Gail started by playing a little game with us. On her TI-Nspire software she drew a triangle and measured one of the sides . Then she locked the “area” and then moved one of the points. She asked “What do you think is going to happen?” Ultimately: What does a trace of all the places you can move one of the points look like? (Try it!)
Next game is what happens if we instead lock the perimeter and trace? What do you think will happen? (Try it – your hint is that it has something to do with the sum of two of the sides of the triangle.)
Gail’s point is that the only reason we ask questions is to find out what students are thinking. To probe or to push their thinking. If we aren’t doing that with our questioning, then our questions aren’t worth it. Tasks that push and probe should be our focus. A possible task – Which glider goes farther: one that starts at 25 meters high and goes 185 meters horizontally, or one that starts at 25 meters high and goes 155 meters horizontally. (One audience member asked which distance) This is an example of different context for the same concept. In terms of the Common Core this type of task hits a lot a the Math Practices.
Next: Draw triangle ABC. Construct the perpendicular bisector of sides AB and BC. Make a conjecture about the perpendicular bisector of AC. Move point A. What do you observe? Cool – but how can we make this problem more interesting? October recipes from No More Cookbook Math (Harper and Edwards 2011) has a rubric for thinking about Teacher Centered vs Student Centered.
Stein 2000 talk about choosing solutions, sequencing solutions, managing solution strategies, ask questions, consolidate the math using student work. Gail would call this “purposeful walking”. The work on formative assessment says that hands should never be up unless the student is asking you a question. You do the planning and choosing.
Say you poll the class on a particular problem (maybe TI Navigator style) what do you do with disparate results? You could have a representative from each solution justify their responses…or what about just asking the whole class what the people who answered A. were thinking, and what were the people thinking that chose whatever. Or what about pairing kids up with the goal of convincing each other that they are right. Then re-poll the class. Now you can deal with the outlying kids one on one.
Next we looked at the Nspire activity What_is_a_Solution. A simple and brilliant activity.
Lastly we did a sequence activity with the Fibonacci sequence and I’ll try and recreate it here if I can find time. In the mean time – here are Gail’s slides from the presentation:
Day 3 of Green Lake is a completely perfect day. The Lake is beautiful.
Glen teaches at BSU in Bemidji, Minnesota. I just noticed his shirt. It says WE ARE # .9! (with a bar above the nine). If you Google Glen’s name his site will be the first one that comes up. Glen had us look at some distance versus time graphs and had us try to walk them while the CBR kept track of our movements. The before and after shots look like this:
As I look at these I’m thinking about linking the discussion to transformations for the times when someone walks the graph in the correct shape but they started too close or too far away.
In Stage 2, I was facing away from the graph so I couldn’t see it and my 2 teammates described what I had to do. We started the graph and they walked me through it.
Here students start to use the language of slope. “Walk backward toward the ranger about 2 meters in 1 and a half seconds.” The beauty here is that the math serves the conversation. It is compelling and necessary to start using mathematical language. As a side note Glen mentioned that for the students he teaches (in a higher education setting) it makes the most sense to use Excel. He sees the kids getting more algebra benefit (than from, say, a graphing calculator) because they are labeling the columns in Excel and also seeing that a given input produces an output.
That was about it for the “slope” portion of the session and we spent some time talking about some recent research by University of Minnesota about NSF vs. traditional students that tracked them through high school and college. I’ll try to find this and link it up here. We also talked about the fact that Calculus should not be the holy grail anymore, but rather statistics. Glen mentioned that 80% of college students will need to take at least 1 to 3 stats classes in college for almost all professions. He also related a story about talking to the Engineer of the year in MN who hasn’t done any calculus since her sophomore year in college but does statistics every day.
If you send Glen an email he will send you an Intro to Mathematical Sciences Class Notebook which he and Dr. Derek Webb worked on. Ask about the islands activity also.
See also the Discrimination or Not? activity from the Navigations in statistics series.
Well, here we go. The Lake was beautiful on the way in and I am very excited to start another year at Green Lake. Apparently we will be the first group in WI or IL to use the new CX (color) version of the Nspire.
Ray’s main points:
The TI-Nspire is a computer, not a calculator and you have to adjust your thinking.
The relationship between Documents – Problems – Pages is key.
Anytime something is bold, it is defined.
Escape and Tab are key. If one of them doesn’t do the trick, the other one probably will.
Look at the corners of the screen to give you an indication of what is happening and what mode you are in.
In list and spreadsheet pages, a list has a name and spreadsheets are blank.
Adding a “problem” is only done one way (Doc –> Insert –> Problem) because it is a special thing to do that requires you understand item 2 above.
Adding a “problem” clears out all variables and you can start fresh.
delete, delete, delete will clear your history or graphs or whatever you’re looking at
Geez, let’s do some math already!
Ok, not quite to the math yet but here are some quotable quotes:
“The commutative property of exponentiation. The one property that every kid knows”
“The kids won’t always believe me, but they will always believe their calculator.”
Here’s a little math for you:
I’m doing this on my computer but it is exactly what the kids would do and see on their TI-Nspires.
Finally! The color CX’s are here.
They are quite a bit thinner and completely rechargeable (No AAA batteries!).
How about importing a picture and fitting a curve to it:
Lastly then, I’ll show you the last activity that we did. I’ve left out any discussion of the pedagogy of the activity and focused on what the Nspire can do. You can determine the value and implications for yourself. Cheers!
