除数是两位数除法学习路径研究：口诀试商，看余调商

A Study of Learning Paths for Division with Two-Digit Divisors: Test Quotients by Mnemonics and Adjust Quotients by Looking at Remainders

摘要: 结合实践探索了基于算法一致性的“试商调商”学习路径，该学习路径为：算法衔接——提炼算法——熟悉算法——巩固算法——迁移算法，以“口诀试商，看余调商”的统一算法贯穿所有除数非整十数的除法运算，该优化算法能够帮助学生能深刻体会到除法运算算法的一致性并且能够有效迁移，在处理四位数除以两位数和四位数除以三位数具有较高的计算正确率。提出以下建议：教材编写可以参考该路径；教师要精心设计活动任务，重视引导学生经历试商、调商的过程，尤其是要重视建立起学生对于余数和除数关系的敏锐性。

Abstract: The learning path of “test quotient and adjust quotient” based on the consistency of algorithm is explored in practice, which is as follows: Algorithm articulation—Refinement of algorithm—Familiarization with algorithm—Consolidation of algorithm—Migration of algorithm—Consolidate the algorithm—Migrate the algorithm, and the unified algorithm of “test the quotient with the mnemonic, look at the balance and adjust the quotient” runs through all the division arithmetic operations whose divisors are not integers. The optimized algorithm can help students to deeply realize the consistency of the division algorithm and be able to transfer the algorithm effectively, so that they can have a high rate of correct calculation when dealing with four-digit division by two-digit numbers and four-digit division by three-digit numbers. The following suggestions are made: The teaching materials can refer to this path; teachers should carefully design the activity tasks, emphasize on guiding students to go through the process of trying quotients and adjusting quotients, and especially emphasize on building up students’ sensitivity to the relationship between remainders and divisors.