# Category Archives: Math

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….

July 18, 2012, 9:44 am

# For proofs, just click “play”

This week I am adding to the playlist of screencasts for the inverted intro-to-proofs class I first mentioned here. There are seven chapters in the textbook we are using and my goal is to complete the screencasts for the first three of those chapters prior to the start of the semester (August 27). Yesterday I added four more videos and I am hoping to make four more tomorrow, which will get us through Chapter 1.

The four new ones focus on conditional (“if-then”) statements.  I made this video as the second video in the series as a prelude to proofs, which are coming in Section 1.2 and which will remain the focus of the course throughout. Generally speaking, students coming into this course have had absolutely no exposure to proof in their background with the exception of geometry and maybe trigonometry, in which they hated proofs. Watch a part of this and see if you can figure out my …

July 16, 2012, 3:02 pm

# What does it mean for kids to be “ready” for math?

USA Today has this op-ed (h/t to Joanne Jacobs) from Patrick Welsh giving thoughts on why kids hate math:

I worry that we’re pushing many kids to grasp math at higher levels before they are ready. When they struggle, they begin to dread math, and eventually we lose thousands of students who could be the scientists and engineers of tomorrow. If we held back and took more time to ground them in the basics, we could turn them on to math.

We’re asking young kids to move up in mathematics too far, too soon, in other words. Patrick goes on to focus especially on a push in California to get more younger kids taking Algebra and cross-references it with a Duke University study showing negative effects of the same sort of program in North Carolina.

I’m in complete agreement with this op-ed, although thankfully I haven’t felt that push so much with my own kids, ages 3, 6, and 8. There have…

July 13, 2012, 8:17 am

# Screencasting for the inverted proofs class

Here’s the first (and so far, only) screencast that students will use in the inverted transition-to-proof class:

This one is a bit more lecture-oriented than I intend most of the rest of them to be, so it’s a little longer than I expect most others will be. But I do break up the lecture a little bit with a “Concept Check”, which is the same thing as a ConcepTest except I’ve never warmed to that particular term (the word “test” puts students on edge, IMO).

If you have tried out any of Udacity’s courses or read my posts about taking Udacity courses, you will see some obvious inheritances here. I tried to keep the video short, provide simple but interesting examples, and give some measure of formative assessment in the video. I am exploring ways to make the Concept Check actually doable within YouTube — Camtasia 2 has an “interactive hotspot” feature I am trying to figure out — …

July 10, 2012, 11:38 am

# Inverting the transition-to-proofs class

When I see the first back-to-school sales, I know it’s time, like it or not, to start prepping classes for the fall. This fall I am teaching two courses: a second-semester discrete math course for computer science majors and then two sections of “Communicating in Mathematics” (MTH 210). I’ve written about MTH 210 before when I taught it last fall. This fall, it’s going to be rather different, because I’m designing my sections as inverted or “flipped” classes.

If you’ve read this blog for any length of time, you know I’ve worked with the inverted classroom before (here, here, here, etc.). But except for a few test cases, I haven’t done anything with this design since coming to GVSU. I decided to take a year off from doing anything inverted last year so I could get to know the students and the courses at GVSU and how everything fits together. But now that I have the lay of the land, I…

July 5, 2012, 4:13 pm

# Looking for evidence?

Amid all the shuffle of the #mtt2k phenomenon and my piece on Khan Academy this week — which is well on its way to being the most-read and -retweeted article I’ve ever done — Konstantin Kakaes put up a response to critiques of his Slate piece on educational technology. In it, he addresses both my critique and that of Paul Karafiol. I wanted to give just a few counter-critiques here. I haven’t had a chance to read Paul’s piece, so I’m just going to focus on the part of the response that referenced my post. (Here’s the full post I wrote about the Slate article.)

Let’s go back to the original Slate piece, which said:

Though no well-implemented study has ever found technology to be effective, many poorly designed studies have—and that questionable body of research is influencing decision-makers.

The Slate piece suggests that researcher bias, brought on by having a financial stake in…

July 3, 2012, 9:08 am

# The trouble with Khan Academy

At some point around the beginning of February 2012, David Coffey — a co-worker of mine in the math department at Grand Valley State University and my faculty mentor during my first year — mentioned something to me in our weekly mentoring meetings. We were talking about screencasting and the flipped classroom concept, and the conversation got around to Khan Academy. Being a screencaster and flipped classroom person myself, we’d talked about making screencasts more pedagogically sound many times in the past.

That particular day, Dave mentioned this idea about projecting a Khan Academy video onto the screen in a classroom and having three of us sit in front of it, offering snarky critiques — but with a serious mathematical and pedagogical focus — in the style of Mystery Science Theater 3000. I told him to sign me up to help, but I got too busy to stay in the loop with it.

It…

June 29, 2012, 2:23 pm

# The summer of BYOD

So, the six-week Calculus 2 class is over with — that didn’t take long — and there’s beginning to be enough distance between me and the course that I can begin to evaluate how it all went. Summer classes for me are a time when I like to experiment with things, and I wanted to comment on the outcomes of one experiment I tried this time, which is using a bring-your-own-device setup for clicker questions.

I’ve been using TurningPoint clickers ever since I started doing peer instruction, and I recommend these devices highly. They have a lot going for them in terms of classroom technology: They are small and unobtrusive, relatively cheap (\$35), exceedingly simple to use, rely on no pre-existing infrastructure (for example, whether or not you have decent wifi in the room), and are nearly indestructible. They are about as simple, dependable, and inexpensive as a radio-operated garage door…

June 12, 2012, 7:00 am

# Misunderstandings vs. misconceptions

The first speaker in the Model-Eliciting Activities (MEA’s) session Monday morning said something that I’m still chewing on:

Misunderstanding is easier to correct than misconception.

She was referring to the results of her project, which took the usual framework for MEA’s and added a confidence level response item to student work. So students would work on their project, build their model, and when they were done, give a self-ranking of the confidence they had in their solution. When you found high confidence levels on wrong answers, the speaker noted, you’ve uncovered a deep-seated misconception.

I didn’t have time, but I wanted to ask what she felt the difference was between a misunderstanding and a misconception. My own answer to that question, which seemed to fit what she was saying in the talk, is that a misunderstanding is something like an incorrect interpretation of an idea …

June 5, 2012, 8:00 am

# Taking time and giving time on assessments

I haven’t given many updates lately about, well, anything, but especially about my Calculus 2 class. Freakishly, we are 2/3 of the way through the course now. First of all let me say that there’s something seriously wrong with having a midterm in a class after three weeks, and then a final exam three weeks later. Students should have more time to dread those things.

I kid, but actually the biggest adjustment I’ve made in the class — and teaching a class that’s as compressed as this one is all about paying close attention to everything that happens and being nimble about making adjustments — has been the testing scheme. I know that I posted earlier about my idea of having in-class assessments that were smaller than the usual test, more frequent, and which leveraged student collaboration and the real-life social network of the class. But after a couple of tries with this, I dropped it…

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