Teaching Graphing Transformations

Submitted by Tracy Fitch on Sep 05, 2018
APH graphing board

This was definitely a “think outside of the box” moment for me. Transformations are difficult to understand in the beginning for many students, sighted and visually impaired alike. Making it hands-on simplifies it a bit and builds the foundation of understanding for students. Before you try to incorporate higher level technology for graphing, it is important first to teach the foundational concepts using graphics and tactile materials.

What are Transformations? 

The different transformations when graphing are:

  1. Rotation: Rotating an object about a fixed point without changing its size or shape
  2. Translation: Moving an object in space without changing its size, shape or orientation
  3. Dilation: Expanding or contracting an object without changing its shape or orientation
  4. Reflection: Flipping an object across a line without changing its size or shape
A typical sighted student will use graph paper to draw the different movements of the shape. They are able to use color and/or rename the new graph A1, B1, C1 and A2, B2, C2, etc.
 
Graph showing dilation and reflection
 

So, the question is, how do we present the concept in an understandable way to our students who are blind or visually impaired and how do we give them a way to produce the work themselves?

 

Strategies for Teaching the Concept

  1. Rotation:
I will cut out a shape (to scale) using cardstock and place it using a push pin on the graph. You can also add another tactile element to the shape by outlining with puff paint and or puff painting a dot on each point. Literally have the student rotate the shape using the push pin pushed into the point that remains constant. They can turn the shape 45, 90 or 180 degrees, etc. (This would of course be done with card stock shapes on the rubber graph board and push pins.)

Rotation graph with card stock triangle

Rotating triangle on graph paper

When it is rotated the correct amount of degrees, place push pins into the other two corners of the triangle. They can then identify where the shape has moved on the coordinate plane. 

Triangle after rotation

 

  1. Translation:

Using the different types of push pins, plot the original shape with one type of push pin, then when they are translating by counting left, right, up, down, they will place a different type of push pin in the new spot of where the shape is moving to. 

Push pins on graph

 

  1. Dilation:

Use the same method as with translation using a different type of push pin to show how the original shape has grown.

 

 

  1. Reflection:

Use the same method as with rotation. Have student literally flip the card stock shape from one side of the x or y axis to the other side, reflecting it over the axis.

Triangle in top left of graph
 
Reflection demonstration
 
Triangle is flipped over axis
 

The push pins are great for allowing them to produce their own work as well. Once they’ve learned the concept of rotation and reflection, the push pin method can also be used.

Push pins on graph

The importance of the push pins is that they allow the student to keep the original shape that was plotted stationary, while manipulating and altering the new location of the shape with a different type of push pin. This is also a way for them to “label” their shapes.

 
Materials: 
  • Rubber Graphing Board (can be purchased through APH)
  • Card stock
  • 2-4 different shapes of push pins
 

Collage of teaching graphing transformations

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