I am very gruntled after listening to Michael Enright’s
Reflections in a Bay of Fundy tidepool
interview with Andrew Hacker, Professor of Political Science at Queens College in New York City about teaching advanced algebra in high school and college. In part I am delighted to have learned a new word – gruntle, opposite of disgruntle. How cool is that.
But let me focus on the conversation about algebra and why it might be a good idea to drop our insistence on advanced algebra in high school and college because it is the single biggest cause of students dropping out and not finishing their education.
I couldn’t agree more with the premise that we are wasting far too large a proportion of the intellectual capital of our young people by insisting on dragging forward old ideas about what constitutes a good education. Wake up people; start thinking differently instead of simply plodding forward with historical beliefs that are never re-examined.
When life is more than the sum of its parts!
I spent the first 30 years of my life being a math-phobe. I didn’t finish high school because I was terrified of having to do algebra and trigonometry in Grade 13. I had several math teachers who were horrific in terms of their inability to teach and their concomitant ability to humiliate those of us who were slow on the up-take. Except for Mr. Dube, my grade 9 Math teacher. I simply couldn’t cotton on to the notion of x and y. This poor man worked with me for 6 weeks before the light bulb finally went on. I am eternally grateful for his persistence because I may not have made it to Grade 12 otherwise.
University came late in life to me. I was 29 when I began my studies in the social sciences (39 when I got my BA) and I put off the required stats course as long as humanly possible. But having begun a degree on a part-time basis my work fortunes improved dramatically. I got myself a job as a manager in a major telecommunications organization. The horror was that I was hired into a department filled with statisticians, economists and systems analysts. One of my bosses thought it was pathetically funny that when I was presented with a graph with several lines on it my first response was to panic, followed very quickly by tears. Talk about embarrassment and feeling intimidated.
After several years of this nonsense I forced myself to take an introductory economics course. It was perhaps one of my most uncomfortable educational experiences but I persisted. I was fascinated by the assumptions made by this social science that pretends it is a hard science. And some of the math even started to make sense. At one point we had a take home exam which I did fairly well on except for one question that was worth a large number of marks. As the professor was reviewing the assumptions to the question I realized that I had read the assumptions quite differently. I found the courage to put up my hand and let him know that to me the question meant x, not y as he had stated it. He worked the numbers through based on my assumption and it turns out I had the right answer based on that different starting assumption. When he checked with the class, about 20% of us had read the question differently than he had intended. He was a big enough man to give us full marks if we had either an x or y response. Yay!
From that moment forward a huge portion of my math phobia fell away. Because I realized that what I had been calling ‘math phobia’ wasn’t that at all. I wasn’t afraid of numbers: I was afraid of looking like a total loser because I clearly didn’t understand and couldn’t play with them the way I could with words. My moment in Economics class showed me that I did understand; I just often started from a different point than more mechanically oriented brains seem to.
A couple of years later I could no longer avoid that dreaded stats course so I very reluctantly signed up. Lo and behold I got a young lecturer who didn’t believe that traditional statistical analysis were the only way to gain results. Sure we did a bit of stuff around chi squared, etc. but mostly we looked at qualitative rather than quantitative survey methods. What a brilliant course that turned out to be.
By then my job had migrated into the marketing domain and doing customer surveys was a big and important topic. This qualitative approach to stats was a massive benefit to me because it taught me how important language is to creating great, useful and bias free questions. I also discovered that it was okay for me to focus on that stuff and leave the actual manipulating of data to the statisticians who could do it with elegance and accuracy. In this course I also learned a saying that has stayed with me to this day. I think of it always when I hear ‘experts’ flogging their data to prove a point. It is: If you torture numbers long enough, eventually they will confess.
By this time I was married to a man with an advanced degree in statistics and an undergraduate minor in English. Interesting combination. And he helped me to recognize that mathematics is a language where number combinations rather than letter combinations carry meaning. I am clear that it is a language that I have only the most rudimentary knowledge of, kind of like my knowledge of German. And yet, despite having only a basic understanding of the manipulation of numbers, I get many of the messages that math has to offer us. Before I ended my corporate career I had actually become quite formidable in the boardroom for asking tough questions about the math behind positions, policies and propositions people were putting forth.
I love Professor Hacker’s idea of liberal art courses on, say, the history of mathematics or what’s so important about certain mathematical concepts or even how qualitative and quantitative approach support one another. I’ve kept a small book by John Allen Paulos on my bookshelf for decades now. Whenever I begin to doubt my mathematical abilities I have a read of one of its chapters and it reminds me that I am far from a mathematical dummy. Get hold of Beyond Numeracy is you want to read about math in a way that makes sense to the non-mathematical mind.
I’d also like to thank my ex husband for helping me to understand this domain which used to terrify me so much. Greg is a part-time math tutor whose specialty is working with adolescent boys who aren’t doing well with their math studies. A big part of his success comes from the fact that he treats them as adults, but a bigger part comes from the fact that he finds out what their world is about and then finds ways to make math relevant to their lives or potential futures. I’ve watched as he’s helped steer many young men and women onto a productive and meaningful path after they’ve teetered on the edge of educational failure for some time. We need more math teachers like him.
So in closing I’d like to say that I agree that it is time that we take a long, hard look at the whole domain of algebra in our high school and college system. We’ve stopped demanding that kids know how to spell and write a proper sentence (and even to handwrite, it seems) and they still manage to find work and be productive citizens. Why can’t we lighten up around algebra? If it means that a greater proportion of our children make their way through the school system and actually graduate with some self esteem still intact, who knows how our society will benefit.
And that thought gruntles me very much.