We just finished our unit on similar triangles, and as par for the course, there were the typical shadow problems. I know from past experience that students have problems with these: they draw shadows going in 2 different directions .... they don't know how to set things up .... etc. BUT. I thought it was a geometry misconception problem. No. From deeper questioning of various students today, I see that some students have no concept of shadows.
* What makes a shadow ... or how is it made?
* How would you make your shadow longer if it's coming from a light post?
- move closer to the light?
* Draw the picture and point to the shadow.
- points to the hypotenuse.
How did I miss this scary fact in 12 years of teaching geometry? I guess I just made assumptions on why they were struggling, and didn't probe deeper.