We started this conversation on Twitter and I don't want to lose all the great ideas we came up with there (in fact, searching the hashtag #rethinkgeo already gets no hits on twitter!). For now I will just copy and paste, later we should parse out the good ideas and expand on them elsewhere. Of course, since this is twitter, read bottom to top. Not sure what's up with all the stars, they input themselves automatically!


**__Matt Enlow__** ‏@**CmonMattTHINK**
Thought: Would replacing "always"/"sometimes"/"never" questions with "must be"/"could be"/"can't be" questions help students with the logic?
I just feel that they understand a sentence like "A rectangle COULD BE a square" better than "A rectangle is SOMETIMES a square".


**__Matt Enlow__** ‏@**CmonMattTHINK**
@**PamLPatterson** @**crstn85** @**druinok** Anyone used Edmodo? A non-math colleague is a big fan. Creating & sharing diagrams always a challenge, tho.

**__Matt Enlow__** ‏@**CmonMattTHINK**
@**druinok** @**crstn85** Like, "Is it possible to have a 30-60-90 triangle whose sides are all whole numbers?" Leads (probably) to conjecture: "No"

**Matt Enlow** ‏@**CmonMattTHINK**
@**druinok** @**crstn85** Well, I'm thinking more "What if..." kinds of Qs. Taking ideas and tweaking them. Conjectures are great too.‪#**rethinkgeo**‬

**Tina C** ‏@**crstn85**
@**CmonMattTHINK** @**druinok** Matt's original idea was have them try to make lots of triangles based on criteria, then ask questions‪#**rethinkgeo**‬

**__Tina C__** ‏@**crstn85**
@**CmonMattTHINK** @**druinok** I do a lot of conjecture now but my experiments are narrow, I'd like open exploration with lots of ?'s‪#**rethinkgeo**‬

**Matt Enlow** ‏@**CmonMattTHINK**
@**__crstn85__** Yes. I am a technology skeptic in general, but I think something like a wiki or Moodle would be a good way to do this.‪#**rethinkgeo**‬

**__Tina C__** ‏@**crstn85**
@**__CmonMattTHINK__** it would be great to find a way to keep track of open questions that we might need to come back to later‪#**rethinkgeo**‬

**Matt Enlow** ‏@**CmonMattTHINK**
@**crstn85** I also think that their Q's might not be ones that can be solved quickly, & we should help the students be OK w/ that.‪#**rethinkgeo**‬

**__Tina C__** ‏@**crstn85**
@**CmonMattTHINK** @**PamLPatterson** @**mathislife22** school is out, I'm ready to have this conversation! Agreed on them asking the ?'s‪#**rethinkgeo**‬


**Matt Enlow** ‏@**CmonMattTHINK**
@**PamLPatterson** I guess I personally would want the focus to be on getting them in the habit of asking genuine questions. ‪#**rethinkgeo**‬

**Pam Patterson** ‏@**PamLPatterson**
@**CmonMattTHINK** Nice start. Will try to get some thoughts together soon. Hope to get my new dept members involved too. ‪#**rethinkgeo**‬

**Tina C** ‏@**crstn85**
@**CmonMattTHINK** cool. Kelly P, Jarred R and I are intrigued. We will have to discuss further when my brain is unpacked, still a week left!

**__Matt Enlow__** ‏@**CmonMattTHINK**
@**crstn85** Yes, that's a big focus, getting them to ask their own questions. I figured you'd smell the PROMYS all over it... :-)

**__Tina C__** ‏@**crstn85**
@**CmonMattTHINK** so the goal is to encourage them to ask lots of questions beyond the prompts? We are intrigued (3 PROMYS alums in my apt now)

**__Matt Enlow__** ‏@**CmonMattTHINK**
@**crstn85** I think a lot of students will already have seen A=bh/2, and I'd be fine with not deriving it. GeoGebra would be good here too.

**Matt Enlow** ‏@**CmonMattTHINK**
@**crstn85** I figured they'd go all-analog for the most part (paper, pencil, rulers, protractors, etc.), but GeoGebra certainly has its place.

**__Tina C__** ‏@**crstn85**
@**CmonMattTHINK** do we assume they know the area of a triangle, do they use GeoGebra?

**__Matt Enlow__** ‏@**CmonMattTHINK**
.@**PamLPatterson** @**druinok** @**crstn85** Here are some initial thoughts about how a "Unit 1" might begin. ‪#**rethinkgeo**‬https://www.
https://www.dropbox.com/s/bjlewii2q0klwnh/triangle%20questions.docx

**Matt Enlow** ‏@**CmonMattTHINK**
@**druinok** @**crstn85** I figure we could go "backward" to logic after Δs, hopefully having created a NEED for it while trying to talk about Δs!

**__S T__** ‏@**druinok**
@**crstn85** @**CmonMattTHINK** we start geometry w/ the logic chapter (how to write definitions, counterexamples, etc)

**Matt Enlow** ‏@**CmonMattTHINK**
@**gogeometry** These are all so great. Do you create these problems yourself, or have you found them somewhere? Thank you for sharing them!

**__Antonio Gutierrez__** ‏@**gogeometry**
‪#**Math**‬ ‪#**Geometry**‬ Problem 760: Isosceles Triangle, Circle, Diameter, Altitude, Chord, Measurement. High School, College:http://www.gogeometry.com/problem/p760-i …

**__Pam Patterson__** ‏@**PamLPatterson**
@**CmonMattTHINK** I like it. While starting w/elements makes sense, it also causes students to disengage immediately.

**Matt Enlow** ‏@**CmonMattTHINK**
Our textbook does 3D stuff in its 1st (e.g. intersecting planes) and last (e.g. polyhedra) chapters only. What kind of sense does that make.

**Matt Enlow** ‏@**CmonMattTHINK**
What if we were to begin the year in Geometry not with points/lines/planes but with triangles? And then go both "forward" AND "backward"?