四、关于估算教学

　　美国的《学校数学的课程标准和评价标准》指出估算是一种能够用于非常规问题解决情境的技能，是学习者能够用于问题解决的一种情景性工具。它应该通过与其它概念的整合进行教学。 [34] 研究也表明 估算技能可以通过仔细设计的、成序列的系统教学而得到发展。尽管还没有发现某种方法比其他的方法能更成功地增进儿童的估算技能，但研究已经证明估算教学对不同年龄和不同能力水平的儿童都是有效的。 [35] 然而，对关于何时开始进行估算技能教学的意见却是不一致的。

　　德汉尼等人（ 1998 ）提出估算是源于对数量的近似和比较系统，从一定程度上说，前言语的婴儿就已表现出这种能力。 [36] 但凯斯的理论表明，真实的计算估算产生于他们所提到的精致的二维思维以后，即不低于 10 岁。 [37] 而事实上，有的研究表明许多成人也仅是低水平的估算者。富森（ K.C. Fuson ）和霍尔（ J.W. Hall ）指出，估算技能应该在小学的中期和后期进行教学。其他人则提倡，估算教学应该发生在初中阶段。 [38] 美国的《学校数学的课程标准和评价标准》中对 2 岁起的学前儿童和小学 1-2 年级阶段的数学教育就提出了能进行合理估猜的教学目标。 [39]

五、结束语

　　认知领域和教育领域中对估算研究的兴趣都在于试图决定估算产生的具体时间，以及它与其他数学技能的关系，它的发展过程等问题。

　　在现有研究文献中，大多数是关于测量估算和计算估算的研究。许多研究已分析了计算估算中所使用的策略种类，也有研究已经接触到计算估算技能与其它能力之间的关系。但关于数量估算的研究很少。根据现有的研究，估算能力不是一种整体的能力。即不同类型的估算任务，如数量估算和计算估算似乎需要不同的能力，并且在各种估算任务之间似乎不容易进行能力的迁移转化。 [40] 一个好的计算估算者并不必然是一个好的数量估算者。估算任务的多样性和儿童在这些任务上的表现是研究中一个重复的主题。

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