How Arithmetic is Not Mathematics and Why Children Need to Learn Both
“What is math?”
If you ask this question, you will likely get a response like, “Well, math is adding, subtracting, multiplying, or dividing numbers.”
Guess what? That’s not math, that’s arithmetic.
If you were to pose the same question to Galileo he would have said, “Math is the way to understand all sorts of things in the world around us.” In fact, he did say that. He also expressed it this way, “The great book of nature can be read only by those who know the language in which it was written. And that language is mathematics.”
In short, arithmetic is the use of numbers in calculations, where mathematics is the study of the relationships among numbers, shapes, and quantities. Just a matter of semantics, you say? It helps to think of it in this way. Mathematics is like writing a story and arithmetic is spelling. Yes, they go together, but are very different nonetheless. There have been many great authors who have written amazing stories and were admittedly not great spellers. To be sure there are many who can memorize a list of words to spell correctly but could not create characters or a plot if their life depended on it!
Children need to learn BOTH arithmetic AND mathematics. Everyone acknowledges the importance of arithmetic. After all, how could anyone survive without a grasp on basic addition and subtraction?! But what’s the big deal with mathematics?
Thinking Skills Striving to understand number concepts and how numbers relate to one another develops good thinking skills. To study mathematics is to hone your logical and critical thinking skills. Mathematics teaches the brain to look at problems from different angles and to concretely map out a solution. It is immensely important for a developing brain (a child) to practice and refine these skills.
Science Should a person desire to study and/or work in the fields of physics, chemistry, astronomy, etc. then a strong math mind is a must. As Galileo said, these sciences speak the same language and that language is math.
Arithmetic! Studying mathematics actually makes you better at arithmetic. For example, if you have a concept of 10 as being two groups of 5(a mathematical way concept of 10) – if that is how you think of 10, then multiplying 5×2 is simple. Mathematics helps a child see how numbers fit together and that understanding makes calculations easier as well as more meaningful.
So how can we ensure our children are learning mathematics as well as arithmetic? I would suggest the following:
*Be sure the curriculum used teaches both. If “math” is only memorizing facts and operations, it is lacking. If there is not adequate arithmetic practice, it is lacking. Look for a balance. The goal is for a child to know how and why the numbers work together. Global Student Network has a wide variety of curricula. You can find a curriculum to suit your student’s needs at www.globalstudentnetwork.com
*Offer plenty of open-ended problems and puzzles. Puzzles and problems that do not have an obvious solution encourage children to look at it from various angles and calls upon their creative problem-solving skills. Puzzles requiring manipulation (tangrams, matchsticks, etc.) are excellent for younger children.
*Encourage children to notice patterns. Recognizing patterns is to learning mathematics what recognizing rhyming words is to reading. It helps to set the stage, to prepare the mind for understanding.
It’s the start of a new school year and we are giving great thought toward what we hope our children will. Let’s give them as much mathematics AND arithmetic – it all adds up to stronger minds!!
Sources:
http://www.math.umn.edu/newsletter/2004/mathimportance.html
http://www.livestrong.com/article/255620-why-is-math-so-important-for-kids/#ixzz2dTYAqQnh
http://www.mathmedia.com/whatisdifbet.html
Copyright © 2013 J. Hoffman / GSN
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Email: JHoffman@GlobalStudentNetwork.com