Teaching For Proportional Reasoning
As any experienced teacher will attest, it is not sufficient to simply tell a student his/her answer is incorrect and then instruct the student to use the correct solution. The incorrect strategy has not been “unwired in the brain” and would re-emerge after the current lesson has been completed.
Also the additive strategies noted above cannot simply be labeled as “incorrect” since they do correctly match other real world situations. For example, consider the following problem:
On Independence Day this year Mr. Tall was 6 years old and Mr. Short was 4 years old. On a future Independence Day Mr. Short is 6 years old. How old will Mr. Tall be on that Independence Day?
Similarly the constant sum relation can be correct for some situations. Consider the following problem.
There are four beavers on the left side of a river and six beavers on the right side of the river. At a later time with the same group of beavers there are eight beavers on the right side of the river. How many beavers will there be on the left side?
So there are situations where the additive relations (constant difference and constant sum) are correct and other situations where the multiplicative relations (constant ratio and constant product) are correct.
Read more about this topic: Proportional Reasoning
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