Related: Academics, Mathematics, Students

Voices of Trinity: Nyamekye and Chiang on Algebra


No surprises here, Trinity’s faculty provide strong and passionate reasons why Algebra — and so many other subjects — are essential for our students and graduates.  The “algebra doubters” of the world seem to miss the point about the inter-relationship of knowledge and the formation of advanced reasoning.  While many of us found math daunting in our high school and college courses, we also cannot imagine being college graduates without the foundations that algebra, calculus and statistics provide for almost all disciplines.

As Dr. Nyamekye points out in her comments below, the real problem is the pedagogy of K-12 math educators, a topic that we need to take on and solve in our teacher education programs.

Here are the thoughtful comments from Math Specialist Dr. Farhaana Nyamekye, and Associate Professor of Mathematics Dr. Lee Chiang:

Dr. Farhaana Nyamekye on the “Is Algebra Necessary?” Question:

Thinking and problem solving are necessary skills used in daily activities, and algebra can serve as one avenue for helping students to develop these skills. I would agree that certain topics covered in algebra are related to quantitative reasoning that students may need on the job, while others are not.  The use of equations for example is utilized in fields of business (calculating costs) and health (calculating BMI) and are necessary, while operations of factoring trinomials and completing the square are likely not as necessary and/or relevant to many fields. The question of whether algebra is necessary in part depends on what the goal is for American students. If the goal is for helping students build a certain type of intellectual capital and to have a technological advantage, then yes, I would argue that is it necessary. If the goal however is for students to use algebra efficiently on a daily basis in their everyday lives, then for a musician or actor for example, it is probably not necessary.  For these students, there should be alternatives to algebra that still develop numerical thinking.

In response to Hacker, I think that the issues of students struggling and failing are inappropriately used to warrant a claim or sentiment about algebra being unnecessary.  The act of questioning algebra’s necessity, evades the real questions of “why are millions of students struggling?” and “why is algebra feared?”  The main impediment to college graduation on the surface might appear to be freshman math, but in reality, is the often non-existent or poor mathematical foundation that many American students receive in the K-12 system of education, coupled with deep-seated math anxiety and negative mathematical experiences. There is much educational research to support that many teachers of mathematics are inexperienced, afraid of mathematics, not qualified to teach mathematics, lack proper certification, and the list goes on.

Like algebra, English is also a stumbling block for all kinds of students, but we dare not say that it is wrong to expect all students to master English, or that English is not really necessary for nursing or applied mathematics. I personally have never been asked to identify linking verbs or provide an analysis of Steinback as a part of my job, but someone felt these skills were necessary for me to learn. When a teacher asks a first grader to fill in the box for box + 3 = 5, the student is in essence doing algebra; it is just not referred to as “Algebra” at that level.  There are first graders that stumble with the task of finding the number that should go in the box.  If we take Hacker’s perspective, first graders should not be subjected to this ordeal, and expecting them to do this problem will cause many of them to drop out of elementary school.  Where do we draw the line?

Many questions arise from reading this Hacker piece. If we view algebra as unnecessary, then technically could we not also view trigonometry, geometry and calculus as unnecessary since they are probably not needed for the jobs that the majority of students will have? Does that mean that these subjects should not be made mandatory either?  Many college programs require students to learn history, religion, philosophy, and environmental science.  Hacker suggests that there is no evidence that  being able to do an algebraic proof leads to more “credible political opinions”, but neither is there evidence that understanding sedentary rock formations in Environmental Science  or the way of the Dao in Religion 101 will lead to these, nor are these topics needed to function in various types of employment.  Yet still, these topics are deemed necessary.  Should we not “subject” American students to these topics either?

We could technically argue that demanding subjects like religion and history (I found history to be quite demanding) are also an attempt to “elevate a profession’s status” as Hacker suggests, but we typically do not. Algebra is unfairly painted as the villain in students’ quest for academic recognition because students struggle with it, while English which also plays a political role in our educational system via its dominance in high schools exit exams and college exit, remains virtually unscathed (perhaps because it is not as objective in nature as mathematics).  I think that an alternative to critiquing the utility of algebra, is to focus on improving access to quality mathematics education at the K-12 level.

Dr. Lee Chiang Comments on Is Algebra Necessary:

I read Prof Hacker’s article and got shocked that he concluded “But there is no reason to force them to grasp vectorial angles and discontinuous functions.” He does not seem understanding that these angles and broken functions(like on/off switches) are everywhere in our daily life, including the statistics he used to support his points. But statistics is established based on algebra and geometry. If statistics is a must, how could we skip algebra?

Many majors at Trinity require Math110, Intro to Statistics and Math210, Inferential Statistics, for an obvious reason: Students need statistics knowledge and skills after graduation. In the past ten years, math faculty members have worked closely to develop new curriculum for these majors. In addition to teach theories and applications, we keep up with new computer software developments. SPSS, a real stat software at work, is used to enhance teaching statistics at Trinity (though not adopted by almost all textbooks for too complicated). The two SPSS workbooks developed for these statistics courses, co-authored by Sita and I and sponsored by President’s 2003 Summer Grant, have been updated every year to match up the newest version of SPSS.  Students graduated from Trinity and took Math110/210 can start using SPSS at work right away.

We do require students to complete algebra and more before taking statistics. In my opinion, no algebra, no statistics.

I just came back, on behalf of Trinity, from an international math conference in China, titled “Mathematics in 21st Century, Advances and Applications”. During the conference, many presenters reported new applications, for example oceanography, traffic control, tax collecting, and etc. I myself presented my new research in simulating interaction between counterinsurgency and insurgency.

Thanks to all Trinity faculty who contributed to this conversation!

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Patricia A. McGuire, President, Trinity, 125 Michigan Ave. NE, Washington, DC 20017
Phone: 202.884.9050   Email: