## Notes from the Learning Lab: How to Dull My Curiosity Friday, Dec 14 2012

I know I say this kind of thing a lot but I’m sitting here studying for a final, and this truth is just glaring and throbbing at me:

If you want to dull my curiosity, tell me what the answer is supposed to be.

If you want to make my curiosity vanish completely, do that and then add in a little time pressure.

There is nothing as lethal to my sense of wonder as that alchemical combination of already knowing how things are going to turn out (without knowing why), and feeling the clock tick.

## This Is What Democracy Looks Like Sunday, Sep 16 2012

The Chicago Teachers Strike

## Purging Thursday, Jul 5 2012

This is an impulsive and probably self-indulgent post.

When I moved to New York almost 6 years ago, I stowed two crates of hanging files in my grandmother’s closet. They are artifacts of my 2000-2005 teaching career in Boston. One crate, curricular materials; the other, student work. They had made it past one round of purging – this was the stuff I chose to bring with me to New York.

But they’ve been gathering dust since 2006 and I figured I owed it to my grandmother to get them out of her hair, so I picked them up on Tuesday. They’re sitting on my living room floor. I have absolutely no sensible place in my apartment for them. I am next to them, on the couch, a bag of paper recycling at my feet.

I didn’t budget time for these guys, and the time efficient move is to not even think about it; just dump it all.

I can’t bring myself to do this. That said, knowing how I get, if I start going through it paper by paper then (a) I will be here till next week and (b) at least half of it I will not be able to throw out.

Maybe I can make this blog post some kind of middle ground.

* Here’s the Jeopardy game I played with my Algebra I and Calculus classes they day before winter break! Optimization for $300: This is the maximum amount of money you can make selling cookies if you know that you could sell 100 cookies for$1 each, and that every time you raise the price $0.25, you lose 10 customers. Final Jeopardy (Algebra): $x$, given that $a=4, b=2, c=-1, d=37$, and $ax+b=cx+d$. Mr. Blum-Smith trivia for$200: Mr. Blum-Smith’s grandmother was kissed by this former US president. (Same grandmother whose apartment has been housing all this sh*t! Correct response: who is Bill Clinton?)

* Here are my various attempts at teaching about proof in Algebra I! My first year, I tried to teach a “proof unit.” It culminated with a “proof project,” where I had students attempt to prove one of six eclectic elementary theorems (e.g., sum of first $k$ odd numbers is $k^2$; any composite has a factor $>1$ but $\leq$ its square root; …). I remember being essentially unsatisfied. In the notes I made to myself after implementation (ed note: HOW CAN I THROW THESE OUT! F*CK!) I was starting to realize the whole thing was ill-conceived. I was smashing together the problem of actually figuring out what’s going on (interesting, unexpected, no guaranteed outcome) with the formal process of making it into an argument. I was setting the kids up. In my fourth year, I revisited the idea except with more coherence because the whole thing was based on creating a “number trick” (“think of a number; add 6; multiply by 2; … ; you got 42!”) and proving it worked. Still, the proof aspect of the unit was stilted and poorly motivated because the kids couldn’t see the need for the amount of formality I was insisting on.

* Here is a unit I wrote my student teaching year, about tessellations and symmetry, based on Escher. Here are pages of transparencies with Escher prints and other tessellations. Here are the 5 envelopes of tessellating polygons (triangles, rhombi, a nonconvex quadrilateral, some special pentagons…) I designed on the computer and lovingly cut out of paper. I never taught this unit again.

* Order of operations. I used to use this activity I stole from my own 7th and 8th grade math teacher, Steve Barkin, an institution of the Cambridge public schools. Take the year (I used to use the kids’ birth year, or just make it 1994 if I wanted it to be easier), and using the digits in that order, put any math symbols you want between them to get as many of the numbers from 1 to 100 as you can.

* Ah! And an inheritance from Steve I never actually made use of: a kind of integer number sense activity where you label the vertices of a graph with integers so that the numbers on adjacent vertices differ by 10, or else one of them is double the other. Like this! Fill in the blanks: $12\leftrightarrow ? \leftrightarrow ? \leftrightarrow 13$. Solution: $12\leftrightarrow 6\leftrightarrow 3\leftrightarrow 13$.

* CAN THEORY. This was the name of my linear-equations-in-a-single-variable unit, the core topic of my Algebra I class. I took the name and the idea from Maurice Page, then the math coordinator of the Cambridge Public Schools. The unit became what it was in my classroom in collaboration with my awesome colleagues Jess Flick (then Jess Jacob) and Mike Jenkins. The whole unit was based on physically modeling the equations with plastic cups and poker chips on a table; I put a piece of tape down the middle of the table and the rules were, all cups have to hold the same number of chips and both sides of the table have to have the same number of chips total. You figure out how many chips go in the cup. I beat that model to death every year. I tweaked the model in various ways to accommodate negative and fractional coefficients and solutions. That was the one topic I would have counted on nearly all my students still having mastery of the following year.

* Qualitative graphs! One of the years of my collaboration with Jess and Mike, we implemented an idea Mike brought to the table of a unit in Algebra I that was about interpreting qualitative features of cartesian graphs. The culminating project was, you picked a container (we had all kinds of shapes – beakers, vases, wine glasses, etc.), you filled it steadily with water and measured its height against the amount of water it contained, and you drew a graph of that. Before you did the experiment you predicted what the graph would look like. Afterward, you wrote an explanation of the features of the graph (changes in slope; concavity; inflection points) and discussed how they related to the shape of the container. My experience of the unit was that it was very difficult for kids, but it definitely felt like some proto-calculus skills.

That was the easy stuff. (I know; I’m being dramatic.) STUDENT WORK:

No, I can’t even open this up. GRRR. To every student I taught in 2000-2005: I am about to dump into a bag of paper recycling a whole lot of both your and my blood, sweat and tears. RRRRR okay. I have to immortalize a few memories. This will be spotty and haphazard, please forgive me. I am leaving most of you out in the below, but to all of you let me say that I hope you learned half as much from me as I did from you.

W: Best handwriting ever. Every homework assignment literally looked like the inscription on the One Ring. May you bring that level of love to everything you do.

D and M: The two black women in a calculus class I had allowed to be dominated by the personalities of cocky (mostly white) boys, you had the courage, and the respect for me and my potential for growth, to tell me what this felt like. I am grateful you did and sorry you had to. You are both rock stars and I regret that my class wasn’t a better environment for expressing that.

N and M: You stand out in my mind in your willingness to put in time and effort to understanding what you didn’t before. You put in after-school time to the degree it could have been a part-time job. That kind of commitment got you past hurdles higher than many adults I know have ever had to face. In my life I have come to understand that anybody can learn anything, and you guys helped teach me that.

W: As a math student you were an amazing combination of depth of thought and engagement, on the one hand, and desperate difficulty mastering computational techniques, expressing yourself in writing, or doing anything at all in a subinfinite amount of time, on the other. You asked some of the most thoughtful and interesting questions in class that I have ever heard. You practically never finished a test, even if you came after school for 3 hours to work on it. You were uniquely gentle and generous with myself and your classmates at all times. Rest in peace, W.

## Technology Advice Request Tuesday, Apr 19 2011

So I am going to begin a PhD in math at NYU’s Courant Institute of Mathematical Sciences in the fall.

(Congratulations me! EXCITED.)

Do not for a second think this means I am abandoning Team Teacher. K-12 education 4eva. More on this another time.

Anyway, for a math teacher blogger I am sort of a luddite so I could use some internet advice.

I’m trying to start a study group for my cohort at NYU. (We have to pass a written exam during the first year of study; a lot of folks e.g. me want to get it done in the fall.) So far nobody who’s written back is going to be in New York over the summer, so an online study group seems indicated. Question: what’s a good platform for an online study group?

We need to be able to ask, answer, and reason through stuff. We need to be able to write stuff. My thoughts so far:

Idea A: a group-authored WordPress blog. I have never done anything group-authored on WordPress so I don’t know how to think this through, but it supports LaTeX so we can typeset stuff. Somebody can post on a question or problem they’re struggling with and other folks can answer in the comments. Drawbacks: everybody needs a WordPress account, right? And writing a post is not the most user-friendly thing compared to commenting. And we’d need to be deliberate about how to make it easily navigable.

Idea B: somehow get our hands on the platform used for MathOverflow and Stack Exchange. It’s already set up for questions and answers and also has full LaTeX support. Drawbacks: how will we get our hands on the platform? Also, the “reputation” part would be bad for our purpose – can we omit it?

Idea C: One of my classmates suggested a Facebook group. I’ve never used a Facebook group for anything and somehow the idea seems lame to me, but I don’t have a valid basis for that. Do you have experience with them? What are they good for?

Okay, do you have other ideas for me? Do you have any additional thoughts/advice about these ideas?

Thanks for real.

UPDATE 4/20:

To clarify what I think we need (although if you have experience with online study collaboration, I want to hear what you think we need too) –

We need to be able to ask, answer and discuss math problems. I think that means we need to be able to typeset math, so LaTeX support is a plus; we need to be able to have back-and-forth discussions, so support of comment threads or the like is a necessity; and we need to be able to participate in multiple conversations at once, so some sort of easy-to-navigate organizational structure would be nice. (The last of these is the primary drawback of a WordPress blog as I see it.) Also, the ability for multiple people to contribute content in a user-friendly way would be nice.

UPDATE 5/2:

When I sensed this turning into a much bigger project than I intended, I went with WordPress. I got lots of great suggestions that I’m looking forward to learning more about when I have the time.

## Bob Moses in NYC Thursday, Apr 7 2011

I just found out that one of my heroes, Bob Moses, founder of The Algebra Project, and an important leader in the civil rights movement (specif. the SNCC voter registration movement), will be speaking at NYU this afternoon, and I can’t go. GRRR. Maybe you can.

The title of the talk is:

Working the Demand Side: Mississippi, SNCC and the ’60s struggle for the Right to Vote. The Algebra Project, the Young People’s Project and the current struggle for a Quality Public School Education as a Constitutional Right.

The info:

Thursday April 7, 4:00-5:30pm
King Juan Carlos Center Auditorium (NYU)
53 Washington Square South, 1st floor

The talk is sponsored by The DOE History in the Classroom Project and NYU’s Department of Teaching and Learning. Bob will have a book signing afterward for his two books Radical Equations and Quality Education as a Constitutional Right.

I don’t have time at this second to properly introduce you to Bob Moses’ work if you aren’t already familiar with it but let me at least say that if you are interested in the relationship between math education and democracy, there isn’t a deeper thinker on the subject anywhere.

## Still Here, Still Learning Friday, Mar 11 2011

I last posted in October. I wrote a review of Waiting for Superman that generated more traffic than I’d ever seen before on this blog. Since I had been intending to continue my series on the idea of mathematical talent since the summer, I decided not to post again until I was done with the next installment of that series. But because it involves some research, and I care about it a lot and want to get it just right and tend to get kind of obsessive about things like that, and because there’s been a lot of other stuff going on so I haven’t been working on it consistently, this has kept me from posting anything at all for 4.5 months. So maybe it was time to revisit that agreement with myself?

And a few days ago, JD2718 wrote me an email to the effect of, “yo, what happened to you?”

So, here’s a partial answer -

a) I learned a lot about leadership. One of my jobs this year has been to facilitate the weekly math department meeting at a high school, and plan the agenda for this meeting. This has gotten me involved with the communication channel between the department and the principal. I feel really grateful to have had the opportunity to do this. It has caused me to start to develop a completely different skill set than I’ve ever had to use before. (To give you a whiff of what I mean, it inspired the following facebook status: “Ben Blum-Smith thinks it is important to be a straight-shooter and a diplomat, and that you do each better by doing the other one.”)

b) I learned a lot about training new teachers. Another of my jobs this year has been as a faculty member of an MAT program. In the fall, my colleague Japheth Wood and I taught a “math teaching 101″ typed course for our cohort of 12 preservice folks; this winter we taught the “math teaching 102″ installment. They’ve been in apprenticeships for 9 weeks and we’ve just gone through observing them actually teach a few times, so now on my mind is – what am I happy with in their teaching? What’s missing? And what implications does all that have for our fall and winter courses?

c) I’ve continued to design and implement a graduate course on algebra and analysis for the faculty of a high school. This has been both awesome and very challenging. We chose to organize the course to culminate with the Fundamental Theorem of Algebra. At the beginning of the year I thought this was a reasonable goal and the course would not feel hurried. Now, 2/3 of the way in, somehow I’ve found myself feeling pressure to go through significant chunks of material at breakneck speed. That tension is of course absolutely part of the lives of all the participants in their own classrooms, so in a way it’s cool that this is parallel; but still. I am implicitly making a case with this course for the principles of math teaching I believe in, so I’d better be living those principles in my teaching of it. A few of them I feel like I’ve been 100% consistent with:

* Every day I will bring you questions that are worth your time, questions that even I think are exciting to think about even though I already know the content.
* A math course should have a plot, with beginning, middle, end, dramatic tension, resolution. (Math teaching as storytelling.)
* Central to learning math is the interplay between formal/rigorous thoughts, definitions etc. and intuitive notions. I will always stress the connections between the two.

Other principles I feel like I’ve nailed some of the time and totally let slip away other times in my concern to make sure we get to the content:

* (Closely related) The most powerful certification of new knowledge is consensus of the learning community, the same way new knowledge is certified in the research community.

3 classes ago I had them prove the irrationality of $\sqrt{2}$, spent the whole period on it, left them all the heavy lifting, noticed and brought out points that were bothering people, and generally aced these last two principles. The last two classes have felt the opposite way. I think I was talking 80% of the time in the most recent class. Lots of questions never got answered because they never got aired; lots of productive thoughts never got formed because they never had time to. Anyway, getting this course right will continue to be an engaging challenge.

d) I applied to doctoral programs in math. Now I need to decide where to go. The choices are NYU, CUNY and Rutgers. I feel very excited and torn.

e) If anybody remembers the ellipse problem that Sam Shah brought back from PCMI, and which I wrote about back in August… Japheth and I have completely solved it. I am going to tease you with this tidbit and not the solution itself because we wrote a manuscript on it which we hope to get published.

f) Okay this doesn’t fit under the rubric of “what happened to me” but here are some links you might enjoy:

* A Teacher Story by Anna Mudd. Anna’s blog, Drawmedy, is a beautiful kind of writing which I won’t try to describe. It’s not an education-themed blog so I was delighted to see her take on her experience as a teacher.

* This gem from Vi Hart: Wind and Mr. Ug

* Taylor Mali’s What Teachers Make. This poem is definitely amazing, and if you’ve never seen it, I think you won’t be sorry if you watch it before reading the next sentence. <pause>Pause while you watch the video.</pause> It brings up some ambivalent feelings in me too – these are a story for another time, but here’s the short version: It’s related to the tone of the current national conversation about education, which is all about how the incompetent slovenly dumb*sses in front of our children are f*cking everything up. In this context, Mali’s piece is an eloquent testament to the value of our work, but it also makes me uncomfortable. Mali appears to have been amazingly happy with the job he was doing as a teacher when he wrote and performed this. But I don’t think that (especially in light of the current climate of the conversation) feeling like you’re doing an amazing job should be in any way a requirement for testifying to the value of your work; especially since most of us do not feel that way, most of the time.

* Speaking of the current national conversation about education, a new study by the National Education Policy Center came out on New York City’s charter schools, which are often touted as models for the nation.

* It’s weird to experience yourself as an unwitting participant in a historical zeitgeisty trend, but I do. I have the strong feeling that the traditional distance between the mathematics education community and the mathematics research community is closing, and I, a classroom teacher and teacher trainer entering into a math PhD program, am like completely an example of that. Another is the latest issue of the Notices of the American Mathematical Society, which is the research community’s professional association. It is devoted to education. You can download it for free.

(Thanks, JD2718, for making me write all this.)

## Kate Nowak Is Such a MF Bad*ss and Other Stories Friday, Sep 17 2010

Kate is walking the talk.

And writing about it, which, because it’s Kate, means she’s writing about what makes it hard, which means she’s putting into words the core of maybe the biggest obstacle I can see to the improvement of math education in this country.

I haven’t used the Regents exam as a threat, not one time. I casually mentioned it on day 1. I’m doing my best to ignore it.

Problems like Solve: x + |2x – 4| = 4x – 8 just piss me off to an alarming degree. Only if you tell me what x represents and what relationship those expressions describe and why you think they are equivalent, NYSED. Then maybe I’ll solve your equation, but right now I think it’s too uninteresting.

Nothing about what I just wrote does not provoke anxiety.

And then she’s tying her thoughts together with a nautical metaphor?

Oh right. She used to be in the navy.

* * * * *

I am working on the Talent Lie series but I don’t think I’ll have anything up for a good long while. I’m teaching two courses for teachers this fall, one for inservice folks and one for preservice folks, and I foresee a need to actively reflect on those courses, so if you hear anything from me in the next month it’ll probably be about that.

## An Odd Request Wednesday, Aug 25 2010

We interrupt our regularly scheduled programming to ask you an admittedly strange question:

A bunch of brand new young enthusiastic preservice math teachers sit down in front of you. If you could pick 3-5 things about math education that you most want them to understand, what would they be?

Comment with whatever quick and dirty brainstorm you have. I know some of you have given this, or something like it, a stab in the past – in that case I’d appreciate a link. (I remember Dan did this semi-recently – others?)

## There Is No Reason for You To Read This Post (I Mean It) Wednesday, Aug 4 2010

The purpose of this blog has evolved since I started it. I’m just declaring that here for the sake of my own integrity. This is really no use to you.

Originally, the plan was to engage with research on math education from a practitioner point of view. The goal was so I could try to stay vaguely current on the literature by processing it out loud on this blog so when I read something it will be easier to remember.

* First of all, what I engage with has ballooned to include anything I read about math or education, not just the fairly narrow category “math education research,” although I plan on continuing to read math education research and post about it among other things.

* I’ve found myself using this as a platform to articulate thoughts and values about math education that I want to go on record with because I believe they’re important.

* I’ve been using this as a place to hash out and process thoughts about teaching and learning that are inspired not only by reading but by conversations, classes I teach or observe, etc.

* I’ve occasionally indulged the impulse to enthuse about math itself.

* I haven’t done much of this so far, but in the coming months I foresee the need to use this blog from time to time as a place to actively reflect on my own practice.

* Combinations of any and all of the above.

My original intent was for 1 post a week. This has been hard to maintain. I hereby retract this as a declared intention, but retain it as an approximate goal.

While I’m chewing on what this blog has become, it seems appropriate to once again shout out Kate Nowak (my fairy blogmother), and Jesse Johnson (my fairy blog-big-sis).

Okay! Integrity restored! I’ll be back on topic soon…

## Alright, here goes… Friday, Oct 2 2009

This blog is a math education research digest.  I’ll post weekly about something I read – a study about teaching, learning, cognition; a book or article about pedagogy; anything that provoked my thinking about math education.  My hope is that people will find it thought-provoking and useful for reflection, and possibly also useful as a source of information about research.