Before responding to your post let me go on with the train of thought I started last week in my post about All of high school math in one year?
Teaching math to students who’d rather not be there is not anyone’s idea of a good time. Can anything be done about that? One solution is to not teach math to those students, or to teach them much less math. Another is to help those students change their attitude, but unfortunately, that is difficult. It is difficult because by the time they reach high school, students’ attitudes towards the subject are already formed. It is difficult because we live in an anti-intellectual culture, where everything is measured by its short-term utility. It is difficult because most of us teach the way we were taught, and we were taught with no awareness of how people learn. Worst of all, it is difficult because, well, algebra is difficult. (Algebra being the main obstacle to entry into high school math.)
Back in the day, the problem was solved by having only some students pursue high school math, and condemning the majority to endless rehashing of paper and pencil computational techniques. As concerns about equity increased following the 1960’s, and as many good jobs in manufacturing went offshore, the idea of “algebra for all” took off. Legendary civil rights leader Bob Moses considers algebra to be today’s front line in the struggle for equality. See his Algebra Project.
Unfortunately, the way “algebra for all” was implemented in practice in most schools was by taking the 1970’s version of Algebra 1 and requiring mastery of that material as the entry point to high school math. This has not worked well, as it ignores cultural shifts, technological advances, and the fact that we are addressing a much, much broader population. It leads to a superficial, rote approach that rewards obedience over understanding. And thus it leads to students hating math, and wanting to get out of it as soon as possible.
I’ve written a fair amount about my ideas for a new algebra (see also this shorter article.) And in fact, I co-wrote a book based on these ideas. The book failed to become a best-seller, to say the least, but I have been able to implement this approach with my colleagues at the Urban School, and we manage to keep students “in the game” for three or four years of high school math. This approach, or something close to it, works just as well when it is implemented in public schools, as Jo Boaler‘s research shows (see this post about complex instruction.) It’s not easy, but it works.
My fear is that limiting math instruction to just one year for most students would set us back forty years, to the days where only well-off white boys would take three or four years of math in high school. That meant that all engineers, all statisticians, all scientists were white men. Because believe me, the children of the privileged will NOT be limited to 100 hours of high school math. Of course, that’s not your intention, but if your proposal were adopted in public schools, it would only get more middle class families to move their kids to private schools where they would get the three or four years that colleges require.
I’m running out of steam, and I didn’t respond to your post. I will as soon as I can find the time! And I didn’t even get to the topic I promised to address (how do we differentiate what we teach to most kids vs. what we teach to future mathematicians.)
Well, like I said last time, stay tuned!
2 thoughts on “Algebra for all?”
Henri,I appreciate the continuation of our conversation. I'll try to stick to responding to one post at a time :)I am quite concerned about the equity issue, as you are, and I have read Bob Moses' book on his experiences in the Civil Rights movement and how it informed his opinions about algebra as a gatekeeper class – bringing more students through it successfully provides opportunities that cannot be equaled elsewhere.I don't really believe that all students should have one year of math, as I've said, but I do believe that most need no more than one year of specific mathematics instruction. However, if that is insufficient time, then I am certainly willing to entertain the ideas of slowing down, teaching differently, and providing more authentic exploratory experiences for our students over a longer interval. I am skeptical, however, that: 1) Students who enter high school disengaged from and often actively opposed to mathematics will change their opinions using this longer/alternative model; 2) this is a workable model for public high schools, especially as all students will be expected to pass 3 exams in mathematics (of the PARCC variety, for us in New Jersey) covering all topics from the Common Core State Standards. To be completely honest, my own proposal has a similar difficulty with point 2, so that's a push. To be even more completely honest, the fact that I even have to worry about point 2 is one of the greatest frustrations I have to deal with; it would be much easier for me to imagine alternatives if I was not working in a system that so actively tries to forestall real ones. Anyway….I think we both believe the teaching of mathematics in America is in need of serious work and change, and I am impressed with what you have been able to accomplish in the Urban School. On to the next post!-Mike
What we've accomplished at Urban took a long time to create, and was largely facilitated by the fact we're a private school and don't have to struggle with external mandates. (At least not too much. If our students did poorly on SAT's, and if none of our students took the AP's, we'd be under tremendous pressure to change our ways.)But I encourage you to look at the research mentioned above to read about public school implementations of a program that is in many ways similar to Urban's. The school Jo Boaler studied (“Railside”) also took a long time to create a humane and effective program, but it was an impressive case of doing this work in spite of external mandates and bureaucratic short-sightedness.Bottom line: this is not easy and it does require a team effort, but it's worth it.