Almost Homeless

One of the top study tips many of us try to impart to our students is how mathematics (to a degree greater than any other discipline) builds on itself, with every day being an absolute requirement for what comes next. Much like a metal chain (I will say), if you break any single link, then the whole structure falls apart.

Several weeks ago, I met a visitor at an open-house for my girlfriend's art studio. We get to chatting, and I say that I teach college math; it's a good place to work, my boss treats me great, and there's an enormous need for help on the part of community-college students trying to pass remedial courses. He agrees, saying he was one of those students, and fortunately he did get the help he needed. I say: “For any of us, including myself, the limit on our careers and our aspirations is almost always how much math we were able to master in school.” He says: “I think possibly, maybe three or four days in elementary school, I either zoned out or something wasn't explained clearly... and directly because of that, twenty years later, I almost became homeless.”

Sometimes I use that anecdote on the first day of my remedial classes now, and it does make quite an impact.


  1. Yes, I know how that feels. I've spent most of my life almost homeless, aside from those weeks in Michigan where i was, in fact, homeless.

    Seriously, i hope he fleshed it out a bit. I sometimes think of myself as "almost homeless" when I see a storm cloud. Just one tornado away from destitution.

  2. Discussions around education (and MOOCs) have exposed me to ideas that have apparently been around for some time but haven't received much mainstream exposure. One of those is the idea of 'mastery' as opposed to 'passing'. The idea that you move on in lock step with your age cohort while not understanding up to 50 percent of the material seems ridiculous to me now although while in school I accepted it as the way things were. Math (and the way it builds on itself) especially seems like it would be harmed by this pressure to move on. Anything that facilitates immediate recognition of a lack of understanding and addressing it right then has to be better than just moving on, whether that is a great teacher or doing problems interactively on a computer. We need to set higher expectations and then help students meet them.

    I was actually successful at school, did fine on tests, eventually got a BSc in Math and Computer Science. I was somewhat pleased with myself but realize now that a lot of it was just an ability to memorize and perform on demand a series of operations and get the right answer. I did fine on tests so the teacher saw no need to address what I didn't know, and neither did I. My grades slowly declined over the years but remained acceptable for moving on. I also had little idea of how to apply the math to real problems. I believe that only some of the difficulty people have with more advanced math is due to its being harder or more abstract. I bet a lot of it is just the accumulated ignorance of previous years catching up with them.

    I expect the size of your remedial classes shows how many students were just moved on, and the detective work with each student to determine where they got off track must be daunting. I wouldn't even have ended up in one of your classes but now believe I probably should have. I am currently doing my own remedial work (why I am excited about MOOCs) and was surprised how far back I had to go to find a truly solid base that I could claim to have mastered. I hope that a full curriculum of quality courses becomes available and that by setting my goal at mastery I can actually achieve what my degree would seem to claim.

    1. Good observations, and I totally sympathize. Honestly, teaching any of my own courses has been an opportunity for self-reflection and identifying my own places where I had shaky or half-baked habits and really making them air-tight. I had to retrain myself on how I write my own math, for example, looking at lot more closely at good textbooks than I ever had in the past. Teaching even remedial algebra there's been a shocking amount of extra investigation I could do to really deeply understand why things are the way they are (all the way down to say, Peano Axioms), so I can launch an explanation at any abstraction level someone might ever surprise me with.

      Like the way some musicians or martial-arts teachers talk, there's probably an unending amount of practice that anyone could do to keep refining their abilities in this regard.