Abstract
The adaptive use of strategies, that is selecting a strategy which allows an efficient solution for a given problem, can be considered as an important individual ability relevant in various domains. Based on models of subjects’ skills of adaptive use of strategies, two idealized instructional approaches are suggested to foster students in their strategy development. The explicit approach aims at reducing cognitive load by demonstrating and practicing strategies combined with an explicit identification of criteria for strategy efficiency by contrasting problem solutions. The implicit approach capitalizes on the generation effect and stimulates students to generate their own strategies and efficiency criteria based on the analysis of task characteristics and the comparison of problem solutions. In a 1-week experimental study (16 lessons) with 73 third-graders, we examined the effectiveness of these instructional approaches in the domain of multi-digit addition and subtraction. Results from post- and two follow-up tests after 3 and 8 months did not yield different effects of the two approaches on students’ skills in adaptive use of strategies. A comparison of strategies used by the students showed that the students of the explicit approach more frequently applied complex strategies whereas the students from the implicit approach showed a more sustainable use of self-generated strategies. Hence, for the adaptive use of those strategies students are able to generate, the implicit approach turned out to be more effective than the explicit approach. However, this generation effect does not hold for strategies which are too complex to be generated by students.
Highlights
Cognitive variability— the ability to adaptively apply a strategy to characteristics of a given problem in a given situation so that an efficient solution is possible—can be considered as an important part of human cognition
We will present empirical findings on primary school children’s skills in adaptive use of strategies for multi-digit addition and subtraction problems— the domain we addressed in our own study
The results presented in the previous sections give no clear indication about the theoretically assumed effectiveness of the implicit instruction of an adaptive use of strategies
Summary
Cognitive variability— the ability to adaptively apply a strategy to characteristics of a given problem in a given situation so that an efficient solution is possible—can be considered as an important part of human cognition. There is empirical evidence that children do not necessarily show an adaptive use of strategies concerning task characteristics, even when they know relevant efficient strategies (e.g., Siegler 1996). This phenomenon is well-known for arithmetic where many children use one favorite strategy to solve all addition or all subtraction problems (e.g., Heinze et al 2009). This restriction to one favorite strategy might occur in domains in which universal and task-specific strategies exist. Universal strategies can be applied to all problems of a domain (i.e., all subtraction problems) with a similar efficiency whereas task-specific strategies are highly efficient for a specific class of problems and hardly efficient for other problems
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