How I Taught Geometric Transformations

Starting geometric transformations I had two goals. 1) Be as student centered as possible. 2) Get the kids to do a bunch of mental gymnastics.

I wanted my students to develop their own understanding of the ideas surrounding translation, dilation and rotation. I did not want to rush them from the concrete to the abstract. They worked in small groups, 3 or 4, a few choose to work more or less alone. I didn't explain a thing to them, at least not as a whole class. I simply showed them examples of transformations and asked them to describe the results and create the rules...

I continued on like this with each type of transformation. The students did not find them difficult, but I was also never asked "whats a _______ transformation?"

I gave them examples of transformations asking them to identify and describe the transformation that had occurred.

Here the questions began, but often they were addressed to another student and not to me, "the teacher." I kept marching on, letting students work in small groups at their own pace. I asked questions forwards and backwards, inside and out, anyway that I could think of to let students more fully explore and create their own understanding.

The result was a solid 2-3 week unit. The unit needs revision, but it worked well especially for a first iteration. All of my files can be found in a Google Doc folder, the naming convention is a bit non-conventional, but hopefully it is clear enough. Any comments or suggestions would be welcome.

To give credit where credit is due, many of the ideas and some of the questions came from Visual Math. All of the images were created by Geogebra. 

For those who prefer bullet points:

Topics addressed

• Translation, rotation about a point, reflections across lines
• Dilation in one direction and two, by negatives and by values less than 1
• Vectors as a way of describing translations
• Transformations of coordinate points
• How to find the point of rotation
• How to find the line of reflection

What was awesome?

• It was nearly 100% student centered.
• Students could work at their own pace resulting in varying amounts of homework
• Homework was at a minimum, students worked and learned socially not in isolation
• My students are solid on ideas of translation, reflection and dilation - all ideas they'll encounter again with functions

What was less than awesome?

• Treatment of vectors was superficial - need quality problems to reinforce their use(fulness). 
• Rotation bits were rough, but not terrible. Could be fleshed out more.
• Finding the point of rotation and line of reflection were in the form of "follow these directions" not a structured or scaffolded inquiry 
• I need more open ended investigative questions for the students to explore and extend their understanding - These could function as a final assessment
• Ideas of symmetries could/should be added