On July 28, 2012, the New York Times published an article by Queens College Political Science Professor Andrew Hacker that aroused mathematicians and educators everywhere to respond with alarm and alacrity to the simple question of whether algebra needs to be a requirement for all students. Hacker’s indictment of algebra as the cause of everything from high school dropout rates to the depletion of American brainpower evoked a remarkable critical reaction proving that passion for great education is neither moribund nor lost in the dreck of ed policy quagmires and school reform debates.
Fascinated by this controversy, I asked Trinity’s faculty to weigh in with their views on the role of algebra in the portfolio of a learned person. To their credit, the mathematicians rose to the challenge with brilliance and eloquence. For the next week, I will be sharing their responses on this blog, and I invite other colleagues, as well as students and Trinity graduates — and all readers of this blog — to send me your comments by clicking on the “comments” link below or sending messages to me at email@example.com
Math Specialist Joseph Sheridan wrote this essay with the participation of Luce Professor Kerry Luse, Math Specialist Jennifer Rivers, and Dean Elizabeth Child:
A Response to Andrew Hacker: By Joseph Sheridan, Kerry Luse, Jennifer Rivers, Elizabeth Child
At the end of reading Andrew Hacker’s article “Is Algebra Necessary” I wanted to open the window and scream until I was left voiceless and exhausted. Just because a thing is hard, do we need to eliminate it or change it?
In the fall of 2011, in a small ceremony at the White House, President Obama announced the launch of “Change the Equation,” a public-private partnership of people in America excited about STEM (Science, Technology, Engineering and Mathematics). The idea is great, but our American culture has rejected the idea.
Linda Rosen, CEO of Change the Equation stated in their press release:
“‘I can’t do math’ has become an iconic excuse in our society. Many Americans have expressed it, but I do not believe it’s an accurate reflection of who we are or, more importantly, what we can do . . . . If we don’t encourage our children and students to get excited about math as well as science, technology, and engineering, we are denying them the chance to reach their potential and be prepared for a future filled with opportunity. . .”
We’ve probably all been at a restaurant with a group of people who want to pay individually when one bill arrives. You find yourself in the position of trying to determine how much each person owes. What happens? You look over the bill and you say, “I’m no good at math” you proceed to pass it to the next person who immediately responds the same way you did. Eventually and usually with some hesitancy, one person takes ownership over the bill and calculates the individual costs or divides the total by the number of people at the table. Did you notice how quickly people say that they are no good at math? Did anyone say, I’m no good at reading or I can’t read? When and why is it acceptable in our society to say we’re no good at math? We’d be embarrassed to declare that we’re no good at reading, yet it’s quite acceptable in our society to say that we can’t do math! In today’s information age, mathematics is needed more than it ever was before – we need math! Problem solving skills are highly prized by employers today. There is an increasing need for math, and the first step needed is a change in our attitudes toward and beliefs about math.
Even highly educated people that are not in a STEM field will state in public “I’m not so good at math”, or “I can’t do math.” I have heard some of my own colleagues that are in other disciplines state this. When this socially acceptable, cultural norm began is unclear, but what is maybe a more important question is: “how educators can make this type of statement socially and culturally un-acceptable.” Cultural and social acceptance of “chosen” ignorance or refusal to tackle that which seems a difficult task runs counter to all that academic settings hope to foster in students but also sets the stage for a society of people who shy away from tackling the challenges that could catapult them onward to new and innovative ideas.
The problem lies neither within mathematics nor in the sub-topic of algebra. For the most part, teaching mathematics has not changed since the days of Pythagoras, Plato, Euclid, Archimedes and Muhammad Al-Khwarizmi. The problem lies with our cultural conversations surrounding the subject.
A quick look at statistics across the country shows, as Andrew Hacker points out, that math is the greatest barrier course to students, and students that fail math in their freshman year of college are likely not to return. Andrew Hacker also points out that students in other countries score better on mathematics tests – which is indeed true. But, he states that “it’s their perseverance, not their algebra that fits them for demanding jobs.” It follows, then, that eliminating algebra from the math curriculum would not only be teaching our students to quit math, but would teach them to forego attempting to persevere when faced with difficulty. If mathematic success is so closely tied to academic resilience, the simple statement “I can’t do math” becomes increasingly problematic—as it is a commentary on a person’s belief that failure is his inevitable future. It is imperative, then, that the cultural conversations surrounding mathematics must change.
Dr. Hacker’s solution of teaching “Math for the Liberal Arts,” with a focus on applications such as the Consumer Price Index misses the big picture in that a thorough understanding of applications requires comprehension of algebraic manipulation and mathematical modeling. After all, what is a mortgage calculation other than an exercise in changing the values of one or more variables and watching how they interact? Algebraic applications taught in a vacuum are of little value in terms of teaching students how to think. Teach a student how to solve a CPI, and they will be informed in one specific content area. Teach a student how to model a real life situation with algebraic concepts, and they will know to think analytically.
Algebra and other 100-level mathematics courses do not have to be seen as barrier courses to higher education; rather, they should be viewed as gateway courses to the future. The best way to change the cultural view of mathematics—from barrier courses to gateway courses—is by employing pedagogy in the very first freshman algebra course that focuses on building the student’s self-efficacy. Students with a high self-efficacy believe that difficult tasks, such as algebra, are to be mastered rather than avoided. Additionally, students with a high self-efficacy will persist in their educational goals. A penchant for persistence must be ingrained in the students of today if they are to become the problem solving aficionados of the future. The primary focus of those professors teaching freshman in any discipline is to teach the students to think. In the case of mathematics, algebra is just one of the avenues used.
What we, as educators, all know is that “placing blame” cannot continue. Placing blame, as seems to be vogue, with grade school to secondary school teachers, curriculums and the “teaching to the test” modes is fruitless and serves no purpose. Colleges that attempt to remediate high school mathematics, finding fault with previous teaching methods, do nothing more than compound and extend the problem. Instead of continuing this “blame game,” colleges need to rewrite their algebra course content summaries (discontinuous functions, for example, is not a topic typically considered in an algebra course) and curriculum in their entirety focusing primarily on improving and building the student’s self-efficacy.
Teaching algebra to college freshman that have struggled with math their entire lives and have heard how hard the subject is, reinforced over and over again by many adults, is the culture that math instructors are teaching in. While this is a difficult cultural climate, standards and rigor should not be abandoned for the sake of student self-esteem. Rather than giving students a shoulder to cry on, or “extra credit” so that they can pass, mathematics instructors should foster in them the tenacity to strive for mastery of those things that initially proved difficult to grasp! Record the student grade in bright red ink – with a note for them to see you for help.
It is interesting how in sports, when the game is difficult, it isn’t made easier or even eliminated. Society doesn’t say, “This game is too hard. It should no longer be played.” Instead, society looks to coaches to encourage their players, change plays, reassess the starting line-up in an effort to ensure the team’s overall success. Teachers, much like coaches, must work tirelessly to build students’ self-efficacy so that during moments that seem like defeat, students believe that they can solve impossible looking math problems; that they can discover the answer to the problems set before them.
Yes, students might still encounter difficulty in algebra even after their self-efficacy is built up, but that doesn’t mean that algebra should be eliminated. Like our students we should be willing to reconsider, over and over again, the answer to the problem set before us—we should, first, consider changing our approach to the equation.
The solution is not easy; in fact it is very hard. We are teaching our students to persevere in the face of a difficult concept. We are putting into practice exactly what we preach— students and instructors should not give up even if it is a difficult subject to master and equally difficult to teach. We shouldn’t overlook institutions that are making the best use of all of the resources available to them and achieving measurable success in their algebra courses, because they prove it can be done.*
Contributors are Elizabeth Child, PhD, Dean of the College of Arts and Sciences; Kerry Luse, PhD, Clare Boothe Luce Assistant Professor of Mathematics; Jennifer Rivers, M.A., Writing Specialist and Joseph Sheridan, M.Ed., Mathematics Specialist at Trinity Washington University in Washington D.C.
*Of entering freshmen at Trinity Washington University that successfully complete their introductory algebra course, 70% or higher pass.
Next: Dr. Sita Ramamurti