Blog Archives

Curvature (part 2)

In my last post Curvature, I showed how the curvature, along a path is equal to: . I then asked a “challenge” question about how one could compute the curvature without referencing a velocity or acceleration vector. I have slightly rephrased the question below: Is

Posted in Multivariable Calculus


There is a natural way to compute the curvature for a curve whose position is given as a function of time, . The following is the vector proof which shows how the velocity and acceleration vectors can be used to compute the curvature at any time. Is there

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Posted in Multivariable Calculus

Apple juice and vinegar — Chemistry prompts about weak acids

Generating interest in weak acids We started a unit this week applying equilibrium concepts to acid base chemistry. To motivate this discussion, we used prompts to engage students in the critical thinking skills of problem solving and lab design. Apple juice and vinegar

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Posted in Advanced Chemistry

Geometry: Circular Billiards and Fractal Design

Circular Billiards Circular billiards can be used as an entry point for students to discover the generalized inscribed angle theorem. Inspired by Henri Picciotto’s Lab 1.9 on page 18 (PDF: on the generalized inscribed angle theorem and N. Chernov and

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Posted in puzzles

Lewis Structure and Function

I wrote the following pre-lab activity as a practice for Lewis Structures and to use in conjunction with a great PhET activity. Enjoy!

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Posted in Advanced Chemistry

Can class work be meaningful?

The problems After watching Cal Newport’s wonderful lecture, a question comes to mind: “If you believe that deep work is important for the development of rare and valuable skills, what is the purpose of a teacher?” As a teacher, I

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Posted in Deep work, Philosophy

Deep chemistry questions

I have been using ridiculously challenging (and interesting) chemistry questions for my 1st year chemistry class. To the extent that I have made the questions harder and had students focus on deep practice (as opposed to grades), I have found

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Posted in Deep work, quiz

Rare and Valuable Skills

In Cal Newport’s book “So Good They Can’t Ignore You,” Newport argues that to become world class in a field, it is necessary to dedicate relatively more hours of deep work to the relevant skills than others. Young people who

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Posted in Deep work

Christmas Fractal Competition Vote!

Your SAS Multivariable Calculus Class presents… The Second Annual Christmas Tree Competition! Vote for your favorite here!

Posted in Multivariable Calculus

An end and a new beginning…

Check out the prezi for a summary of our 2 week experiment You’ll find out what our students thought of the experiment. I hope you enjoyed it as much as we did and find their reflections helpful!

Posted in Advanced Chemistry, Multivariable Calculus