访友脚印
学生间的口耳相授更重要学生间的口耳相授更重要
闲来无事，整理以前及时写就，但未来得及打印的文字，以赡自己及曾经的2010—2011学年度的六年级。
苏教版六年级下册数学书第52页有一小长方形和将其按比例放大后得到的图形，要求学生先分别量出它们的长和宽，写出对应边长的比，再估计一下，大长方形与小长方形面积的比是几比几，最后估算，看看估计对不对。
学生先各自测量出：
（1）小长方形的长是3厘米，宽是1厘米；
（2）大长方形的长是9厘米，宽是3厘米；
（3）大长方形与小长方形长的比是（ 3 ）∶（ 1 ），宽的比是（ 3 ）∶（ 1 ）。
再估计大长方形与小长方形面积的比是几比几。
李昊远积极举手发言，看上去胸有成竹，所以我就请他估一估。结果，他的估计方法大出我的意料，显得异乎寻常的精彩。
他说，我们可以用小长方形来量一量大长方形的面积。把小长方形的长与大长方形的宽对齐可能更加准确，把小长方形的宽与大长方形的长对齐。因为9厘米里面有9个1厘米，所以要9个小长方形才能把大长方形盖满，大长方形与小长方形面积的比是9∶1。
天哪！方法好，说得也好！是什么原因促使他能做出如此巧妙的估计，精辟的分析呢？
课后，我向其了解情况，原来是他课前请教了其他同学。其他同学用自己的理解说服了他，使他能够完整表述。从认知科学的角度出发，学生与学生之间因年龄相仿，认知特点相近，因而有更多的认知的倾向和认知选择，也更容易沟通和相互理解。这是师生之间的交流与沟通所无法比拟的。
《数学课程标准》也明确指出：有效的数学学习活动不能单纯地依赖模仿与记忆，动手实践、自主探索与合作交流是学生学习数学的重要方式。生生之间的合作交流，甚至是口耳相授具有师生交流所不可替代的作用。
今天，从李昊远的发言中，我更清楚的看到了这一点。
因此，每种理论，每种要求都应是有其实际根据的。当我们在实践中看到这种实例时，就不能让其悄悄溜走，而应抓住它，用它来促进自己更好的理解理论，明确做法，即需要教学反思，并以教学随笔的方式记录并呈现。
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