January 28, 2013, 7:45 am
This is the second post in a series on the nuts and bolts behind the inverted transition-to-proofs course. The first post addressed the reasons why I decided to turn the course from quasi-inverted to fully inverted. Over the next two posts, I’m going to get into the design of the course and some of the principles I kept in mind both before and during the semester to help make the course work. Here I want to talk about some of the design challenges we face when thinking about MTH 210.
As with most courses, I wanted to begin with the end in mind. Before the semester begins, when I think about how the semester will end, the basic questions for me are: What do I want students to be able to do, and how should they be doing it?
This course has a fairly well defined, standard set of objectives, all centered around using logic and writing mathematical proofs. I made up this list that has…
January 25, 2013, 9:27 am
Elaine Seymour and Nancy Hewitt’s book Talking About Leaving: Why Undergraduates Leave the Sciences is considered one of the seminal works in the literature about STEM education in higher ed. It’s certainly one of the most cited. Even though it’s 15 years old, it still wields a powerful influence over a lot of thought about university-level STEM education.
Mark Connolly, a researcher at the Wisconsin Center for Education Research, recently reached out to me to make me aware that he and Anne-Barrie Hunter of the University of Colorado Boulder are conducting a follow-up study to re-evaluate one of the claims made in the original 1997 study by Seymour and Hewitt study. Mark asked me to post about this to the blog and solicit your help in conducting the study. This involves taking a two-question survey. Here is the announcement from Mark and Anne-Barrie, and I hope you can find the time…
January 22, 2013, 8:00 am
It’s been a month or so now that the inverted transition-to-proofs class drew to a close. A lot of people, both here at my institution and online, have been asking questions about the design and day-to-day operations of the course, especially if they have ideas of their own and want to compare notes. So starting with this post, I’m going to publish a series of posts that describe exactly how this course was designed and managed throughout the semester. I’m not sure how many of these posts there will be. But the idea is to pull everything together so that people who want to try this sort of thing themselves will have a detailed accounting of what I did, what worked, what didn’t, and how it all went.
Some background on the course (MTH 210: Communicating in Mathematics) is in this post. The short version is that MTH 210 is a course on reading and writing proofs. It’s a…
January 15, 2013, 9:10 pm
I’m currently taking a MOOC called Computing for Data Analysis through Coursera. Ths is my fourth MOOC (the sixth one, if you count the two that I started and then dropped). It’s an introduction to the open-source statistical computing environment known as “R”. I got interested in R after learning about this modeling-based Calculus project that uses the statistical and plotting capabilities of R as well as some special symbolic packages as the centerpiece of introductory calculus. I’m leading a taskforce in my department to draft a plan for technology use in the Calculus sequence, and while I don’t think we’ll be using R, I like very much the spirit behind this calculus project, which puts programming at the heart of learning the subject and uses an open-source platform. Plus, I thought R might come in handy for analyzing my own data, and anyway, it’s free, and the course…
December 31, 2012, 9:01 am
Here’s a piece of a conversation I just had with my 8-year old daughter, who is interested in becoming a teacher when she grows up.
Daughter: Dad, if you want to become a teacher, do you have to take classes?
Me: Yes. You have to take a lot of classes about how to teach and a lot of classes in the subjects you want to teach. You need to be really good at math to teach math, for example.
D: Then do you have to go out and teach in the schools, like Mr. D___ [the young man who student-taught in my daughter's elementary school this year]?
Me: That’s right. You have to take classes and you have to go into the schools and practice.
D: Do you have to practice with the little kids?
Me: That depends on who you want to teach. If you want to become an elementary school teacher you work with elementary school kids. If you want to teach in a middle school, then you work with middle …
December 21, 2012, 8:00 am
Paul Pintrich was the creator of the Motivated Strategies for Learning Questionnaire, which I used as the main instrument for collecting data for the study on students in the flipped transition-to-proof course this past semester. Now that the data are in, I’ve been going back and reading some of Pintrich’s original papers on the MSLQ and its theoretical framework. What Pintrich has to say about student learning goes right to the heart of why I chose to experiment with the flipped classroom, and indeed I think he really speaks to the purpose of higher education in general.
For me, the main purpose of higher education is to train students on how to be learners — people who take initiative for learning things, who are skilled in learning new things, and who above all want to learn new things. My goal as an instructor is to make sure that every student in my class makes some form of…
December 18, 2012, 4:17 pm
I’m excited and happy to be teaching linear algebra again next semester. Linear algebra has it all — there’s computation that you can do by hand if you like that sort of thing, but also a strong incentive to use computers regularly and prominently. (How big is an incidence matrix that represents, say, Facebook?) There’s theory that motivates the computation. There’s computation that uncovers the theory. There’s something for everybody, and in the words of one of my colleagues, if you don’t like linear algebra then you probably shouldn’t study math at all.
Linear algebra is also an excellent place to use Peer Instruction, possibly moreso than any other sophomore-level mathematics course. Linear algebra is loaded with big ideas that all connect around a central question (whether or not a matrix is invertible). The computation is not the hard part of linear algebra — it…
December 4, 2012, 4:23 pm
Right after my last post — nearly a month ago — I began to ask myself, Why is it taking so much effort to blog? The answer was readily apparent by looking at my OmniFocus inbox, which was filled with orange-colored “Due Tomorrow” tasks having to do with making screencasts for the flipped transition-to-proofs course. I realized that I could have any two of my sanity, screencasts completed in time to deploy to the class, or regularly-appearing blog posts. I resigned myself to the fact that this semester I was screencasting instead of blogging. But now — it hardly seems possible — the screencasting is done and we’re moving toward exams next week. So it’s time to release the pent-up blog posts.
I have a lot to say about my experience going full-on flipped classroom with the proofs course. I regret that I couldn’t give more of a day-by-day accounting of how the class has …
November 9, 2012, 7:00 am
Speaking of faculty adopting research-based instructional strategies, Theron Hitchman (who blogs at Circles and Tangents) wonders aloud in the direction of math education researchers: Why didn’t you tell me? That is, referring to research-based instructional strategies that seem to work really well with students,
Why do I stumble on these things only to find that they have been understood for decades? Why didn’t someone knock on my door and tell me I was doing it wrong?
My basic point is this: If you do research on teaching and learning, you owe it to society to share what you know. Scholarly publication doesn’t count. The mathematics education community talking to itself is a necessary condition for sorting out the truth of things, but it is insufficient for educating the public and for changing practice on a large scale.
If you know that the standard lecture-homework-exam …
November 7, 2012, 7:00 am
I’m really excited to be working next semester as a co-PI on a National Science Foundation grant with my Grand Valley State colleagues Scott Grissom (Computer Science), Shaily Menon (Chemistry), and Shannon Biros (Chemistry). We’re going to be interviewing a large number of GVSU faculty to try to understand why some of us adopt research-based instructional methods like peer instruction and why others don’t.
As we were putting together the grant proposal earlier this year, one statistic really impressed the importance of this study on me. GVSU is a fairly big place – we have nearly 25,000 students on multiple campuses with both undergraduate and graduate degrees offered. I don’t know how many sections of courses we offer in a given semester, but it’s got to be in the thousands. We have over 40 sections currently running for just College Algebra! And yet: How many sections…