Starbird’s IBL

During MathFest a month ago, I was fortunate to have dinner with Dana Ernst, Matthew Leingang, Stan Yoshinobu, and Mike Starbird.

Photo courtesy of Stan Yoshinobu. Pictured (right to left): Matthew, me, Dana, and Mike. Mike is playing the game Wuzzit Trouble for the first time on my iPad.

Mike is pretty famous in the mathematics community: he is a well-known topologist, and for a while now has been one of the more public faces of inquiry-based teaching in college mathematics. Mike is a wonderful storyteller, an entertaining speaker, a good listener, and so positive and friendly with everyone, it is easy to see how he would have a good impact on students. I was pleased that events conspired so that I got to spend some time talking with him.

We walked a couple of blocks from the conference site to the place Matthew had picked out for dinner, and so I got ten minutes of beautiful Portland evening to talk with Mike one-on-one. During our short conversation he mentioned something about how he and Ed Burger (now President of Southwestern University) went about writing their book The Heart of Mathematics. The key point was that in writing the book, he had to give up some of the IBL approach, but he could keep other parts which he found essential. He said something like, “IBL really has two parts, and though we had to give up on students doing all of the development of the mathematics for themselves, we could keep the other part.”

At this point, my ears picked up. Stan had asked me last summer to formulate my own definition of what it is to do IBL. Regular readers (‘sup Vince and Paul), might recall I wrote about that a while back. Dana took a step forward to catch up and listen, too. He had overheard, and the two of us were in the middle of planning for the workshop in Wales to happen a few weeks later. Here was a big chance: we would get an attempt at what it means to teach with an IBL bent from one of the masters. Since Mike’s definition is a little different from what I had, I filed it away to share with you someday. Today is that day.

Mike Starbird’s two part definition of what it means to run an IBL class

  1. The students are responsible for developing and presenting the mathematics.
  2. The mathematics is presented with what might be called a “plausible false history,” in that questions are presented in a natural order that gives them some meaning.

That first part I expected. The second one is close to addressing the issue of intellectual need that I read about in some of Guershon Harel’s work. Why should students care about what you are teaching them? Well, if you can connect the ideas to questions that they can imagine asking and build a sequence of tasks so that this motivation stays with them, they just might care.

Certainly Mike’s definition challenges me to reexamine the way I have structured my courses. I don’t have to follow the history of a particular question, but have I invented a reasonable alternate one?

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A reminder to myself: Sell the process

Here is a short report on the big experiment for this term, and a related note on a realization from today with wider applicability. I expect that this will start well, and then ramble on as I fiddle with some ideas.

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A reflection on “Assessment Interviews, Phase 2”

I have spent a large portion of today in one-on-one conversation with the students in my Euclidean Geometry course. To prepare the students for these meetings, I asked them to complete a one page reflection paper, with this prompt. If you don’t want to click through, I basically ask the students to read through the “standards for assessment,” which is just a fancy name for my student learning goals, and do a self-assessment. Then I want them to make a plan of action for improvement during the next three weeks.

The striking part is the strength of the negative correlation between student self-assessment and my assessments.

Students who I recognize as having developed strong skills come it with focused critiques and tight plans for how to improve.

Students who I recognize as having not yet demonstrated many of our foundational skills show up with some confidence that they are doing everything just fine, and weak plans for self-improvement.

(This relationship is not perfect. Some students were spot on, of course.)

I have enough experience that I expected this, but to watch in unfold all day was really something.

Opening Week for a Moore Method Course: Getting Comfortable

I am teaching iteration number ten of my Modified Moore Method Euclidean Geometry course. This semester I am making an effort to refocus on the basics: managing and mentoring the students as much as I can.

At this point, my theorem sequence is very stable. (I am no longer surprised much by what happens in this course.) This allows me to work on the other aspects of the course. I feel like I have started to let some important things go in the last year or so, and now I want to sharpen up. What has been lacking? I don’t think I have kept on top of the students to keep them engaged as well as I might. And I don’t think I have done a good job selling the method of instruction, either.

So, I was much more deliberate about introducing myself to each of my sixteen students on the first day. I have been very explicit about my expectations and my willingness to help them meet those expectations (which are rather high). And I will be making a conscious effort to check in with as many students as possible each day.

The first week was a rousing success, I think. Each day we got at least one theorem. We have already set the expectation for what counts as an argument. (Well, surely, there is still some work to be done.) The class has made two conjectures. We took some time to discuss some basic points of what acceptable writing will look like. I even successfully navigated our first potential difficult situation and found something positive in it. All in all, I am feeling pretty good about this.

I think our next test comes when we have to finish conjecture 1.1. They haven’t addressed the second statement in that, yet.

And sometime next week I will have to steal ten minutes to talk with them about my Standards Based Assessment experiment for the term.

A Big Class

Update on that big IBL class:

A little over a week ago, I posted a plea for help on Google+, and a note here. I will soon be running a mathematics for liberal arts students (“math for those who might not wish to be there”) course. In the past I have run the class as an IBL experience, using group work heavily. This was working at an acceptable level for sections of 30-40 students. This semester I have 68 enrolled. And my friend Doug Shaw has two sections of 72 each.
After reading and thinking it through, I will take the combined advice of Bret Benesh, Robert Talbert and Vincent Knight. I can’t quite count on my audience to be as self-directed as Vince’s, but I am happy to stay within the family of student-centered, active, social-constructivist teaching techniques and use a form of peer instruction/guided practice. (Is that your term Robert? Or did you borrow it?)

Poll Everywhere

As a practical matter, I will be using www.polleverywhere.com as a student response system to help run classes. UNI has a site license which will make it possible to use polls with more than 40 respondents. The advantage of PollEverywhere is that it allows the use of any web enabled device or any cell phone with a text messaging plan to post a response. That will bring the number of students who don’t already have a useful piece of technology down near zero. I hope it is zero. I am working on a back-up plan in case the number is not exactly zero.

The downside to Poll Everywhere is that questions are only really allowed to be short strings of text. At least, that is what fits in their web app naturally. I can imagine times I want to ask questions based on a picture or a graph. fortunately, they allow you to embed a poll into any web page by generating a little snippet of javascript. I will be investigating this tomorrow to see if it is useable without destroying all of my prep time.

Other Materials

The other big hiccup is that I was planning on using an IBL script. This isn’t appropriate for my new course structure. But it is far too late to order a textbook as a reference. So it looks like I will be writing a different style of course notes this term. I think I want to keep the “discovery” feel. (I doubt I can get all the way to “inquiry” with this many students.) So, I shall be looking through the materials on the Discovering the Art of Mathematics site for inspiration, but not outright plagiarism.

When I get moving, these materials will start showing up in my github repository for course notes. Feel free to follow along.

At the moment, I still plan to discuss Cantor’s theory of the infinite, something significant about probability and statistics, and something topological. I usually lead a unit on classifying surfaces, but I might switch that up for something about knots or tangles. Frankly, anything past Monday feels so far away, I am unqualified to talk about it.

Here goes nothing.

MathFest 2013: Hartford

Yeah, Hartford was not that exciting, but I still had a good experience at MathFest 2013. It was a very full week, so I have lots of things to share—way too much to fit in one post. I’ll pick out one thing or another and try to write a little bit for the next few days as I process.

The first thing on my mind is my Math 1100: Math in Decision Making course for the coming fall. I had a few discussions with people about this course during the conference. In particular, David Pengelley encouraged me to make the course more tactile. This seems a good idea. I have no doubts that with some work I can realize this for my unit on topological ideas.

Also, I got to thinking that a major problem isn’t so much what my students know, but rather what they “know” that isn’t true. This is especially acute during the probability and statistics unit. I am reminded of the approach taken by Derek Mueller in his Veritasium series. He points out the importance of confronting misconceptions in order to encourage genuine learning. In fact, watch this TEDx Sydney talk he gave.

So, I want to design some sort of hands on probability & statistics unit that puts common misconceptions front and center. Now I just have to figure out what those are.

I have attempted to teach this course 3 times, and I have had classes with enrollment between 30 and 40. This is large for a “presentation based” IBL style, but I adapted some group work. I figured for this coming semester I would try out a version of Dana Ernst’s felt tip pens structure. But today, I checked my enrollment.

I will have 68 students.

I emailed my comrade Doug Shaw. We have embarked upon this experiment of teaching Math in Decision Making in parallel. (I’d say together, but we don’t talk often enough. Seriously, Doug. We should chat more.) His two sections are 72 students each.

Time for rethinking.

Robert Talbert and Matthew Jones dropped some tips over on Google+. I’m going to investigate some peer instruction ideas, some details about using classroom response technologies, and even more group work flavors of Inquiry Based Learning. I have to design something that will work.

If you have ideas, I am happy to hear them.

Standards Based Assessment for a Moore Method Course

Motivation

I have been working on developing a reasonable assessment model for my IBL Euclidean Geometry Course for a while now. I have several reasons for this:
1. It would be more fair, and better for my students, if I found a way to communicate with them about their progress. At the very least, I need to open the line of communication, so students feel they can have a conversation with me about how things are going.
2. So far, I have been going with a “you will have to trust me” approach. I have gotten away with it. But someone who wants to raise hell will make my undocumented life difficult.
3. This class is conducted as a lightly modified Moore Method course. Standard assessment with homework, quizzes and exams just doesn’t feel right.
4. The accountability movement is coming. Sooner or later, I will have to deal with a top-down mandate to deal with how I assess my students, and how I assess my teaching. I choose to start, on my own, with the parts I can control before that pressure gets here. First up: how I assess students.

The Main Idea

I will try to use a Standards Based Assessment scheme. I will attempt to focus on this mainly as a feedback mechanism. Grades will only happen to the minimal extent that is required.

What didn’t work well enough, and why.

I tried to implement a simple SBG/SBAR scheme in each of the last two semesters. Neither worked because I had not found a method of dealing with the administrative details. At first, I asked too much of myself. Then, I asked even more of myself, but on deadlines. Ugh.

What is working

I am happy with my set of standards (read that as learning goals). I am very proud that they are weighted toward process goals: what one does and how one behaves as a mathematician. This is intentional—I want students to become acculturated to doing mathematics, and to acquire some of a mathematicians habits of mind.

A New Attempt

For next semester, I have devised a two-prong approach to administering a standards based assessment mechanism.

The First Prong: Face to face meetings

In order to make for better communication about expectations, I will meet with each student individually every three weeks. This will involve splitting the class. I will meet with half one week, half the next, and then take a week break.

Before each meeting, I expect the student to write a one page reflection about their progress in the course. To tighten this process up, I have written specific prompts to which the students must respond. This must be done before the meeting. It can either be sent to me electronically, or it can be brought to the meeting on paper, but it has to be done before the conversation. Really, the paper is not important. But the time for reflection is crucial. The meeting could too easily be wasted without it.

Second Prong: Professional Feedback at each Assessment Opportunity

Each time a student participates in some sort of assessment opportunity (a presentation at the board, turning in a written paper), I will provide feedback. I have a little electronic system built (with the help of my friend Stephen Hughes) using a Google Docs form/spreadsheet/script combo. I have a web form into which I will type comments. When I click the “enter” button, my comments are saved in a spreadsheet, emailed to me, and emailed to the students.

It is too much to manage class and write out feedback at the same time, so I will be doing this during the hour after my class meeting. I normally take time to convert my notes into a blog post for the students anyway. Now I will just add a little bit to the “post meeting decompression” that I do.

What is left to do?

I need to think some more about how I will provide feedback. I want this to be a narrative process, but what are my aims? What constraints should I observe?

That should be my next post. 🙂

Where is all of my stuff?

Well, I keep a blog for the students, and it has a page all about assessment. Go have a look. Not all of the links are live, yet, but they will be at the appropriate time of the semester.

In the end, what about grades?

Here, I have no substantive changes, but Ed Parker has pushed me a bit…