There are many tricks that can help students solve math problems
by Joan Reissman, Blended Learning Specialist
It’s not news that many students struggle with math. According to the Programme for International Student Assessment (PISA), the triennial test given to 15 year-olds by OECD, the United States ranked 38th out of 71 countries in 2015.1 Every three years we slide a few more notches. Something has to be done. But what?
Many mathematicians feel that only deeper conceptual understanding will improve math learning and provide lasting results. Some math experts look at computational tricks as cheating. Linda Gojak, the former president of the National Council of Teachers of Mathematics, says “I envision students dragging a big bag of tricks into standardized tests and not really thinking about the questions.”2 There is some validity to this position. Tricks alone without deeper instruction are only a schtick. But if success with a trick can give students confidence, is that a bad thing? I don’t think so.
There are many tricks that can help students solve math problems, particularly when preparing for standardized tests. One typical example is plugging in. Students take an equation and try to solve it working backwards from the given answer choices. In order to find the right answer, they still need to solve the equation. They still must work through the problem by employing mathematical operations to solve the equation. Is that bad?
One of the challenges in working with high school students is that they don’t want to do what they consider elementary school math, even if they need to re-learn it. They will just look at a fraction and think that they have always hated fractions and have never understood them. They don’t even want to try.
When I was teaching math, borrowing with fractions was always a trouble spot. I found a convenient trick to teach it. Let’s take an example. Solve 2 3/8 minus 1 5/8. If you make the 2 into a 1 (because you’re borrowing) and then add the two numbers of the first fractions (3 and 8) you will get 1 and 11/8. This is the same as borrowing the 1 in the form of 8/8 without the hassle. Of course, you still have to remind students to convert all denominators when they are not the same. Students would often ask me why nobody had ever taught them this way before. It’s a simple trick but it helps build confidence.
Are tricks a substitute for deep conceptual math learning? No, they are not. But can they help in certain circumstances? Yes, they can and do. Tricks help students build confidence and feel better about math. That’s an outcome every teacher wants for her students. Halloween or not, math tricks can be a treat for students and teachers.
1 U.S. Students’ Academic Achievement Still Lags That of Their Peers in Many Other Countries, Drew De Silver 2/14/17 http://www.pewresearch.org/fact-tank/2017/02/15/u-s-students-internationally-math-science/