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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.
The two most common responses when I tell people I meet that I’m a math teacher are:
- People tell me how much they admire and even like math;
- People tell me how bad they are at math, squirm uncomfortably, and kind of sidle away.
In the second, much more common option, I seem to represent all the inadequacies they have felt about math for much of their lives. They try and fail to put on a polite face, instead looking at me as they would a particularly disgusting plate of food. It’s an occupational hazard to have these awkward moments at parties.
Both responses more or less make an assumption that I love numbers and all things numeric. But, as much as I enjoy learning about and teaching math, I don’t love numbers. I love people and ideas. For me teaching is pretty close to a perfect combining of these two: I get to talk to people about ideas. Teaching statistics, in particular, is about helping people sort through all the individual stories they know, looking for a trend or trends; students learn to organize and communicate about data, helping them make decisions in the world.
And as a teacher, the stories my students tell me about struggling with math and with education in general are often heartbreaking. Everyone has a math autobiography, too often filled with a teacher or relative who said something like “math is hard and it’s not for everyone” — a backhanded way of saying telling the student he or she doesn’t cut it. Sometimes it’s more direct (“Math is not your subject” or even “You’re not smart enough to do math.”) and usually these messages are delivered to children at ages 8, 9, or 10.
Another common narrative is of the young person who enjoys math till a certain class or till a certain teacher — frequently around 9th or 10th grade — where the student gets the message that they have “reached their math level” and anything beyond it is impenetrable for their meager talents.
There are, of course, many other stories (and I invite you to share yours in the comments) and this kind of introduction often leads people who are pro-math-and-science to exhort our society to change its attitude toward math, moving to a more math-positive message for children or to calls for increased time and emphasis on math in school. And while that would be nice, I don’t think it’s the job of society to change its attitude toward math and science. I think it’s the job of teachers to change society’s attitude.
Clearly, many people have been trying for generations to do just that, so I’m not suggesting I have all the answers or that I know what everyone should do. But I would like to share some of my experience co-creating a math course using the principles of backward design, just-in-time remediation, attention to the affective domain, and the assumptions that students are capable of high-quality work and that context is important for learning.
Three years ago, a colleague of mine and I set out to create a course that would prepare students to take college-level statistics using these principles. Unlike myself, my colleague was an experienced statistics instructor and as we talked about what to put in the preparatory course and explored the curriculum together, I constantly asked “why do we cover that topic?” and “what’s the purpose of that skill?” To her credit, she never responded that we do it that way because we always have. She never said “trust me.” She always gave me a good reason — or we tossed out that topic. The result is a course in which, unlike every other math course I have ever taken or taught, there are no extra topics; that is, in our course (“Preparation for Statistics”) every topic and every activity and every assignment are directly relevant to preparing students for the next course.
And while statistics is in general easier to contextualize than algebra, if a student does ask why we are studying a particular topic, the answer is always, in addition to any other uses, that it will be used again next semester.
This intentionality about everything we do in the class creates more buy in for students. Combine it with the assumption that students are capable of doing the work and the practice of appropriate support and we have a course that alters students’ perceptions of math (toward being more useful to them) and of themselves (toward being capable of understanding and using math).
For generations math teachers have debated amongst themselves and with others about the best ways to justify and explain the importance of mathematical education, with more and less success. Arguments about the development of problem solving and reasoning skills assume a privileged place for math that is disciplinarily arrogant and willfully ignorant (or even insulting) of the intellectual rigors in every other discipline. Discussions of the utility of skills such as factoring polynomials, solving inequalities, and calculating the volume of a frustum (much as I enjoy these topics) are unconvincing and potentially disingenuous.
It is our job to do better. And from my experience, when we do a better job of connecting what we’re doing in class to something the students want to know, the students respond with curiosity and engagement — the kind of engagement that leads to empowerment, learning, and a new attitude toward math.
And when that happens, people no longer have feel that sinking feeling inside when they see some numbers in an article they’re reading, they no longer have to cringe when they meet a math teacher, and my social life gets a little less awkward.
(*Big ups to the work of the California Acceleration Project and its founders Myra Snell and Katie Hern – my work and the assumptions it’s based on could not have happened without their leadership, intelligence, and support. Snell and Hern are among the finest educators I know.)
Here’s a cartoon that, not only does nothing to refute my argument in the previous post, it also speaks to the entitlement the folks coming out of college appear to have. The not-so-subtle subtext is that getting a job and life in general after college is supposed to be free from pain and misery. Wasn’t my experience and wasn’t the experience of most people I know.
About a year ago, a friend of mine told me he wondered why he had bothered to get an education. He felt that the job prospects and earning potential he had did not balance against the time and money he had invested in getting his Ph.D. He speculated more broadly that college degrees were becoming less and less valuable in our country and asked why we should continue to place such a high priority on college as a nation.
My friend’s thinking, plus the fact that I teach at a California community college, got me paying attention to some of the conversation that our society having about college degrees. In particular, over the last year I’ve been noticing more and more people questioning the value of a college degree. The script for these articles, videos, rants, complaints goes something like: 1) college costs a lot of money and finishing requires taking on significant debt, including some statistics on the amount of debt taken on by college students; and, 2) a college degree doesn’t guarantee a good job like it did in the “good old days,” followed by an anecdote about a college graduate’s job search and maybe some questionable statistics.
A recent (6/13/11) Time magazine article (“Now What? Mortarboards and diplomas don’t get you as far as they used to. These new graduates are in for a bumpy ride.”) is a good example. Along with anecdotal evidence, the author cites a Rutgers University study finding that 30% of college graduates from 2006 to 2010 didn’t find employment within six months of finishing school (there’s no comparison with unemployment for folks without a college degree during the same time). Further, a Twentysomething Inc. poll found that 85% of “graduates are taking shelter under Mom and Dad’s roof.” (The timeline for this statistic is not clear—is it within one year of graduation? Or two years? Certainly, it doesn’t mean that 85% of all college grads are still living at home for the rest of our lives.) These two stats exhaust the quantitative data supporting the article’s title and it concludes that, although science and engineering majors are more likely to find jobs than their colleagues in liberal arts (U.S. Labor Department data), the nationally high unemployment numbers are promoting choosy employers.
Belying the faux-profound conclusion, the tone of the article is decidedly alarmist, ignoring that fact that people with a college degree continue to enjoy higher employment percentages than people without degrees; more education still promotes greater employment, in general, and graduates know it—the same Rutgers study found that 62% of those with a Bachelor’s degree believe that more education is needed to be “successful.” In addition, according to the U.S. Census Bureau, more education tends to increase your income.
More thoughtful approaches to what a college degree means today include Sherry Linkon, at the Center for Working-Class Studies, who discusses the value of getting an education for people headed toward professions such as accounting, education, communications, and social work, for whom getting a college degree is a crucial step on the way to being certified to do the work. At the same time, Linkon points out that colleges force these essentially vocational students into general education classes that don’t seem to have anything to do with their chosen field of work. Importantly, she also discusses the knowledge that working class folks bring to these (and all) professions, much of which is not taught in school.
Then there is a New Yorker article by a college professor who tries to answer his students’ question: “Why do we have to read this book?” He believes that college should exist to educate citizens for democracy, but he’s not sure that’s how our society still uses higher education.
One could legitimately ask if we ever did use it that way. Indeed, self-improvement blogger Brian Kim writes:
Back in the day, everything that was said about getting a degree was true. If you had a degree, you separated yourself from the pack. Not many people were able to get degrees because not many people were able to afford college. It was normally reserved for the rich or upper middle class. And that’s precisely why the degree was so valued . . . because it was scarce. Scarcity creates value.
Like Kim, I think our society has always used college to reinforce the status quo elite, but I also think that in at least the last 50 or so years we’ve also used it for more democratic purposes. The facts are that in the last 50 years, our country has made a college education more available to women and people of color and they have taken advantage of it. According to the U.S. Census Bureau, women outnumber men in college and in degrees earned. In addition, the number of people of color earning degrees is increasing for every group.
The blog posts and articles go on and on, including a paranoia-inducing video put out by the mysteriously obscure, apparent scam organization “National Inflation Association” telling us that our education system sucks and that we should buy gold and silver to survive the coming economic apocalypse.
At the same time, College Board blissfully continues to tell us that “one of the best things about getting a college education is that you have more careers to choose from” and produces lists of the “Hottest Careers for College Graduates — Experts Predict Where the Jobs Will Be in 2018”
Trying to make sense of this cacophony, I’ve begun to think that its purpose is two-fold: to complain about the loss of privilege for those who used to be “entitled” to good-paying jobs; and, to promote the impression that by continuing to democratize college degrees for more and more segments of our society we further devalue a college degree. It’s not a big leap to think college degrees are being devalued by white men precisely because more women and people of color have them.
But beyond the more or less explicit racist, classist, and sexist agenda, these arguments ignore the issue of what happens to degree earners when they enter the job market. It would be great if jobs were equally distributed across all demographics of the degree earners — that would imply that hiring practices had improved greatly and that race, class, gender, and other forms of oppression in our society have diminished — but I don’t believe that is the case. Instead, as we all know, in most jobs white men continue to be more likely to get hired and be promoted than other people.
That means that the crying over the uncertain job market for college grads is almost entirely a tactic to protect white male privilege and entitlement; that is, it’s the same old discrimination in play. And, the people questioning the value of their degrees — whether knowingly racist, classist, and sexist or not — at least all ignore the reality of the privilege that most of them have. As a white man from an middle-class background, my friend’s analysis of his degree may be accurate for him. But for everyone else, the statistics say that a college degree remains a viable path to a better job and economic improvement.
Tonight on Marketplace from American Public Media, they ran a story about a couple and their struggles to make it in the current depression/recession. Part of the dialog between the show’s host, Kai Ryssdal, and one of the guests, Caitlin Shetterley, illustrates people’s expectations about a college degree and the way that is changing:
Ryssdal: So there you are, first week of January 2009, you have a brand new baby, but your husband’s jobs have all been canceled; he’s getting no contracting, no freelancing. The whole country is literally thinking that this is it, because we’ve had the crash in the fall of the previous year. What was going through your mind?
Shetterley: What was going through my mind? I mean, I was angry. I think many of us, many people in my generation anyway — I can’t speak for say, my grandparents’ generation who went through the Depression — but we’ve grown up believing that if we work hard and strive for our dreams, they will come true. And I believed that.
Ryssdal: Past tense, you’re speaking in the past tense. “I believed that.”
Shetterly: Yeah, I did believe that. Now I don’t believe it anymore. I don’t know that just hard work makes it. I don’t know, I think a lot of luck makes it.
Shetterley is critiquing the myth of the United States as a meritocracy. Of course, her comments come in the context of an economic crisis, but I maintain that even in good times, luck, connections, skin privilege, and privilege of all kinds have almost always trumped merit in our society.
This blog post gives a sense of what people are feeling like on the ground. I’ve heard similar sentiments from several people, mostly white middle class folks. What it looks like to me is that as those people are increasingly competing in the work place with people with whom they didn’t used to have to compete. Makes them mad, because they feel entitled to a job — after all, they’ve been told all their lives that a college degree is the key to a good job. The result is a more or less deliberate devaluation of the college degree. That is, as some of us work to democratize a college education, others work to maintain the privilege they’ve enjoyed in the past.
This article is an example of the some of the ways that college degrees have been and continue to evolve. In the past, academia offered degrees in only traditional disciplines. More an more we have professional degrees designed for very specific fields and purposes, often by region (for example, you don’t usually have viticulture degrees outside of a wine-producing region). These trends point to an increased focus on the college degree as a job-producing tool for people from all socio-economic backgrounds. Historically, a college degree was much more a social class marker and a luxury of the leisure classes or the clergy.