Diversity and dispositions

Another post that touches on my professional life as an educator / researcher. This too may take multiple installments to get the thoughts fully fleshed out, but I want to start sketching out the issue.

In a previous post on education I brought up the issue of diversity and variation. Here’s a snippet of what I wrote:

Variation, dispersion… it’s no exaggeration to argue that life itself could not function without it. Biological evolution critically depends on variation, in particular variation in “fitness” for passing on one’s genes. Fitness is a relative concept – an organism is not universally “fit,” but is fit insofar as it can function well within its environment. Change the environment, and the organism’s fitness may rise or fall.

Now, there are places where we want to tame variation. Manufacturing comes to mind, particularly when safety is a concern. In producing turbines for aircraft engines we don’t want variation in the stiffness of the material or the weight of the individual fan blades. Variation in that case is a problem – drift too far away from the center and things start to go wrong very quickly. So let’s bear in mind that in some cases, variation is a good thing, and in other cases variation is to be avoided.

Education is a process of guiding human development. So, do we want lots of Darwinian variation, whereby some people are more “fit” for their environment than others, or do we want aircraft manufacturing, with very tight tolerances for assuring uniformity in the components? (Hint: it’s not a black or white answer. “It depends.”)

I want to come back to this question of where we desire variation, where we want to control or eliminate it, and what a “healthy” balance looks like both within and between individuals. In particular, i want to discuss interests, attitudes, and dispositions. This is going to draw on some ideas I’ve been sketching out on standards and standardization, as well as attitudes among middle schoolers.

Let’s start interests writ large (I’m not going to analytically parse an exact definition of “interest” – let’s stick with the colloquial). It’s not controversial to hope that children and adults have a variety of healthy interests: sports, music, arts, academic subjects, Civil War re-enactments, bird watching, you name it. It also seems to be a generally agreed desire that children at least try a variety of things, and probably adopt a much smaller number as “main” interests, while continuing to cultivate a habit of curiosity and openness to new experiences.

Now let’s dive down a level. Parents and adults will differ on some of the particulars. Most would hope that their children develop some sort of strong interest in a socially acceptable, personally fulfilling and economically beneficial domain – arts, engineering, business, and the like.  But I doubt most parents would find a complete lack of interest in any of these things perfectly okay – we’d worry about the child, not just for their future but for their present sense of well-being. A child who exhibits little interest in anything may be exhibiting signs of depression. (Yes, I realize a child can have strong interests in anti-social domains, too. If I try to footnote every exception this will start to read like an academic journal article. I’m trying to avoid that).

So I’m going to postulate this: we care that our children develop interest(s) in some domains that we would consider “healthy” (a shorthand for fulfilling, productive and pro-social). But we don’t necessarily care about the particulars: computer science of culinary science; martial arts or fine arts. Or rather, across a society, individuals may care about these distinctions, but as a whole there’s a healthy mix of healthy interests.

It almost goes without saying that there are activities, pursuits, and lifestyles that few of us would wish for our children. Drug addiction leads to varying circles of Hell. Does anybody really want – as a first choice – that their child grow up to be an assassin for a gang? Backing off the obviously criminal, most of us would probably want more for our children than to sit on a sidewalk begging for spare change.

We have a healthy mix of positives, and a somewhat clear set of universal negatives. Are there any “must have” positives, something that pretty universally every adult wants for his/her child? And I mean this with some degree of specificity – not just “I wish my child to be fulfilled and happy.”  (This reminds me of a joke about a Jewish mother telling her son he can be anything he wants: a cardiologist, a neurologist, a dermatologist, a surgeon…)  At the moment I can’t think of any that jump out. Perhaps grow into a healthy romantic relationship of their own?

My main point, though, is that while we may have universal wishes for our children at a particular level of generality (I want my kids to find fulfilling work), we may disagree or even have no opinion about the particulars.

Now let’s talk about the “STEM crisis.” (STEM stands for Science, Technology, Engineering and Math). Lots of hand-wringing about how we aren’t producing enough STEM graduates in our schools. In particular, there are too few women choosing STEM careers. I’m asking – are these really problems?

What does it mean that we aren’t producing enough STEM-ready graduates? Generally it means that there are open jobs available on the market and not enough qualified individuals to fill them. In the US, that also means lobbying Congress to open up visas for skilled immigrants. But as economists and others have argued, this is not a STEM problem, it’s an economics problem. Basic supply-demand theory says if you raise the salaries for STEM employees, you’ll end up with a greater number of qualified applicants knocking on the door. So it’s not that there’s a STEM worker shortage – there is a shortage of workers willing to work for the current salary ranges. Edit: this article from Businessweek makes the same claim.

I believe the supply-demand argument works up to a point. At some point, though, we’re going to bump into an interest limit. That is, there are reasonable, intelligent people who would say “I don’t care how much you want to pay me; you couldn’t pay me enough to major in engineering. I’d rather starve and live on the streets.” Perhaps this is a first-world problem, that those who have grown up in true poverty and suffering just couldn’t understand. But anybody who has been to an American university has run into students with this attitude. And it isn’t just STEM – change the subject to social work, kindergarten teaching, marketing… you’ll find people who would rather gouge their eyeballs out than partake of that work.

Likewise, what does it mean that there aren’t enough women interested in STEM careers? Superficially, it means that the proportions of women are lower than those of men in terms of STEM interest. Some of this, as has been documented, is due to barriers to women’s entry, including discouragement from teachers and an exclusionary culture in some STEM fields. So let’s assume that some of that gender disparity is due to structural impediments imposed from the outside. Still, at some point we’re going to hit the barrier defined by intrinsic interest – surely not every woman or man wants to go into a STEM field. And if not every, what is the “natural” base rate of interest? (again, given that this base rate is partially sensitive to the perceived rewards).

I’m choosing career interest as my illustrative case – we care that children become interested in something positive, but may care less about the actual details. What other choices are we happy with leaving up to general variation? Not every child will want to take up music for starters, and those that do will have different preferences for instruments and genres.

If we step back and think of our education system, there is not a lot of respect or room given for diversity of interests, at least until the upper levels of high school. The curriculum from K to roughly grade 10 is relatively standard. We give all kids a taste of everything – some they will take to, some they will want to reject, but they are required to at least try it (sort of like making sure kids eat their vegetables?). And we select winners (at least for university admissions) based on whether they were able to succeed (i.e., get A’s) at subjects whether or not they actually enjoyed them. There’s a whole other topic for discussion, but I wouldn’t be the first to question the social consequences of that selection policy.

Specialization appears to be something that is left to the after-school or non-school part of a child’s life. Perhaps that is fine. I just want to mark that as the case.

That’s all I’m going to write for now. My main point was to push back a bit on the hand-wringing over the “STEM crisis” and distinguish between general and specific wishes for our children. This is a work in progress, but at some point I want to develop a clearer idea of how variation plays out in society and education.


Back to my roots – middle school math

Once upon a time, I was a high school math teacher. Twice upon a time, actually. Both times I flunked out. Well, not really flunked out – voluntarily withdrew from the profession. The first time I was 23 and teaching in a private school that turned out to be a bit of a cult (no exaggeration). Six years later I was in a public school with a “mentor” teacher who would leave the class with me when he needed to meet with his real estate clients (guess what his moonlighting job was). Sure, I could blame my early exits on the particulars of the situations, but the second go-around also taught me that I really didn’t want to work with adolescents so intensely day after day. I thought I did, but when push came to shove I preferred working with adults, which I’ve done ever since.

Now I live with two 7th graders. It’s homework time. The distributive property. Simplifying algebraic expressions. And everything I’ve been studying about middle-school mathematics teaching and learning is coming to the surface. There’s the basic “how do you teach algebra” question, but I had that pretty well down from the get-go. Then there’s the attitude question: “why do we have to learn this stuff?” Tonight’s sticking point – developing the metal habit of careful accounting for terms and signs. It’s not that the procedure for distributing terms is difficult, but it entails really understanding each component of the process, why a particular transformation is used, and careful book keeping. That’s tonight’s struggle.

An example: simplify 6b – 2(2b – 7) = 21.  The tricky part here is keeping track of the minus signs. Actually, working through this has exposed some confusion in the student between unary minus (“eyebrow level minus”, as my old teacher called it) and binary minus (“belly-button minus”). So, what gets distributed here?  There are a couple of ways to approach it. One is to treat the term 2(2b-7) as the basic unit to be unpacked, and you get:

6b – [2(2b) – 2(7)] = 21

Then you’ve got to deal with that minus sign before the expression in brackets – essentially distributing a (-1) again.

Or, you can try to distribute (-2) across the expression, and end up with

6b -2(2b) -2(-7) = 21

My student was not tracking the minus signs accurately, in part due to some odd (but not entirely incorrect) use of parentheses that obscured what was happening to the signs of each term.

Here’s where we hit the wall – I had started with a simpler version of this where all signs were +. Then I moved to just having a minus sign inside the parenthesis – no problem. Then I switched to a minus sign after the 6b but a + sign within the parentheses – trouble! That’s where the diagnostic flag went up. How to either distribute that pesky minus sign, or block out the whole expression in parentheses. Both were not making sense to the student. Blocking out the whole expression in parentheses (my first expansion example above) was a non-starter. But distributing -2 as a factor ran into trouble because “that’s not a negative 2, that’s a minus!” (in the way only a 7th grade girl can whine).  In the end she worked enough examples that she’s learned to be aware of the -a(b-c) forms, and this expands to -ab + ac, but the learning is not robust. She hasn’t yet seen, for example, -a(-b-c) expressions, and I’m sure she’ll struggle as soon as she sees one.

Attitude. As soon as I tried to work an example I got the “just tell me if it’s right!” impatience. She’s not really trying to “get” it, but “get through” it. And – tonight at least – there isn’t a lot I’m going to do to change that attitude. That’s a longer term… I was going to use the word “battle,” but that frames the situation as one of domination. How to get her to take an interest in how algebra works? That’s the question. If she had some degree of curiosity tonight, I could steer her energy in a productive direction. But what I’m feeling is a sense of drudgery, that the homework is something to be gotten through and then moved past.

(Her sister, on the other hand, has an entirely different set of issues: she grasps the concepts quickly, is actually curious about how things work, aces tests, but is “rebelling” by not actually handing in her work and lying about what she actually has to do in a given night. That’s a later story…)

So what to do? This situation, right here, repeated day after day as a high school teacher, is where I hit a wall. If a student isn’t really latching onto the problem, how do I inspire? I had a high school senior once say to me “Mr. G., I know you’re trying hard, but really, I’m gonna take this course again in community college next year anyway, so I just don’t care.”  Anybody who has ever found a passion – or even a modest interest – in life knows that feeling of “latching on.” One long-term question I’ve been really curious about is how to “transfer” that attitude of curiosity from situations where it occurs naturally to those where it might take a little work.

Then again, why *should* a student be deeply curious about the ins and outs of algebra? I was, but I wouldn’t claim that everyone *should* be. I was never that curious about British literature as a student, and still am not. But if I were in school right now with a general ed. requirement that included British literature, I would try to understand what the instructor saw in the subject matter. In fact, that’s one of the joys of getting to know somebody new – understanding what they’re interested in even if it’s not my own personal interest. But as a 7th grader, I was either interested in something or I wasn’t… but I have to wonder how my interests may have been shaped by talented teachers. I had a 6th grade social studies teacher who made world history fascinating for a year, and that was the only time I enjoyed a social studies class through 12 years of schooling.

I actually just asked the 7th grader about this – whether she was “interested” in understanding. She said she was actually interested when she started the homework, “but then it got hard.” She agrees that she’s not always interested in math, “not like that boy in class who gets excited whenever the teacher is about to do something new.” It makes me wonder, how much interest is enough?

To be continued…