Thursday, August 23, 2007

Pattern-recognitional mathematics

Another best answer by me :)


Asked by quantum_dot: Why do children make zero and decimal position mistake while dividing?
For e.g.: 21 divide by 2 is 10.5, but many times children end up with 1.5 as the answer

1 year ago - 6 answers
Best Answer - Chosen by Asker

I suspect this error is possible because the child is not learning maths, but merely pattern recognition. If the child learns numbers and calculation the mathematical way, she (from my experience, higher chance is a she) will know 1.5 is very unlikely to be the answer, since it is so much smaller than what would be expected for when a value near to 20 is divided by 2.

However, if she were pattern recognizing, 1.5, 10.5, 15, 15.0 are similar patterns.

I recommend more focus needed on the 'feeling' of values and their representations using Arabic numbers. I think more practices on estimation might help. E.g. ask them to estimate, using their perception on the values that are represented by numbers to give rough descriptions of the answer. E.g. before applying method to exactly calculate the value of 21/2, ask them to describe the answer. Will it be bigger than 21? Will it be smaller than 2, will it be near to 0, 10, 20, 30, etc.? Will there be decimals? Etc.

Another advice, forbid the use of calculators! Lower the importance of getting the exact answer.

Just to share, I was amazed when a 20+ year-old working adult couldn't figure out why 3/2=1.5, but he can tell you in split seconds that a meal that cost $3.00 shared by 2 persons means each has to pay one dollar and fifty cents, or one-fifty, which in numeric form is $1.50! Why, 3/2 is so different from 1.5, and he probably find it complicated to rationalize the pattern-transformation in order to transform 3/2 to 1.5, but $3.00 and $1.50 are money to him, not numbers, and he has good sense of money :)

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