Active Calculus

On Tuesday 10/2, I was honored to speak in the MIT Electronic Seminar on Mathematics Education.  The recorded video from the seminar is now available to view; my slides are also posted.  If you watch/listen to the recording, I apologize in advance for the fact that I struggled with my voice and a cough as I was getting over a cold.

I promised the participants that I’d follow up by reading through the chat stream from Zoom, responding to any issues that I didn’t get to in the seminar and sharing resources that others suggested.  First, here are a two lists that I think others will find interesting and useful, most of which come from the many participants:

Phrases that people suggested to describe active learning:

+ inquiry based learning
+ making thinking visible
+ student centered
+ students drive the mathematical agenda: the discovery of the mathematics
+ actively engaging students in the classroom in authentic mathematical problem solving
+ the instructor inquires into student thinking as students inquire into mathematical content
+ productive struggle

Examples of free or open-source materials the participants use:

+ Desmos classroom activities – https://www.desmos.com/
+ We use OpenIntro’s statistics textbook – https://www.openintro.org/stat/textbook.php?stat_book=os
+ “find the error” by doug shaw – http://uni.dougshaw.com/findtheerror/index.html
+ I get lots of ideas from http://www.iblcalculus.com/, whether or not I implement them as an IBL activity or not
+ Poll Everywhere – https://www.polleverywhere.com/
+ http://mathlets.org/
+ Also Active Calculus multivariable – https://activecalculus.org/multi/
+ This is K-12 but has great tasks. Some of the higher grade level tasks can be used with college students: https://www.illustrativemathematics.org/content-standards
+ I am planning to use this next semester for an Abstract Algebra Course for Secondary Pre-service Teachers https://taafu.org/ioaa/index.php
+ Wolfram Demonstrations Project – https://demonstrations.wolfram.com/
+ Siefken’s linear algebra notes (I think the following link is right) – http://iola.math.vt.edu/
+ Good Questions Project at Cornell for “clicker” questions – http://pi.math.cornell.edu/~GoodQuestions/
+ wolframalpha.com for quick calculations and checks between pairs/groups
+ https://www.artofmathematics.org
+ CalcPlot3D – https://www.monroecc.edu/faculty/paulseeburger/calcnsf/CalcPlot3D/
+ geogebra – https://www.geogebra.org/
+ http://math.colorado.edu/activecalc1/index.html
+ pretextbook.org (this is Rob Beezer’s new publishing language that Active Calculus is written in)
+ MIT Opencourseware https://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/
+ These Desmos Activities have some additional questions that are not in the Preview Activities in the book https://github.com/sergeballif/sergeballif.github.io/blob/master/Desmos/DesmosActivities.md
+ Mathquest at Carroll College: http://mathquest.carroll.edu/
+ David Austin’s Understanding Linear Algebra:
http://merganser.math.gvsu.edu/david/linear.algebra/ula/ula/ula.html

Questions.  Participants asked a host of great questions.  I’ve listed below all of the ones that came through by chat.  If memory serves, I responded to all of them but one.  I will refer people to the seminar recording for almost all of these, and here I want to respond to the one that I didn’t get to, which is noted in red below.

> I’d be really interested to hear more about how you went about developing the activities — this would be really helpful for me in thinking about other classes where something as great as AC doesn’t yet exist.

I started small.  Early in my time at GVSU, I wanted my students to engage in more active learning.  So I started writing individual activities.  Usually I tried to think of these using the following criteria:

  + provide a rich and meaningful context that is accessible to students
  + ask a sequence of questions that is clear and focused
  + plan for each activity to be do-able in 15-20 minutes by students who are engaged
  + challenge students to reason in multiple ways and from different perspectives

After I’d taught calculus 4-5 times, I had a collection of maybe 20 such activities, adding to the list each time I taught the course.  Then I learned that several of my colleagues were doing the same kinds of things and asked them to share.  After some light editing and additional writing, my collection of activities for calculus 1 grew to 50 or more; when I printed it as a coursepack and had students buy it for $6, it was about 100 pages (activity statements with room to work).  That pack of activities for calculus 1 was pretty fully developed over a 10-year window of time.  I used that as the basis for the textbook, for which I was granted a 1-semester GVSU sabbatical to write the first four of the eight chapters.

My advice for developing your own activities for courses where you can’t find good resources is:  play a long game.  It’s completely fine to start small and build on your work over an extended time.  While the status quo might not be what you aspire to, the status quo is still ok.  Just work to make the course better every time you teach it.  Over a long career, it’s amazing (still almost astonishing to me) how these resources accumulate over time and can end up producing something that others find useful.  And:  share your work with others.  We have a lot of power to develop rich materials when we share with one another since it lowers the duplication of effort and improves the ideas that we often develop in isolation.

The rest of the questions people asked that are addressed in the seminar recording follow.  I’m very grateful to everyone who participated and contributed, and again to Haynes Miller and MIT for the invitation to speak and hosting this ongoing seminar.

> why is workbook by request?
> Do your students bring their own computers to class?
> How do you grade writing assignments?
> Are these webwork problems available to be added to other problem sets (not linked to the text)? do students need to create an account?
> How large is your class?
> What do your meeting times look like? (That is, how many times per week and for how long?)
> Can this work with 50-minute lectures?
> in class are students all working on a set of shared problems, or is it more individualized for each student
> How many students actually complete the pre-class activities?
> What is discussed during the ‘daily debrief’?
> I notice there is no “wrap up” at the end of class. Is that on purpose?
> Would you be comfortable using the same structure in a class of size 200?
> Are all students comfortable with working in groups? Is individual work welcomed? I am also wondering what a student would do if they finish the exercises quicker than others
> could you talk a little more about structures to provide for different learning pathways for students with varying prior experiences with mathematics and confidence in their abilities
> deskwork vs groups at a blackboard?
> How did you handle the “coverage” issue? Did you have to give up content?
> Do you collect pre-class activities? How do you handle all the paper?