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Winter 2003 Table of Contents

Versión Español de este artículo (Spanish Version)

Susan Osterhaus, Secondary Mathematics Teacher, TSBVI

*Editor's Note: In the author's words, "Although graphing calculators
are mainstays of most secondary math classrooms, it is important for all students
to understand the concept of graphing on a coordinate plane before they move
to the graphing calculator." This is especially important for visually
impaired students, and Susan Osterhaus, math teacher at TSBVI, ensures that
her students learn to do so manually _ they must physically plot points, graph
lines, and find slope. Below are her answers to questions about how to teach
this skill, and her suggestions for students, teachers, and parents. *

Most academic blind students, even those with spatial orientation problems, are quite capable of graphing, and as one of my students exclaimed, "Not only can we do it, it's fun!" There are several tools they can use to do so:

**The Graphic Aid for Mathematics**, from the American Printing House for
the Blind (APH), is excellent for graphing algebraic equations. It can also
be used in geometry, trigonometry, etc. It consists of a cork composition board
mounted with a rubber mat, which has been embossed with a grid of 1/2-inch squares.
Two perpendicular rubber bands, held down by thumbtacks, can create the x- and
y-axes. Points are plotted with pushpins at the appropriate coordinates. Points
are connected with rubber bands (for lines), flat spring wires (for conic sections),
or string (for polynomial functions). I like for my students to graph extensively,
and they can do so incredibly fast on the APH Graphic Aid. In fact, many print
students also like using it because it is fast, fun, and allows them to learn
graphing skills in another modality. You can make your own graph board by affixing
a piece of raised line graph paper (also available from APH) to a **cork board
**and proceeding as described for the Graphic Aid.

If a student needs to turn in copies of graphs for homework, he can use **Wikki
Stix **and **High Dots **on **APH graph paper**. This method can be
quite expensive, however, and is very time consuming. It also tends to be more
of a test of artistic ability than a demonstration of understanding of graphing
concepts.

** **The **ORION TI-34** talking scientific calculator (from Orbit Research)
and the **Accessible Graphing Calculator **(from ViewPlus Technologies) are
examples of more high tech solutions for graphing activities. I described them
in a previous *See/Hear* article (Winter, 2002), but strongly recommend
that students be able to graph manually as well. It is important for visually
impaired students to be able to use a variety of tools, and know when to use
each of them. For example, a former student decided to graph a quadratic function
manually because it was "too easy to bother with the computer." Yet,
he will use the AGC to graph an exponential function.

The APH Graphic Aid described above works well. Plot the points with pushpins and connect them with a rubber band when the boundary line is to be included in the solution (a solid line in print). Leave off the rubber band when the boundary line is not included in the solution (dotted or dashed line in print).

When graphing one inequality in two variables, I simply have my students place their hand on the shaded side. I check each graph as my students complete them. When graphing a system of two inequalities, the student places one hand on the shaded side of the first inequality. Then they place the other hand on the shaded side of the second inequality. Where the two hands overlap (including the boundary lines where applicable) is the solution. Pretty soon most of my students are able to handle three or more inequalities without multiple overlapping of hands. We even progress to linear programming problems involving four or more inequalities. In these problems, a bounded area with vertices is often found, and it is pretty obvious where the shaded portion (the solution) is located.

If a student-made, manually produced paper copy is required, the student could use APH graph paper attached to a corkboard. She could plot her points using stick-on high dots, puff paint, etc. and could form solid lines using Wikki Stix. She could actually use a colored pen, pencil, or crayon to color the shaded area of the solution. This would take much longer, however, and would be very labor intensive. It will be important to know the purpose of the assignment and the concept(s) being taught. A paper copy of a single function can be created on the AGC (it can't graph multiple functions on the same graph). Often, it is possible for a sighted person (teacher, peer, parent, teaching assistant) to make a print copy of the student's graph _ the visually impaired student graphs on the Graphic Aid and someone copies it exactly onto a piece of paper to turn in. You can also divide the Graphic Aid into 4 to 6 small, separate coordinate planes for multiple problems. If you have a digital camera, you could even e-mail or print a picture of the student's graphs. Better yet, have the student take her own photos!

Please be sure that visually impaired students are allowed to participate in all kinds of graphing activities and that they are supplied with the proper tools. I would rather see them become proficient using a rubber graph board because they will learn so much more with this method, and they can do so independently. Creative exploration should begin in the early grades and allowed to blossom. Remember, the beauty of a tactile graphic is found in the fingertips of the beholder. And there can be no more beautiful and meaningful graphic than one created by those very same fingertips.

APH Graphic Aid for Mathematics and APH Graph Paper: www.aph.org

Wikki Stix: www.wikkistix.com

High Dots: www.exceptionalteaching.com

ORION TI-34 Talking Scientific Calculator: www.orbitresearch.com

Accessible Graphing Calculator (AGC): www.ViewPlusSoft.com

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Last Revision: August 25, 2003