## August 14, 2011

### End of Year Reflections: Geometry Favorite vs. Hard

Continuing analysis of student's reflections... (see first post for a full description)

Geometry CP students' Favorite Topics:

Ch 1
Ch 5
Ch 10
Ch 12
Triangles
Triangles
Solving Triangles
Similar triangles
Ratio/proportion
Proportion
Area
Area
Area/Volume
Trig (interesting)
Pythagorean thm
Pythagorean thm
Translation
Polygons
Polygons
SAS etc. Theorems

Geometry CP students' Hard Topics:

Nothing
Nothing (if I paid attention)
I don't know
I don't remember
A lot
Everything
Everything
Everything
Everything
Everything
Everything
Triangles
Finding lengths and angles
Ratios/proportions
Trig
Trig
Trig
Trig
Trig
Trig
Trig
Trig
Trig
Trig
Trig
Trig
Trig
Proofs
Proofs
Proofs
Circles
Area formulas

What's the most striking thing? The million Trigs!
That pattern isn't surprising to me at all. I haven't figured out yet what I will do next year (suggestions??), but Trigonometry was the only section where I had students asking "When will I ever need to know this?" We studied plenty of topics that were difficult (at best) for students to see the applications of, but they never stopped to ask that question because they were interested, involved, curious and they understood enough to be able to work toward the problem. In trig, that didn't happen. I saw confusion, frustration and kids giving up. It may have started when the first investigation we did gave data that was too far off to see real patterns (perhaps technology would be better than measuring by hand for this?) or perhaps when we started synthesizing too many ideas at once. When 'solving a right triangle' (finding all the side and angle measures given a few) we applied angle sum rule, pythagorean theorem, trig ratios and a lot of algebraic manipulation. Next year I'd like to do more problems throughout the year that synthesize topics so hopefully that won't be so overwhelming. Last, but certainly not least, trig was the first topic we did after MCAS (the state exam, required for graduation) and students feel like they should be done when they've finished that test (even though it happens mid-May and we didn't finish until June 29 this year). Overall, trigonometry got a bad deal last year. I'll try to do it more justice in the future.

Proofs are another challenge, and I believe that a lot of that is related to how they are presented. Student in my classes are accustomed to "defending their answers" and usually can do so well. However, when it comes to writing a proof they get caught up in format, and formal language. Precision is key and I certainly want my students to be able to write concise and carefully worded explanations, but I wish that they were more willing to just write something to start with. Does anyone have a method of draft proofs or easy entry formats?

Otherwise, I appreciate the overlap of favorite topics and hard topics. Different students had different preferences, and geometry has plenty of variety so most students get to experience a balance of topics they enjoy and others that they struggle with.

Take aways:
Do multi-step, synthesizing problems (before Trig)
Make proofs more 'low threshold'