Everything Counts: Can children add and subtract before knowing arithmetic?
June 1, 2007 by Kristina Chew, PhD
Filed under Health
Charlie learned his numbers from 1- 10 quickly when he was 2 1/2 years old and long had a fascination with just looking at some of the numbers, especially 3 and 5. He is not hyperlexic and only really knew the alphabet with certainty last year (and he still confuses capital B, D, and G, and i, l, L, t, T). His IEP is coming up in two weeks and we have been considering very basic math goals for him. An earlier attempt to have Charlie match number cards to quantities of objects proved frustating.
I have often wondered if, evidence to the contrary, Charlie has some sense of addition and substraction. Research under Harvard psychologist Elizabeth Spelke and published in the May 31th Nature suggests that children have the ability to use “nonsymbolic arithmetic” to perform rough but accurate calculations (addition and substraction) before being formally taught arithmetic. Notes an article in the May 30th Scientific American, the researchers
wondered if children could apply that ability, called nonsymbolic arithmetic, to Arabic numerals after learning to count but before they learned to add and subtract.
To find out, they gave several groups of children a laptop-based audiovisual test that asked whether one person had more or fewer candies or other objects than another person. The screen showed numbers to be added, such as 21 and 30, or subtracted, such as 64 and 13, followed by another number, such as 34, with which to compare the added or subtracted value.
The children answered correctly from 64 to 73 percent of the time…..
Math goals will be added to Charlie’s IEP.
I am not sure what a million would look like if it were spread out on the floor as I am not a bean counter.
I do remember learning numbers by the patterns of counters however and to me my fingers are my digits in a crisis (yes I know what that means in latin)
It is odd I can’t do the simplest of sums in my head, yet I can work out algorithms to help. For instance when SBC was taking an interest in calendrical savants, I was able to explain the method of calculation but could not possibly do it without a calculator.
I have a poor digit span when a series of numbers is read out, yet I can recall complex phone numbers by rhythm and sound, in effect they become music which I can recall well, but not read.
We are all a mass of contradictions, because the brain divides up various tasks which we think are one task and apportions them to different parts of the brain so that if one part is damaged in some way the other parts may be in tact.
I discovered during testing that I have what I call “holes” in my cognition, things that make no sence because they cannot make sence as I obviosly don’t have that bit of hardware that binds them into cohesion and comprehension.
Hi, Kristina–
Tobey has a very hard time with mathematical problems, like 2+2=4 and the like. I was trying to explain it to him and it’s just so difficult to rationalize why 2+2=4. I know the answers 4, and it makes “sense” to me. But, to explain even what “adding” means is just too hard for him to understand.
I think we (in the collective, general sense) just accept these kinds of concepts and they only make sense because we accept them as rational.
Something else I’ve learned that I take for granted without much forethought as to why or how.
I hope you’re having a great weekend…
Larry and Rochelle, thanks for sharing all of this: It has long puzzled us that Charlie has seemed interested in numbers, and struggled beyond learning the numbers themselves.
So much I take for granted—so much I have yet to learn!
Math research keeps growing and growing, for neurotypicals as well as children with various disabilities that affect their learning. Keep those goals in the IEP for Charlie! There will be a way to teach him.
Kristina, I recommend the TouchMath system. It incorporates a tactile component, where the student actually touches points on the numerals. The points are gradually faded until the student doesn’t need them any more since they are in the “minds eye”. The materials are colorful and appealing using animals, insects, and other fun items as “points”. It progresses from elementary math all the way to high school. My daughter is doing three digit addition and subtraction, and learning to solve word problems.