What to Teach? What NOT to Teach?

Posted: April 11, 2011 in Teaching and Learning Philosophy

We teach during a very exciting time in the history of mathematics education. Technology allows us to do things that we could not have done in years past.  As a result, I often think to myself…what SHOULD I be teaching my students to prepare them to succeed in this modern, high-tech world? And more worrisome for me…what should I NOT be teaching?

For example, students used to learn paper and pencil methods for approximating roots of numbers that are not perfect squares. Now, students use calculators. Are there other such topics that are, should be, or might become obsolete?

  • What about the rational root theorem? We can find zeros (even irrational) using technology.
  • What about those “tricky” integrals (that I actually love)? wolframalpha.com is easy to use, powerful, and gives much detail about any antiderivative we wish to find.
  • What about factoring quadratics? I find that, with technology, students can use the graph of a quadratic to factor the quadratic rather than to factor the quadratic in order to graph the quadratic!

I don’t know about you, but I often feel that I lack a sense of authority and confidence within myself as I struggle to “cover” a laundry list of topics each semester but feel unable to do so in such a way that allows students to learn deeply big ideas.  I think that many mathematics faculty lament the fact that there is so much material to cover in so little time. Students are not able to learn mathematics in a well connected way that allows them to experience future success as they learn more mathematics. Is it time to engage in professional conversations where we make wise (but difficult?) decisions about what might be eliminated or deemphasized in order to create a classroom learning environment where students are allowed to learn profoundly the foundational mathematical ideas that permeate the mathematics curriculum? I deeply desire that, in the long term, students will experience success in important areas such as problem solving, sense making, and argumentation as they learn to think like a mathematician. How do we empower faculty to transform their curriculum, assessment, and instruction to accomplish this goal?

What do you think? Are we preparing students for a 1950’s world or a 2011 and beyond world?

Scott Adamson

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