Kindergarten Math - Addition

Date: 12/21/96 at 18:03:26
From: Monica M. Corbin-Simon
Subject: Kindergarten math

My daughter Gabrielle is in kindergarten.  She is doing fine in the 
areas of math she studies at her school.  How can I continue to 
enhance her skills in math without making her feel overwhelmed?

When I first started her with math I would use beans, pasta pieces, 
and other objects for addition and subtraction.  Now that she is 
getting older I want to do something new but I don't know what to try.

Date: 12/21/96 at 20:35:04
From: Doctor Ceeks
Subject: Re: Kindergarden math

Hi,

After addition and subtraction are mastered, the next step is often 
multiplication.

You can still use beans for multiplication.  (Arranging beans into 
rectangular patterns corresponds to multiplication.)

When you do this, there are three things to keep in mind:

First, you should aim to get to a stage where the particular objects
being counted are seen as irrelevant... beans, people, bananas... it 
doesn't matter what you use (from a mathematical viewpoint!).

Second, there is the technical aspect of counting which should be
mastered.  This includes knowing how to write numbers and say numbers,
and also knowing how to actually produce a number which is the sum
or product of two given numbers.  That is, it is one thing to 
understand that addition of two numbers is like putting together two 
piles of beans, and it is another skill to be able to compute this sum 
without actually counting all the beans every time.

Third, there are mathematical principles worth noticing (or
discovering).  For instance, when putting two bags of beans together,
it doesn't matter whether you count the first bag, then the second,
or the second, then the first... you get the same answer.  It's not as 
important to know that this is called "commutativity of addition" as 
it is to simply know it.  That is, it doesn't hurt to say the phrase 
"addition is commutative", but it's probably not a good idea to make a 
big deal about the word "commutative" - treat it like any other word.  

As another example, 5 times 9 = 9 times 5 because the rectangle that 
represents 5 times 9 can be rotated to look like the rectangle that 
represents 9 times 5.  More generally, "A times B equals B times A".  
(There is no end to the sophistication at which this simple law can be 
viewed!)

The above three things to keep in mind were written in that order for 
a reason.  First, you have to know what you are talking about, then 
you can try to invent algorithms and vocabulary for what you are 
talking about, and finally, you can notice patterns and principles in 
whatever it is you're talking about.  Also, there is no shame at all 
in going back to a simpler stage when trying out the next.

So for instance, when trying to master the algorithm of addition,
if your daughter goes back and counts on her fingers for a moment 
that's fine.  At least she's trying to get the answer.

Since there's plenty of time, if you can, try to have the patience
to let your daughter discover the mathematical principles for herself
(though perhaps with suggestive examples).

These opinions are my own and may not reflect the opinions of other
Math Doctors here at the Math Forum.

-Doctor Ceeks,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/