Let me say this about Phillips Exeter Academy – the showers in the dorms are FANTASTIC.

I wrote a note to myself this morning to share this fact. After living in an old house for years, and vacationing in rustic cabins for even more years, the strong steady water pressure with adjustable but stable temperature (uninterrupted by sudden flushes) is just one more bonus to this conference, whose end is, sadly, in sight.

Leaping from the start of the day to the end, Dan Meyer (@ddmeyer) spoke [inspiringly] this evening about Perplexity. I am an avid follower of his blog, dy/dan (http://blog.mrmeyer.com/), and an advocate of his approach to infusing the classroom with an empowered spirit of inquiry as a means to meet the myriad challenges of teaching math in an era of omnipresent, rapidly and continually changing technology. But in addition to engaging (in the best sense of the word), perplexing, and enlightening his audience, Dan gave us concrete suggestions (thank you!!!) for how to categorize/organize/efficiently store the overwhelming amount of information streaming toward us, how to employ readily available technology (e.g. our phones) in service of that process, and how to enliven our own spirit of inquiry in order to provide ‘perplexing’ opportunities for our students. It was yet another mind-expanding event in this week of continual enrichment and enlightenment. Did I mention he has a great sense of humor?

Other highlights of the day included a great lesson on Parabolic Art in Desmos by Mary Bourassa (http://mathgeek.ca/), putting together a chapter for a class iBook project on Louis Kahn, the architect of the Exeter Library (which, by the way, has a grandfather clock in the lobby and a grand piano upstairs), and some great group work in Number Theory, during which I actually articulated and modeled a pattern for one of the problems (a major academic breakthrough!). I am preparing a very brief presentation on Flatland for Friday’s class, and learned that the author, Edwin Abbott Abbott, was not only a mathematician, but a celebrated classicist, theologian and Shakespearean scholar. Not bad for the son of 1st cousins (hence the 2 Abbotts). And in my work on the Louis Kahn book, I discovered that the Trenton Bath House which he designed in the mid 1950’s is neither in Trenton nor a Bath House. It did, however, have an incredibly mathy design and mural.

In my Higher Mathematics course today, we were discussing the Socks and Shoes Property, a way of explaining inverses – in order to put on your socks and shoes and return your feet to their normal barefoot stage again, you must complete the actions in reverse. Our quantum mechanist posited the idea that if the sock was ‘fundamental’ [to be honest, I’m not sure what he meant by that] then you wouldn’t be able to tell which sock you put on first, whether both socks were on the same foot, or whether you could even tell them apart. He admitted that this did make him sound like a bit of a wingnut, and then tried demonstrated this with pieces of paper. Following this, we began a discussion in which we imagined ourselves fleas crawling around on a surface, not being able to tell whether it was flat, or a torus, or indeed how many holes were in the torus, and how we might use a string to help us determine that. This discussion intrigued all of the wingnuts in the room, myself included.

One final bit of entertainment, a video in which exponential growth is illustrated in one of the most entertaining ways I have seen. Enjoy!

My sojourn to New England enabled me to have a lovely Korean dinner with a long, long time friend (I believe we have known each other since birth….) who lives outside of Boston.  She is the head of school for a small private school in Grafton, and it is interesting to hear how an administrator must approach the needs and [well-set] attitudes of a long-time staff.   Politically I have big issues with the idea of independent [read: private] schools, but it is tempting to look at what education can be when it is divorced from the scrutiny that attends public funding, even if the vast majority of the population doesn’t have access to it.  Nevertheless, it was clear to me that my friend, the daughter of teachers and teachers-of-teachers, is a wise and judicious school leader.   I wish we saw each other more often.

Today was another day of intense academics, fun math teacher bonding, and new ideas.  The emotions I went through in my higher mathematics class covered a wide spectrum, and as I am typing this very sentence, I realize that this can be a powerful empathetic tool for me as a teacher.  Thirty minutes into class, after proudly putting my homework problem on the board (I arrived early to make sure I could post the one question I felt confident in answering!), I was completely lost, almost in tears, and plotting my escape.   I envisioned begging the conference administrator to transfer me out of the class, explaining to the impossibly young teacher that I am not getting anything out of the class, nor am I contributing anything, trying not to cry (hmmm…this sounds familiar…I think this happens in our guidance department…).   I did not, however, run out of the room, especially after I discovered that several of my classmates were also confused, and much more willing to let it all go and move on.  We changed topics halfway through the session, and suddenly I understood what was going on!  We received these lovely little squares, and were charged with defining and composing all of their symmetries.  Geometry! My one true mathematical love!   I was able to understand the assignment on my own terms and participate [finally].  I was doing great until one of my classmates said, “This reminds of me of Physics graduate school when we were studying Quantum Mechanics…”

After morning class, my new math buddies and I went on a bit of a treasure hunt in the science center where our classes are held.  Not only is the building filled with all of the amazing skeletons I have been sharing with you, but it turns out that the interior design of the building reflects scientific material as well.  What do these tiled walls evoke?

If you said the Periodic Table and a DNA molecule, you are right!! (BTW, inclusion of bathroom fixture was for context.)

It’s way past my bedtime, and I haven’t had time to share the Goat Problem, the spiked Icosahedron, or more iPad fun.  But there’s always tomorrow….

Today was an incredible day – I don’t even know how to describe it.  I have been surrounded by math teachers before, but at this conference, I am surrounded by people who are interested in learning, sharing, exploring, and elevating the level of their own and their classroom discourse, and doing so with a good-humored spirit.  Everyone seems to be open to an exchange of information and ideas, and so many people are friendly.  There are people from all over the country – all over the world in fact – including several teachers on their first visit to the U.S.  The academic facilities are incredible; this skeleton of a humpback whale is suspended from the ceiling of the Phelps Science Center, where most academic activities are held.

  I am taking 2 courses, which seem to be at opposite ends of the academic spectrum.  The first course – Greatest Hits of Higher Mathematics – is taught by a woman from Brown University; the topics include Real Analysis, Number Theory, Topology, and Proof – and a project!!!  I am completely intimidated by the material – we began by proving that √2 was irrational (just in case you weren’t convinced).  In fact, when I am done with this post, I have homework to do!!  Did I mention that the teacher looks like one of the student volunteers?  No matter – I am here to tackle this higher mathematical inhibition of mine.

The other class – iPads in The Classroom – is completely hands-on, much more relaxed, and I am much more in my element. We had a lot of fun today uploading pictures of ourselves to a wall on padlet.com, and doing the homework assignment (yes, homework in BOTH classes!), which involved scanning QR codes and downloading a series of color-coded messages.  Very cool.

The social hour before dinner and evening program was very lively – lots of laughter, mathematical banter, discussions of classrooms and standards – with graphing calculators, iPads and other mathematical toys in evidence.  And dinner – oh wow – a Middle Eastern station, a carving station, an Indian station, a dessert station and a fresh fruit table – oh, I forgot the shrimp and sushi table.  Amazing!!

I am sitting now in my room, which is sort of like a monk’s cell – very bare bones – unlike the rest of the opulent campus.  I guess a dorm is a dorm is a dorm, even if senators’ children live in it.   However, it does boast a commemorative shrubbery.

 

No more procrastinating – must face my homework!  More on the morrow. 

Final photo – last night’s Super Moon at Exeter.

 

SOOO excited – I am leaving tomorrow morning for the Anja S. Greer Conference on Math, Science & Technology at Phillips Exeter Academy – a full week of learning, talking, living math and math education.  I am so incredibly grateful that I was given a scholarship to attend this event.  I will be taking a class on using iPads in the math classroom and another entitled “Greatest Hits of Higher Mathematics” taught by Diana Davis of Brown University, as well as attending lectures and programs by mathematical notables including Dan Meyer (@ddmeyer).   Even as I am typing this, I can’t believe my good fortune.

I have just finished my 7th year (where has the time flown to??) of teaching – and even though I spent #$!*# years doing other things before this, I cannot remember ever feeling as comfortable and identified with what I do now.   For the past 7 summers, I have avoided making plans, attending conferences, taking classes – I needed to recede, restore and regroup in order to face another school year.  And I have had some really difficult summers, dealing with personal and health issues.  But this summer I feel energized by the coming events – this conference, a week on the Appalachian Trail quilting, and Math Twitter Camp (@TmathC) – to be topped off by my beloved 2 weeks in Vermont on Lake Dunmore in August.I am looking forward to posting more about the goings-on this coming week.  I’ll see you in prep school!

With 9 class days to go (gasp – just finishing circles…), I cannot believe the year is almost over.  It’s been a good year – despite my early early schedule (arrival at 7 am) – and I am already looking at myself as I teach, planning what I will do better next year. 

1. Increase class participation, perhaps by cold calling? – or finding SOME way to get everyone participating.  I can see so clearly that many students are just letting their classmates do the heavy lifting, but it also varies from class to class.  I teach 3 sections of Geometry (and thus the same lesson 3 times each day), and there is a wide variation in the number of hands that will be raised to answer any given question.  But in one of my classes, I can now see a number of students who look down, look at the window, look anywhere but at me or at the board when a question is asked.  Not a heartening thing to see.  I think that if I begin the year with a lot of cold calling, then all students will get used to answering in class, and being ready to answer.  I have made this resolution before, but I would REALLY like next year to be the year I make it stick.
2. Get the students to do more of the work – I have been told on occasion that I am ‘doing too much of the work’, which means that (a) the class is too teacher-centered, and (b) I could be a little easier on myself!  In my Discrete Math classes, I have done a good job of giving the work over to the kids – they have been working in pairs/groups for most of the current unit, Linear Programming, although the beginning of the unit was heavily teacher-centered because they needed that support to learn the process.  But in Geometry, with the end of term and Regents exam bearing down on me, I am delivering content as fast as I can.  This is not to say it has been this way all term – in fact, quite the opposite – but I really feel it, and don’t like it.  Yesterday, we covered tangent and secant segments, and I could feel how dry the lesson was, especially by the 3rd go-round.  Luckily, my 3rd Geometry class is the most good-natured and has the highest level of participation, so the proof of those theorems was the liveliest it had been all day.  I love that I end my day with that class.
3. Employ helpers like crazy – Along the lines of the previous bullet, I need to give over mundane tasks to the kids, who enjoy doing them (erasing boards, distributing papers – or less mundane, tekky tasks) and even earn a sense of pride from their execution.  I don’t think I want any help grading –  although I should perhaps think of some grading tasks that students can assist on – but anything that will help (a) lessen my load and (b) help them feel special is a win-win.
4. Incorporate fun more frequently – This I am definitely NOT good at, even though I do inject a lot of humor into my lessons.  But the fun games and activities do not come naturally to me.  There is such a wealth of resources out there, particularly in the Math Twittoblogosphere, and a lot of people generously sharing their implementation ideas, that I am committing to pushing myself in this direction.  I will set a measurable goal for myself.

But I have done many good things this year as well, and I am going to REFLECT and write about them this coming week.

BTW – the picture has nothing to do with math, but it is a sketch that my daughter included as part of her senior portfolio for her recently acquired BFA in Costume Design from Rutgers University.  Proud mama?  You betcha!

Cheers!

As we dive into the unit on Circles – a long and difficult unit for the students – I wanted to create an intuitive idea of how arcs, chords, and central angles are related.  We have used patty paper only once before this term, and the students seemed nervous – what did this crazy Geometry teacher want them to do NOW?

But as I posed questions – how do you prove congruence with patty paper?  Or confirm parallel lines with corresponding angles?  How can you find a perpendicular bisector?  How can you bisect an angle? – the room grew quiet, except for the sound of rustling.  Patty paper being traced upon, folded, played with.  And private smiles and light bulbs going off as they figured out how to manipulate the paper to prove – everything.  When I asked them to make a conjecture regarding congruent arcs and their chords, and then try to prove it, they began to get creative.  One student said “I don’t really need an entire circle, do I?”  and just drew a segment of a circle to work his proof.  Some students played with 2 arcs in one circle, while others drew 2 circles to create their congruent arcs.

That was all we had time for today; I can’t wait to watch them discover some of the other chord theorems with them tomorrow.

Yesterday was the aforementioned Quality Review visit to my classroom. The effort to have the iPads synched and running the appropriate app was fairly Herculean; I am rather proud of the accomplishment which succeeded mostly due to my sheer force of will and refusal to fail. The day prior to the visit was truly a Kodak moment in my classroom (so wish I had remembered to bring my phone); the Lego ‘Funky Furniture’ activity grabbed the attention of those unsuspecting senioritis-afflicted students before they knew what was happening. The amazing power of a baggie with 14 Legos. Thank you, Fawn .

Day 2 (the observation) of Linear Programming (the observation) included an exploration with a pre-made file and Sketchpad Explorer into a problem involving restaurant capacity, adult:child ratio, and profit. The kids were great – attentive, participating, independently working when required. I needed to begin the lesson with a brief recap of the Funky Furniture activity. We ran out of time the day before (as we often do), and thus, my Do Now included actually graphing the system and discussing what the graph meant (introduction of the vocabulary “constraint” and “feasible region”). The visitors arrived right on time. The beginning of the lesson was necessarily teacher-centered; my students had never completed this type of activity before, and it was imperative (to me) that the previous exploration was concluded as planned before they began the second activity on their own.

So I took a little longer than I would have liked with the Do Now (it lasted 15 minutes, inviting a comment on my pacing). As I ran through the material, I willed more students to raise their hands, willed myself to keep my questions open-ended, willed my classroom to scintillate! Why do we inevitably feel awkward doing what we do 5 times a day, 185 days a year, when someone walks into the room? The fact is that the QR doesn’t affect me specifically (it has a much bigger impact on my principal’s life than mine), but the weight of the school’s pending rating was palpable to me. In any case, we got through the Do Now (or Do for A While), I distributed the iPads, and the kids went to work – very independently. When the reviewer, principal and my AP left, we all breathed a sigh of relief. The kids said I was great, but looked nervous (duh!). I owe them some serious candy.

At the end of the day, I went to my AP for feedback. Like a shrink, she asked me “How do you think you did?” I commented on the teacher-centered-ness, but explained (as she knew) that the students would not have been able to complete the activity on their own. I also admitted it took longer than I would have liked. She then told me she thought it was fine and that her only issue was my pacing. She then told me that my written lesson plan received a “Highly Effective” and was going to be used as a model for the department. I left the debrief unsatisfied, a feeling that has remained with me.

My students finished the activity independently today; their homework is to create a similar problem with different constraints, graph the system, and identify the maximum profit. I am truly curious to see how they do. These are students who are not generally successful at math; getting them to the point where they can create and solve a problem – now THAT would be something!