Are We Overemphasizing Manipulatives in the Primary Grades to the Detriment of Girls
Are We Overemphasizing Manipulatives in the Primary Grades to the Detriment of Girls
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我们是否过分强调小学年级的操控性而损害了女孩的利益
DOI：
10.5951/tcm.9.1.0016
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
R. Ambrose
中科院分区：
文献类型：
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作者：
R. Ambrose
在过去的25年里，算术课程包含了更多的实践活动，越来越强调解决问题。根据《原则与标准》中的表征标准，“从学前班到12年级的教学计划应该使所有学生能够使用表征来模拟和解释物理、社会和数学现象”（NCTM 2000，第136页）。表征，如操作，通过为以后使用符号建立基础来帮助儿童发展理解。当让孩子们选择如何解决问题时，他们倾向于使用操纵者，因为他们可以把问题中的情况或关系表现出来。当孩子们可以自由选择解决一位数算术问题的策略时，他们通常会从使用具体的策略发展到使用更抽象的策略。例如，考虑下面的问题：“丽莎收集了8个贝壳。哈尔又给了她5个贝壳。丽莎当时有多少贝壳？”为了解决这个问题，发展初期的孩子会制作一组有8个物体和另一组有5个物体的物体，将这两组物体连接起来，数所有的物体。随着他们的发展，孩子们不需要建立第一套，而是可以从8开始数到得到答案。最终，孩子们可以抽象地解决问题，而不需要问题中任何一个数量的具体模型（参见Carpenter等人[1999]对这些发展阶段的完整讨论）。这种策略的发展是很自然的，即使是五岁的孩子也会在没有指导的情况下从计算所有策略转向计算策略（Groen and Resnick 1977）。有些孩子在多位数加减法的发展道路上也有同样的进展，他们最初使用具体的策略来处理问题中的数量
During the last twenty-five years, arithmetic curricula have included more hands-on activities with an increasing emphasis on problem solving. According to the Representation Standard in Principles and Standards, “instructional programs from prekindergarten through grade 12 should enable all students to use representations to model and interpret physical, social, and mathematical phenomena” (NCTM 2000, p. 136). Representations, such as manipulatives, help children develop understanding by building a foundation for the later use of symbols. When given a choice of how to solve a problem, children gravitate toward manipulatives because they can act out the situation or relationships in the problem. When children are free to choose strategies for problem solving in single-digit arithmetic, they typically progress from using concrete strategies to more abstract strategies. For example, consider the following problem: “Lisa had 8 seashells in her collection. Hal gave her 5 more seashells. How many seashells did Lisa have then?” To solve this problem, children in the beginning stage of development will make a set of 8 objects and another set of 5 objects, join the two sets, and count all the objects. As they progress in their development, children do not need to build the first set but can count on from 8 to get the answer. Eventually, children can solve the problem abstractly without requiring a concrete model of either quantity in the problem (see Carpenter et al. [1999] for a complete discussion of these developmental stages). This progression of strategies is quite natural, and even five-year-olds move from counting-all strategies to counting-on strategies without instruction (Groen and Resnick 1977). Some children progress along the same kind of developmental path for multidigit addition and subtraction, initially using concrete strategies in which they manipulate the quantities in the prob-