Every student in the US has to learn algebra. If this statement is an exaggeration, it’s not much of one. Almost all students take at least two years of algebra before graduating from high school and millions take it again in college. In addition, algebra skills are required in most science, engineering, and other course. But as technology evolves and what it means to be an educated person changes, I think it’s time that we think about why we teach algebra and the way we use it in education. In particular, I think it’s time we stop making algebra skills a barrier to success in college.
Now don’t get me wrong – I love algebra. Really. It’s a beautiful achievement, solving problems that challenged humanity for centuries. It’s also fun, and, as a math teacher at a community college, I enjoy supporting people as they learn algebra’s intricacies. I hope algebra is always available for those students who want to study it. However, if we’re honest about the knowledge and skills needed by 21st-century graduates, workers, and citizens, algebra does not rank high on the list. Even in the technical fields, I seriously question how often algebraic skills are actually required.
The issue is especially relevant in the community college setting because large percentages of incoming students are placed into developmental algebra courses, or below. These are the same courses most of us took in high school, but students have trouble retaining the algebraic skills they learned, especially if those skills aren’t related to their majors. As a result, many students struggle to learn algebraic content that, if they’re not going on to calculus, they don’t need for their next courses – topics like factoring polynomials and solving rational equations with variables in the denominator and synthetic division. The data reveal that students who place into algebra or below are very unlikely to ever pass college level math. And because first-generation college students and students of color are placed disproportionately into low-level math courses, the algebra barrier perpetuates educational and economic inequities.
For all these reasons, in 2010 I partnered with a colleague to develop a new course designed to prepare students who were going on to take college-level statistics. The fact is that relatively little algebra is needed to learn statistics and we thought we could help students succeed in statistics using a different kind of course, a course containing only the algebra students would need for statistics. We hoped to help the majority of students who aren’t heading toward calculus and who need statistics to complete their associate degrees and transfer to four-year colleges.
Fortunately, we were not the only ones working on this idea and we learned a lot from professors at other community colleges already trying this approach. (Learn more about the “pre-stat” community at: http://accelerationproject.org/.) With their help we were able to create our course, called Preparation for Statistics, and piloted it in Fall 2011. In the course, we asked students to engage with real data, using statistical ideas in an interactive and constructive teaching and learning style. We even helped them create their own surveys, collect data, analyze the data, and present it to their classmates. It was work to teach this way, but it was also the most fun I’d ever had in class.
Most important, it worked. Data from our college, combined with other colleges teaching similar courses, show that students from pre-statistics courses are successful in college-level statistics and that they are much more likely to complete their math requirements than students that who took the traditional algebra sequence. The evidence also suggests that the courses helped close achievement gaps for underrepresented students. (http://rpgroup.org/system/files/CAP_Report_Final_June2014.pdf) At our college, the evidence was strong enough to expand beyond the pilot stage. Each year we were helping hundreds of students reach and succeed in statistics.
If taking algebra in college is not necessary for success in statistics, what about other math courses? What about science courses? Isn’t algebra the mathematical foundation of modern science?
Questions like these got me thinking about mathematical prerequisites for general education science courses. These are the science courses that non-science majors usually take to satisfy the science requirement for their degrees, things like astronomy, biology, geology, geography, and basic chemistry and physics. I looked for studies of math prerequisites in courses like these, but have yet to find one (if you have one, I’d like to see it). The marked lack of statistical evidence that either supports or refutes the need for math prerequisites in science courses (or any courses, for that matter) is telling. At my college, most of these courses do not have math prerequisites, precisely because they want to attract non-technical majors to the courses (some of the courses advise completion of algebra, but don’t require it).
I did find some unpublished data, collected at my college and two other California community colleges that offer pre-statistics courses. Aggregating the data from all three colleges, students who took pre-stats courses before statistics were almost exactly as successful in their general education science courses as students who took the traditional algebra preparation for statistics (84% vs. 83%). Even disaggregated, the difference between the success of students at each college was never greater than 10 percentage points and the college (my own) with the lowest success rate for pre-stats students in GE science courses was still 72%, compared to 78% success for their traditionally algebra-prepared peers.
These results beg the question of how students without as much algebra are doing so well in general education science courses. One answer, suggested and bemoaned by some, is that instructors of those courses are reducing the mathematical content of the courses to accommodate students who haven’t had algebra since high school. Another potential answer is that, since almost all students took algebra in high school, a little reminding and prompting enables students to use algebra to the extent that they need to solve the problems.
While both of these are possible, I have yet to see any data that support those answers or any other. In the absence of evidence, I think it much more likely that the real skills needed to do well in general education science courses are things like numerical literacy, critical thinking, the ability to connect evidence to an idea, and academic skills like going to class, reading your book, taking good notes, turning in your homework on time, and, perhaps most important, belief in your ability to succeed. All these skills are taught in both algebra and pre-statistics courses; my experience is that more attention is paid to them in pre-statistics courses than in algebra.
But, what if it were true that science instructors have reduced the algebra content of their classes? Would this be a problem? I say, no. From my perspective, science classes exist to teach science concepts, not to test students’ algebraic knowledge. If, indeed, science teachers are making science concepts more understandable for students with less algebra experience, that would be a testament to the quality of their teaching ability. As I like to say, it’s easy to make an idea complicated and hard to understand; the difficult task is to make ideas simple and clear.
We have been making most science and math courses harder to understand by forcing algebra into them, even though it’s not needed or needed only minimally. For example, in a physics class the height of an object thrown in the air can be modeled quite well by a quadratic equation. Understanding of the scientific principle is demonstrated by setting up the equation. Solving the equation is purely algebraic, but most of the time these “physics” problems aren’t correct until the equation has been solved. In a science class, the science concept should be the primary goal. Solving the equation by hand should be less important, especially when computers with powerful solving algorithms are so readily available.
Here’s another example, from a geometry course:
The geometric concept being reinforced is that the sum of the angles in a triangle is always 180°. But, in order to solve the problem, you have to perform some algebra. We don’t need algebra to understand the geometric idea, but if a student can’t do the algebra they won’t get the problem right.
We force students to do similar (and often more complicated) algebraic manipulations in chemistry, biology, oceanography, geography, economics, trigonometry, calculus, statistics and many others. In my experience it is algebra that trips up most students in these courses, not the non-algebra content. Limits, differentials and integrals are challenging ideas in calculus courses, but factoring from beginning algebra is frequently the biggest barrier to completing a calculus problem.
Of course, reinforcing algebraic skills throughout the math and science curriculum is not necessarily a bad thing, but I think too often we do it because that’s the way we were taught, not because of any considered pedagogical reasons. The cost of this decision is high because algebra courses and algebra’s continued use throughout the curriculum is, as I mentioned earlier, so often a barrier preventing students’ success.
And, while algebra can teach attention to detail, mastery of algorithms, symbol manipulation, logic, critical thinking, problem solving, teamwork, numerical literacy, and more, there are other ways to teach those same skills. My experience teaching pre-statistics suggests that we can teach those skills as well or better outside of the abstract context of algebra.
Higher education is changing at an unprecedented pace. These changes are driven partly by increases in the percentage of the population who go to college, partly by pressures from the federal and state governments for more return on their education dollar, partly by employers’ demands for well-prepared, 21st-century graduates, and partly by huge technological advances. In mathematics, the traditional algebra and geometry sequence, familiar to most of us from our own mathematical careers, is being questioned. The algebra sequence, after all, is designed to prepare students for calculus and beyond. But in a world where the most students are not seeking science, technology, and engineering degrees, do we really need to prepare all students for calculus? I don’t think so and I’m not alone. According to the 2015 report Degrees of Freedom: Diversifying Math Requirements for College Readiness and Graduation, “Alternatives emphasizing statistics, modeling, computer science, and quantitative reasoning that are cropping up in high schools and colleges are beginning to challenge the dominance of the familiar math sequence.” (http://edpolicyinca.org/publications/degrees-freedom-diversifying-math-requirements-college-readiness-and-graduation-report-1-3-part-series) These alternatives are emerging because the knowledge and skills needed by informed citizens of the 21st century can be taught as well or better in other ways and because the cost of continuing to insist on algebra is too high.
I’m open to being persuaded that algebra is as important for college students as we have made it. But, to change my mind, you’re going to need to show that the benefits of algebra are algebra’s alone and that they outweigh the costs of forcing everyone to do it.