Abstract

Concrete-operational thinking depicts an important aspect of cognitive development. A promising approach in promoting these skills is the instruction of strategies. The construction of such instructional programs requires insights into the mental operations involved in problem-solving. In the present paper, we address the question to which extent variations of the effect of isolated and combined mental operations (strategies) on correct solution of concrete-operational concepts can be observed. Therefore, a cross-sectional design was applied. The use of mental operations was measured by thinking-aloud reports from 80 first- and second-graders (N = 80) while solving tasks depicting concrete-operational thinking. Concrete-operational thinking was assessed using the subscales conservation of numbers, classification and sequences of the TEKO. The verbal reports were transcribed and coded with regard to the mental operations applied per task. Data analyses focused on tasks level, resulting in the analyses of N = 240 tasks per subscale. Differences regarding the contribution of isolated and combined mental operations (strategies) to correct solution were observed. Thereby, the results indicate the necessity of selection and integration of appropriate mental operations as strategies. The results offer insights in involved mental operations while solving concrete-operational tasks and depict a contribution to the construction of instructional programs.

Highlights

  • Concrete-Operational ThinkingThe concrete-operational stage depicts an important step in the cognitive development of children (Piaget, 1947)

  • Chen et al (2016) examined processing strategies on matrix completion strategies and could find a more frequent use of processing strategies of high-performing 5- and 6-year-old problem-solvers. These findings indicate that the correct solution of concrete-operational concepts might be explained by qualitative aspects as well as the frequency of the used strategic operations

  • We focus on shedding light on the influence of specific mental operations as well as of pattern of these operations on the solution of tasks depicting concrete-operational thinking in primary school

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Summary

Introduction

The concrete-operational stage depicts an important step in the cognitive development of children (Piaget, 1947). According to Piaget, thinking in this stage is characterized by logical operations, such as conservation, reversibility or classification, allowing logical reasoning. These mental acts cannot be applied in hypothetical situations and are still limited to concrete situations. Concrete-operational thinking is examined using specific tasks depicting concrete-operational concepts. More recent research indicated that it might not be appropriate to assume a concreteoperational stage, but to examine concrete operations as specific and independent (Berzonsky, 1971; Winkelmann, 1975; Lourenco and Machado, 1996).

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