Math Tricks Often Add up to Answers, Not Learning

Math textbooks often contain math “tricks” that solve certain types of problems quickly and reliably. It’s understandable why math textbooks include these shortcuts: they are easy to remember and usually work. But a major concern rises from this: do they actually teach math?

In his presentation at the P12 Summer Institute, Phil Daro, one of the co-developers of the Common Core State Standards for Mathematics (CCSSM), suggested not. They’re great for “answer-getting,” as he puts it, but not for developing understanding.

As an example, he describes the “butterfly method” for adding fractions of unlike denominators, in which students draw “wings” around different parts of each fraction to isolate the numbers they need to multiply and add. This method has both strengths and weaknesses.

“Works every time,” he says, “takes one lesson to teach, kids can remember it… but what the heck does this have to do with mathematics? This is not mathematics. This is answer-getting.”

And answer-getting should raise a number of red flags. As students progress in math, topics build off of each other. Especially at such an early level, learning shortcuts in math sets the stage for students to ask, “Why are we learning this?” A lack of foundational math understanding will make later concepts seem that much more perplexing.

Students with solid math understanding also tend to exhibit some seemingly unrelated qualities: curiosity, creativity, and surprisingly, strength in literacy. Early math researcher Doug Clements believes that this correlation between strong math programs and positive gains in literacy scores might stem from the fact that math encourages students to “reach down” to articulate their thoughts about concepts that are often somewhat abstract.

It stands to reason than that relying on math tricks eliminates what might be some of math’s greatest benefits. Rather than ignoring math tricks outright, however, teachers might consider encouraging students to work together to explain why the trick works! Once they understand the logic, the trick becomes a tool students can utilize to solve problems, rather than a shortcut to avoid them. Number talks can also help students think their way through math procedures, as they encourage students to utilize multiple solution strategies and discuss their logic with their fellow classmates.