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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.
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.
Calcularis is a computer-based training program which focuses on basic numerical skills, spatial representation of numbers and arithmetic operations. The program includes a user model allowing flexible adaptation to the child's individual knowledge and learning profile. The study design to evaluate the training comprises three conditions (Calcularis group, waiting control group, spelling training group). One hundred and thirty-eight children from second to fifth grade participated in the study. Training duration comprised a minimum of 24 training sessions of 20 min within a time period of 6-8 weeks. Compared to the group without training (waiting control group) and the group with an alternative training (spelling training group), the children of the Calcularis group demonstrated a higher benefit in subtraction and number line estimation with medium to large effect sizes. Therefore, Calcularis can be used effectively to support children in arithmetic performance and spatial number representation.