Escaping the Lectureculture

For years now I’ve been a reader of Robert Talbert‘s column Casting Out Nines hosted by The Chronicle of Higher Education. Last week he wrote a post (“Is lecture really the thing that needs fixing?“) that gave me a lot to chew on. Here’s where I find myself today:

  1. Lectureculture is a set of machinery that self-replicates and it has political, social, psychological, instructional, and institutional components. It is pervasive and I find it in the world all around me, and some of the cultural natives don’t even recognize its existence.
  2. When I run a course, my #1 goal is to help learners move from being introduced to a concept to understanding and displaying mastery of the concept. Lecture is not the most effective way to help learners*.
  3. If I do nothing but lecture in my classes, I am helping sustain lectureculture and I am not helping my learners toward mastery the best I can, in violation of my #1 goal.

My plan of action: I’m teaching “Calculus II” again this semester. Although I’m using a standards-based approach, I must fess up that last semester nearly all of our class time was devoted to either lecture or assessment.

I am a lectureculture native and it is hard for me to let go. But I have come up with two ways I want to add non-lecture content delivery this semester (that don’t involve me tossing out all of my old materials).

First, I plan to continue last semester’s “Madness Mondays.” On those days, I introduced my students to ideas not necessarily tied to our course. I wanted to pick topics that I thought would inspire curiosity or happy befuddlement in my students, so they would walk away wanting to know more about what they had heard. (Examples: The Cantor set. Hilbert’s Hotel. Countably infinite vs uncountably infinite). I hoped to approach these ideas using a type of moderated discussion, letting the students ask questions to each other and talk about what was perplexing, interesting, fascinating, confusing, etc.

Second, I was really inspired by a recent video by Jo Boaler about “Number Talks” and I plan to try doing a weekly “Number Talk” (or something like it) with my calculus students.

My husband asked me why I wasn’t combining these things under one umbrella. To me, they hit two different–but equally important–goals for my course that can’t be found directly on our syllabus. They are

  1. I want my students to develop an appreciation for mathematics outside of what will show up on their next exam. I want them to be exposed to the kinds of questions mathematicians ask. I want them to practice the difficult skill of speaking with others about mathematical ideas.
  2. I want my students to become more fluent in numeration. I want my students to practice looking at the same problem from multiple perspectives. I want my students to see mathematics as a creative endeavor and get away from the idea that what mathematicians do is “apply a standard algorithm, proceed the same way, get the right answer.”

[Many of my digital colleagues seem to use some type of presentation requirement in their courses to get at item (1.) above. While I think that having students present math problems, solutions, ideas, etc. to each other would help develop this skill, and other skills too, I remember how terrified I was as an undergraduate at the thought of standing up in front of people and I don’t think I could impose those feelings on anyone in my classroom.]

Hopefully I will come up with other ways to push back against lectureculture in my classroom.

*As I was writing this post, the following MOOC announcement appeared in my Twitter feed & seemed quite apropos:


Reboot of my list of standards

I’m about to start my second semester of using a standards-based approach in Calculus II. One of the things I wanted to change was my list of standards. Last semester, I ended up with about sixteen standards. When thinking about improvements for this semester, I wanted to pull apart my standards in a different way and I wanted to have more of them. Also, another big goal I have is to offer a broader picture of what calculus is really about. I’ve decided to re-categorize my (now) thirty standards under some Big Questions. Here’s what I have so far:

  • What background skills are important before we begin?
  • What kinds of applied problems can we solve using integration?
  • What techniques can we use to evaluate integrals?
  • How can we add infinitely many things together?
  • When and how can polynomials be used to approximate functions?
  • How can we model phenomena if we know how they change over time?
  • What can we say about the motion of objects moving in more than one dimension?*

Here’s a Dropbox link to my current standards list: m220-f2014-standards.pdf (Apologies if this link isn’t stable; this is a working document undergoing continual changes)

* Thanks to Joshua Bowman for help with this last one!