Skemp & Fractions

While my desert island article is the one where Brian Cambourne shares the Conditions of Learning, Richard Skemp's “Relational Understanding and Instrumental Understanding” (reprinted in Mathematics Teaching in the Middle School, September 2006) is not far behind. And it may be better to discuss with preservice math teachers, since it doesn't require transfer from literacy to math. Despite being a rather difficult read, it never fails to provoke good discussion and deep thinking.

Previously on the blog I have: interviewed a baseball coach/math teacher about relational understanding, recorded student discussions, and a post about the article. So thisis only the fourth post, it's not like I'm obsessed.

I don't give a formal homework assignment too frequently, but still do for this reading as support is helpful. (Assignment.) I also have a workshop for use in class:

Skempification

After time to work through the questions, Sam led the start of the discussion. She hit the ideas of relational and instrumental, and solicited examples of the contrast for fraction addition and subtraction. But as she noted - it felt like multiplication and division was where the really interesting bits would be. So I split up the groups among multiplication and division and then recorded their quick explanations.


Loved that the key question "3/2 of what?" came up here. I was fascinated by the "sometimes it works, sometimes it won't" idea. That's a real vestige of instrumental understanding, when we are given rules but often not the conditions under which they apply.


We discussed the grid here for what might confuse students, and tried to connect back to context. Students often want to draw a picture for all the quantities, even though there is not 1/6 of a whole here, but they were taking 1/6 of 1/2.


The lack of a picture was good here, and we discussed how relational doesn't mean with pictures. I tend to ask them about pictures to push their understanding because they are more likely to have rules for the numeric than the visual. Although the grid method can become very rule driven, just like the numberline for integers. This discussion was also grounds for discussing the difference between explaining why a method works and justifying that it does work. 


In the last explanation we were getting close on time, but they posed a couple good why questions to which they struggled to good answers. 

One thing about university classes is that it can be hard to get them to ask each other questions as the duck and cover principle is well learned. I try to stress that the discussion is one of our best tools for pushing understanding, and in math ed classes, I try to frame it as teacher training - you need to practice posing questions. Still tough sometimes.

I'm satisfied that they see a difference in the modes of understanding. Fractions are just such good content for this, as math majors' computational fluency is strong, but they can tell there are things they don't get. One of the gratifying parts is how much they want to get it, and take on the goal of getting their students there as well.

Bonus: as they write their next blogposts, we might see some writing on this as well. First one in is from Matt - Instrumental vs Relational.

Nova Now Notes

This is the school. Srsly.

One of the questions posed during Nova Now 15, a state conference focusing on discussions among teachers, was 'should conferences end with a reflection session instead of a keynote?' Any opportunity to encourage teacher writing.


So now I feel obligated.

As with Twitter Math Camp and EdCamp, this is a conference organized on the principle of creating teacher conversation and collaboration. It's hosted at Kent Innovation High, where, frankly, I wish I could send my kids. It's a tech friendly, open design, project based learning school. Kids attend in the morning for core classes (science, math, ELA, social studies) then return to their home schools all over the ISD for the rest of their schedule. The conference starts off with a tour and chance to see the learning happen, and then several students take the option to stay and be part of the conference, even coming back on Saturday. The single most frequently heard comment for me was about the eloquence, maturity and phenomenal perspective of these students. My favorite #KIHway quote from Peyton: "Students have to shift from doing this to make people happy to 'I'm learning how to be creative and productive'."

Even before the conference started, I had a great talk with Laura Chambless. She's the K-7 math/science support for St. Clair region schools. She's got her resources organized in a protopage. (Free start pages that can also do RSS feeds.) She's a big believer in fact fluency and has been trying to find ways for teachers to get at that constructively.

#michED is our statewide Twitter chat. Wednesday evenings, 8pm ET. The first big session was a meet between the east side and westside collaborative groups, Innovation Now and the Bluewater Group, moderated by Rushton Hurley. He did a good job of guiding a discussion, and using that to also make his points. Some big ideas raised:

• Isolation is the cancer of the teaching profession.
• Good ed leader question: how many times have you deviated from your plans? Because that's a measure of how many cool moments you've facilitated.
• We are not good at sharing successes. Why are you a good teacher? "I care about kids." Who doesn't? Share specific successes as individual teachers and as a school. Share them with voters!
• Gamestorming, co-creation tools.

Derek Braman led a session on student blogging. Mostly ELA teachers - I want to hear how content teachers are using it, too.  My big takeaway was an activity he uses to introduce blogging. Have students write a list of some of their passions. Pick one to write about on paper. Then circulate and leave comments for people on stickies. I'll try that next fall and share how it goes.

'Math: are we doing it wrong?' was led by Rick Jackson, who kept good notes on resources - http://bit.ly/1zWbae1. Dan Meyer came up, PBL in math with the KIH teachers, SBAR, flipped classroom ... all the good stuff. Infuse Learning was recommended for BYOD formative assessment. Teachers were surprisingly reluctant to discuss, surprisingly given the context, but there were two KIH students who killed it in the conversation. 

• "We have to still follow state standards, which have nothing to do with learning or critical thinking."
• "The pioneering spirit is a big part of KIH, shared between teachers and students."
•  "Students have to shift from doing this to make people happy to 'I'm learning how to be creative and productive'."

Ben Rimes led a session the next morning. (His notes, which include the cards.) Out of all the good stuff going on,  he won me with teases about the world premiere of his Keynotes for Humanity game. The game itself was a great discussion piece - I should think about how to use the Cards Against Humanity structure in math class. (Make your own.) The point about the keynote's role in ed meetings was that we need to think about it's purpose and utility.

Jeff Bush (@bushjms) and Rebecca Wildman (@RebeccaWildman) had a session on student centered classrooms. (Their ) One of the hallmarks of a meeting like this is that being discussion driven, the sessions may not go according to plan. Two of their tasks for us took over the discussion. Find a video that represents you as a teacher. The most fun:

• Rebecca thinks about digital natives.
• Jeff thinks teaching is like... this.
• Tara Maynard feels like this some days.

The second task was to make an infographic of a topic. I haven't tried this yet. Rebecca assured us that there are infographics on everything, and that seems to include math topics. Good synthesis assignment. Kate Kling recommends http://piktochart.com for a free tool.

The last session I attended was Jennifer Bond's creative play. (@teambond; her Google site.) What I learned is she has the best toys. The littleBits are very curious. Another good resource is the Imagination Foundation. Best quote: "if you give them open-ended time, you'll have their attention week after week. They don't have time to play." Sad to think about students not having time for real play. Jennifer ran a creative play club for which students applied. Every single form I saw, these elementary students considered themselves creative. By the time we get them in college, few people claim that. What are we doing so wrongly?

My session was on Talking Points.  I'll write about that separately! I had an awesome group of teachers to share them with and discuss them in other disciplines.

Some other neat bits from the conference:

• Ted Talk by @TrevorMuir who led "Do It Big".
• Todd Bloch's (@) storify of the conference.
• David Theune (@DavidTheune) on attending conferences with students
• Tara Maynard (@tmaynard5) What is Flipped Class?
• Ron Houtman's (@ronhoutman) photos from NovaNow

Good or Bad?

Are you a good teacher or a bad one?

Image by Gillian (?)

STOP! It's a trick question. Loaded.

If you say good, you're arrogant, you don't understand how good teachers are always trying to get better, you're not aware of your faults or you're just blind to the signs.

If you say bad, you buying into some kind of talent argument, ignoring growth mindset principles, falsely humble, don't even know what formative assessment or SBAR means or, worse, you're guilty of one of the big teacher sins like low expectations, no classroom management or ...  I gasp to say it ... LECTURING.

Are some teachers better than others? Of course. I see them at work every day, in my case. Do I want to know how to get better? Of course. I think about it rather obsessively. Is it helpful to classify teachers? Of...

I don't know. I'm open to arguments, but everything I know and has experienced leads me to say no.

Part of the academic life at university is this periodic vetting of our colleagues. Who is good enough to stay?

So we have to functionally label people as good teachers or bad. Since we are so bad at measuring teaching, our main tool for this is student evaluations. This is not the purpose for which student evaluations are meant. But they have pithy comments, and numbers we can average! I can pretend it's data about the quality of teaching!

Tenure is a weird construct, and I understand why it makes people fidgety. Ultimately, my view of it is colored by my brilliant advisor, who saw it as freedom. Freedom to pursue interests instead of quantitative measures, which will produce more innovation in the long run. We want to know, what will people do with their freedom? Which is one of the fundamental problems of freedom.

I'm fortunate, in my view, to be at a university where teaching is the major factor in tenure. Getting a little less so, but it's still the case. There are not many public universities like this. Send us your children, because they are going to get a better education here than almost anywhere.

But it also brings us to these moments of passing judgment. If I'm against classifying good and bad teachers, how do I make my decisions?

Photo by VD Veksler

Is the colleague interested in teaching, working on their teaching, selecting good goals, seeking out professional development that will move them forward? If yes, then I hope they are different than I am, teaching for different goals, working on different teaching problems. Because then, as a faculty, we will be the better for it.

I don't want to judge where I think your path is going. I want to hear you talk about your journey. If you're willing to share it, let's get a coffee.

Te invito. My treat.