I read an article a few years ago that really changed the way I talk to my students in math class. The article is called 13 Rules That Expire. It was published inNCTM’s August 2014 issue of Teaching Children Mathematics.
The gist of the article is that there are math “rules” used in classrooms. These are often presented as rules that always work, but in the case of these 13 rules, there is an expiration date. The article goes into greater detail about each of the rules, including the expiration date (or expiration grade). My goal is not to thoroughly discuss all 13 rules in this post, but wanted to at least list them.
- When you multiply a number by a ten, just add a zero to the end of the number.
- Use keywords to solve word problems.
- You cannot take a bigger number from a small number.
- Addition and multiplication make numbers bigger.
- Subtraction and division make numbers smaller.
- You always divide the larger number by the smaller number.
- Two negatives make a positive.
- Multiply everything inside the parentheses by the number outside the parentheses.
- Improper fractions should always be written as a mixed number.
- The number you say first in counting is always less than the number that comes next.
- The longer the number, the larger the number.
- Please Excuse My Dear Aunt Sally.
- The equal sign means Find the answer or Write the answer.
There is one rule I wanted to discuss a little further. Before reading this article, I was a big fan of teaching students to solve problems with the help of keywords. This often included making an anchor chart with the keyword on one side and the meaning on the other side (i.e. in all means add, how many more means subtract).
One common keyword strategy to teach students is that the word altogether means you should add. While that does work most of the time, it doesn’t always work. Take for instance the following problem:
Jimmy read 11 books in fourth grade, and Brian read 8 books. Jimmy, Brian, and Elyse, read 37 books altogether. How many books did Elyse read?
If students attack word problem by simply looking for keywords to help them solve problems, they will most likely see altogether and add 11 + 8 + 37. If students are thinking about the context of problem, and not just the keywords, they will see that they have to subtract 19 (11 + 8) from 37. This requires students to understand what is happening in the problem and not simply use the keyword as their only problem solving tool.
Teaching problem solving to our students is not an easy endeavor. It takes many tools in the mathematician’s toolbox. It takes constant repetition and exposure to many problem types. Teaching problem solving is not easy, but it is one of the most important skills we teach in any subject area.