March 25, 2013, 8:00 am
I have a confession to make: At this point in the semester (week 11), there’s a question I get that nearly drives me to despair. That question is:
Can we see more examples in class?
Why does this question bug me so much? It’s not because examples are bad. On the contrary, the research shows (and this is surely backed up by experience) that studying worked examples can be a highly effective strategy for learning a concept. So I ought to be happy to hear it, right?
When people ask this question because they want to study an example, I’m happy. But studying an example and seeing an example are two radically different things. Studying an example means making conscious efforts to examine the example in depth: isolating the main idea or strategy, actively trying out modifications to the objects involved, making connections to previous examples and mathematical results, and – very …
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…
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…
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 …
October 17, 2012, 7:21 am
I just completed my second MOOC, the “Securing Digital Democracy” course from Coursera. Emboldened by actually completing it with a passing grade I’ve jumped into another Coursera offering, this time “Introduction to Interactive Python“. My colleague John Golden and I are both taking it, and yesterday John tweeted:
Which got this attention-getting reply from Bret Benesh:
Further down the conversation, Bret pointed to this quote in the Coursera terms of service:
Notice for Minnesota Users
Coursera has been informed by the Minnesota Office of Higher Education that under Minnesota Statutes (136A.61 to 136A.71), a university cannot offer online courses to Minnesota residents unless the university has received authorization from the State of Minnesota to do so. If…
October 3, 2012, 8:46 am
The flipped transition-to-proof class is now finishing up its sixth week. It’s hard to believe we are nearing the midpoint of the semester. The management of the class is still something of a work in progress, and I hope to have more posts up soon about how the class logistics have evolved since August. But one thing for which I am really grateful, and which I frankly find surprising, is that nobody in the class has yet to express any kind of longing for the good old days when professors lectured and students sat there and listened. In fact most students who express anything at all say that having the lectures on video, in addition to having a well-written textbook for reference, is hugely beneficial for their work in the class.
Recently. when I’ve asked students what we could do differently in the class that would help their learning, two items have shown up multiple times (and these…
August 14, 2012, 8:00 am
I’ve been sort of quiet on the inverted transition-to-proof course (MTH 210, Communicating in Mathematics) lately, partly due to MathFest and partly because I am having to actually prep said course for startup on August 27. It’s almost ready for launch, and I wanted to share a document that I’m going to hand out to students on opening day and discuss. It’s called “How MTH 210 Works”. I’m fairly proud of this document because I think it says, in clear terms, what I want students to know not only about this class but for inverted classrooms generally.
I’ve written before that the inverted or “flipped” classroom approach always tends to engender a lot of uncertainty and sometimes strongly negative responses. With this document, I am hoping to pre-empt a lot of those feelings by stressing what this is all about: Being realistic about their education in the present day for the things that…