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Meaning for Fraction Activity: Some critical considerations/observations

Meaning for Fraction Activity: Some critical considerations/observations. Yet, we were able to conceive a relationship between the size (amount) of the whole and the parts, and to express the size (amount) of either one in terms of the other.

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Meaning for Fraction Activity: Some critical considerations/observations

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  1. Meaning for Fraction Activity:Some critical considerations/observations • Yet, we were able to conceive a relationship between the size (amount) of the whole and the parts, and to express the size (amount) of either one in terms of the other. In this activity sequence, did we ever know absolute amounts of given quantities? NO! • This is a conceptually powerful relationship that is independent of the absolute amounts. MTE 494, 08/26/09

  2. Foundational images and mental operations that generate meaning of fraction • Iterating/duplicating/conjoining parts of equal size to make a whole amount of something • Comparing the size/amount of each part with that of the whole Partitioning an amount of something into some number of equal sized parts (“equipartitioning”) • Comparing the size/amount of the whole with that of each part • Expressing the size of either (the whole or each part) only in terms of the size of the other MTE 494, 08/26/09

  3. A generative conception of fractions • Reciprocity is embedded in the fact that thinking of amount A being 1/nth as large as amount B means thinking that amount B is n times as large as A, and vice versa. This sequence of activities develops a meaning of fractions as reciprocal relationships of relative size • Fractions do involve partitioning amounts into some number of parts, but the partitions must be of equal size AND the focus must be on thinking of the size of the parts (whole) in relation to that of the whole (parts). [Fractions are NOT absolute amounts or counts of things] MTE 494, 08/26/09

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