This was my warmup today:
Draw a hexagon.
Draw a six-sided shape.
I followed up in our discussion with “Is a hexagon a 6-sided shape?” and “Are all 6-sided shapes hexagons?” Tomorrow they’re going to be in groups to categorize the shapes from Christopher Danielson’s Hierarchy of Hexagons project. These are my probably incoherent notes:
1st Period: Tenth graders were taking the ACT Plan, so they were not writing down warmup. Still had time to have a lively debate about hexagon- I had asked them to draw a hexagon and a six sided shape. Then I asked if they were different? Lots of people said yes, so we had to look up the definition of a hexagon
3rd Period: 4 9th graders only due to testing. Had them do the warmup- they focused on the definition of hexagon as having 720˚ internal angles. Were able to prove a polygon a hexagon by reasoning using the right angles. Then inferred that this example meant their previous notion of what a hexagon was needed to expand. WHOA. Then we worked on groupings- group the hexagons from Chris Danielson however you want. All 4 of them put each hexagon into one category only- I asked them if they thought a hexagon could be in more than one category. They were not convinced, but I could also tell they were rapidly losing interest. Next time I would try to push them more to write down more categories. Pics (disclaimer: one board is mine).
5th period: Got hung up on the terminology “irregular hexagon”. Big argument (unsettled) over if “irregular hexagons” could be called “hexagons”. S: “Why do they have the name irregular hexagons then?” Good question. First time seeing some people draw a six-sided shape as a 3-D rectangular prism or cube- different interpretation of the word “side”. Reminds me of Chris Danielson’s video “One is one. Or is it?”
6th period: Much less debate than 5th period. More students came up to board. Used online definition of hexagons, was able to use that to prove other shapes were hexagons. The 3D shape came up again. I felt good that we forced the need to define hexagon, especially with the 2-D “flat” and the fact that the sides didn’t need to be any particular length.
Many students had an idea of how a hexagon was “supposed” to look, probably based on a vast majority of experience with a hexagon being regular and not as much, or any, experience with irregular hexagons. Makes me realize how important it is to show a bunch of different examples to use to test any definition. Also makes students start thinking about how to go by definitions instead of just looks.
Was able to do small groups with proofs today. I let them self-select into my facilitated group while the rest of the class tried on their own and checked against answer key posted online.
Identified where individual students had trouble
Automatic buy-in because of the self-select
Students who were working independently were excited to try the proofs on their own
Let students get to really talk about ideas- especially one student who hardly participates suddenly jumping in all the time
I know there are some students who should have been in my group who weren’t. This is totally on me because I should have snagged them anyways, but just didn’t have the energy to fight that battle today.
Only got through 1 proof
Still have a nagging feeling I was doing too much talking. Maybe they weren’t quite ready? Fine line where productive struggle separates “blindly following teacher’s method” and “floundering in the dark”
On a related, but separate note, I just came across this article/research paper by Jo Boaler regarding her research on math education. This is a must read!! http://nrich.maths.org/content/id/7011/nrich%20paper.pdf
Today in Geometry we did group presentations. I struggled with this because I had not given very much feedback to the groups on their proofs prior to their presentations. The bad news was, an overwhelming majority of the groups’ proofs were glaringly incorrect. The good news was, this process allowed to me to take specific notes about where the groups’ misconceptions were- did they mix up words and symbols? Did they know how to use a certain piece of given information? Super enlightening. On the other hand, can I justify that if a proof was correct, the entire group knew how to do it?
In dance, we often have to stop and find our center. I need to do that with teaching as well. I’m in my third year and it is feeling scarily like my first year all over again- noone wants that.
Where I’ve lost focus:
Creating quality lessons that highlight problem solving
How I’ll get it back:
Make a point to check on blogs DAILY- other teachers around the country/world inspire me. I need inspiration to feed my growth! MTBoS is like Miracle-Gro for math teachers.
WRITE MY OWN BLOG. As Dan pointed out, it’s been a long long while since anything came out of here. Force accountability by having someone check my blog every day!
Get friends in industry to give highlights for qualities/traits that they have found most useful in their jobs. Shoot a quick video and show to students- rewrite goals for math class. What is most important?
Where I might struggle:
Too much negative re: chatting/classroom management –> As lesson quality increases, student engagement increases, student redirection decreases.
Too much to do –> Focus on priorities, keep running list. Lesson planning/blogging comes first!!
Ok, I think that is good for now. Any comments/suggestions/encouragement/feedback/accountability is more than welcome!