# Tag Archives: Calculus

March 11, 2014, 2:34 pm

# Getting off on the right foot in an inverted calculus class

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 6, 2014, 2:25 pm

# Getting student buy-in for the inverted calculus class

So far, regarding the inverted/flipped calculus course, we’ve discussed why I flipped the calculus class in the first place, the role of self-regulated learning as a framework and organizing principle for the class, how to design pre-class activities that support self-regulated learning, and how to make learning objectives that get pre-class activities started on a good note. This is all “design thinking”. Now it’s time to focus on the hard part: Students, and getting them to buy into this notion of a flipped classroom.

I certainly do not have a perfect track record with getting students on board with an inverted/flipped classroom structure. In fact the first time I did it, it was a miserable flop among my students (even though they learned a lot). It took that failure to make me start thinking that getting student buy-in has to be as organized, systematic, and well-planned as…

March 5, 2014, 2:37 pm

# Creating learning objectives, flipped classroom style

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

# The inverted calculus course: Using Guided Practice to build self-regulation

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:

1. Self-regulating learners are an active participants in the learning process.
2. Self-regulating learners can, and do, monitor and control aspects of their cognition, motivation, and learning behaviors.
3. Self-regulating learners have criteria against which they can judge whether their current learning status is…

March 3, 2014, 9:00 am

# The inverted calculus course and self-regulated learning

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.

1. The learner works actively on optimization problems as the primary form of…

January 27, 2014, 7:55 am

# The inverted calculus course: Overture

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…

September 1, 2013, 1:49 pm

# Week 1 of the inverted calculus class: Failure is an option

Week 1 of the new semester is in the books, and with it the first week of the inverted calculus class. I am teaching two sections of this class, one that meets Monday/Wednesday/Friday and the other Tuesday/Thursday. It makes for tricky scheduling, but as I learned this week it also gives an opportunity for second chances, which is important if you don’t always get the in-class portion of the flipped classroom right.

People always seem to focus on the out-of-class experience when they talk about the inverted classroom. How much time does it take to make the videos? How do I make sure my students do the Guided Practice? But that’s not the hard part, nor is it the part where most of the learning takes place. The in-class experience for students is what makes the inverted classroom more than just a lab or a seminar course, and as the instructor, it’s both hard and crucial to get it …

August 25, 2013, 2:38 pm

# Flipping calculus

In the last post, I said I might be taking a couple of weeks off, and I ended up taking three. Well, the week before classes start is basically a blackout period during which nothing gets done except course preps, so that’s why.

Yes, it all starts back up again here this week. This semester is going to be fuller than usual for a lot of reasons, three primary: First, I’m up for contract renewal in January, meaning that I am approaching the “midterm exam” at the halfway point toward tenure, which requires the usual aggregation of evidence demonstrating that I’m making satisfactory progress. Second, I’m teaching my first upper-level course since arriving at GVSU, one section of our Modern Algebra course, which I have not taught in a few years and I am anxious to get into it. I’m also trying out a new platform for classroom response systems in that course and I will tell you…

June 25, 2013, 12:04 pm

# What math topic do engineering faculty rate as the most important?

I’m at the American Society for Engineering Education Annual Conference right now through Thursday, not presenting this time but keeping the plates spinning as Mathematics Division program chair. This morning’s technical session featured a very interesting talk from Kathy Harper of the Ohio State University. Kathy’s talk, “First Steps in Strengthening the Connections Between Mathematics and Engineering”, was representative of all the talks in this session, but hers focused on a particular set of interesting data: What engineering faculty perceive as the most important mathematics topics for their areas, and the level of competence at which they perceive students to be functioning in those topics.

In Kathy’s study, 77 engineering faculty at OSU responded to a survey that asked them to rate the importance of various mathematical topics on a 5-point scale, with 5 being the…

August 13, 2012, 8:00 am

# A free and open-source calculus textbook

Allow me to make a shameless plug for a very cool project currently underway by my GVSU colleague Matt Boelkins. He is writing a free, open-source calculus textbook that will be available in PDF form online for anyone to use and for any instructor to modify. He has already written the differential calculus portion of the textbook — his Winter semester sabbatical project — and he’s about to begin work on the integral calculus portion. You can download the differential calculus parts here. This is at his blog, where he is promoting the book and soliciting feedback. Matt’s also on Twitter.

Matt and I have talked about this project a lot in the last several months, and I’m deeply impressed by his vision for what this resource could become. He sums it up in this blog post:

While on sabbatical during the winter semester of 2012, I began drafting a free, open-source calculus text….

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