Abstract
If the main goal of educational research and refinement of instructional program is to improve students' learning, it is necessary to assess students' emerging understandings and to see how they arise. The purpose of this paper is to address issues related to assessments of students' mathematical thinking in cross-national studies and then to discuss the lessons we may learn from these studies to assess and improve students' learning. In particular, the issues related to assessing U.S. and Chinese students' mathematical thinking were discussed. Then, this paper discussed the findings from two studies examining the impact of early algebra learning and teachers' beliefs on U.S. and Chinese students' mathematical thinking. Lastly, the issues related to interpreting and understanding the differences between U.S. and Chinese students' thinking were discussed.
Kurzreferat
Wenn Sinn und Zweck von Unterrichtsforschung und-veränderung eine Verbesserung des Lernen von Schülerinnen und Schülern ist, dann ist es notwendig zu untersuchen, wie Verständnis entsteht und wie es sich entwickelt. Ziel dieser Arbeit ist, Fragen im Zusammenhang mit der Erhebung mathematischen Denkens in internationalen Studien anzusprechen und zu diskutieren, wie diese Erkenntnisse zur Beurteilung und Verbesserung des Lernens beitragen können. Insbesondere werden diese Aspekte anhand der Untersuchung des mathematischen Denkens von nordamerikanischen und chinesischen Schülerinnen und Schüler diskutiert. Der Beitrag betrachtet die Ergebnisse zweier Studien über den Einfluss früher Algebra-Lemerfahrungen und der Einstellung von Lehrpersonen auf das mathematische Denken nordamerikanischer und chinesischer Kinder Abschließend werden Fragen der Interpretation und des Verständnisses der Unterschiede im Denken nordamerikanischer und chinesischen Schülerinnen und Schüler erörtert.
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