Thursday, July 15, 2010

Arithmetic vs. Mathmatics

I have been spending a lot of time thinking about arithmetic lately.  Partly it is due to the fact that Determination (10) is really ready to delve into the fascinating world of numbers.  Numbers have always come easy to him and I foresee that he will use numbers a lot in his mission in life. 

It wasn't until I read this fascinating post by Karen here that I began to think of arithmetic and mathematics as two different things.  The idea fascinated me and I begin to do some research.  This was another missing piece of the puzzle in our home education.

Arithmetic is the study of numbers on a basic level learning.  Basic arithmetic includes the ability to compute numbers through addition, subtraction, multiplication and division.  Higher arithmetic includes decimals, fractions, and negative numbers.  Mathematics would be Algebra, Geometry, Trigonometry, Statistics, Calculus, etc.

I realized in my mind I was treating them as the same thing.  When I disconnect the two in my mind I see clearly the skills I need to teach my children before they reach scholar phase when they will begin an in depth study of mathematics.  This study will be possible only after the groundwork of the skill of arithmetic as been accomplished.  (Much the same way that studying literature is only possible after the skill of reading is learned).

I mentioned in a previous post that I am starting to offer skill classes to those interested.  I have been asked repeatedly to teach some math classes by the boys.  I realize now that I need to focus on basic arithmetic with Imagination and Leader.  (Leader has not requested any classes yet and so he will not have them until he does request them).  Determination needs some (and has requested) advanced arithmetic work in fractions and decimals and then he will be ready to begin his mathematical studies when he is ready.

Through my study an awareness as come about what level of arithmetic/math I use on a daily level.  I realized that I do not use mathematics.  I do use arithmetic constantly.  I balance my check book, double a recipe, figure out sales tax, budget for daily needs, etc.  All the activities I pursue are on an arithmetic level.  This reinforced to me that I need to make sure my children have a solid base in arithmetic.

After this they can move on to mathematics in their life.  My husband I now realize uses mathematics.  He computes the square feet of fence needed, the amount of paint we need for a bedroom, the probability of success in our investment accounts, etc.  Mathematics is needed in his world.  I realize now where I can improve.

After doing some research and consultation with my friend who is my curriculum expert, Mr. Patriot and I have determined our curriculum choices. For basic arithmetic we will continue to use Saxon Math to gather problems and explain things.  (I do not like Singapore or Right Start Math.  I am sure they work great for everyone else but me, but my brain does not work in these math programs).  Saxon will be utilized more as a reference.  Basic arithmetic can easily be taught with out a textbook.  I will teach these basic principles in small chucks with a wipe board and pencil and paper.  Then the boys will use real life experiences to reinforce principles learned.  Since my life is full of arithmetic they will have ample opportunity to practice.

For advanced arithmetic and mathematics we have chosen to use The Life of Fred series.  Click the link to learn more about this great program.  There are example pages (link here) taken from each book.  I have seen these books and have found them exceptional.  (If math can be exceptional. : ) I tend to prefer literature and history).

I continue to love to read great posts by all of you that spring board me into ideas that will work for my family.  Thank you all.


Shanny said...

Thanks for the interesting thoughts.

My 2nd and 3rd children struggled with maths at the beginning. They could add things together in real life but put it on paper and all of a sudden they didn't know a thing.

We just gave the bookwork a miss for quite a while in the end. Didn't do them any harm. Now they are flying through their Math-U-See pages.

There is something to be said for real world learning! lol

Karen said...

I really like Life of Fred. I have started studying a book called The Beginner's Guide to Constructing the Universe. I really like it so far. It makes me fascinated by math and I want to learn more. I share little tid bits with the children and they really like it.
Thanks for your thoughts on this. I'm motivated to get on the ball with this again!

Being A Mother Who Knows said...

Shanny-Math is real life. Why did I make it so boring before?

Karen-That book sounds great. I will try to find it. Thanks for the book idea.