Students' Early Mathematical Representation Knowledge: The Effects of Emphasizing Single or Multiple Perspectives of the Rational Number Domain in Problem Solving

This study examined changes in 26 fourth-grade students' early conceptions of rational number representations as a function of receiving one of two curricular interventions. The first group of 12 students received a curriculum that emphasized constructing knowledge through extended problem solving with a single perspective of the rational number domain based on part-whole relations. A second group of 14 students received a curriculum that emphasized a more conceptually diverse multiple perspective view of the domain through problem solving with operator and ratio relations. Analyses of the students' rational number knowledge before and after the interventions indicated that students in the single perspective group produced organizations of knowledge that more frequently diverged from a formal domain analysis than those produced by students in the multiple perspective group. Further, students in the single perspective group increased their focus on superficial surface features. Alternatively, students in the multiple perspective group demonstrated an increased focus on operations that more frequently reflected the underlying mathematical relation conveyed by the representation. The findings indicate that an early exposure to more diverse perspectives of rational numbers assists students in developing more interconnected and viable representation knowledge for rational numbers.     

论法学研究生教育中的法律思维培养——兼论WTO案例教学

法律思维培养是法学研究生教育的主要目标,包括WTO案例在内的案例教学法对于法学研究生法律思维的培养有莫大的助益。其中WTO案例内容丰富、数量充足、说理性强且易于获得,是研究生法律思维培养的宝库。对于WTO案例在教学当中的使用,首先应当在法学全部二级学科当中进行推广;其次应当注重经典案例的积累;第三应当鼓励通过模拟WTO争端解决的辩论赛的方式进行浸入式的双语教学。通过更好地在研究生教育中使用WTO案例,培养出具有国际视野、通晓国际规则、维护国家利益的法律人才。