Systematisch einführen oder selbst entdecken lassen?: Eine experimentelle Studie zur Förderung der adaptiven Nutzung von Rechenstrategien bei Grundschulkindern

Adaptive use of computation strategies, that is solving arithmetic problems with few and simple solution steps, is a desirable goal of elementary mathematics education. With respect to instruction, research indicates, on the one hand, that an explicit teaching of strategies restricts children’s creativity and adaptive use of strategies. On the other hand, in learning environments which ask children to invent their own strategies, children’s strategy repertoires often lack complex strategies. Based on a model of strategy acquisition and following criteria for instructional coherence, a lesson sequence for an explicit teaching of addition and subtraction strategies was developed which especially addresses adaptive use of strategies. This explicit approach comprises the introduction and practicing of strategies as well as comparing strategies for given problems. In a one-week experimental study (16 lessons) with 78 third-graders, this explicit approach was compared with an alternative implicit approach. The comparison group did not receive direct instruction. Students generated their own strategies and efficiency criteria and compared the invented strategies for solving arithmetic problems. Results from a pre-post-comparison and from short intermediate tests indicate advantages for the explicit approach concerning the development of students’ strategy repertoire. Especially, complex strategies were more frequently used by children taught by the explicit approach. The findings for students’ adaptive use of strategies did not yield differences between the two learning environments. Hence, based on criteria for instructional coherence, an explicit teaching of adaptive use of strategies turns out to be effective. Implications for research and educational practice are discussed.