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.
Following an idea suggested by Stan Yoshinobu, I had my students in Math 1100 Math in Decision Making write short mathematical autobiographies. If you are interested in the specifics, the assignment is here. Tonight, I finally finished reading and commenting on all 63 of these. (It took me far too long to do. Partly because I am over-scheduled, and partly because I wanted to comment meaningfully on each one.)
I learned a ton from reading these. I want to keep the contents confidential, but I think it is fair to share a bit about what I learned without taking any quotes.
- Paper after paper described a relationship with mathematics through the lens of a relationship with instructors. It was very clear that the students don’t really experience the subject as much as they follow a person (or not).
- Many papers discussed openly a negative attitude for the subject. But almost as many expressed quite positive feelings. I was a bit surprised by this, and it made me glad I did this assignment. And even those papers expressing negative feelings also said that they were willing to make a new start.
I won’t take any quotes from student papers, but I feel perfectly comfortable sharing those things I found myself writing over and over again as comments on papers. Perhaps that will give you a feel for what I learned.
- We will not race.
- I have chosen topics for this class which are likely new to you. I picked them because I thought they were interesting, and I hope that you find them interesting. Perhaps you can use this as an opportunity to re-evaluate your relationship with math?
- We won’t cover much “every day math.” My understanding is that people have no real trouble learning what they need to when it comes up in context. Instead, we will do things that are new and interesting.
- By the nature of college, you will have to show a lot of independence in this course. Most of the learning will happen when you work outside of class. But don’t let that stop you from asking questions! I like talking about mathematics.
- Feeling frustrated and confused is totally normal when doing math. I feel that way all the time! I have come to recognize that feeling confused just means that I am in a place where it is possible I could learn something new. Maybe that could work for you? Still if you feel really frustrated, don’t hesitate to talk with me.
I would certainly do this again.
I have completed the first week of classes. I also took a good 36 hours to sleep and play with my children, so I am feeling up to getting back to work. The retooling of my liberal arts mathematics course to handle 70 students involved a lot of work. My usual work pattern involves long stretches of thinking and indecision, followed by a short, intense burst of actual production. I had to repeat this for every class meeting this week, so I was very tired on Friday. Labor Day weekend is well-placed for me this term.
So, how did the big experiment with Guided Practice and Peer Instruction start? More after the jump. Continue reading
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?)
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 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.
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.
This week I have started to new ongoing conversations that I am really excited about.
A Formal Discussion Group
First, I joined a small “Talking Teaching and Learning” group on campus. This is a multidisciplinary group of people who wish to have a small community for working on issues related to being an educator. One of the ground rules of this group is that the conversations are confidential, so I will just say that I hope to use the group as an accountability mechanism for me. I shared during our first meeting that I will be working on three things in the near future:
- developing an assessment method I am happy with using (focus on Math 3600 Euclidean Geometry)
- learning to teach Math 2500 Linear Algebra
- refining my approach to Math 1100 Math in Decision Making
I will probably talk about some of my thinking here, as I noodle through things, but this will be the last mention of the group. I think this is a fun idea, and I am looking forward to participating.
An Informal Chat over Tea
Today I had a longish discussion with my colleague Scott Peters. Scott teaches political science at UNI, and we sometimes play soccer together. He was curious about what IBL might mean for a social science course! I am so glad I did this today.
Sometimes you just need to start talking and see what comes out of your mouth. Then you can evaluate it and decide if you really mean it. [Hell, that is why this blog exists. Just replace “talking” with “typing.”] The conversation with Scott was nice because he was very thoughtful and because he comes from a very different discipline. This meant we had to talk about and navigate through to the important commonalities that are really about teaching and learning from an inquiry based learning viewpoint without reference to mathematics. I learned some very important lessons from our talk today. They are important enough that I want to write them down, so I can find them again later and feel guilty when I realize I haven’t internalized them well enough. (Hey, look at that. I wrote exactly that thing down two years ago. What was I thinking?)
Lesson One: Introducing Students to asking their own questions should be done in a narrowly focused context
Scott floated the idea of having students pick their own questions to work on–essentially he wanted them to develop their own small program of study. He has tried something like this lately, and was unsatisfied. I reflected upon my EG experiences and shared that I invite the students into the process of asking questions and making conjectures, but I do it in a very deliberate way.
At the beginning of the course, I set all of the questions, and I model making new questions and conjectures during class when the opportunity arises. Sometimes a presentation doesn’t quite hit the mark the student wants, and then an easy way to “salvage” things is to state a theorem encapsulating exactly what the argument does prove and then make a conjecture that covers the gap in the argument. Sometimes an argument looks juicy enough that I just ask the presenter if they can think of any conjectures that come to mind in the context of their work.
Later in the semester, I explicitly ask students to find and prove unstated theorems that are analogous to ones already in our records. For example, after we have proved a bunch of things about rhombi, I introduce the notion of a kite and set them loose. Even later I can work in a more open-ended way. By mid-semester, some of the students have their own observations to share and they ask permission to make conjectures. (Iowa students are so polite and deferential.)
Anyway, the main point is that without realizing it, I have things structured to slowly acculturate the students into doing mathematics including what it means to ask a question and what kind of question we might have a chance of answering. Importantly, the question-asking is also done in very narrow, specific contexts. That allows the students the freedom to practice asking their own questions, but only gives them a big enough sandbox to do so in an appropriate fashion. I get high-quality work out of them because they come to understand what that means first. Apparently, I am so awesome that even I didn’t recognize it.
Scott pointed out that one of the things going on is that I am only allowing students the opportunity to ask their own questions after they have begun to get a sense of what a proper mathematical process of finding answers is. He felt that this was lacking in his approach. I can’t say for certain if that is true for him, but [expletive deleted] that is definitely true for me! This is a big part of why my Differential Geometry course failed this term. I gave them all the freedom in the world, which is waaaaay too much. What an eye-opener.
Lesson Two: Replicating the Success of Euclidean Geometry might require more faithful replication of the format
Scott asked me about my textbook choices. This gave me a chance to talk about my rationale for using Euclid’s Elements as a text. For all of you, the abridged version is this:
- I want some examples of correct proofs for students to see
- I want students to experience reading mathematical literature for understanding
- I want to be able to assume something or this class will never get anywhere
- I want to infuse the course with a sense of connection to history and wider mathematical culture
- I want the students to learn to critique everything, even Euclid (some of his arguments are wonky)
- I don’t want to pretend the students don’t know anything, even if they really don’t. (They have all had a geometry course in high school. But mostly they don’t have anything but vague memories.) The Elements acts as a convenient bandaid. The facts we need that they are likely to recall from previous schooling are in there.
I tend to think of the course as a mini research community: I am the grand mathematical guru, and my students are new graduate students who wish to be mentored into the professional mathematics community—but all about a millenium ago, when aspects of this planar geometry stuff is still cutting edge. The Elements is our full suite of reference literature, and then I set a research program for the group around it and extending it.
Scott latched onto the idea of using historical sources as a way to structure the development of his material. I have always liked this idea, but I haven’t done strictly that. And this is another thing that hit me! This is missing from my other courses. I don’t have the “extant research literature” for students to grapple with and use as a foundation. But maybe I need to make that. So, for Differential Geometry or Linear Algebra I could make some synthetic replacement for Euclid’s Elements by looking in the historical record. At this point, I don’t expect to find such a convenient piece of ancient scholarship for other courses that plugs into just the right spot, so I’ll have to create something.
This sounds like a lot of work, but it might be just the thing.
Though right now I have my doubts about using such an approach for Math in Decision Making. I don’t know why. I hope it is not a prejudice on my part. More reflection required.