Vorgehensweisen von Grundschüler(inne)n bei Aufgaben zur Addition und Subtraktion im Zahlenraum bis 1000

Profiles of Cognitive Flexibility in Arithmetic Reasoning: A Cross-Country Comparison of German and American Elementary Students

“…The discrepancy between Selter's (2000) results for fourth grade students and those reported here needs additional study. Our results call into question the popularly held belief that German students abandon flexible mathematics strategies once they learn standard computing algorithms.…”

“…But, if this had been the crucial reason, we would have expected a greater grade-level difference in the American sample. In contrast to the research reported by Selter (2000), the different set of problems (Selter used three-digit problems) could be responsible for different results. (2) Approach: Selter (2000) has reported that students act less flexible in solving problems after they have learned the standard procedures in third grade.…”

“…In contrast, German states typically introduce number reasoning in the primary grades and reserve computing algorithms for higher grades. Given these geographic differences, our own teaching and school experiences, and former research (Selter, 2000), we had expected that German fourth graders would exhibit more solution procedure types of reasoning (rigid) than German second graders. Yet, the opposite was found in our data.…”

“…For example, after learning the standard computing algorithms, students tend to prefer them and do not utilize previously learned strategies, even when the latter continue to be more advantageous and appropriate (Selter, 2000(Selter, , 2001. Moreover, when students learn through examples, they tend to learn specific procedures rather than general rules or relationships, which in turn leads to a negative impact on the development of mental flexibility (Heirdsfield & Cooper 2004;Klein, Beishuizen, & Treffers, 1998;Schütte 2004).…”

“…In the United States, the standard addition algorithm is introduced in first grade, as soon as students are engaged with adding two-digit numbers. Based on this important cultural difference and results from former research (Selter, 2000), it was expected that second graders would be more flexible than fourth graders, and that German students would be more flexible than American students.…”