March 18, 2014, 4:34 pm
Yesterday I got an email from a reader who had read this post called What should math majors know about computing? from 2007. In the original article, I gave a list of what computing skills mathematics majors should learn and when they should learn them. The person emailing me was wondering if I had any updates on that list or any new ideas, seven years on from writing the article.
If anything, over the past seven years, my feelings about the centrality of computing in the mathematics major have gotten even more entrenched. Mostly this is because of two things.
First, I know more computer science and computer programming now than I did in 1997. I’ve learned Python over the last three years along with some of its related systems like NumPy and SciPy, and I’ve successfully used Python as a tool in my research. I’ve taken a MOOC on algorithms and read, in whole or in part, books…
March 11, 2014, 2:34 pm
In the previous post about the flipped/inverted calculus class, we looked at getting student buy-in for the flipped concept, so that when they are asked to do Guided Practice and other such assignments, they won’t rebel (much). When you hear people talk about the flipped classroom, much of the time the emphasis is on what happens before class – the videos, how to get students to do the reading, and so on. But the real magic is what happens in class when students come, prepared with some basic knowledge they’ve acquired for themselves, and put it to work with their peers on hard problems.
But before this happens, there’s an oddly complex buffer zone that students and instructors have to cross, and that’s the time when students arrive at the class meeting. Really? you are thinking. How can arrival to class be such a complicated thing? They show up, you get to work, right? Well…
March 5, 2014, 2:37 pm
In my last post about the inverted/flipped calculus class, I stressed the importance of Guided Practice as a way of structuring students’ pre-class activities and as a means of teaching self-regulated learning behaviors. I mentioned there was one important difference between the way I described Guided Practice and the way I’ve described it before, and it focuses on the learning objectives.
A clear set of learning objectives is at the heart of any successful learning experience, and it’s an essential ingredient for self-regulated learning since self-regulating learners have a clear set of criteria against which to judge their learning progress. And yet, many instructors – myself included in the early years of my career – never map out learning objectives either for themselves or for their students. Or, they do, and they’re so mushy that they can’t be measured – like any…
March 4, 2014, 2:59 pm
This post continues the series of posts about the inverted/flipped calculus class that I taught in the Fall. In the previous post, I described the theoretical framework for the design of this course: self-regulated learning, as formulated by Paul Pintrich. In this post, I want to get into some of the design detail of how we (myself, and my colleague Marcia Frobish who also taught a flipped section of calculus) tried to build self-regulated learning into the course structure itself.
We said last time that self-regulated learning is marked by four distinct kinds of behavior:
- Self-regulating learners are an active participants in the learning process.
- Self-regulating learners can, and do, monitor and control aspects of their cognition, motivation, and learning behaviors.
- Self-regulating learners have criteria against which they can judge whether their current learning status is…
March 3, 2014, 9:00 am
A few weeks ago I began a series to review the Calculus course that Marcia Frobish and I taught using the inverted/flipped class design, back in the Fall. I want to pick up the thread here about the unifying principle behind the course, which is the concept of self-regulated learning.
Self-regulated learning is what it sounds like: Learning that is initiated, managed, and assessed by the learners themselves. An instructor can play a role in this process, so it’s not the same thing as teaching yourself a subject (although all successful autodidacts are self-regulating learners), but it refers to how the individual learner approaches learning tasks.
For example, take someone learning about optimization problems in calculus. Four things describe how a self-regulating learner approaches this topic.
- The learner works actively on optimization problems as the primary form of…
January 27, 2014, 7:55 am
As many Casting Out Nines readers know, last semester I undertook to rethink the freshman calculus 1 course here at my institution by converting it to an inverted or “flipped” class model. It’s been two months since the end of that semester, and this blog post is the first in a (lengthy) series that I’ll be rolling out in the coming weeks that lays out how the course was designed, what happened, and how it all turned out.
Let me begin this series with a story about why I even bother with the flipped classroom.
The student in my programming class looked me straight in the eye and said, “I need you to lecture to me.” She said, “I can’t do the work unless someone tells me how to get started and then shows me how, step by step.” I took a moment to listen and think. “Do you mean that you find the work hard and it’s easier if someone tells you how to start and…
January 24, 2014, 8:03 am
Here are some items from around the web for your weekend enjoyment.
- Here’s a great post on Medium by Nik Custodio in which he explains Bitcoin like I’m five. I think the audience level here is rather older than five, but it’s still probably the best explanation of the problems that Bitcoin attempts to solve, and how it solves them, that I’ve seen. (I wasn’t sure whether to file this under “Math” or “Technology” because it’s a lot of both.)
- If you’ve ever been interested in standards-based grading, you won’t want to miss Kate Owens’ post An Adventure in Standards-Based Calculus where she lays out why, and bits about “how”, she intends to use SBG in her Calculus 2 course this semester. Don’t miss the link to George McNulty’s calc 2 syllabus at the end, which is a great example of how to use SBG in actual practice.
- Good report…
December 29, 2013, 1:05 pm
After a bit of a hiatus, here is the newest installment in this Casting Out Nines’ series of 4+1 Interviews. In these interviews, I’ve tapped various people who are doing interesting work in some combination of math, technology, and education to see what they’re up to and what’s on their minds.
In this interview, I had a chance to catch up with Gavin LaRose. Gavin is affiliated with the Mathematics Department at the University of Michigan. He is officially listed as a Program Manager of Instructional Technology in the Mathematics Department, but his areas of interest and accomplishment are a lot more varied than what that title suggests. He’s been involved with Project NExT and other programs in the MAA and is well known for his work with innovative pedagogy and instruction, especially instruction using technology, at U-M.
1. At the University of Michigan, you do some…
December 18, 2013, 1:25 pm
Over three years ago, I wrote a post to try to address a fallacy that is used to refute the idea of novel ways of teaching mathematics and science. That fallacy basically says that mathematics and the way people learn it have not fundamentally changed in hundreds if not thousands of years, and therefore the methods of teaching that have “worked” up to this point in history don’t need changing. Or more colloquially, “We were able to put a man on the moon with the way we’ve taught math for hundreds of years, so we shouldn’t change it now.” I sometimes refer to this as the “man on the moon” fallacy because of that second interpretation.
To understand why I think this is a fallacy, read the post above – or better yet, read this long quote from a 1988 paper by Edsger Dijkstra, one of the great scientific minds of the last 100 years and one of the authors of modern…