中美职前小学教师“教学用数学知识”的发展比较——以分数乘除法为例

Comparison of Development of Pre-Service Elementary School Teachers’ Mathematical Knowledge for Teaching in China and The United States——With the Multiplication and Division of Fractions as an Example

中美职前小学教师对分数乘除法运算法则较熟悉,但知识的教学之用及发展存在一定差异:(1)知识方法维度:中国学生对分数乘除法运算的算法明确、结果准确,美国学生对分数乘除法的概念性理解有局限,有时出现一定偏差.(2)理解表征维度:美国学生的知识理解和表征是发散的、多样化的,中国学生的知识表征和运算方法则比较单一.中国学生倾向于数字和符号的计算,美国学生则关注和擅长于图形与问题情境的表征.(3)教学策略维度:中美学生的教学用数学知识有进步,但进步的幅度不大,美国学生的进步则更明显.中美学生对分数乘除法运算的程序性知识较好,但数学知识的教学实践之用是"捉襟见肘"的.

The pre-service elementary school teachers are familiar with the algorithm for multiplication and division of fractions whether in China or America, but the use of knowledge in teaching and its development are different: (1) Knowledge Method dimension. For Chinese students, they are clear about the algorithm for multiplication and division of fractions and their computation results are correct. The American students’ comprehension of its concept has limits and sometimes has deviation. (2) Dimension of understanding representation. The American students’ understanding of knowledge and representation are divergent and diversified. For Chinese students, their understanding of knowledge and representation are heterogeneous. Chinese students are skilled in the calculation of numbers and symbols. The American students are supposed to be good at representing the problem situation. (3) Dimension of teaching strategy. American and Chinese students’ mathematical knowledge for teaching is extending, but the extending level is modest. By contrast, The American students’ progress is evident. Both of them have preferable procedure knowledge of the operation of the multiplication and division of fraction, but their mathematical knowledge for teaching practice is deficient.