I attended the University of Chicago’s “Many Ways of IBL” conference last week. Here is a brief list of my thoughts for the week, in no particular order.

- It was utterly great to see a couple old friends. I have been blessed to have had good colleagues everywhere I have been, and I wish that I could have taken many of them with me to my current position.
- It was great to meet a bunch of new friends. I hope to stay in touch with many of them.
- Part of the conference was to watch John Boller teach an IBL class on real analysis to a bunch of super-motivated high school students. Both John and the students did a fantastic job. I told John that it was so enjoyable that he could charge admission.
- One big thing I was failing at with IBL last year: I did not discuss the statements and meanings of the theorems before students presented. Boller did this, and it must help students understand everything about the course better.
- Paul Sally continues to be amazing. He is also hilarious.
- In many classes, I have students read the textbook rather than lecture. I have no idea how to mesh this with IBL, but it is something I value. I realized from the conference that the reason why I value this is that it helps students learn how to learn on their own.
- Even though I have been calling my recent hybrid classes “a mix of Peer Instruction (PI) and IBL,” I no longer think that I have been doing IBL. At best, it is IBL-Lite, although it is probably just “students presenting problems.”
- This will lead me to alter a paper that I recently wrote on a PI/”IBL” calculus class; I will now qualify that my IBL is pretty weak.
- I am now fairly certain that my courses for pre-service elementary education majors
*are*IBL. - I might do IBL in my abstract algebra course this spring. If so, I might interweave IBL and PI differently: I might mainly do IBL, but then have some PI days to make sure students understand the ideas that have already been presented.
- In abstract algebra, I might also create a class journal, where students can submit homework problems to an editorial board (of students) for peer review.
- In IBL classes, have students take pictures of the board work. They can then upload the pictures to the course website as a record of what happened.
- Matthew Leingang gave me a nice way of communicating course rules. He has “The Vegas Rule” for his class: “What happens in Vegas, stays in Vegas” where “Vegas” is defined as “the world outside of this classroom.” This is a nice concise way of reminding students to not use previous knowledge and outside sources.
- Leingang also got me excited about paperless grading. Now I just need to find $1200 for an iPad and scanner.
- Ken Gross uses an “adjective-noun” metaphor for fractions, where the adjective is the number and the noun is the whole. That is, you can explain common denominators by doing something like: “units” “units” equals “units” “units,” which is equivalent to “sixths of a unit” “sixths of a units” “sixths of a unit” “units.” Most of the work then is just changing the “noun” and finding the appropriate “adjective” for each of the new nouns.

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Tags: abstract algebra, community, Conferences, Elementary Education, IBL, Math 121, math 331, Pedagogy, Peer Instruction

June 27, 2013 at 9:59 pm |

Bret. Can you elaborate on #4 a bit? Would this be like providing a high-level overview before the students present the gory details?

June 28, 2013 at 3:58 pm |

Hi Joss,

Item #4 might be pretty specific to mathematics. Methods of teaching that are close to the Moore Method (which I am implicitly describing right now) create an outline theorems to prove, axioms, and definitions for the semester, then spend most of the class time having students present their proofs. I didn’t do this particular one, but one example might the Fundamental Theorem of Calculus:

FToC: If f is a “nice enough function,”

1. d/dx \int_a^x f(t) dt = f(x) 2. \int_a^b f'(x) dx = f(b)-f(a).

Students would try to prove this, and then (at least) one student would present her proof in class.

Here is what I was doing: I would say, “Joss: would you like to prove the Fundamental Theorem of Calculus?” You would say “yes,” you would state what the theorem says, and you would present your proof. We would answer questions that the audience has about your proof, discuss whether it was valid, and move on with our lives.

Here is what I should be doing: “Kentavious: could you please read what the Fundamental Theorem of Calculus says?” KCP would read it, I would lead a small discussion about how to think of the FTC, what the significance is, and answer any questions about the statement of the theorem. Then I would say, “Joss: would you like to prove the Fundamental Theorem of Calculus?” And we would proceed as above.

This can’t help but get more students to follow and care your proof, and it would help students understand what the class was about.

I am a little embarrassed that I wasn’t doing that before, but so it goes.

Does this makes sense? Bret

On Thu, Jun 27, 2013 at 4:59 PM, Solvable by Radicals

June 28, 2013 at 4:20 pm

Makes complete sense. I struggle with similar things. Ideally I would take the time to have discussions with the students about where the current topic fit into the conceptual framework of the course or larger topic, both before and after working on the gory details of a clicker question, example or whiteboard problem. But I usually focus all my attention on the gory details and forget about the larger conceptual narrative. The first step to solving a problem is admitting that there is a problem!

June 28, 2013 at 4:28 pm

You put my problem into words perfectly: “I wasn’t focusing on the ‘big picture’ enough.”

On Fri, Jun 28, 2013 at 11:20 AM, Solvable by Radicals

July 1, 2013 at 10:43 pm |

Hi Bret! Nice meeting you at the conference š

One way to incorporate students reading the book is to use an IBL book. I’d highly recommend checking out Carol Schumacher’s Chapter Zero and Closer and Closer to see what an IBL text looks like. The activities and examples are distributed throughout the text so the students are actively working through things as they read.

As far as having students referee proofs, if you are ever interested in having a cross-institutional referee thing (a la Angie Hodge, Dana Ernst, and Andy Schultz), I’m sure someone here at Loras would be interested in pairing up!

July 2, 2013 at 2:35 pm |

Hello!

I will be strongly considering

Chapter Zerowhen I teach our introduction to proofs course. That looks great.Thanks for the offer for the cross-institutional refereeing project. Frankly, I wasn’t even considering the “cross-institutional” part. But I will now!

It was great meeting you, too!

Bret

July 29, 2013 at 3:25 am

Chapter Zero is a great book. It’s what I used for my very first IBL course (as a teacher). I’d love to talk you into using my intro to proof notes, which are free and you can modify them as you see fit. You can find the source here:

https://github.com/dcernst/IBL-IntroToProof

Also, if you and Susan end up doing some cross-institutional peer review, let me know.

August 3, 2013 at 2:32 pm

Hi Dana,

I will DEFINITELY be looking at your notes when I teach the introduction to proof course (I just downloaded them). In fact, I might even request that I teach it next year. Bret

On Sun, Jul 28, 2013 at 10:25 PM, Solvable by Radicals