Twitter+Conversations

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. <span style="background-color: #ffffff; color: #0084b4; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px; text-decoration: none;">[|‪#**rethinkgeo**‬]

<span style="color: #999999; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px; text-decoration: none;">[|**__Tina C__** ‏@**crstn85**] <span style="background-color: #f5f5f5; color: #990000; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px; text-decoration: none;">[|@**__CmonMattTHINK__**] <span style="background-color: #f5f5f5; color: #333333; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;"> it would be great to find a way to keep track of open questions that we might need to come back to later <span style="background-color: #f5f5f5; color: #990000; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px; text-decoration: none;">[|‪#**rethinkgeo**‬]

<span style="background-color: #f5f5f5; color: #333333; display: block; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;"> [|**Matt Enlow** ‏@**CmonMattTHINK**] <span style="background-color: #f5f5f5; color: #333333; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;"> [|@**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**‬]

<span style="color: #999999; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px; text-decoration: none;">[|**__Tina C__** ‏@**crstn85**] <span style="background-color: #f5f5f5; color: #990000; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px; text-decoration: none;">[|@**CmonMattTHINK**] [|@**PamLPatterson**] [|@**mathislife22**] <span style="background-color: #f5f5f5; color: #333333; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;"> school is out, I'm ready to have this conversation! Agreed on them asking the ?'s <span style="background-color: #f5f5f5; color: #990000; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px; text-decoration: none;">[|‪#**rethinkgeo**‬]

<span style="background-color: #f5f5f5; color: #333333; display: block; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;"> [|**Matt Enlow** ‏@**CmonMattTHINK**] <span style="background-color: #f5f5f5; color: #333333; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;"> [|@**PamLPatterson**] I guess I personally would want the focus to be on getting them in the habit of asking genuine questions. [|‪#**rethinkgeo**‬]

<span style="background-color: #f6f6f6; color: #333333; display: block; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;"> [|**Pam Patterson** ‏@**PamLPatterson**] <span style="background-color: #f6f6f6; color: #333333; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;"> [|@**CmonMattTHINK**] Nice start. Will try to get some thoughts together soon. Hope to get my new dept members involved too. [|‪#**rethinkgeo**‬]

<span style="background-color: #f5f5f5; color: #333333; display: block; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;"> [|**Tina C** ‏@**crstn85**] <span style="background-color: #f5f5f5; color: #333333; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;"> [|@**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!

<span style="background-color: #f5f5f5; color: #333333; display: block; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;"> [|**__Matt Enlow__** ‏@**CmonMattTHINK**] <span style="background-color: #f5f5f5; color: #333333; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;"> [|@**crstn85**] Yes, that's a big focus, getting them to ask their own questions. I figured you'd smell the PROMYS all over it... :-)

<span style="background-color: #f5f5f5; color: #333333; display: block; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;"> [|**__Tina C__** ‏@**crstn85**] <span style="background-color: #f5f5f5; color: #333333; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;"> [|@**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)

<span style="background-color: #f5f5f5; color: #333333; display: block; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;"> [|**__Matt Enlow__** ‏@**CmonMattTHINK**] <span style="background-color: #f5f5f5; color: #333333; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;"> [|@**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.

<span style="background-color: #f5f5f5; color: #333333; display: block; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;"> [|**Matt Enlow** ‏@**CmonMattTHINK**] <span style="background-color: #f5f5f5; color: #333333; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;"> [|@**crstn85**] I figured they'd go all-analog for the most part (paper, pencil, rulers, protractors, etc.), but GeoGebra certainly has its place.

<span style="background-color: #f5f5f5; color: #333333; display: block; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;"> [|**__Tina C__** ‏@**crstn85**] <span style="background-color: #f5f5f5; color: #333333; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;"> [|@**CmonMattTHINK**] do we assume they know the area of a triangle, do they use GeoGebra?

<span style="background-color: #f5f5f5; color: #333333; display: block; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;"> [|**__Matt Enlow__** ‏@**CmonMattTHINK**] <span style="background-color: #f5f5f5; color: #333333; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;">. [|@**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

<span style="background-color: #f5f5f5; color: #333333; display: block; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;"> [|**Matt Enlow** ‏@**CmonMattTHINK**] <span style="background-color: #f5f5f5; color: #333333; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;"> [|@**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!

<span style="background-color: #f6f6f6; color: #333333; display: block; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;"> [|**__S T__** ‏@**druinok**] <span style="background-color: #f6f6f6; color: #333333; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;"> [|@**crstn85**] [|@**CmonMattTHINK**] we start geometry w/ the logic chapter (how to write definitions, counterexamples, etc)

<span style="background-color: #ffffff; color: #333333; display: block; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;"> [|**Matt Enlow** ‏@**CmonMattTHINK**] <span style="background-color: #ffffff; color: #333333; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;"> [|@**gogeometry**] These are all so great. Do you create these problems yourself, or have you found them somewhere? Thank you for sharing them!

<span style="background-color: #f6f6f6; color: #333333; display: block; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;"> [|**__Antonio Gutierrez__** ‏@**gogeometry**] <span style="background-color: #f6f6f6; color: #333333; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;"> [|‪#**Math**‬] [|‪#**Geometry**‬] Problem 760: Isosceles Triangle, Circle, Diameter, Altitude, Chord, Measurement. High School, College: http://www.gogeometry.com/problem/p760-i …

<span style="background-color: #f6f6f6; color: #333333; display: block; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;"> [|**__Pam Patterson__** ‏@**PamLPatterson**] <span style="background-color: #f6f6f6; color: #333333; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;"> [|@**CmonMattTHINK**] I like it. While starting w/elements makes sense, it also causes students to disengage immediately.

<span style="background-color: #f5f5f5; color: #333333; display: block; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;"> [|**Matt Enlow** ‏@**CmonMattTHINK**] <span style="background-color: #f5f5f5; color: #333333; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;">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.

<span style="background-color: #f5f5f5; color: #333333; display: block; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;"> [|**Matt Enlow** ‏@**CmonMattTHINK**] <span style="background-color: #f5f5f5; color: #333333; font-family: 'Helvetica Neue',Arial,sans-serif; font-size: 14px;">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"?