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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.
Brown is the New White is the most hopeful, optimistic book about politics in the US I have read. Phillips’ subtitle captures his main argument, made concrete in his first chapter and backed up by thorough evidence: people of color and progressive white folks are the new electoral majority in the US and, if we organize and take advantage of that majority, we can change the course of the nation, making it a better place to live for all.
Phillips’ prime example is the election of President Obama. Through a careful analysis of the voting trends, he shows that the new majority elected the President and debunks the myth that of a backlash against that mandate in the off-year elections. He demonstrates that the Democratic losses in the US House and Senate were, instead, the result of the new majority not voting in those off-year races, precisely because the Democrats failed to engage progressives on the issues they care about.
In addition, Phillips looks at the history of White privilege in this country and how both the major political parties continue to dedicate the vast majority of their energy and resources to winning the White vote, despite the demographic shifts we are experiencing. He shows how those shifts are rooted in the anti-discrimination, voter rights, and immigration policies enacted in the 1960s, now coming to fruition. And, importantly, Phillips outlines the policy priorities for the new majority, the issues that will energize and bring progressive voters to the polls.
Brown is the New White is not a Pollyanna look at the US — there is chapter entitled “Conservatives Can Count” toward the end of the book that warns the other side is aware of the same trends he outlines and is moving to attract those voters as I write — but it is unrelentingly hopeful. When I saw Phillips speak in person, I asked him how he maintains his optimism in the face of so much cynicism in today’s political landscape. Without hesitation, he explained that 16 million Americans have health care today that didn’t eight years ago, that unemployment is down across all demographics, that life for regular folks all across the country is better today than it was before we elected President Obama. The trends, he said, are up and there is every reason to believe that we can continue to improve.
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.
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.
An article from the San Francisco Guardian confirming my assertions about who is going to public school and who is not.
A little more research reveals that the 20,000 school age children not in San Francisco public schools are not all white. However, what I’m now hearing at least anecdotally (but apparently backed up by data I have yet to see) is that the children of middle and upper class parents are going mostly to private schools. And since income breaks down by race, with Whites and Asians topping the statistics in San Francisco, middle and upper class parents are paying to create a racially unequal society.
Furthermore and contrary to what I initially thought, people (mostly parents) are talking about this problem. (I’ve been insulated from this situation because I don’t have kids.) The problem is that voting patterns and political influence are also correlated to class status, with working class and poor parents being least likely to be politically engaged. And so the parents who are most likely to impact the public school systems are paying to remove their children from that system.
At least that’s part of the educational and racial justice story in San Francisco. Is it like this elsewhere? Is the same dynamic playing out in cities across the country?
The San Francisco Chronicle recently published an article, entitled “Latino kids now majority in state’s public schools,” describing the unsurprising news that the Latino kids are now officially more than 50% of all the children in our public schools. The article goes on to discuss the real and potential impact of demographic changes on the political landscape, both local and statewide.
But for me the real news—which may not be news for many—was when I saw the demographics for the more than 55,000 San Francisco Unified School District students:
There’s nothing wrong with these numbers—except for the fact that, while whites make up a little more than 50% of San Francisco’s population, white kids are only 10.7% of the total number in public schools. A little more looking reveals that there are about 75,000 school age kids in San Francisco and 20,000 of them are not in public schools.
These numbers suggest to me that 20,000 white kids—75% of all the white kids in San Francisco—are going to private schools. If I’m misunderstanding these numbers, or if I’m missing some important piece of information, I’d like to know. Really. Please tell me. I’d like believe that white people aren’t deliberately and at great cost to their personal finances creating an unequal and unjust educational system and, therefore, an unequal and unjust society. I’d like to believe that white parents aren’t taking their kids out of schools with children of color in them, thereby depriving all kids the chance to get to know children from other communities and backgrounds.I’d like to believe that there’s a very good reason for the numbers. Please explain.
But if you can’t explain, then let’s start talking about the racism we are perpetuating and what we’re going to do about it. I think we could start by leaving our kids in public schools and by working and paying together to make those schools the best they can be.