Category Archives: Teaching

Why the graphing calculator doesn’t matter anymore…

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I read a recent blog post Why the graphing calculator still matters in an ipad world. My intent is not so much to refute but to deflate.
I was at a technology firm focus group recently and they asked me how they could make sure their product was well incorporated into the high school environment and I offered the TI calculator as an example of how no matter how much you want to push your product, math classrooms are remarkably resistant to change. TI (thanks to our students, parents, governments, school boards and districts) have poured a fortune over the past twenty years into professional development for teachers, textbooks & resources for classroom use and classroom sets of (over-priced, in many cases) TI calculators. And yet, if I were to throw a stone at a random classroom (even if I were to only use those with classroom sets) would I see much effective TI calculator usage? Our Ontario ministry textbooks often look like a TI calculator manual, with step-by-step procedures and screenshots of the TI calculators for reference. Having been in classrooms throughout the Greater Toronto Area (and in conversation and observation of teachers around the province) I see very little usage (let alone sophisticated and deep immersion of the technology within the classroom) and certainly not of a type that would require the purchase of an individual device solely for math class.
I would argue that it is more cost-effective from the teacher, student, parent and tax-payer perspective to emphasize the use of portable devices (read: smartphones and tablets) that are inexpensive relative to their usage (the graphing calculator being a device little used outside of math class), ubiquitous and push the technology envelope in a far more competitive way than graphing calculators (the TI84+ uses a chip introduced in 1976). The use of mobile web-based resources to replace the functions of the graphing calculators would level the playing field; the burgeoning group of math educators blogging and twittering would expand on and distribute materials that would result. This is an environment far more likely to foment more real change than the past twenty years of effort on the part of TI.
Lucas closes with his insistence that the requirements of the AP & SAT tests will mean the TI calculators will continue to be a staple of classrooms. However, the AP Calculus exam is lessening the graphing calculator component and the use of CAS will become an issue of equity relatively quickly as they become more common. The Core Curriculum in the States will produce a whole new testing regime and one could easily envision an online testing scenario with the calculator built in … that online calculator will be what will be available to every students’ phone and tablet in short order.
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p.s. The sycophantic tone of the article (ex. TI has “an army of millions of devoted followers“) speaks to a common problem in the math community. TI has shown such largesse to well-intentioned, well-motivated educators that it often seems that the graphing calculator, in particular, the latest TI incarnation is the sine qua non of the exceptional math educator. While I have great respect for many of the teachers who are TI aficionados, it is occasionally difficult to separate their individual voices from the one they are typically paid to espouse in their roles as TI trainers or paid participants in TI training. Upton Sinclair put it best: “It is difficult to get a man to understand something, when his salary depends upon his not understanding it!”
Fair disclosure: I attended a free training twenty years ago on the TI81 and was a passionate user of the graphing calculators (requiring my students to purchase one) for the following ten years. Then I was fortunate enough to work at a 1:1 school and discarded them in favour of a more useful technology (except in my AP Calculus courses, when they had to be shown the six functions useful on the exam).

 

Conway’s Law

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We spend a great deal of time planning for the work we do during the Reflecting on Practice (RoP) time at the Park City Mathematics Institute (PCMI). We meet as a whole group for three days in the fall to get a global picture of what is going to happen, then we meet again in our smaller group (of six staff members, teams of two do the planning for one of the three weeks of the program) for another three day session focused on just the one week of work. Then, there’s online discussion of the materials before we meet again in Park City.
Each day after the RoP finishes, we do an analysis of the 75 minutes, how each of the three rooms worked (or didn’t) and take extensive notes on the materials so we (or anyone else who wants to use it) can modify it for the next time. Then we turn to the next day and make adjustments as a result. That’s an hour or two of time each day — okay, we are all a bit perfectionists but what we like is that the participants often push (or inspire) us to make the program the best it can be.
There’s a wide range of experience, from pre-service teachers to 20 year veterans. Some use no technology, others are dyed-in-the-wool techies. Some have just finished their Masters, others haven’t been a student themselves for years.
What does that have to do with Conway’s Law? Surprisingly, it is not JOHN Conway, who has inspired a lot of the work at PCMI. Instead, Conway’s Law is from a computer scientist Melvin Conway who said
“…organizations which design systems … are constrained to produce designs which are copies of the communication structures of these organizations.”
I think part of the strength of the RoP time (and indeed, throughout the PCMI program) is that it is developed by mathematics educators who struggle with the same issues in their classroom as the participants. The communication structures we use are based on collegiality, respect and an emphasis on criticism of content and process rather than individuals. The five people (and three “administrators”, although they never pull the admin card) are each extraordinarily passionate individuals and have strengths each within their own spheres. But we talk. Discuss. Throw out ideas that are way out there. Some are discarded. Others challenge us, we spend hours working on them and then, if it’s not going to work, we throw them out. No hard feelings. No obsession with credit or responsibility. We know we’re there for the participants and not for ourselves. And I think that environment in which we build the professional development is translated into our sessions with the participants.
Who designs your PD? And how?

 

Who am I to speak up?

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One of the (many) blogs I subscribe to, “PhD Talk” recently had an entry titled “Who am I to speak up.” While it had to do with the author’s encounter with the Imposter Syndrome as she worked on her research, it spoke to me as I considered both my own PhD research (Imposter syndrome writ large!) but also my role within the larger educational community.
There is a reluctance on the part of independent school teachers to engage too readily with the outside world. For one, it is a competitive environment for students, especially in this economy. If we share the best of what we are doing, then others benefit from our expenditures. Fortunately my school has always had the spirit of openness and sharing and has encouraged us to share whatever we have or created with others. We’re also a bit of a closed society; everything is very self-contained. We’ll often joke about how we seldom know what is going on in the real world. But, I will endeavour to share what I have collected over the past twenty years of teaching. It will not be perfect but that’s not entirely the point, is it?
Secondly, there is a strong public school / Catholic school community in Ontario in line with the teachers’ union through which most of the educational change discussion is filtered. The voice of independent schools is a slight whisper from the back of the chorus. It’s not a discussion table I get invited to; this has been particularly noticeable in my work at the university this past year. It’s also stung, when my registrations have been declined for online and summer programs in Ontario because of which students I teach. I don’t think we ever get out of high school — you have to learn to make your own friends and let the cliques to their own.
So it was interesting to find myself, a Canadian, deeply involved in a discussion of the Common Core State Standards with a wide assortment of teachers at PCMI this summer. It is a fascinating time during which we see the American school system try to re-invent itself to match more closely the approach taken in Ontario, at least as far as mathematics is concerned. I look forward to seeing how the Mathematical Practices, intended to be the tail that wags the dog of the “Standards”, negotiates with the American addiction to standardized testing.
That experience, to be recounted later, of thinking about and discussing with others the intent and ramifications of this approach to mathematics education reminded me that my intent has never been to change the world but only to change myself. To make my own understanding more clear and thus my work with others more profitable for them. That those others may turn out to be Americans rather than those in Ontario is merely an accident of geography, I suppose.
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Changing the world is too big. But I can do small things… and I’m a Calculus teacher. I know small things add up. So my goal is to publish some small bit each workday over this month before school starts anew to try to get into the habit. (I can’t commit to the weekend as it is often consumed by volunteering.)
For those Americans who may read this, Monday was a holiday.

 

OAME 2011 Presentation(s)

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I had a great time down in Windsor for the 2011 OAME conference. It was fun to see a lot of old friends and meet some new ones, particularly now that I meet so many math teachers on Twitter first. (memo: if you’re not on Twitter, how many new math teachers do you meet each year?)
My presentation was on mobile learning. As I mentioned at the beginning of the session, teaching at a 1:1 tablet computer school as I do, I have often felt guilty that when I was discussing the use of technology in class I was well aware of the huge equity gap. With modern smartphones and tablets, that gap is steadily closing. The conference organizers had me do the session twice and I was pleased with both the turnout and the contributions of the participants. The second time I used an auto-tweet tool (SAP – link) so that as each slide of my presentation appeared, a tweet with the slide’s major point was sent out with the #oame2011 tag.
I’m looking forward to Kingston in 2012!

Presentation: http://bit.ly/kCMgiO in 5Mb PPTX
Handout: http://bit.ly/liooRC in 1Mb Word DOCX
or
Presentation: http://bit.ly/jI38cN
Handout: http://bit.ly/lIVwun
(these are synced versions of Office 2010 files so formatting may be off in GoogleApps)

 

ECOO Reflection

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And the ECOO Conference has wrapped! What a great experience!
A number of people asked me how things went… I think the most extraordinary remembrance of the conference was the amazing group of people I had an opportunity to work with. I’ve been so lucky in the past to work with great groups of people at Appleby and at PCMI so it was wonderful to find another organization with similar energy and dedication. I can’t wait to work with them all again for next year’s conference.
How many sessions did I get to? Well, I got to all of them! Since my responsibility was the Presentations, I visited each one, although often it was peering through the door to ensure that everything was going okay. I kept reminding myself that my role at ECOO was not to attend sessions for myself but to make sure everything was in place to ensure that others could enjoy and learn. And I did get to meet a lot of educators from around Ontario and Canada interested in good teaching. I almost said technology but ECOO has moved far beyond being just a tech conference — it’s about teaching and learning and curriculum and assessment from all perspectives of the classroom and ed office. It’s such a rich and vibrant learning space for educators.
I loved my role… I got to communicate with presenters, some experienced and some novice. Their energy is contagious and their willingness to share is a credit to their profession.
I got to learn about mobile app programming, having started with one framework (iWebKit), getting it to work, tossing it out and using a new framework that offered more (jQTouch) and Chrome/Safari portability. I’ll start from scratch again next year — these frameworks are developing so fast that by then the possibilities will blow away this year’s planner! It was great getting back into database programming, too. I love the logic of SQL and PHP.
I also put QR Codes on all of the room signs so that folks could access the full description of each session through their smartphones. I strongly believe in a paperless environment even if it does put people outside their comfort zone (and they’re happy to tell you they’re outside their comfort zone!) Next year, expect to see QR Codes on a lot more material to make the flow of the conference even better.
So, get your proposals ready… only 4 short months before I post up the submission form! We’d like to make sure we broaden the focus (pedagogically, technologically, geographically) while deepening the experience for those attending. Your suggestions, comments and feedback are always welcome.

 

Teaching is hard

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I’ve been given the opportunity to sit in on a colleague’s class and offer feedback on his teaching. Now, as I mentioned to him, it’s a bit like gilding the lily: he’s already what I would consider a masterful teacher. I shall learn as much from him as he shall receive from me, I’m sure.
But Deborah Ball offers some advice that is helpful.

“No single issue is the essential one; none is definitively inappropriate. The traditional isolationist culture in teaching — that everyone has to find his or her own style, that admitting to reaching an impasse or having a hard time is tantamount to an admission of incompetence — has a crippling aspect of our work as a community of educators. (p. 34)

By opening his door, and by offering the example of opening his door he’s a great role model for the rest of us. And the discussion we’ll have about his choices will be valuable. I would argue that Ball doesn’t go far enough. It’s not just “reaching an impasse” but thinking that you’ve got the teaching process “down pat” that’s dangerous. I cringe, remembering “the book” at one of my first teaching placements — it contained the script of all my lessons I was meant to teach, all the examples, all the homework. They were well worn pages, too, and I was cautioned not to damage anything so that they could continue to be reused by all the sections in the coming years.

At the same time, although we know better, we seem to talk as though ‘a right way’ exists to motivate students, to teach place value or to respond to certain kinds of questions from students. On one hand, then we have pretended that we have nothing to learn from one another. And on the other, we have pretended that teaching is simple and straightforward. (p. 38)

Our focus will be on the discourse in classroom; who’s talking, when, why and how? Although this is just a personal project and nothing will be noted here, I hope it will serve to inspire not only my research but improvement in my teaching when I return to the classroom.

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Ball, Deborah. (2008). What’s all this talk about ‘discourse’?. In P. Elliott (Ed.) & Elliott, C., Getting into the mathematic conversation (pp. 32-39). Reston, VA : NCTM.

 

Dimensions

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Just a reminder of a group assignment from last year. I was actually doing a coverage of an AP stats class and wanted a record of their work for the teacher so I pulled out the cellphone camera; using the Share option, I could quickly email it to the teacher. All the tech? For the past decade i’ve been teaching at a 1:1 tablet school; very practical for math given that a laptop only gives you the option of typing — and math is not conducive to typing (most students do not view Latex as an option).

 

Changing directions

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(I thought I should squeeze this in given a link from a popular blog, Continuous Everywhere.)
I closed off my teaching this June for a year; in the fall I’ll be returning to life as a PhD student at OISE, the Ontario Institute for Studies in Education at the University of Toronto. I’ll be working in the Curriculum Studies and Teacher Development program — two big areas of interest for me. Stay tuned for updates.
I’ll hopefully have considerably more time to write & reflect. The only external responsibilities I’ve kept are the Auxiliary, the ECOO conference in November and PCMI, of course. For me, that’s not a lot. And I’ll be commuting in on the GO train (public transit) so there will be about 90 minutes of downtime each day in which to put pen to paper (electronic, that is).
I’m looking forward to have the time to “think deeply of simple things”. My focus will be on teacher development, an interest developed over my time with the folks at PCMI. It’s so energizing being around these folks — how do we capture the experience at PCMI and make it more accessible to math teachers everywhere, efficiently & effectively?