Month: February 2013

Total 12 Posts

An Aggravating And Energizing Hypothetical

Andrew Leonard:

All we need is one superb remedial algebra course that can be effectively delivered online and, theoretically, the demand for a zillion remedial algebra courses taught at a zillion community colleges suddenly drops off a cliff.

This hypothetical drives me up the wall, oblivious as it is to all the very interesting things that can happen in a brick-and-mortar classroom that can’t yet happen on the Internet.

The Internet is like a round pipe. Lecture videos and machine-scored exercises are like round pegs. They pass easily from one end of the pipe to the other.

But there are square and triangular pegs: student-student and teacher-student relationships, arguments, open problems, performance tasks, projects, modeling, and rich assessments. These pegs, right now, do not flow through that round pipe well at all.

So I’m aggravated by the hypothetical and, especially, its seductive allure to money-men and policy-makers.

But it also energizes me. It makes our job rather clear, doesn’t it?

Promote the hell out of the square and triangular pegs.

Push them into the plain view of anybody who’d love to believe math education isn’t anything more than a set of round pegs ready for a trip down the round pipe.


Great Classroom Action


Frank Noschese’s Texting While Driving:

How far does your car travel while you drive and one-handedly text “LOL” to your friend? Kids were immediately engaged. They asked questions like “How fast am I driving?” and “How long does it take to text?” I told them to assume whatever speed you wanted, we’d share out later.

Nik Doran’s Mini Feltron Project:

I set them first to the task of collecting information about how many text messages they sent over the course of a few days, and then we jumped into the idea of recording more about yourself over the Christmas holidays. I got on board as well. I anticipated some students would not have collected the data (and was unfortunately not proven wrong) so they get use my super boring data. What I did not anticipate was this.

Liisa Suurtamm & Jessica Drake’s Orangiest Orange Juice:

Although I have tried this problem several times with teachers and students and am not surprised when many of them guess which solution is the “orangiest” — I am still surprised at the variety of strategies that people use to prove this and how rich the discussion is. In this particular class the common theme in the strategies that the students used was the need to make something the “same” in order to compare. Some adjusted their ratios to find the amount of water needed for 1 cup of orange juice, others turned everything into percents so that they “were all out of 100″ and it would be easier to compare, some drew circle graphs so that their “whole” looked the same. What was nice is that many students recognized this similarity in their solutions even though they looked quite different.

Mr. Owen’s Contagion:

Generalize it! We then discussed a general form for the equation. They needed to make a connection between the R-0 number from the video and the multiplier they used to generate their charts. As soon as I brought up the question, they noticed that it was just (1 + R). At this point, my head almost exploded from awesomeness.

Twin Pressures On Good Novice Teachers

Shawn Cornally:

Hence, the argument for higher teacher pay: we’ll stay in the classroom longer, rather than jumping ship when our salary schedule is incremented less than inflation (i.e. making less the older I get, like my second year of teaching). In other words, it’s not student achievement you’re directly paying for, it’s avoiding turnover.

“Maybe that’s not a bad thing?” you say. “Some of my best teachers were young and excitable.” you opine.

So here’s the rock: there are certain teachers who thrill a great deal more to the challenge of good teaching than to any missional obligation to care for children. (See: McMatherson, Mathy; Nowak, Kate; Pershan, Michael.) As teaching gets easier, these teachers are forced to impose tougher and tougher challenges on themselves (because teaching itself doesn’t offer that kind of differentiation) just so they can stay interested in the field.

And then there’s the hard place: the demands of good teaching, particularly in charter systems, are often unmanageable for anybody but the young, single, and childless – long hours, comparatively low pay, and only a thin veil of separation between you and your work.

Without even glancing at a census table, it’s possible for us to see that the rock and the hard place close in on good novice teachers at almost exactly the same time. The job becomes untenable at about the same time that it becomes unchallenging.

Kate got out. Vegas oddsmakers have Pershan out of the classroom in another six years. I don’t know McMatherson all that well but his writing has me scared. I don’t know the solution either. (Shawn’s post offers a few.) I barely understand the problem. I’m happy we’re all still here, at least, still buzzing somewhere around the periphery of math education in various service roles if not actually inside the math classroom itself. (Blogging is so a service role, okay?) I’m just worried more and more that classroom teaching is shaping up to be an entry-level job.

2013 Feb 12. Jason Buell reminds me that Kilian Betlach coined “The Ledge” years ago.

2013 Feb 12. Riley Lark and Ben Chun both say this post describes their situation fairly well. Kate Nowak dissents.

Featured Comments

Tom Hoffman:

This is the kind of issue that seems increasingly insolvable because the solution is so straightforward. Everyone needs lighter teaching loads, less time in front of students, and budgets that have a bit of slack so that it is possible to pursue interesting ideas, go to conferences, etc.

Lighter teaching loads, more free time, and a little extra money don’t improve things on their own, but they are a prerequisite for just about anything interesting happening.

Tom Woodward:

I’m not sure enough people care about keeping teachers of that quality. My bet is that the powers that be will opt for consistency and repeatability over powerful teachers they can’t easily replicate.

I fear many pieces are already lined up for the (further?) McDonaldization of education- increased focus on scripting, rigid pacing guides with standardized lessons plans, adaptive path LMSs etc. Not too far a stretch to record the “best” Disney approved edutainers and then pay low skill workers to manage the bodies. It’s not far from what I saw at the School of 1 in NY a few years ago. They’re franchising.

I’d like to be very wrong.

P.J. Karafiol:

I’m not sure I agree with this analysis. For me, a teaching certification program I did about five years in—one that required a lot of reflection—woke me up to the fact that I had a LOT of room to grow; I spent the next five years trying to do the stuff I realized I wasn’t doing yet. Maybe what we need to do is take these not-quite-novice teachers who have mastered the basic skills of getting stuff done and help them see how much more they have to learn.

Andrew Shauver:

What strikes me about my profession is that if I, with my newly-acquired master’s degree, want to advance my career, it REQUIRES me to leave the profession. There isn’t a structure in which I stay in the classroom, but advance my career in the traditional sense of that term.

There are lots of moral victories and self-actualized achievements, and I’m certainly welcome to take on more responsibilities, but it doesn’t do a whole lot more than add to an already-heavy workload.

That’s the main motivator for me going forward. If I decide that I want to engage in policy-making, observation and evaluation, work strongly on curriculum matters or assessment, I really have to strongly consider leaving the classroom because those advancement opportunities don’t exist in my current assignment.

There aren’t offers for half-time teacher/half-time teacher evaluator or half-time curriculum support person or half-time data-analyzer. If I have interests in those things, I have to pick one or the other.

2013 Mar 12. By “unchallenging” I should have said something to the effect that “the challenge of the job transmutes into something less satisfying than it was, while the costs of the job remain constant.” Maybe that’ll still spin up the Internet indignation machine, but it’s more accurate anyway.

Tweet-Sized Tasks

Here is one of my favorite quotes on task design from one of my favorite math educators:

A good problem seems natural. A good problem reveals its constraints quickly and clearly.

Is it possible to pose a task so quickly and clearly that it would fit in a tweet?

I asked and lots of you gave it a shot. Here’s mine as well as a few of my favorites:

Extra merits for roping in your personal life:

Extra demerits for trolling:

I’ll depart from Sallee briefly and say that it’s nice, sometimes, when the constraints aren’t fully revealed. I’d like the task to be clear, but in life the constraints often require clarification. When you ask yourself, “What extra information do I need here?” you’re doing the work of mathematical modeling.

Feel free to play along in the comments, but you’ll have to constrain yourself to 140 characters.

Featured Tasks


Two points A and B on a paper, 13″ apart. You have a pencil and a 12″ ruler. Construct the line segment AB.

Caitlin Browne:

How many squares are on a standard checkerboard?

Bowen Kerins:

Is it really possible for Steven Seagal to have “millions of hours” of weapons training?

2013 Sep 22. From Nat Banting on Twitter:

Give students the sums when rolling two irregular dice. Ask them to design the dice based on data.

Any Questions?

Nobel laureate Isidor Isaac Rabi:

My mother made me a scientist without ever intending to. Every other Jewish mother in Brooklyn would ask her child after school: So? Did you learn anything today? But not my mother. “Izzy,” she would say, “did you ask a good question today?” That difference – asking good questions – made me become a scientist.