# Daily Archives: September 29, 2011

## Goodbye Paperless Classroom, Hello Collaboration

After a three-week experiment, I’ve decided that I’m going to downgrade my classroom from “paperless” to “minimal paper usage.” Every student in our school is given a tablet computer, which is awesome, yet very few teachers take advantage of the tablet capabilities of these computers. I thought I would try this year and had every student bringing their tablet to every class. We have been taking notes and doing homework with Microsoft OneNote. The cool part about this is that I have their notebooks shared with me on our school network, so I can check out their notes if I want, AND no one has to rip out paper from their notebook to hand in, only to lose it when I hand it back (or, on the rare occasion, have me lose it). OneNote automatically syncs with their shared notebook on the network,* so I can grade their notebooks on my computer without them sending anything to me, and then they can automatically see my marks on their homework notebook the next time they open up their computers and sync – without me sending anything to them*. This, I have found, is absolutely awesome. It’s more efficient and more organized and I think saves a considerable amount of valuable class time.

But the in-class tablet usage is another story. Here are the downsides:

**It has taken them like an average of 6.8 minutes* to start-up their computers**and get going every class, which is possibly the most annoying thing in the world. My hairline recedes a little bit at the beginning of each class from the stress of the wasted time – I couldn’t have kept that up for very long.**Our tablets are not reliable**. Every class, someone’s computer wont start, the pen wont work, the screen wont flip to the right orientation, a computer will spontaneously light itself on fire etc. etc. I’ll get a hand raised every lesson with someone asking me an annoying tech question that I can’t answer and I have to make the choice of whether to help them out or to keep going with class and let them fend for themselves. As an efficient/impatient person, I choose the latter, sorry kid!- Most importantly,
**there’s a weird invisible barrier between everyone with computers in front of them**. I have found that the level of collaboration in the class went way down. I could have predicted this with regular laptops, but I would have thought that the tablet would feel just like a regular notebook. But something about that extra weight over a notebook keeps people from scooting over to see what a neighbor is doing, keeps the computer flat on the table instead of being able to show someone else, and keeps students eyes down more often than up.

Final decision: I’m keeping the tablets for the homework (where efficiency is paramount and collaboration doesn’t really matter), but ditching them for in class stuff. Though I’m sad it failed, it helped me really realize what I value in my classroom. Frank’s famous $2 Interactive Whiteboard post really captures well how technology can actually *restrict* modalities of learning though it can expand our abilities to visualize and manipulate things. And even though I read that a few times this summer, it took the experience of the tablets to make me really understand what he was talking about.

So what did I do? I had the school order whiteboards for the math department. And we used them today to play the Mistake Game, where students present the solution to problems and purposely hide a mistake in their solution. And it was awesome. My favorite math class of the year by far.

I guess I’m willing to sacrifice a tree or two for mathematics sake.

*[See the mistake(s)?? Kind of a silly one.]*

**Educated guess. I’m not ridiculous enough to actually time that and record the data.*

## Students Identifying Misconceptions (Instead of Me)

At the Klingenstein Summer Institute this past summer, a really transformative experience that I think is going to help me bridge the gap from rookie teacher to low level intermediate teacher (I set ambitious goals), we talked a lot about identifying **MISCONCEPTIONS** as one of the roots of good teaching. In the math teacher group, one of the challenges that we decided would challenge ourselves with was* to design an activity/lesson where the students would realize that they had a misconception on their own without me explicitly telling them*. Here was my inadvertent attempt…

**THE ISSUE:** In a extraordinarily weak non-AP Calculus class* (for now! and only compared to last year’s group, – growth mindset!!),* we just spent about a week and a half talking about limits. Nothing fancy, basically just graphical and numerical limits. I had a really hard time getting going this year and do not think I did a good job at all of creating a student centered, constructivist classroom… and it showed. We had a quiz on numerical and graphical limits, and… wow. I was genuinely surprised at how low the conceptual understanding was of the main idea of limits.

**THE MISCONCEPTION:** Among many misconceptions, the biggest one seemed to be that the limit as *x* approaches a certain value is affected by the value of the function there. This mainly manifested itself with tabular limits* (in which students put that the function is undefined at a point, and conclude the limit does not exist)*, and with open and closed endpoints on piecewise functions *(closed meaning – in the teenage mind – that the limit does exist, open meaning it does not)*.

**THE ACTIVITY:** I made a four stations around the classroom and each one had 3 or 4 different functions represented either graphically or algebraically. The goal was to determine the left, right and overall limits of each function. For the tabular limits, I put a green piece of paper over the approached x-value of the function in the tables. I asked them to first determine the limits before lifting up the green piece of paper. Then lift it up, check out what the behavior of the function is like at the approached point, and see how their answers change.

The catch was that all the limits were the same. This was patently obvious with the green strip over the function values – I could see the students at each station talking and being like *“What? They’re all the same…”* Then, they lifted them and were like *“What?!? How can that be?”* The other stations were similar, except that I represented the functions graphically instead, covering up the whole x-value on the graph:

After everyone passed through all the stations, we debriefed. We talked about what changed when you lifted up the paper and what didn’t (okay, maybe this is explicitly pointing out the misconception, but only after most students realized it on their own). I asked what the point of the activity was and one student eagerly raised his hand to say, *“I think the point was to show that when you lifted up the green strip, EVERYTHING about the limit changed because how the function is defined underneath.”* Right, except… wait no, exactly wrong. But, from that we ended up having a good discussion and I really saw the right idea finally click in a few students heads. I really wish I had done this in the beginning instead of defining a limit more mathy-mathlike.

So the reason I decided to post about this? I got this encouraging bit of metacognition as part of a Reassessment Request:

on the table, in our last quiz i assumed that since there was an error at the limit the limit did not exist. we did the activity in class and it helped me learn that even though there might be an error or a weird number, there is still a limit if it is going to the same number from both sides

Success! Misconception realized. Exactly right young mathling. Even with the rough start, maybe this will be a great year after all.