Maria H. Andersen, August/September 2012
Bringing Color to the Classroom
I adore using color to bring attention to important steps or concepts when I am going over problems, theorems, or definitions with students. When I was a graduate student, I did this with colored chalk. When I was a new faculty member (at a school with whiteboards), I did this with colored markers. Later, when we got a document camera in our classroom, I did it with colored highlighters on worksheets. And today, I use the highlighting tools on my tablet PC to do it (in OneNote).
Despite my use of color, I realized many years ago that students were taking notes in monochrome.When a student looked at his or her notes, the “layers” of the steps that I had so carefully laid out in multicolor during class had disappeared.
If students are going to bother to take notes, they will benefit the most from the colored steps, not me. For many years, I provided students with a classroom set of highlighters and colored pencils. But this year, I required that the students purchase yellow, green, and blue highlighters and a red pen—these are the annotation tools I use all the time in OneNote.
This issue’s column is about a low-tech technology—how we use those highlighters and red pens in the classroom.
Below are examples I made using Microsoft OneNote and some of the student notes that result from some of these lectures, highlighted with their own tools.
Supposedly, a picture speaks a thousand words. Here are some of the many ways I use these tools to help students to understand topics better.
The chain rule:
I have students highlight the “inside” and “outside” pieces of function compositions to help them see why the chain rule is necessary when taking derivatives.
The Chain Rule
Integration by substitution:
Highlight the u and du in different colors (and highlight the corresponding parts of the integrand in matching colors). This also works nicely for the u and dv of integration by parts.
Integration by substitution
Highlight each piece of the equation (and its corresponding section of the graph) in a different color.
Partial fraction decomposition:
In the coefficient balance, highlight all the x terms (or coefficients) in one color (and their corresponding equation); the x2 terms in another color (and their equation); and so on.
Draw the basic function in red, then all the transformation steps in pencil. Highlight each transformation in a different color, and write the transformation in words or an equation and highlight that in a matching color.
When you’re performing an operation such as R1 + 2R2 → R2, highlight the old R1 and the entries for 2R2, then add them. Highlight the new R2 in the same color. Switch colors for the next row operation.
Volumes of rotation:
I draw the solid in black, and then a representative slice, disc, washer, or shell in red.
Watch a slideshow of more examples of Bringing Color to the Classroom:
It is very important that the students use the same colors that you do when you’re working with complex concepts. It’s too much for a student to think “her blue highlighting is my pink highlighting and her yellow is my orange” on top of thinking about the mathematics.
And I keep a few highlighters in the classroom for students who chronically forget theirs.
This column appeared in the August/September 2012 issue of MAA FOCUS.
Maria H. Andersen is a Learning Futurist for The LIFT Institute and a Math Professor at Muskegon Community College. She is also president of Edge of Learning LLC (formerly Andersen Algebra Consulting LLC), an educational consulting business. Follow her on Twitter @busynessgirl or visit her official website.