Having fun with Math

by Dr. Sandra Cookson

Few subjects elicit as great emotional response as mathematics. People tend to either love it or hate it. They see themselves as capable of ‘doing’ math or they don’t. Several theories offer insights on why this might be. You don’t have to agree with any of these ideas completely, but give it some thought.

Theory 1 … People who don’t like math are still trying to remember all of the rules that go with math. The unfortunate thing about this way of learning math, is that rules change. True story! For example, “multiplication is repeated addition.” While this seems to hold true in some cases [3 x 4 = 3 + 3 + 3 + 3], students struggle to apply this rule to fractions. [ ½ x ¾ = ½ + ???] In this case, the rule is just not useful.

In other cases, rules become over-generalized. “Two negatives make a positive.” This rule is meant for multiplication and division but students over-generalize it to addition and subtraction. [ -5 x -3 = 15, but -5 + -3 = -8] Instead of learning rules, students need to understand what is happening when numbers are being combined (constructed) and deconstructed.

For more examples of math rules that expire, search Google using the key terms ‘math rules that expire.’ For examples of math rules that expire in middle school, check out this article from 2015: https://www.nctm.org/Publications/Mathematics-Teaching-in-Middle-School/2015/Vol21/Issue4/12-Math-Rules-That-Expire-in-the-Middle-Grades/

Theory 2 … Students need more work developing number sense. Students are much better served when they are able to make sense of numbers and patterns and then gradually apply their understandings to more complex numbers. There is a reason why students first learn to manipulate single-digit numbers, then double-digits, then multi-digit numbers, fractions, decimals, and irrational numbers.

Students can build number sense by playing with numbers in their environment. Given a bag of M&Ms, how could you divide them evenly to make them last over several days? If there are 28 M&Ms, you could divide them out evenly to eat the same number each day. Day 1, you eat 4 M&Ms; Day 2, 4 M&Ms; etc. Thinking about this from a fraction perspective, each day you eat 1/7.

Be willing to see numbers in your world.

How many eggs are in a carton? Are there other ways to arrange them that would take less space and a smaller carton?
How many stairs between the first and second floor? Are they evenly spaced? Can you estimate the vertical distance between the first and second floors based on the number of steps?
Ceiling tiles? Floor tiles? Bricks on the wall? How do these help us make estimates about size, area, and volume?

Things are scary because we don’t understand them. Don’t be afraid to play with numbers. Flexibility is what math is all about. Math is not about having just one correct answer. Think of 5 ways you can make 75 cents. You can do it using coins other than quarters!

Theory 3 … Many people think that Common Core math is ridiculous. First, there is no such thing as Common Core math - unless some textbook company has created a series that they call Common Core Math. But Common Core State Standards for Math are just standards. These standards do not prescribe a single way to teach math or say that students must learn math in a particular way. As a matter of fact, the Common Core standards DO specify points by which students should be able to use the standard algorithms. In other words, students should be able to use the traditional method (the standard algorithm) of adding and subtracting multi-digit numbers by end of 4th grade, the standard algorithm for multiplying multi-digit numbers by the end of 5th grade, and the standard algorithm for dividing multi-digit numbers by the end of 6th grade.

People get caught up in the Common Core argument because of a lack of understanding about the importance of number sense and over-emphasis on the use of rules and procedures. If you rely solely on the standard algorithm with all of it’s borrowing, carrying, subtracting, and lining up, you could easily make a mistake in computation and then not have enough number sense to determine if your solution makes sense or not. People who blame ‘Common Core Math’ for their struggles with mathematical concepts are generally expressing frustration. The real reason for the struggle is much deeper though.

Every student can learn math. My best advice is to approach math with a mindset of discovery. Be willing to try new strategies and play with different combinations. Math involves thinking, problem-solving, and communicating about the world. Similarly, science, social studies, and reading also involve these same skills. Thinking, problem-solving, and communicating with numbers is the purpose of math. Embrace it!