Let me clarify. I'm not asking do you believe in algebra in the same sense as do you believe in the tooth fairy (full disclosure: I do not). I'll posit that algebra exists. Rather I'm asking if you believe in algebra as a separate course/curriculum that we should teach in high school.
After my last post, Dean Shareski wrote a thought-provoking post that asked whether it was possible to offer a customized educational experience in a standards-based system of education.
Our current system and structure fights personalized learning with nearly every new policy and protocol it can generate. The system craves standardization while we desperately need customization. These competing ideals butt heads constantly and for those teachers who do believe in personalizing learning, they live in perpetual frustration... In the end, without a restructuring of time and current curriculum requirements the best we can hope for is small pockets of success or the 0.02 percent of students whose passion happens to be trigonometry or Shakespeare.
Dean later acknowledges, however, that while he wants personalization, he also wants students exposed to a broader range of ideas:
While I'm busy advocating for changes that might support an education that fuels and fosters students' passions, I worry that we lose sight of what a liberal education is all about. They don't know what they don't know. Providing students with broad experiences that invites them to develop a variety of skills, understand and appreciate diverse perspectives and potentially uncover hidden talents and interests speaks to a fairly well accepted purpose of school... If we were truly starting education from scratch today, I can't imagine we'd build the same system we have. There would be lots of discussion as to what types of content all students need. Even if core content and skills could be determined, we'd never teach them all as segmented subjects taught in isolation in 45-minute increments.
And therein lies the dilemma -- is it possible to provide in a systemic way a customized educational experience for all students that both allows and encourages them to pursue their passions, but also exposes them to the wide range of human endeavors that they may have little or no knowledge about and therefore wouldn't be able to even know if they were passionate about in the first place?
Which brings us back to algebra. I teach in Colorado, which recently adopted the Common Core State Standards. In general, I believe the Common Core Math Standards (pdf) are much better than most standards that came before them. First, there are fewer of them, with 156 standards for grades 9-12. In addition, 38 of those standards are identified as "advanced" standards, which leaves us with 118 standards for all students spread out over four years of high school, or just under 30 per year. That's much, much more doable then what we had before, and I believe targets much more of what I would consider mathematics that is essential for people to know.
But it still begs the question of whether all students need these 118 standards. For example, do you believe that all students (scratch, that, all people) need to know that "there is a complex number i such that i = -1, and every complex number has the form a + bi with a and b real?" (CCSS, N-CN 1). Or how about "prove the Pythagorean identity sin(x) + cos(x) = 1 and use it to find sin(x), cos (x), or tan(x) and the quadrant of the angle?" (CCSS, F-TF 8).
(My not-so-modest proposal is that no state legislature is allowed to require standards that they couldn't demonstrate proficiency on themselves. Since they are clearly successful adults and they are saying that these standards are necessary for all students to be successful, surely they'd be able to demonstrate proficiency by taking the same tests our students do. But I digress.)
As G.V. Ramanathan recently asked in the Washington Post:
How much math do we really need?
In an age of information abundance, when Wolfram Alpha can do pretty much all of high school math quickly and at no charge, do all students need to be able to know all 118 standards? When instructional videos (either homegrown or created by others like Khan Academy) exist that replicate many aspects of a traditional math classroom and allow students to learn the skills at a time and a place of their own choosing, what activities should be taking place in our math classrooms?
Consider these statistics:
1985: 3,800,000 Kindergarten students
1998: 2,810,000 High school graduates
1998: 1,843,000 College freshman
2002: 1,292,000 College graduates (34 percent)
2002: 150,000 STEM majors (3.9 percent)
2006: 1,200 PhD's in mathematics (0.03 percent)
(source: presentation by Steve Leinwand, American Institutes for Research at NCTM Regional Conference in Denver on October 7, 2010. His source U.S. Statistical Abstract)
There's lots we could talk about with those statistics, but I'm just going to focus on what percentage of our students truly need the Common Core Math Standards. I would suggest that it's most likely somewhere between the 3.9 percent and the 34 percent, which makes me wonder how "core" they really are. While I think Common Core, combined with replacing calculus with probability and statistics as the capstone to high school mathematics for most students, would be an improvement on much of what we're currently doing, I'm still not sure whether teaching algebra as a separate course is the best way to accomplish it -- even for that small subset of our student population that is passionate about math and science.
Can we find a way to have students whose passion is math and science explore rich, meaningful mathematics that isn't divided up into courses (Algebra), semesters (first semester linear, second semester non-linear), and units (Chapter 5: Writing Linear Equations)? Can we do this in a meaningful way for all students, even those who currently don't have a passion for math and science? Can we do it in a mathematically coherent way that doesn't impact a student's ability to progress to higher-level mathematical thinking should they choose to do that? Can we do this within a system that -- at its heart -- is an assembly-line model designed to mass produce a fairly standard product?
I think this is essentially what Dean -- and many of us -- are asking ourselves. Is there a way to combine the best of both? The best of passion-based learning and a liberal arts education that exposes students to some "standard" body of knowledge that we believe all people should be exposed to. Can the current system -- with all its flaws and all its successes -- adapt to a personalized, on-demand, anytime, anywhere learning environment? Or do we have to start over with a system that is designed to meet the needs of the learner and one that -- at its heart -- is antithetical to a standards-based system?
I honestly don't know. Because while I do believe the current system is designed to meet the needs of a rather small portion of our students, I'm not sure I can clearly define what mathematics education would look like in such a new system. As I stated in a previous post, I believe we can have high standards without standardization, yet like Dean I struggle to envision exactly what that looks like in practice in any kind of systemic way.
So, do you believe in Algebra as a separate course/body of study in high school? Or, like the tooth fairy, is algebra -- and standards-based, one-size-fits-all education -- something we should've outgrown by now?