Graphical use in a Geometry Course

1. Graphics for Learning in
Geometry
By Liam Downey

3. 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.

5. 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.

7. 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.

9. 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.

11. 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.

13. 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

15. 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.

16. 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.