# Teaching with Tech

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.

#### 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.

#### Piecewise functions:

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 *x*^{2} terms in another color (and their equation); and so on.

#### Graph transformations:

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.

#### Gaussian elimination:

When you’re performing an operation such as *R*_{1} + 2*R*_{2} → *R*_{2}, highlight the old *R*_{1} and the entries for 2*R*_{2}, then add them. Highlight the new *R*_{2} 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 the Director of Learning and Research at Instructure. Prior to this position, she taught mathematics at Muskegon Community College for more than a decade, and directed the MCC Math and Technology Workshop for five years. You can find Maria on the Internet at busynessgirl.com or @busynessgirl on Twitter.