Reply to FYI: Indiana withdrawing from Common Core standards

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Reply to "FYI: Indiana withdrawing from Common Core standards"

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[quote=Anonymous][quote=Anonymous][quote=Anonymous]One problem with kids who onlye know the "algorithm" for subtraction (Start at the right in the ones column, borrow one from the tens column, cross out the 5, make it a 15, now subtract) is that they are so busy just applying the algorithm that they don't stop to think what those numbers really represent.  So if they make a computational error, they don't recognize that their answer is wrong, even off by an order of magnitude.

For an absurdly easy example, say a child is asked to solve:

300
-  201
_______

Really should be able to just do that in her head.  She shouldn't need to cross out the 3, make it a 2, cross out 0, make it a 10.  Now cross out the 10, make it a 9, cross out the 0, make it a 10.  Now, subtract.

Kids who only know this way, and NO OTHER, for subtraction, become the store clerks  who are completely unable to make change if the cash register is "down".   You hand them a $20.00 bill and try to buy a 4.99 item, and they have NO CLUE how to make change, because they can't do all that crossing out in their head.

Use a mental number line, and go back $10 from $20 to $10, then go back $5 to $5 and then go back one cent.  Your change is $15.01 -- a 10, a 5 and a penny.[/quote]

Here is what is wrong with CC (or if you wish, how it is being implemented):

Any math problem can be solved many ways.  Any reasonably motivated student, even if "only" taught the standard algorithms, will naturally and gradually came up with [b]his/her own mental shortcuts and intuitive visualizations that are useful/meaningful to him/her[/b].  Doing so will be driven by the student's own urge to save time and reduce errors.  And [b]each student will probably come up with somewhat different shortcuts and visualizations[/b], and that is fine.   
It is important to keep the lessons centered on the the standard algorithms because:  
1) Those standard algorithms [b]always[/b] work.  Yes there is a nice shortcut for 300-201 or $20-$4.99, but you need a more general method for $21.27-$8.69 
2) There needs to be a universal method that all students can use to communicate and "prove" the correctness of a result to others.  The standard algorithms are best suited for this.

I see teachers giving questions that require the student to make sense of some wacky visual or verbal interpretation for solving some particular math problem.  If that interpretation doesn't happen to "click" for a particular student, then the whole exercise is counterproductive.

Kids are smart and creative.  They will develop their own innate ability to understand/visualize.
[/quote]

+1000[/quote]

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