Extra-scope transfer in learning mathematical strategies.

Abstract

The notion of a restricted rule or strategy was introduced. It was hypothesized that extra-scope transfer depends on the extent to which a statement of strategy may be viewed as a restriction of a more general strategy. 66 high school Sa were taught a restricted statement (S', SG', or G') of 1 of 3 strategies of varying generality, 8 (= S') < SG (SG') < G (GO. 22 Sa served as a control (C). All /Ss were tested on 6 problems, the 1st 2 within the scope of the most specific strategy (S), the 2nd 2 within the scope of only the more general strategies (SG and G), and the last 2 only within the scope of strategy G. Statements S', SG', and G' were directly applicable only to the 1st 2 problems. Groups SG' and G' evidenced extra-scope transfer. Groups S' and C did not. In addition, performance on the 2nd problem of each pair was contingent on performance on the corresponding 1st problems indicating that "what is learned" may be determined by performance on single test items and used to predict performance on additional similar-scope problems. Suggestions were made for future research.

Memory Structures and Learning Outcomes

“…His research on rule generality (Scandura & Durnin, 1968;Scandura, Woodward, & Lee, 1967) has led to the formula tion of the general conclusion that rule application may be performed Vol. 48,No.…”

Role of rules in behavior: Toward an operational definition of what (rule) is learned.

“…While this Einstellungtype assumption may still have some merit, it is not a necessary requisite for making predictions about behavior potential. data over the past few years which suggests that this is the case (Roughead & Scandura, 1968;Scandura, 1966Scandura, , 1967bScandura, , 1969aScandura & Durnin, 1968;Scandura et al, 1967). Whenever the response given by an 5" to one unfamiliar test stimulus was in accord with a particular class of rules, so was the response to a second test stimulus which was of the same "general type" as the first.…”

“…In effect, whenever an 5 responded to the first test stimulus in accordance with one of these principles, he almost invariably responded in the same way to the second. Since this study was conducted, a relatively large amount of relevant data has been collected with essentially the same results (Roughead & Scandura, 1968;Scandura, 1967bScandura, , 1969bScandura & Durnin, 1968;Scandura et al, 1967).…”

“…Furthermore, the results of the Scandura and Durnin (1968) study suggest that actual behavior potential can often be determined in a systematic manner. It was found that successful performance with two stimuli, which differed along one or more dimensions, implied successful performance with new stimuli which differed only along these dimensions.…”

A plan for the development of a conceptually based mathematics curriculum for disadvantaged children

“…The technique is described in its original form in Scandura (1968) and is based on experimental results of Scandura and Durnin (1968). This involves a technique for assessing behavior potential on classes of tasks which vary along a set of independent dimensions.…”