Consider the following statements (which my teachers taught me and I have taught to my students). For each one, decide whether or not the statement is TRUE or FALSE. I encourage you to write down your answers.
If you suspect that each and every one of these statements is false (or at least not ENTIRELY true), you are correct. In their article, “13 Rules That Expire” (Teaching Children Mathematics, NCTM, August, 2014), the authors challenge us to rethink common “tips” and “tricks” that we often use with students to learn a procedure. Our intentions are good. Perhaps they are the same tricks we were taught. Unfortunately, these tricks and tips often “expire” and aren’t always true. The result is that we leave students with partial understanding of the mathematics and misconceptions that we “hope” someone will correct later. We also leave students with the idea that math is about a “mysterious series of tricks and tips to memorize rather than big concepts that relate to one another.”
The authors go on to give examples of why the statements are simply not always true.
Here are a few of their examples.
1) When you multiply a number by ten, just add a zero to the end of the number.
Does this rule always work? Consider: 0.25 x 10 = 0.250 Not so much.
2) Use keywords to solve word problems.
This approach often leads students to pull out the numbers and do the operation that the key word suggests, rather than focus on what is happening in the story. When students see “altogether,” they may think they always add. But what about this story: There were 9 dogs in the yard. Some more dogs came and altogether there were 18 dogs. How many dogs came? (You’d probably subtract to get the answer.) Or perhaps this one: I had 3 boxes of crayons with 8 crayons in each box. How many crayons do I have altogether? (Most people would multiply.)
3) You cannot take a bigger number from a smaller number.
Image the temperature is 10° and it drops 15 degrees. In this case, 10-15 can (and does) happen and the result is -5°. Even from young ages, we can start looking at a number line with negative numbers. Students often think that subtraction only means “take away,” but they also need to understand that subtraction can be the distance between two numbers on a number line.
14) The equal sign means Find the answer or Write the answer.
Students often believe that the equal sign means “the answer comes next” instead of understanding it as “is the same as” which is a relation between the two sides. When they think that, they will struggle with equations such as:
4 = 4 (They will say this is false because there isn’t an operation.)
8 = 3 + 5 (They will say it is false because it’s backwards.)
Every time we use statements that are not entirely true or tricks that are not grounded in conceptual understanding, we hinder student learning in the long run. This article is great food-for-thought for all teachers of mathematics!
The whole article (with discussion of all 13 statements) can be found here.
This post brought to you by Carol Lucido, the K-8 District Math Coordinator
13 Rules That Expire by Karen S. Karp, Sarah B. Bush, and Barbara J. Dougherty (Teaching Children Mathematics, NCTM, August, 2014)
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