More Motion Sketches

These sketches are to investigate the composition of motions, starting with reflections.  For a schema activation, I asked my preservice teachers to think about compositions.

Schema Activation:  What happens when you do two of a motion?  (Same type, not necessarily the same motion.)  Please guess if you don’t know.

Motions	Result-type	Know/Guess?
Translation then a translation		K/G
Rotation then a rotation		K/G
Reflection then a reflection		K/G
Glide reflection then a glide reflection		K/G

This brings up the idea of orientation both in terms of turning and in terms of face-up/face-down.

For a focus we have the following:
Focus:  Today we’re just going to concentrate on reflections and their compositions.  We have three different sketches to consider, and will also consider the questions that could be asked about each.  A composition of motions is when you make one movement and then another.  The combination is still a motion, as the original and image are still congruent.

We're also going to consider using questions to move us forward.  The types of questions described by literacy instructors are:

1. Literal - factual answer available or quickly available by recall, or can be found directly in the text.
2. Application - answer found by applying known method or looking up with slight modification.  The method of getting the answer is known.
3. Inference - answer requires prediction or extension from known information.  Can be an outright prediction or come from reading between the lines.
4. Analysis/synthesis - answer requires combination or deduction from other known information, possibly requiring a method not currently known by the respondent.

In the three sketches, the students are asked to take more and more responsibility for the questions they are answering.

Activity:

  Two Reflecting Lines:  webpage or geogebra file 

  Two Skew Lines:  webpage or geogebra file

   Two Parallel Lines:  webpage or geogebra file

We discussed these sketches together.  They asked about finding the center of rotation and saw a neat connection with the reflecting lines.  They also saw a neat connection between finding the center of a rotation and finding the center of a circle, but couldn't remember or figure out how.  They found a cool relationship between the direction and distance between parallel lines and the resulting direction and distance of the translation. 

Reflection:  What did you do during this workshop?  So what did you learn?  Now what would you want to consider next about motions or questioning?

Bonus: (or... extension)

Two Glide Reflections: webpage or geogebra file







Coming Soon:

• a tale of two lessons - why can't everything work?
• Sue's MathMama Dialogue:  what's wrong with math education?