Tomorrow is the last day of this school year – the most miserable teaching year in my memory. I wrote a whole series of posts in which I vented against, students, parents, administrators and also against many of my fellow teachers. Certainly the (educational) system is broken and all the segments in it have their share of blame.

However, in thinking back over this last year, I find myself coming back to one thought: there is a tremendous, vast, humongous difference between how teachers look at learning and at their subject matter and how students look at it. Probably this should not be much of a surprise – after all, we have years of experience in our field (e.g. math) and chances are we would not have stuck with it if we did not like it. Plus, sticking with one field over the years, probably qualifies us as experts; certainly with respect to the average level of math knowledge in the country, we are “experts.”

But what I find hard and frustrating is my (and my colleagues’) inability to convey the beauty of math and how interesting it is to the average freshmen I have seen this year. When one has students who dislike school, learning in general and math in particular, it is very difficult to convey to them the delights of thinking and solving math problems.

My guess is that, if one were to plot high school freshmen interest in math, one would get a probability distribution like this.

Here, the horizontal axis would be a measure of “interest in learning (math)” (increasing to the right) and the vertical line would be “% of freshmen” (increasing up).

I don’t think many teachers would quarrel with the qualitative truth of this graph – it is significantly right skewed. The problem is that if we were to plot the same horizontal axis, but replace the vertical one with “% of (math) teachers”, we would get the opposite – a left skewed curve (may be not as steep though). There is a big gap here – “What we have here is a failure to communicate” (Cool Hand Luke, 1967 – I am dating myself!)

Well, my thesis is that it is extremely difficult – if not impossible – to reconcile these two distributions, specifically to make a dent in the shape of student interest. Furthermore, I am not sure to what extent we should make that effort (and I know this is not at all PC).

Here is my reasoning. High school freshmen who dislike math – a vast majority in my experience – have had years of reaching and honing that level of dislike. Chances are that they were abetted in this by poor teachers, parents who say “ I wasn’t very good at math either” and a culture that in general does not value learning and math in particular. As a result, somewhere along the road they started performing poorly in math, but lo and behold they still were promoted from one grade to the next, even when they failed. Now they are in high school and their poor performance is no longer rewarded – they can and do fail and they have to repeat the course. So now, to intrinsic dislike is also added a performance dislike.

I don’t think one can motivate these kids. It is like trying to motivate a child to eat some food s/he intensely dislikes – say spinach. It is no good and not productive trying to deconstruct why that food strikes the child’s taste buds the wrong way – it just is. One can still make the kid eat the food through extrinsic rewards, but the kid will still not like the taste and will relapse into not eating it once the rewards are absent. And extrinsic rewards are not what ed schools call “motivation”.

What can one do? Two things. Concentrate on the right end tail of the curve. We should put our efforts into that part of the curve that wants and/or likes to absorb the knowledge. In other words, cook all kinds of “gourmet” spinach for those who like or want to eat spinach. Show these kids how good/healthy/”interesting” spinach can be.

The second thing to do is to stop putting so much effort into telling the other kids how good spinach is and forcing them to eat it – it makes both parents and kids mad. Instead, if despite your best efforts the kids still don’t want to eat spinach – *and that effort should be made* – cook some other meals. To continue the analogy, spinach is not the only vegetable and indeed some meals can do with a little bit of spinach. When will the vast majority of our kids have to use polynomial division? I am advocating here a much more practical math curriculum.

Let’s see if the next year will be better…Have a great summer everyone!

A different meal! Good idea! Something practical (but better than “consumer math”) is what we need, I agree; in my fantasy about this, every ninth-grader (whether you’re ready for Algebra 2 or Geometry or just Algebra) takes a non-tracked course (Modeling, Data, and stuff like that) while they become more developmentally ready for and interested in abstraction—or not.

Your post recalls another non-PC idea that has been making the rounds: maybe not so many kids actually need to go to college. An intriguing thought. In this fantasy, we’d need decent alternatives for those who would opt out of math or college, and a society with more realistic job requirements, and more respect for non-college jobs. But (fantasy again) we also would benefit from, say, a mandatory year or two of farm work, construction, and forestry, round about middle school.

I like your idea of an initial non-tracked course – it would be interesting to put together a curriculum for such a course. I think it should be case-based and perhaps computer based. I know that there are equity questions with computer based courses, but the kids do tend to get into the problems when they are interactive and on the screen.