How Do I Love Thee? Perceiving

Module 2: Assignment #1

For this project I needed to choose something well-known or familiar from the content we teach, observe it, and re-image it in a new form.  I thought right triangles would be a great image to observe and re-imagine.  Right triangles are a crucial part of Geometry and connect many different topics and ideas together.  Learning about right triangles dates back to elementary school math class, however they still tend to be a tricky concept for students to grasp.  There is so much to learn with their properties including their angles, names of sides, and how to apply various theorems and postulates to them.  As I observed my topic I found it easy to list characteristics and examples, but hard to describe the triangle with “non-mathematical terms”.  As I continued observing I tried to use all of my senses and although this sounds crazy, imagine what it would be like to be a right triangle.

At first I really struggled with re-imagining a right triangle.  It was difficult to “see” the image in another way other than what was in front of me.  As a former college athlete and huge sports fan, I started to imagine myself becoming the right triangle in sport.  I chose to write a basketball poem where I was the right triangle and detailed my multi-sensory experience.  It describes the last few plays of an exciting basketball game where I end up completing a right triangle as the hypotenuse to win the game.

For some readers, this piece may seem to have nothing to do with math or triangles.  I wrote it purposely without any math terminology to give a real life experience.  I sketched a picture of triangle that I see in case someone has trouble visualizing it.  The highlighted portion is the hypotenuse of the right triangle (c).


This re-imagining process forced me to really step back and look at something that has always been familiar to myself and my students in a completely different way.  By presenting the material this way, I may reach more students and bridge some gaps in understanding.  My head is spinning as I see several possibilities for lesson plans relating the Pythagorean Theorem and right triangles to sports: baseball, soccer, basketball, and football.  The most common question I am asked is, “when will I use this in real life?”  By using re-imaged right triangles for problems in math students will discover that they use this content without even realizing it.  I could have students go to the gym/field and act problems out, or create their own word problems.  Word problems are very difficult for them to understand when no diagram is given.  They also seem fake or scripted in the textbook.  By perceiving and re-imagining we can make math real and bring it back to life for our students.  Perceiving is a powerful cognitive tool that we need to bring into the classroom more often.  By using all of our senses we can discover new meanings, experiences, and a deeper understanding beyond what is there on paper.