by a carefully structured sequence of questions (intermediate guidance) and (2) teaching by stating each concept with illustrations and then having the students practice the behavior embodied in these concepts (maximal guidance). One of the studies used fourth grade subjects and a programed presentation of addition and multiplication of integers; the second used sixth grade subjects and a programed presentation of modulus seven arithmetic; the third used eighth grade subjects and a programed presentation of selected topics from vector arithmetic. Within each of three ability subgroups, the subjects were randomly assigned to one of the two treatments. The results of the studies indicated that (1) the high ability subgroup had mean scores significantly greater than those for the middle ability subgroups which in turn had mean scores significantly higher than those of the low ability subgroups, and (2) the significant differences pertaining to treatment effects favored the maximal guidance treatment. It was concluded, therefore, that when mathematics instruction is provided by means of a linear program, a relatively high level of guidance should be provided. (RP)

This study was designed to compare the relative effectiveness of word problem instruction based on Polya's approach to problem solving with Dahmus' word by word translation approach. When ninth-grade students were randomly assigned to one of these approaches, no differences in mean number of problems solved were observed. (SD)

Briefly reviews important research dealing with the effectiveness of non-directed (discovery) learning as compared to guided learning. Describes experiment designed to assess the relative effects of intermediate and maximal guidance in learning selected mathematic concepts using programed materials. Results reveal no reliable difference between maximal and intermediate guidance. (PR)

Describes a study to determine the relative effects of formal deductive presentations versus informal inductive presentations and the effect of the number of exercises completed with each learning set on seventh grade students. No reliable difference between the modes of instruction was shown; the number of exercises per set made no significant difference. (PR)