I've been thinking quite a bit today about DS's math abilities.  It seems he 'gets' the concept of addition.  He understands that if he has $4 now, on allowance day, he'll have $6.  He can count on his fingers if I give him an oral addition problem.  He knows some without having to count.  But put numbers on a page, and he's clueless.  Well, sort of.  I've given him a sheet of math problems, and he usually can do them without much trouble. 

Yesterday was different though, and what spurred my research into kid's thinking processes. 

We played Kismet.  At the end we were adding up his total score and he had such a hard time with the problems.  I'd write it all out and we'd take it one column at a time (which we just learned about) but the problems he normally knew were just too much.  I'd ask 1+1 and he'd say 14 or something completely random.  Then he'd grasp at straws, just saying random numbers until I had him focus again and count out the answer.  This happened with almost all the problems.  Another problem was 9+7 and I told him he should draw circles so he could count them.  Well, I obviously didn't specify because he just kept drawing circles until he was into 20something and I stopped him and showed him how he should draw 9 and then 7 and then count them to get the answer - which he'd seen me done before. 

The most odd one was 6+6 - he said the answer was 6.  I can see why he said that, but I wondered - why does this kid not see that this is obviously wrong.  It left me (and him) very frustrated. 

 

So it led me to look into the development of children's abstract thought, which brought me to this article. 

http://goliath.ecnext.com/coms2/gi_0199-7823508/Enhancing-early-numeracy-by-promoting.html

It's a bit of a hard read, but interesting (to me anyway)  :) 

 

The premise is that some kids are behind in their abstract though processes due to various reasons, and there are some fun tests (disguised as games ;) that you can do to find out their level of thinking.

So today, for math class, we're going to try it out and see how DS does. 

It was a little disheartening that these tests were done on kindergardeners and DS is 8, but hey, I try hard not to compare, and just focus on where we are now (I get lots of practice at that).

 

Here's the tests

-The oddity principle - Take three objects that are the same and one that is different (shape, color, size, orientation, various).  Have the child pick out the different one.  Do many of these with different objects, but also have the opposites  - ie first problem has 3 big paperclips and one little, second problem has 3 little and one big.  What happens sometimes in the second problem is the child will insist that the little ones are still the 'different' and pick them away from the one big one. 

-Insertion - Show a number line with numbers missing and ask them which number goes in between.  Also have a line of progressively bigger/smaller/redder/etc. objects and ask them to insert objects the correct place in line. 

-Conservation - This deals with the rule that 4 will be 4 forever until someone adds to or subtracts from it.  This can be tested by having a line of 5 beans, then expanding that line and asking if there are more or less or the same number of beans.  Also, have a largely written number, and the same number but written very small, and ask which one has more value. 

 

If you scroll about halfway down the page of the article, it will show specific ways to adminster them and make them more fun. 

I can see these tests coming in handy in the future too when we're learning about alphabetical order, reading, etc.  All of them seem like they'd have some type of letter/reading counterpart.