As part of preparing for our impending move from Indy to Grand Rapids, my family and I have made a couple of visits to the area. These by necessity combine business with pleasure, since our three kids (ages 2, 5, and 7) don’t handle extended amounts of business well. On the last visit, we spent some time at the Grand Rapids Childrens Museum, the second floor of which is full of stuff that could occupy children — and mathematicians — for hours. This “exhibit” was, for me, one of the most evocative. Have a look:

I asked this on Twitter a few days ago, but I’ll repost it here: In the spirit of Dan Meyer’s Any Questions? meme, what questions come to mind as you watch this? Particularly math, physics, etc. questions.

One other thing — just after I wrapped up the video on this, someone put one of the little discs rolling on the turntable and it did about a dozen graceful, perfect three-point hypocycloids before falling off the table.

Filed under Geometry, Math, Problem Solving

## Thoughts on the culture of an inverted classroom

I’ve just finished up the spring semester, and with it the second iteration of the inverted classroom MATLAB course. With my upcoming move, it may be a while before I teach another course like this (although my experiments with targeted “flipping” went pretty well), so I am taking special care to unwind and document how things went both this year and last.

I asked the students in this year’s class about their impressions of the inverted classroom — how it’s worked for them, what could be improved, and so on.  The responses fell into one of two camps: Students who were unsure of, or resistant to, the inverted classroom approach at first but eventually came to appreciate its use and get a lot out of the approach (that was about 3/4 of the class), and students who maybe still learned a lot in the class but never bought in to the inverted method. No matter what the group, one thing was a common experience for the students: an initial struggle with the method. This was definitely the case last year as well, although I didn’t document it. Most students found closure to that struggle and began to see the point, and even thrived as a result, while some struggled for the whole semester. (Which, again, is not to say they struggled academically; most of the second group of students had A’s and B’s as final grades.)

So I am asking, What is the nature of that struggle? Why does it happen? How can I best lead students through it if I adopt the inverted classroom method? And, maybe most importantly, does this struggle matter? That is, are students better off as problem solvers and lifelong learners for having come to terms with the flipped classroom approach, or is adopting this approach just making students have to jump yet another unnecessary hurdle, and they’d be just as well off with a traditional approach and therefore no struggle?

I think that the nature of the struggle with the inverted classroom is mainly cultural. I am using the anthropologists’ definition of “culture” when I say that — a culture being a system whereby a group of people assign meaning and value to things.

In particular, the way culture places value on the teacher is radically different between the traditional academic culture experienced by students and the culture that is espoused by the inverted classroom. In the traditional classroom, what makes a “good teacher” is typically that teacher’s ability to lecture in a clear way and give assessments that gauge basic knowledge of the lecture. In other words, the teacher’s value hinges on his or her ability to talk.

In the inverted classroom, by contrast, what makes a “good teacher” is his or her ability to create good materials and then coach the students on the fly as they breeze through some things and get inexplicably hung up on others. In other words, the teacher’s value hinges on his or her ability to listen.

Many students who are in that other 25% who never buy into the inverted classroom think that teachers using this approach are not “real” teachers at all. As one student put it, when they pay a teacher their salary, they expect the teacher to actually teach. What is meant by “teaching” here is an all-important question. Well, on the reverse side, if there were such a thing as a group of students who had only experienced the inverted classroom their entire lives and then entered into a traditional classroom, those students would think they are experiencing the worst teacher in the history of academia. The guy never shuts up! He only talks, talks, talks! We have to fight to get a word in edgewise, we get only brief chances to work on things when he is there, and we’re always booted unceremoniously out of the lecture hall (we used to call them “classrooms”) and left to fend for ourselves on all this difficult homework!

I’m convinced that bridging this cultural gap is what takes up most of the time and effort in an inverted classroom — forget about screencasts!

## Three things I wish Google Documents would let me do

Let me preface this article by saying that I really like Google Documents. It’s a fantastic set of tools that extends basic office functionality to the web in really compelling ways. I’ve been incorporating Google Docs pretty centrally in my courses for the last few years — for example, I no longer hand out paper syllabi on the first day of classes but instead write the syllabi on GDocs and distribute the links; and I’ve given final exams on Google Docs with links to data that are housed in Google Spreadsheets. I love being able to create a document on the web and just leave it there for students (or whoever) to come see, collaborate, and comment — without having to keep track of paper and with virtually zero chance of losing my data. (If Google crashes, we have much bigger problems than the loss of a set of quiz data.)

But like anything, Google Documents isn’t perfect — and in particular, there are at least three things that I wish Google Documents would do that would push my really like-ness to unqualified love:

1. Bring back the old Equation Editor. A couple of years ago, Google rolled out an equation editor for Google Docs that was just beautiful — a small editor that had point-and-click features for adding equations and the ability to parse $\LaTeX$ commands. In other words, it was a mini-$\LaTeX$ editor built right into Google Docs that would implement almost any of the essential functionality of $\LaTeX$, including matrices, multi-line equations, and more. I remember discovering this editor two years ago and promptly writing up every single one of my linear algebra activities as Google Documents. Then, inexplicably, Google replaced this sweet $\LaTeX$ goodness with a stripped-down equation editor that pales in comparison, supporting only a tiny fraction of $\LaTeX$‘s command set, and in particular no matrices or multi-line equations. And the “new” editor is clunky and doesn’t seem to produce very good results. I have yet to hear a satisfactory explanation of why this change to a clearly-inferior editor was made. It can’t be because it was overtaxing Google’s system! This is Google, for goodness’ sake, and it’s 2011 — can’t we have a real $\LaTeX$ editor for Google Docs? There’s already one for GMail, you know.

2. Allow comments and discussion threads on PDF’s uploaded to Google Documents. From a teacher’s perspective, one of the most compelling possibilities for Google Docs is to have students upload their class work on Google Docs and then initiate a running discussion thread on that work. Such a thing would replace the usual system of handing in work and having the teacher write comments on it, thereby turning the grading process into something more like a conversation. You can do this with documents created in Google Docs. But if you want students to create mathematical work — since, as I just noted, the current equation editor for GDocs doesn’t get the job done — students would have to create their work in MS Word or $\LaTeX$, convert to a PDF, and then upload it. No problem, except that discussion threads and comments aren’t allowed on uploaded documents. The option simply isn’t there in the menu system. Google acknowledges that comments and comment threads are only available on newly-created documents, and functionality is coming for older documents — but no word on uploaded documents. If this could be made to happen, grading student work suddenly gets a whole lot more interesting (and valuable for students).

3. Auto-shorten URL’s of links to documents. OK, this is pretty minor, because all I have to do is copy the URL given to me by Google and run it through bit.ly. But since Google already has its own URL shortener, why not just auto-compress the URL using that shortener at the moment the URL is generated? It saves a few clicks and makes users happier because we don’t have to deal with URL’s that are multiple dozens of characters long. And more practically, it makes Google Docs easier for novices to use — many new users (I’m envisioning a good portion of students in my classes who I’d like to get to use Google Docs) have no idea that URL shorteners exist.

What else would you add to this list? Better yet, are there hacks or workarounds that resolve these issues? (Or, thirdly, am I just mistaken on any of this?)

1 Comment

Filed under LaTeX, Social software, Teaching, Technology, Web 2.0

## The “golden moment”

We’re in final exams week right now, and last night students in the MATLAB course took their exam. It included some essay questions asking for their favorite elements of the course and things that might be improved in the course. I loved what one of my students had to say about the assignment in the course he found to be the most interesting, so I’ve gotten permission from him to share it. The lab problem he’s referring to was to write a MATLAB program to implement the bisection method for polynomials.

It is really hard to decide which project I found most interesting; there are quite a few of them. If I had to choose just one though, I would probably have to say the lab set for April 6. I was having a really hard time getting the program to work, I spent a while tweaking it this way and that way. But when you’re making a program that does not work yet, there is this sort of golden moment, a moment when you realize what the missing piece is. I remember that moment on my April 6 lab set. After I realized what it was, I could not type it in fast enough I was so excited just to watch the program work. After hitting the play button, that .3 seconds it takes for MATLAB to process the program felt like forever. I actually was devastated that I got an error, and thought I had done it all wrong once again, but then I remembered I had entered the error command so it would display an error. I actually started laughing out loud in the lab, quite obnoxiously actually.

Yes!  As somebody once said, true learning consists in the debugging process. And that’s where the fun in learning happens to lie, too. Let’s give students as many shots as possible to experience this process themselves.

## Understanding “understanding”

This past Saturday, I was grading a batch of tests that weren’t looking so great at the time, and I tweeted:

I do ask these two questions a lot in my classes, and despite what I tweeted, I will probably continue to do so. Sometimes when I do this, I get questions, and sometimes only silence. When it’s silence, I am often skeptical, but I am willing to let students have their end of the responsibility of seeking help when they need it and handling the consequences if they don’t.

But in many cases, such as with this particular test, the absence of questions leads to unresolved issues with learning, which compound themselves when a new topic is connected to the old one, compounded further when the next topic is reached, and so on. Unresolved questions are like an invasive species entering an ecosystem. Pretty soon, it becomes impossible even to ask or answer questions about the material in any meaningful way because the entire “ecosystem” of a student’s conceptual framework for a subject is infected with unresolved questions.

Asking if students understand something or if they have questions is, I am realizing, a poor way to combat this invasion. It’s not the students’ fault — though persistence in asking questions is a virtue more students could benefit from. The problem is that students, and teachers too, don’t really know what it means to “understand” something. We tend to base it on emotions — “I understand the Chain Rule” comes to mean “I have a feeling of understanding when I look at the Chain Rule” — rather than on objective measures. This explains the common student refrain of “It made sense when you did it in class, but when I tried it I didn’t know where to start“. Of course not! When you see an expert do a calculation, it feels good, but that feeling does not impart any kind of neural pathway towards your being able to do the same thing.

So what I mean by my tweet is that instead of asking “Do you understand?” or “Do you have any questions?” I am going to try in the future to give students something to do that will let me gauge their real understanding of a topic in an objective way. This could be a clicker question that hits at a main concept, or a quick and simple problem asking them to perform a calculation (or both). If a student can do the task correctly, they’re good for now on the material. If not, then they aren’t, and there is a question. Don’t leave it up to students to self-identify, and don’t leave it up to me to read students’ minds. Let the students do something simple, something appropriate for the moment, and see what the data say instead.

This may have the wonderful side effect of teaching some metacognition as well — to train students how to tell when they do or do not know something.

Filed under Education, Teaching

## Targeting the inverted classroom approach

Image via Wikipedia

A while back I wondered out loud whether it was possible to implement the inverted or “flipped” classroom in a targeted way. Can you invert the classroom for some portions of a course and keep it “normal” for others? Or does inverting the classroom have to be all-or-nothing if it is to work at all? After reading the comments on that piece, I began to think that the targeted approach could work if you handled it right. So I gave it a shot in my linear algebra class (that is coming to a close this week).

The grades in the class come primarily from in-class assessments and take-home assessments. The former are like regular tests and the latter are more like take-home tests with limited collaboration. We had online homework through WeBWorK but otherwise I assigned practice exercises from the book but didn’t take them up. The mix of timed and untimed assessments worked well enough, but the lack of collected homework was not giving us good results. I think the students tended to see the take-home assessments as being the homework, and the WeBWorK and practice problems were just something to look at.

What seemed true to me was that, in order for a targeted inverted classroom approach to work, it has to be packaged differently and carry the weight of significant credit or points in the class. I’ve tried this approach before in other classes but just giving students reading or videos to watch and telling them we’d be doing activities in class rather than a lecture — even assigning  minor credit value to the in-class activity — and you can guess what happened: nobody watched the videos or read the material. The inverted approach didn’t seem different enough to the students to warrant any change in their behaviors toward the class.

So in the linear algebra class, I looked ahead at the course schedule and saw there were at least three points in the class where we were dealing with material that seemed very well-suited to an inverted approach: determinants, eigenvalues and eigenvectors, and inner products. These work well because they start very algorithmically but lead to fairly deep conceptual ideas once the algorithms are over. The out-of-class portions of the inverted approach, where the ball is in the students’ court, can focus on getting the algorithm figured out and getting a taste of the bigger ideas; then the in-class portion can focus on the big ideas. This seems to put the different pieces of the material in the right context — algorithmic stuff in the hands of students, where it plays to their strengths (doing calculations) and conceptual stuff neither in a lecture nor in isolated homework experiences but rather in collaborative work guided by the professor.

To solve the problem of making this approach seem different enough to students, I just stole a page from the sciences and called them “workshops“. In preparation for these three workshops, students needed to watch some videos or read portions of their textbooks and then work through several guided practice exercises to help them meet some baseline competencies they will need before the class meeting. Then, in the class meeting, there would be a five-point quiz taken using clickers over the basic competencies, followed by a set of in-class problems that were done in pairs. A rough draft of work on each of the in-class problems was required at the end of the class meeting, and students were given a couple of days to finish off the final drafts outside of class. The whole package — guided practice, quiz, rough draft, and final draft — counted as a fairly large in-class assessment.

Of course this is precisely what I did every week in the MATLAB course. The only difference is that this is the only way we did things in the MATLAB course. In linear algebra this accounted for three days of class total.

Here are the materials for the workshops we did. The “overview” for each contains a synopsis of the workshop, a list of videos and reading to be done before class, and the guided practice exercises.

The results were really positive. Students really enjoyed doing things this way — it’s way more engaging than a lecture and there is a lot more support than just turning the students out of class to do homework on their own. As you can see, many of the guided practice exercises were just exercises from the textbook — the things I had assigned before but not taken up, only to have them not done at all. Performance on the in-class and take-home assessments went up significantly after introducing workshops.
Additionally, we have three mastery exams that students have to pass with 100% during the course — one on row-reduction, another on matrix operations, and another on determinants. Although determinants form the newest and in some ways the most complex material of these exams, right now that exam has the highest passing rate of the three, and I credit a lot of that to the workshop experience.
So I think the answer to the question “Can the inverted classroom be done in a targeted way?” is YES, provided that:
• The inverted approach is used in distinct graded assignments that are made to look and feel very distinct from other elements of the course.
• Teachers make the expectations for out-of-class student work clear by giving an unambiguous list of competencies prior to the out-of-class work.
• Quality video or reading material is found and used, and not too much of it is assigned. Here, the importance of choosing a textbook — if you must do so — is very important. You have to be able to trust that students can read their books for comprehension on their own outside of class. If not, don’t get the book. I used David Lay’s excellent textbook, plus a mix of Khan Academy videos and my own screencasts.
• Guided practice exercises are selected so that students experience early success when grappling with the material out of class. Again, textbook selection should be made along those lines.
• In-class problems are interesting, tied directly to the competency lists and the guided practice, and are doable within a reasonable time frame.
These would serve as guidelines for any inverted classroom approach, but they are especially important for making sure that student learning is as great or greater than the traditional approach — and again, the idea of distinctness seems to be the key for doing this in a targeted way.
What are your suggestions or experiences about using the inverted or “flipped” classroom in a targeted way like this?

Filed under Clickers, Inverted classroom, Linear algebra, MATLAB, Screencasts

## Four lessons from my Lenten social media fast

Image via Wikipedia

This past Sunday was Easter, of course. Easter marks the endpoint of Lent, and therefore it was the end of my 40-day fast from Facebook and Twitter. I do admit that I broke cover once to announce my upcoming job change, and will also admit that I lurked a lot on both services during the last 10 days or so, reading but not commenting. Otherwise, though, I did manage to stay off both Facebook and Twitter for the duration (auto-posted tweets didn’t count).

I’ll have to say my first real tweet after breaking the fast felt awkward — like I’d been out in the wilderness for 40 days and had stepped back into a once-familiar place with people who had never left. I’m gradually getting back into the swing of it, but I also feel like I have a much different perspective on my social media involvement after giving most of it up for 40 days. I’ve learned a few things about the role of social media in my work and life:

Lesson 1: Denoising your life is good. I found this out within days of starting the fast. I didn’t realize until I gave Twitter and Facebook up for a few days just how dependent I’d become on checking status reports every few minutes, not to mention creating status updates myself. There is a tremendous amount of time bound up in these little 2- to 5-minute bursts of social media that I really benefitted from reclaiming. But more than that, I found that once I went cold turkey on Facebook and Twitter, the pace of my life slowed down several notches. I felt less hurried and more relaxed. When you make yourself try to keep up with a continuous stream of status updates, you soon begin to feel like Lucy and Ethel on the candy wrapping assembly line:

But that’s not all I learned.

Lesson 2: Getting rid of the noise is good, but losing the signal in the process is not so good. Many times over the last couple of months, I’d catch myself leaning over the keyboard about to compose a tweet asking for help or ideas on a question, or looking at Facebook to see what my friends all over the world were doing. But I had to catch myself because I was on a fast. I learned through all this that I really value the thoughts and ideas of the people and groups I follow — these thoughts and ideas enrich my life, fire my imagination, make me laugh at silly stuff, and generally make me a better person and professional. I missed all that, and the people behind them, a lot.

Despite the value I place in my connections, I also learned that:

Lesson 3: It’s good not to share everything. I remember quite clearly having lunch with my dissertation advisor one day, and he gave me a piece of advice I’ve never forgotten: Always keep secrets. Work on things that nobody knows about but yourself. While sharing is generally good, and while the power of being able to share yourself quickly and on a large scale through Twitter and Facebook creates a powerful opportunity to connect with others, I think there’s a point of sharing past which the individual starts to get diluted. For example, during the first couple of weeks of Lent, I attended the ICTCM in Denver. There was no tweeting from there, although there was ample opportunity. Instead, I kept notes, talked to people, and made myself social in real life. It was good, and I think it would have been less good if I had taken time away from the here-and-now to tweet about the here-and-now.

Then, the Wednesday after I returned from Denver, I noticed on my right leg a series of painful, angry-looking red streaks going from my lower right calf all the way up to the top of the thigh. I went to the doctor to have it checked out, and they sent me directly to the emergency room, and from there they sent me directly to a hospital room. I was diagnosed with cellulitis, an infection of the subcutaneous tissue under the skin that I probably picked up from walking around barefoot in my Denver hotel room. I spent three days in the hospital getting IV antibiotics around the clock to fight the infection. Had I waited till Thursday morning to go to the doctor, the infection would have made it to my femoral artery and I likely would have gone septic, and it would have gotten considerably worse from there.

I’ll admit it: I was scared, frustrated, and sorely in need of people to connect with during those three days. Had I been using social media, I would have been posting Facebook and Twitter updates, probably with pictures, about as often as I was getting antibiotics. But by choice, I kept this experience to myself, to share with my wife and kids, my doctors, and with God. Instead of tweeting, I prayed and wrote and talked to my wife and children. I watched a lot of Netflix and got some grading done. So while it would have been a comfort to have social media as an outlet for sharing with others, by concentrating my sharing to the real people in my life who matter the most, and keeping the rest a secret (till now), the whole experience somehow has more meaning and lasting power in my memory.

Finally, I learned:

Lesson 4: Social media is a permanent part of who I am, and when managed well it is a powerful force for good. Early on during Lent I realized I liked the slower pace of life so much that I wondered if I would go back to Twitter and Facebook once it was all over. Honestly, I can’t see giving those two services up. I’ve carefully groomed and built my list of people and groups to follow so that whenever I look in on the Twitter update stream, I learn something. Facebook is the same way except on a more personal level with friends from real life. So I can’t see just giving these things up. They are an antidote to stagnation. But I do like taking a more minimal and focused approach to engaging with social media — which, by the way, leaves me more ideas and energy for blogging — so that the signal-to-noise ratio is high.

So ends my Lenten social media fast, with results that I consider successful. I feel that I’m now more apt to use social media outlets to grow and learn and connect in positive ways, less prone to share indiscriminately and inappropriately. Like most things, it takes some time away to help you appreciate what you have.

Filed under Christianity, Family, Personal, Social software, Technology, Twitter, Web 2.0

## News of the day: I’m moving

I wanted to announce to all you readers of this blog that some big changes are coming up soon for my and my family. This doesn’t really affect the blog, but you might like to know. I’ll be leaving Franklin College, my place of employment for nearly ten years, after this semester to accept a new position as Associate Professor of Mathematics at Grand Valley State University in Allendale, Michigan. My first official day at GVSU will be August 8, and we’ll be moving up to the Grand Rapids area probably in mid-July.

This has been a truly gut-wrenching decision to make, since Franklin has been extremely good to me for the last 9+ years, and I hope that I’ve done some good for the college and its students as well. It’s also a decision that’s been cooking for months, but for obvious reasons I couldn’t blog about it. In the end, though, I made the choice to go to GVSU for three reasons.

1. I was really impressed by the university, which is just 50 years old and has an enrollment of 25,000 students — that’s double what it was 10 years ago. It’s an active, dynamic, forward-thinking institution that has all the accoutrements and resources of a large public university but hasn’t forsaken excellent undergraduate education as its primary focus. The math department, in particular, is loaded with talent and intellectual energy, both in mathematics and in teaching, which is rare to see in a big university.
2. My family really liked the area, particularly those lovely beaches along Lake Michigan just a few minutes away and the small-but-big feel of Grand Rapids. My wife and I honeymooned in the Upper Peninsula and we’ve always felt like Michigan would be a cool place to relocate if it came to that. West Michigan has a low cost of living and a high quality of life, and it’s a great place for us to try to accomplish some personal and family goals we’ve set for ourselves.
3. Above all, the people I encountered at GVSU — faculty, administrators, students, support staff — have been so kind, generous, and thoughtful throughout this whole process. Being an academic is about having ideas, but being a successful and happy academic is about surrounding yourself with people who support you, believe in you, and make you better at what you do. This is what makes good ideas take root and become great ideas. That’s what GVSU has to offer, and that’s the main thing that made my mind up in the end.
We will really miss Indianapolis, which is a great city and a terrific place to live and start a family. And we don’t look forward to trying to get our house sold in this terrible real estate market. (Referrals, anyone?) But it seems like the right place and the right time to do this, and my family and I are tremendously excited about what lies ahead.

## Finding passion

I’m finally through one of the busiest three months I think I’ve ever spent in this business, so hopefully I can get around to more regular posting here. The last big thing that I did as part of this busy stretch also happened to be one of the coolest things I’ve done in a while: I got to do a clicker workshop for some of the senior staff of the Johnson County Humane Society.

It turns out that someone had donated a set of 50 TurningPoint RF cards and a receiver to the Humane Society for use in educational programming — but nobody at the Humane Society knew how to use them or had any idea what they could do with them. One of the leaders in the Humane Society saw an email announcing a workshop I was doing on campus and contacted me about training. We had a great workshop last Friday and came up with some very cool ideas for using clickers in the elementary schools to teach kids about proper care of animals, in training new volunteers at the animal shelter in identifying animal breeds and diseases, even in board meetings.

The thing that stuck with me the most, though, about the folks from the Humane Society was their authentic passion for what they do. They really care about their work with the Humane Society and want to think of new and creative ways to express and share it with others.

This got me thinking: How can you tell what a person or small group of people are passionate about? It seems to me that there’s a two-step process:

1. Give those people a break and let them do whatever they want. Remove all the programming you have planned for them, just for a little bit. And then:
2. See what it is they talk about when there is no structure.

Whatever gets talked about, is what those people are passionate about — at least at the time. If they don’t talk about anything, they aren’t passionate about anything.

For teachers: What does this observation, assuming it’s not totally off-base, say about how we conduct our teaching? It seems to me that we fill the spaces that our students have with all kinds of programming — more topics, more homework, more of everything — until there is no space left to fill, and then when there is time to discuss anything students want, they’d rather stay silent. The passion has been beaten out of them. Might students benefit from a little more space, a little more time to play, and a lot less time trying to get to the next topic or the next example or prepare for the next test?

Filed under Clickers, Education, Life in academia, Peer instruction, Teaching

## Speaking of the inverted classroom

On Wednesday, I gave a talk at Indiana University – Purdue Universty – Indianapolis (IUPUI, for short) to the teaching seminar for math graduate students on the inverted classroom. It was sort of a generalization of the talk I gave on the inverted linear algebra classroom back at the Joint Mathematics Meetings in January. Carl Cowen was in attendance at that talk and invited me to make the 20-minute drive from my house to IUPUI to do something like it, and I was happy to oblige.

Since putting the talk up on Slideshare yesterday morning, it’s gotten over 200 views, 2 favorites, a handful of retweets/Facebook likes, and is currently being highlighted on Slideshare’s Education page. So I thought I would share it here as well. Enjoy and ask questions!