Reversed Teaching

Teaching transformations in the past looked like this...
1. Pre-assess students on transformation vocabulary and understanding by having them describe Ms. PacMan's movements.
2. Introduce vocabulary and what each transformation looks like.
3. Describe sequences of transformations.
4. And finally introduce the coordinate plane to get to the math behind each transformation...written in coordinate notation.

This year, I reversed it.
I kept the video game theme, but sought out Mario instead.
I pre-assessed with graphing coordinate points to see where the misconceptions popped up.
And then we set to work...
Analyzing Mario on a coordinate plane when he
     jumped up,
         ran forward,
            slid down a pipe,
                jumped forward,
                    grew bigger,
                         shrank,
                             flipped around,
                                 and when he turned.
Our goal was to understand the math in coordinate notation.
Along the way we reviewed ordered pairs, quadrants, vocabulary, and negative numbers.
We ironed out misconceptions and constructed new learning.
And after each movement of Mario, we were able to model his movements on the screen abstractly with coordinate notation.
Not only could students write the coordinate notation, but interpret what each notation meant in reference to movement on a coordinate plane.

By starting at the end and moving in reverse, we were able to treat the little things along the way as little side trips, while we continued to focus on the main concept of coordinate notation.

Now, as we move into sequencing, I'm excited to see the depth at which it will go.  My goal is just have to students understand how a shape can undergo a series of transformations to move from one spot to the next.  But my guess is that some students (or classes), will take it much farther than that and want to record this sequence in the most efficient coordinate notation possible.

Observations:
In the past, students have struggled with understanding rotation despite my attempts at starting at the concrete and moving to the abstract.  This year, by creating their own understanding for translations, dilations, and reflections, rotations seemed to be much easier.  Students were adept at analyzing data and were quickly able to see the structure in the ordered pairs (math practice 8).  By them creating their claims, including evidence and discussing their reasoning, the understanding was far beyond when I tried to "teach" it.