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Absolute and relative thinking in mathematics - Coggle Diagram
Absolute and relative thinking in mathematics
What is absolute thinking?
is additive thinking
What is relative thinking?
is called multiplicative thinking
requires change in perspective
activities provide the opportunity for students to expand the range of applicability of certain words ie: more
It is important that they are able to understanding change in two different perspectives: actual growth and relative growth, actual change and relative change
in order to adopt more powerful ways of thinking, it is necessary to move beyond counting and
absolute thinking.
Relative thinking entails more abstraction than absolute thinking and, through relative thinking, we create more complex quantities.
relative thinking and understanding fractions
crucial in initial fractions instruction.
entailed in the understanding several important notions:
the relationship between the size of pieces and the number of pieces.
• the need to compare fractions relative to the same unit.
• the meaning of a fractional number. Three parts of five equal subdivisions of something conveys the notion of how much in the same way that the above example conveyed the notion of crowdedness.
• the size of a fractional number.
• the relationship between equivalent fractions. The fraction numeral 1, for example,
5
names the same relative amount as when the unit is quartered (;�)or halved ( 1
� )-
• the relationship between equivalent fraction representations.
It may take time until a child begins to think relatively across a variety of situations, so it is important to present children the absolute-relative choice in many different contexts.
For example, when we ask "Which is larger?" in the context of comparing two
lengths, additive or absolute thinking is appropriate. However, if we ask "Which is
larger?" in the context of an area problem or an enlargement problem, multiplicative thinking is required. In other words, part of the challenge is to attach new meanings to old words
and to associate contexts with appropriate operations-additive or multiplicative.
One difficulty is that our language does
not supply us with new words with which to ask multiplicative questions.