问题描述：
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.”
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.”
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