Continuous Reflection

"If others would but reflect on mathematical truths as deeply and as continuously as I have, they would make my discoveries." - Carl Friedrich Gauss

Continuous Reflection
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Author: Laura

A function defined by an integral

My daughter shared a lovely problem she had encountered in her calculus class: I was inspired to make a Desmos animation: FTC (Evaluation part)


Our Precalculus Text

Here’s what my colleagues Travis Ortogero, Robert Machemer, and I have come up with as an alternative to expensive, heavy textbooks for our precalculus classes. Some sections are more fleshed out than others. We make incremental improvements as we have the time and energy.


Letting the Students Come Up with the Questions: AP Calculus Day 1

The homework assignment I gave my AP Calculus class on the first day of school this year was inspired by Michael Pershan’s well-worth-a-read post I don’t focus my classroom on solving problems. (This was his contribution to Sam Shah‘s fabulous Virtual Conference on Mathematical Flavors). In developing Read more…


Intercepts and Asymptotes and Holes, Oh My!

I’ve been teaching for 27 years. This morning during a discussion of rational functions in a precalculus class, I had one of those why-didn’t-I-think-of this-years-ago moments, when I found myself drawing a Venn diagram on the board in response to massive confusion about holes. My hypothesis about Read more…


Why I Teach [Math]

Inspired by Annie Perkins and her post “For Those Hesitant to Protest” and prodded by a friend to share the following more widely, I offer here the following passage which was my contribution our family’s Christmas letter to family and friends this year. While I do enjoy Read more…


Making Sense of Exponential Models

Exponential growth is a topic that deserves especially thoughtful treatment as part of a high school education because a person who has thought deeply about this ubiquitous phenomenon pays attention to and conceptualizes certain critical issues in, for example, science, economics, and social science, in a fundamentally different way than one who Read more…


Quadratic Functions with Desmos Activity Builder

I thoroughly enjoyed using an activity I created using Desmos Activity Builder over the course of the past couple of days with my precalculus students to help them think in new ways about quadratic functions. These are intelligent people who have graphed plenty of parabolas and solved plenty Read more…


Fresh eyes on end behavior of rational functions

Over the past few years of teaching precalculus regularly, I’ve experimented with a variety of approaches to rational functions in an attempt to find one that will result in students discovering and eventually truly understanding how the equation of a rational function determines its graph. I have never felt very Read more…