Calculus is the first step into a rich mathematical and personal exploration. Photo: Istockphoto.

Scared of first-year calculus? Just grow with it

First-year calculus isn’t what you imagine. It can be the ultimate gateway to personal growth and critical thinking.

By Stephanie van Willigenburg, UBC Department of Mathematics

“Why do I have to take first-year calculus? I’ll never use anything I learn in that class!” is a lament I often hear as a math professor. My response: You’re wrong.

Sure, first-year classes are gateways to more focused upper-level courses with content you’ll use in your career, whether you’re a director at GlaxoSmithKline (Math 442: Optimization in Graphs and Networks) or a business professor (Math 340: Introduction to Linear Programming). However, these classes aren’t only gateways to intellectual and career growth, but also to personal growth.

I see it most vividly in Math 444: Mathematical Research and Writing, a course I’ve designed and taught over the past four years. Students get an authentic research experience by spending 12 weeks in small groups, making discoveries they then teach to the rest of the class. The class culminates with each group writing a research article that they submit on the last day of term. Sounds daunting? You bet, but I’m there with the students every step of the way to cheer on their successes and help them through the stumbling blocks.

Student passions drive the course content — they choose the research topic and focus on their discoveries. My students pursue their interests and strengths: data generation, finding patterns within sequences of numbers, explaining those patterns. Choosing what you want to solve is very different from being told what to solve. You learn to identify a good research question, a good answer, and when to quit when the answer won’t come.

A second stage of growth comes when the students lecture the rest of the class. For many of them, it’s their first try at public speaking. They’re challenged to overcome stage fright and learn how to think, write and speak at the same time. The class provides written peer feedback, which I process into personalized tips for the speakers. In final reflections, students often write that all this growth is what they most appreciate about the course, and they are ready to face their future with confidence being able to work in a team, present their findings and decide what paths are wise to follow.

All math classes can nurture growth. Photo: Paul Joseph/UBC.

As their professor, I’m reminded of what it felt like to give my first lecture and how much I’ve grown since then. Through their eyes, I also learn new teaching tricks or ways of looking at research. Most rewarding is watching my students blossom into confident critical thinkers and team players. I’m always really touched when I’m told: “I’m so grateful, you changed my life!”

But all math classes, including first-year calculus, can nurture growth — improving your communication skills as you explain your homework to a friend, or improving your teamwork skills as you vanquish practice questions together.

So the next time you wonder what first-year calculus is all about, it’s about rate of change — both in math and in you.

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