Graphics for Learning in Geometry

By Liam Downey

Mnemonic Graphic• A simple mnemonic graphic, but of exceptional use to students.

Instead of having to memorize six steps (parenthesis, exponents, multiplication, division, addition, and subtractions) the students need only memorize 2 syllables (pem, das). This graphic alone would be an excellent scaffolding tool to use as a poster in the classroom to keep students comfortable in the proper order of operations.

Decorative Graphic• This is a common themed graphic found in middle and high school

mathematics classes, yet as warned in the reading, these can be more distracting than beneficial. As an educated professional, we know that the square root of negative 1 is i, but to put that fact in a geometry class at the high school level is likely just to add extra clutter, as the students will not be working with i. Worse yet, it could confuse them further, as they likely have learned that one cannot take the square root of a negative number, and now they see it on a poster everyday that they can.

Interpretive Graphic• For the construction unit of a geometry course, this graphic would

serve as a diagram of the parts of a perpendicular line, constructed with only a compass and a straight edge. No order of steps is listed, preventing this from crossing over into being a transformational graphic.

Relational Graphic• This graphic is a review of algebraic properties that come into play

again in the proofs section of a geometry class. It is important for students to remember the relation between 3+2 and 2+3, as the communicative property of addition, and 2+3=5 as the substitution property. Both of those are necessary properties for the execution of basic proofs.

Transformational Graphic• This transformational graphic is a nice little animated example of the

relation between pi and circumference. From this graphic alone, a student may be able to deduce the equation for circumference in relation to radius.

Organizational Graphic• Without getting into the numbers behind the shapes, this graphic

shows why a circle is so much easier to work with than an ellipse, hyperbola, etc. Just by looking at it, a student can tell that a circle lays flat, while the other shapes have some degree of slope that must be accounted for. It also provides a visual representation for which of the shapes could trend towards infinity mathematically, and which are bounded

Representational Graphic• The best use I can think of for this graphic is to project large scale,

while the students hold their calculators in their hands. The number of keys on a modern calculator can be daunting, but with a Representational Graphic, the teacher can point to a large scale example visible to the whole class, to draw each students’ attention to where a particular key is located.

Copyright and the Teacher• The main rule for using material seems to be “never deny a profit.”

Any material a teacher wishes to use must be common domain or purchased properly and used in such a small part that it does not render the purchase of the actual material pointless. A good rule of thumb is 10% of a music clip, picture catalogue, video, etc. can be used. An exception is media that has the explicit use of instructional purposes, but not entertainment or reward.