Guest Post: The Common Core and a Right Brained Math Approach to Math

Editor’s note: Although I’ve been thinking of you during my time away from the blog, grad school + new baby make it terribly difficult to sit down and write. Lucky for me (and now you) Thomas Burwell has reached out and offered to write a guest post. Hopefully I’ll rope him in to continue posting.

The term “right-brained” has become almost synonymous with creativity over the past few decades. To what extent this usage is scientifically backed requires some qualification. As Kara Federmeier rightly observes, “One problem with answering this question is that we would first have to agree on what ‘logical’ and ‘creative’ even mean.” What has been established is that the left-brain typically handles mental functions that are routine and predictable, whereas the right-brain handles events that follow a non-predictable pattern. A perhaps more appropriate description is to refer to left-brain processes as “inside-the-box” and right-brain as “outside-the-box” thinking.

Properly learning any subject requires a BALANCE of left and right-brained thinking. You need to be able to deal with both the routine and the unpredictable aspects of the field. The reason why I like “right-brain” label for math education is because the standard approach to teaching math in schools today is overwhelmingly left-brained. An emphasis of right-brained thinking is needed to create a balance.

For any individual problem, both parts of the brains are almost always working to different degrees, so we should be careful when using the left-brain and right-brain labels. That being said, a proper diagnosis of a student’s thinking approach can reap real benefits to the student and the class as a whole if that student becomes a more active participant.

A student who answers “positive” to the question “what happens when we add two negatives?” is displaying a typical left-brained strategy. They are giving a “correct” answer but to the wrong question. Your left-brain hemisphere seeks to differentiate new information from your day-to-day winning strategies. When presented with a new situation, the left-brained approach is to try out one of your go-to strategies, and then (hopefully) check to see if that result is good.

On the other hand, a right-brain response to the same question might be to draw a number line and count backwards. The right-brain handles the (mathematically more complex) task of “lumping” knowledge, which means to look for connections. Your right-brain hemisphere seeks to store new information for future reference. Even if it is never useful to you personally, it could be useful to someone else someday! A right-brained approach asks “what strategy that I have encountered at some point in my life feels like the right approach here?” Unfortunately, mathematics, being entirely symbolic, has very few surface-level connections to be found. In mathematics, the useful connections are almost always on the deeper, structural level, such as the logic that dictates that the distance formula can be derived from applying the Pythagorean Theorem on an X-Y axis or that the Quadratic Formula can be derived by completing the square from the standard form quadratic equation.

The Common Core addresses the problem with the overly left-brained, approach to teaching mathematics, stating:
“Mathematics is not a list of disconnected topics, tricks, or mnemonics; it is a coherent body of knowledge made up of interconnected concepts.”

As the Common Core points out, mathematics is incomplete without attention to these structural-level connections. “[It] is not a list of disconnected topics.” Understanding mathematics on some level MEANS understanding the underlying patterns. Fortunately for math teachers, students who possess this deeper understanding of math will also perform better on assessments.

How can teachers use knowledge of the left-brain vs. right-brain approaches in their classrooms? One strategy is to try to appeal to both thinking styles within lessons. For example, a right-brain approach to the topic of, say, quadratics for instance, is to start with a concrete experience such as dropping a ball from the ceiling, or showing a video of a car accelerating at a constant rate. An equally good, but left-brained, approach would be to draw upon students prior knowledge of rectangles, by presenting the following problem:

Displaying rectangle quadratic.jpg

A not-as-good, left-brained approach is to start the lesson with a powerpoint slide titled “QUADRATIC EQUATIONS.” Instead of seamlessly activating the correct prior knowledge, students now must use a lot of their brain real-estate deciding where in their existing math schema to put “quadratics,” which is still nothing but an empty label for them at this point. It’s much easier to just copy the words down in a notebook, and not think about it at all, which is what most students will do.

As the following table outlines, the left-brained approach starts with language, next explains the procedure being taught, and lastly discusses what situation to use it. The right-brained approach is the opposite order, starting with the problem, next encouraging students to figure out a procedure to solve it, and only at the end applying a label, such as “the quadratic equation” to what has been covered. The left-brained approach is preferable when students have a lot of prior knowledge with a similar topic (like the rectangle problem when introducing quadratics), whereas the right-brained approach is preferable when prior knowledge is not so easily activated.

Left-Brained Right-Brained
Label-> Procedure -> Situation Situation -> Procedure -> Label
Results-oriented Process-oriented
“Does this procedure always work?” “Is this the only procedure that works?”

Tom is a math educator in Greensboro, NC. His interests include the history of physics and the study of psychology as the discipline of interiority. He believes math should be taught as “the pleasure of figuring things out”, using Dan Meyer’s approach of starting each class with a concrete problem, and also exploring the etymology and historical context of math symbols.