As a teacher of mathematics, you have no doubt had multiple students ask what is actually a very complicated question: “Why do I have to learn this?” At one time or another, perhaps while grinding through a series of context-free symbolic manipulation exercises, nearly every one of us has struggled to provide our students with an answer they, and/or we, find satisfactory. But the student “why?” question raises an equally important, but less often-asked question: “Why do we teach math?”
Francis Su, past president of the Mathematical Association of America, has argued that this is a very important question because how we answer it strongly influences who we think should do mathematics and how we will teach it.
So why do we teach mathematics? Paul Ernest (2010), emeritus professor of philosophy of mathematics education at the University of Exeter, UK, offered three major reasons (and additional sub-reasons) why we teach mathematics:
- Necessary Mathematics – mathematics for employment and the economy. Ernest included functional numeracy; practical and work-related knowledge; and advanced specialist knowledge under this reason.
- Social and Personal Mathematics – mathematics for personal and social relevance. Here Ernest included mathematical problem posing and solving; the development of mathematical confidence, including mathematical persistence; and social empowerment through mathematics.
- Appreciation of Mathematics as an Element of Culture -- the importance not only of appreciating mathematics itself, but also its role in history, culture and society in general.
Mathematics education has traditionally emphasized what Ernest labeled “Necessary Mathematics” over other reasons for teaching and learning mathematics. This bias has long historical roots stretching back to the fourteenth century when European mercantile schools first began teaching arithmetic out of an economic need for efficient calculation.
Similarly, arithmetic was added to the curriculum in the American colonies largely in response to the needs of business. And the current standards-based mathematics education reform effort, which continues to be driven by discussion of national economic interests and the associated emphasis on college and career readiness, has its roots in national defense and economic concerns stretching back to WWII and the Soviet launching of Sputnik. (For those interested in the history of school mathematics education in the United States, I highly recommend NCTM’s two-volume set, A History of School Mathematics.)
As early as An Agenda for Action (1980) NCTM argued that students should learn mathematics for more than economic reasons stating that “all reasonable means should be employed to assure that everyone will have the foundation of mathematical learning essential to fulfilling his or her potential as a productive citizen” (p. 16).
In Principles and Standards for School Mathematics (2000) the Council strongly stated that students need to learn mathematics, and by extension we teach mathematics, for reasons beyond, but including, “necessary mathematics.”
- Mathematics for Life – knowing mathematics can be personally satisfying and empowering.
- Mathematics as Part of Cultural Heritage
- Mathematics for the Workplace
- Mathematics for the Scientific and Technical Community (p. 4)
The recent emphasis on college and career readiness standards has certainly emphasized the latter two reasons over the first two as the primary reasons for teaching and learning mathematics. I admit I have more than once told a student that the reason they have to learn something is because “they will need it for college” or “the next course.” Today I appreciate that this response was lazy on my part, and from my perspective, while critically important, not even the primary reason why we should teach mathematics.
I believe the answer as to why we teach mathematics is in part answered in the NCTM Vision statement. The NCTM vision statement in part states that “We envision a world where everyone is enthused about mathematics, sees the value and beauty of mathematics, and is empowered by the opportunities mathematics affords.” In this statement we find an emphasis on the first two reasons for teaching and learning mathematics first offered in Principles and Standards.
What does it mean to be empowered by mathematics? In addition to preparing students for careers and post-secondary education, I believe it means we also teach mathematics in order to equip students for active participation in our democratic society. We accomplish this goal by emphasizing analysis and critical thinking with mathematics so that individuals can identify and interpret claims made by those in power as truthful or false and misleading.
We live in a world where mathematics is increasingly used to characterize societal problems and formulate proposed solutions. Without mathematics literacy, and a strong mathematics identity and sense of agency, members of our society will increasingly find it difficult to comprehend and critique, let alone challenge, many of the decisions and actions of those in power in political, social, scientific, and economic institutions.
Ultimately, I believe we should teach mathematics (and students should learn mathematics) for multiple reasons – a theme that NCTM will expand upon in the forthcoming publication Catalyzing Change in High School Mathematics: Initiating Critical Conversations, which will be released at the Annual Meeting in Washington. In most cases this means we need to increase our emphasis on teaching “Mathematics for Life” and “Mathematics as Part of Our Cultural Heritage.” Teaching mathematics as part of cultural heritage means that we do not just emphasize the dominant culture and heritage. By valuing and developing a better understanding of each other and other cultures, including the multiple contributions various cultures have made to mathematics, we cultivate and nurture student identities. If we teach mathematics so that students are empowered by it, preparation for college and careers will largely take care of itself.
We should never forget, or fail to appreciate, that as teachers of mathematics, each and every one of us is engaged in something much more important that our daily tasks of instruction, curriculum, and assessment. We are engaged in empowering our students so that they can improve not only their own lives, but can also better understand and critique the world around them.
I challenge you and your colleagues to discuss the following:
- Why do you teach mathematics?
- What are your school or math department’s learning goals for students? Do those goals need to be broadened?
- Are your school or math department’s learning goals clear to students and parents?
- Are your school or math department’s learning goals reflected in your curriculum?
If we start by engaging in critical conversations around these questions, many of the debates in mathematics education and how we resolve them concerning our instructional tasks, our curriculum, and our assessments, will suddenly have more clear direction.