We’re a week into the fall quarter—sweating out a hot August in class—and there are a few things I’ve done that I’d like to record for posterity:
- new wall diagrams (and seating layout)
- collaborative rule-setting
- Talking Points for communication skills
- traditional vs. standards-based grading in Haiku
Inspired by the great book Icons of Mathematics, I spent some time in the classroom this June and July, painting new diagrams on the walls. Eventually I would like them to reach all the way around the room and encompass topics beyond geometry. My diagrams now depict these topics:
- basic concepts (points, lines, planes, etc.)
- vertical angles and linear pairs
- concave vs. convex polygons
- basic constructions
- the arithmetic and geometric means
- centers of triangles
- the trig ratios for right triangles
- various depictions of the Pythagorean Theorem
- geometric transformations: translation, reflection, rotation, dilation, and projection
Some good candidates for future diagrams:
- the distance formula
- unit-circle trigonometry
- Venn and Euler diagrams
- Napoleon’s triangles
- mappings between sets (injective, invertible, composed, etc.)
- tangent lines
- integration via trapezoids or rectangles
Mainly, I’m looking to put up diagrams that will give students a vivid visual memory to associate with the topics we discuss in class. None of them are captioned, and that’s deliberate; I want students to be curious about the diagrams before we even get around to discussing them.
(To be clear: I wouldn’t blithely recommend this undertaking to all other teachers. Yes, there are instructional benefits, but it represents at least a good fifty hours of work after painting the base color. I freely admit I did it largely because it makes me happy to look at the walls and see the images as an integral part of my classroom environment—a not-inconsiderable benefit when I think about how much time I spend there.)
Furniture-wise, I scrapped a big table and replaced it with three desks, to have three groups of three desks, plus a table with room for four—enough for my classes this year. (Yay for small classes. Yes, I’m fortunate and thankful.)
Setting the rules
With the class seated in threes per my new room layout, we had some small-group discussions aimed at developing rules for us to live by this year. I present my main rule...
Let everything you do here demonstrate respect—for yourself, for your classmates, and for your teacher.
...and the students, in discussion, define “respect” and come up with a few rules—stated positively and always in effect, I require—per group. Most are pretty standard; for example:
- Call people by their preferred names.
- Use tools as they are intended.
- Give everyone their own personal space.
I have several students helping me out by setting a few rules each in large type, for me to laminate and place around the room.
For the second time, I’m using a communication exercise called Talking Points, which I acquired from a workshop from this post’s author at last fall’s CMC-North.
The link above describes how the Talking Points activity works. The biggest difficulties I have are that we tend to reply out of turn, and that students often have difficulty coming up with something to say in the second round. Here’s how I have addressed those problems:
- Frame Talking Points as a listening activity. (Which it is, at least in part.)
- Encourage students to use their second turn to reply and reflect on what others in the group have said. “If you have been listening closely the first time around, there should be something you can usefully say or restate.”
Last year I didn’t implement Talking Points until second semester (because I didn’t learn about it until December), but it did seem to help discussion quality as the students got more heavily into proof problems. I’m still a bit awkward with it, but it’s going better this time around. I expect that, between experience and an earlier start, I’ll find it helps get the students to discuss more productively, sooner.
This year the school has switched over to Haiku as our LMS, and for some of our SIS functions. I’m optimistic about the grading platform, though we found its attendance tracking doesn’t yet seem ready for use at our school. Happily, it does have clean support for standards-based grading, and I’ve set it up with two gradebooks: A traditional gradebook titled “Work Completion” (tracking only required work), and a standards-based gradebook, populated with my own learning objectives and my set of eight “mathematical habits” that roughly parallel the CCSS Standards for Mathematical Practice:
- Attend to detail and precision.
- Make and use models.
- Name quantities and figures.
- Bound and estimate.
- Seek elegance; remove needless detail.
- Use rules and patterns to be productively lazy.
- Prove facts deductively.
- Measure and quantify: apply numbers to shapes.
(I’ve also put those into an attractive poster form for my classroom walls.)
Now my only concern is whether the recording of SBG will be onerous. It never worked to kludge it into the traditional gradebook of PowerSchool (and my school didn’t enable SBG in PS), but logging multiple scores per standard should suffice.