英语翻译Existing knowledge may not be appropriate in a new situation and so thelearner needs to adapt their approach to cope with new knowledge.Wesuggest that this need for adaptation is a major factor in causing a range ofdifficulties for studen

英语翻译Existing knowledge may not be appropriate in a new situation and so thelearner needs to adapt their approach to cope with new knowledge.Wesuggest that this need for adaptation is a major factor in causing a range ofdifficulties for studen
英语翻译
Existing knowledge may not be appropriate in a new situation and so the
learner needs to adapt their approach to cope with new knowledge.We
suggest that this need for adaptation is a major factor in causing a range of
difficulties for students learning mathematics.Sowder (2000) described the
enormity of the changes in thinking and adaptations necessitated as students
move “from operating on whole numbers to operating on signed numbers and
rational numbers (that is,fractions and decimal numbers) and from a primary
focus on addition and subtraction to multiplication and division as well.”
Hiebert and Behr (1988) noted that recognition of how the nature of the unit
changes requires a shift in thinking that is “a fundamental change with farreaching
ramifications:a change in the nature of the unit.” Sowder argues
that,“when teachers do not understand the significance of these subtle
changes in how numbers are used,their students can become very confused”
and lists three examples of this change:
• Students move from singleton units to composite units when they
multiply; that is,what counts as a number changes:A set of things
can now be thought of as one whole; I have two sets of three
pencils; I have four six-packs of Coke.
• Students create new types of unit quantities when they divide:
Dividing 30 cookies by 6 children yields 5 “cookies per child.”

英语翻译Existing knowledge may not be appropriate in a new situation and so thelearner needs to adapt their approach to cope with new knowledge.Wesuggest that this need for adaptation is a major factor in causing a range ofdifficulties for studen
现有的知识可能不适合新的形势,所以
学习者需要适应他们的应对新知识的方法.我们
表明,这需要适应是引起一系列的一个主要因素
学生学习数学困难.索德（2000）描述
巨大的思想变化和适应需要的学生
移动”工作在全数字签名的数字和操作
有理数（即,分数和小数）和从主
围绕加减乘除一样.”
希伯特和贝尔（1988）指出,如何识别性质的单位
变化需要转变思维,是“具有深远的一个根本性的变化
结果：在单位的性质发生了变化.“索德认为
说,“当老师不理解这些微妙的意义
如何使用的变化的数字,他们的学生可以成为非常困惑”
列出这三个例子的变化：
•学生从单一单元的复合单元时
繁殖；那就是,什么是数的变化：一组东西
现在可以被看作一个整体；我有两套三
铅笔；我有四六个包的焦炭.
•学生创建新类型时,将单位数量：
将30的饼干,6个孩子的产量每孩子5“饼干”