“去方程”后解决分数除法应用题的三个视角

Three Perspectives for Solving Fraction Division Application Problems after “Removing the Equation”

分数除法应用题是小学数学的难点,现有教材大量借助方程处理分数应用题中的复杂数量关系。《义务教育数学课程标准(2022年版)》将方程内容从小学移出后,需直面分数除法应用题的教学变革,即在不借助方程的情况下,如何帮助学生更好地解决分数除法应用题。通过文献梳理,发现存在三个视角,并分析其优劣:(1) 几何直观视角:明晰“量”“率”对应关系;(2) 单元整体教学视角:综合运用分数内涵;(3) 构建数量关系式视角:借助符号表示未知量。据此,提出以下教学建议:从学生认知角度出发,基于三个视角综合考量,相互融通,提升问题解决的效率。Fraction division application problems are a difficulty in primary school mathematics. Existing textbooks largely resort to equations to handle the complex quantitative relations in fraction application problems. After the equation content was removed from primary school in the Mathematics Curriculum Standards for Compulsory Education (2022 Edition), the teaching reform for fraction division application problems needs to be faced directly, that is, without resorting to equations, how to help students better solve fraction division application problems. Through a literature review, it is found that there are three perspectives, and their advantages and disadvantages are analyzed: (1) The geometric intuitive perspective: clarifying the correspondence between “quantity” and “rate”;(2) The unit-integrated teaching perspective: comprehensively applying the connotation of fractions;(3) The perspective of constructing quantitative relation formulas: using symbols to represent unknown quantities. Based on this, the following teaching suggestions are proposed: Starting from the students’ cognitive perspective, based on comprehensive consideration of the three perspectives, and integrating with each other, the efficiency of problem-solving can be improved.