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?

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Salman Khan on the inverted classroom

Salman Khan, of the Khan Academy, sounds off on the potential of pre-recorded video lectures to change education in the video below. He calls it “flipping” the classroom, but around here we call it the inverted classroom.

I like especially that Salman made the point that the main effect of inverting the classroom is to humanize it. Rather than delivering a one-size-fits-all lecture, the lecture is put where it will be of the most use to the greatest number of students — namely, online and outside of class — leaving the teacher free to focus on individual students during class. This was the point I made in this article — that the purpose of technology ought to be to enhance rather than replace human relationships.

I hope somewhere that he, or somebody, spends a bit more time discussing exactly how the teachers in the one school district he mentions in the talk actually implemented the inverted classroom, and what kinds of issues they ran up against. Ironically, the greatest resistance I get with the inverted classroom is from students themselves, namely a small but vocal group who believe that this sort of thing isn’t “real teaching”. I wonder if the K-12 teachers who use this model encounter that, or if it’s just a phenomenon among college-aged students.

Technology making a distinction but not a difference?

This article is the second one that I’ve done for Education Debate at Online Schools. It first appeared there on Tuesday this week, and now that it’s fermented a little I’m crossposting it here.

The University of South Florida‘s mathematics department has begun a pilot project to redesign its lower-level mathematics courses, like College Algebra, around a large-scale infusion of technology. This “new way of teaching college math” (to use the article’s language) involves clickers, lecture capture, software-based practice tools, and online homework systems. It’s an ambitious attempt to “teach [students] how to teach themselves”, in the words of professor and project participant Fran Hopf.

It’s a pilot project, so it remains to be seen if this approach makes a difference in improving the pass rates for students in lower-level math courses like College Algebra, which have been at around 60 percent. It’s a good idea. But there’s something unsettling about the description of the algebra class from the article:

Hopf stands in front of an auditorium full of students. Several straggle in 10 to 15 minutes late.

She asks a question involving an equation with x’s, h’s and k’s.

Silence. A few murmurs. After a while, a small voice answers from the back.

“What was that?” Hopf asks. “I think I heard the answer.”

Every now and then, Hopf asks the students to answer with their “clickers,” devices they can use to log responses to multiple-choice questions. A bar graph projected onto a screen at the front of the room shows most students are keeping up, though not all.

[…]

As Hopf walks up and down the aisles, she jots equations on a hand-held digital pad that projects whatever she writes on the screen. It allows her to keep an eye on students and talk to them face-to-face throughout the lesson.

Students start drifting out of the 75-minute class about 15 minutes before it ends. But afterward, Hopf is exuberant that a few students were bold enough to raise their hands and call out answers.

To be fair: This is a very tough audience, and the profs involved have their work cut out for them. The USF faculty are trying with the best of intentions to teach students something that almost assuredly none of them really want to learn, and this is exceedingly hard and often unrewarding work. I used to teach remedial algebra (well short of “college algebra”) at a two-year institution, and I know what this is like. I also know that the technology being employed here can, if used properly, make a real difference.

But if there’s one main criticism to make here, it’s that underneath the technology, what I’m seeing — at least in the snapshot in the article — is a class that is really not that different than that of ten or twenty years ago. Sure, there’s technology present, but all it seems to be doing is supporting the kinds of pedagogy that were already being employed before the technology, and yielded 60% pass rates. The professor is using handheld sketching devices — to write on the board, in a 250-student, 75-minute long lecture. The professor is using clickers to get student responses — but also still casting questions out to the crowd and receiving the de rigeur painful silence following the questions, and the clickers are not being used in support of learner-centered pedagogies like peer instruction. The students have the lectures on video — but they also still have to attend the lectures, and class time is still significantly instructor-centered. (Although apparently there’s no penalty for arriving 15 minutes late and leaving 15 minutes early. That behavior in particular should tell USF something about what really needs to change here.)

What USF seems not to have fully apprehended is that something about their remedial math system is fundamentally broken, and technology is neither the culprit nor the panacea. Moving from an instructor-centered model of learning without technology to an instructor-centered model of learning with technology is not going to solve this problem. USF should instead be using this technology to create disruptive change in how it delivers these courses by refocusing to a student-centered model of learning. There are baby steps here — the inclusion of self-paced lab activities is promising — but having 75-minute lectures (on college algebra, no less) with 225 students signals a reluctance to change that USF’s students cannot afford to keep.

Computers, the Internet, and the Human Touch

Image via Wikipedia

This article first appeared earlier this week on the group blog Education Debate at OnlineSchools.org. I’m one of the guest bloggers over there now and will be contributing articles 1–2 times a month. I’ll be cross-posting those articles a couple of days after they appear. You’d enjoy going to Education Debate for a lively and diverse group of bloggers covering all kinds of educational issues.

It used to be that in order to educate more than a handful of people at the same time, schools had to herd them into large lecture halls and utilize the skills of lecturers to transmit information to them. Education and school became synonymous in this way. Lectures, syllabi, assessments, and other instruments of education were the tightly-held property of the universities.

But that’s changing. Thanks to advancements in media and internet technology over the past decade, it is simpler than ever today to package and publish the raw informational content of a course to the internet, making the Web in effect a lecture hall for the world. We now have projects such as MIT OpenCourseWare, Khan Academy, and countless initiatives for online education at US colleges and universities providing high-quality materials online, for free, to whomever wants them. It brings up a sometimes-disturbing question among educators: If students can get all this stuff online for free, what are classrooms and instructors for?

Tech author Randall Stross attempts to examine this question in his New York Times article “Online Courses, Still Lacking that Third Dimension”. In the article, Stross mentions “hybrid” courses — courses with both online and in-person components — but focuses mainly on self-contained courses done entirely online with no live human interaction. He correctly points out that learning is an inherently human activity, and technologically-enhanced coursework is successful insofar as it retains that “human touch”.

However, Stross casts the relationship between computer-enabled courses and traditional courses as a kind of zero-sum game, wherein an increased computer presence results in a decreased human presence. He refers to universities “adopting the technology that renders human instructors obsolete.” But it’s not the technology itself that makes instructors obsolete; it’s the adoption of practices of using that technology that does. There are numerous instances of traditional college courses using computing and internet tools to affect positive change in the learning culture of the institution. There are also plenty of cases, as Stross points out, where technology has replaced human instructors. The difference is an administrative one, not a technological one.

Nor is the supposed obsolescence of the instructor all technology’s fault. If universities and individual professors continue to hold on to a conception of “teaching” that equates to “mass communication” — using the classroom only to lecture and transmit information and nothing else — then both university and instructor are obsolete already, no technology necessary. They are obsolete because the college graduate of the 21st century does not need more information in his or her head to solve the problems that will press upon them in the next five or ten years. Instead, they need creativity, problem-solving experience, and high-order cognitive processing skills. A college experience based on sitting through lectures and working homework does not deliver on this point. The college classroom cannot, any longer, be about lecturing if it is to remain relevant.

And notice that an entirely self-contained online course can be as “traditional” as the driest traditional lecture course attended in person if it’s only a YouTube playlist of lectures. What matters regarding the effectiveness of a course isn’t the technology that is or is not being used. Instead it’s the assumptions about teaching and learning held by the colleges and instructors that matter, and their choices in translating those assumptions to an actual class that students pay for.

What we should be doing instead of choosing sides between computers and humans is finding ways to leverage the power of computers and the internet to enhance the human element in learning. There are several places where this is already happening:

• Livemocha is a website that combines quality multimedia content with social networking to help people learn languages. Users can watch and listen to language content that would normally find its place in a classroom lecture and then interact with native speakers from around the world to get feedback on their performance.
• Socrait, a system proposed by Maria Andersen, would provide personalized Socratic questions keyed to specific content areas by way of a “Learn This” button appended to existing web content, much like the “Like This” button for sharing content on Facebook. Clicking the button would bring the user to an interface to help the user learn the content, and the system contains social components such as identifying friends who also chose to learn the topic.
• I would offer my own experiments with the inverted classroom model of instruction as an imperfect but promising example as well. Research suggests this model can provide in significant gains in student learning versus the traditional approach to teaching by simply switching the contexts of lecture and activity, with lecture being delivered via video podcasts accessed outside of class and class time spent on problem-based learning activities in teams.

Rather than view college course structure as a pie divided into a computer piece and a human piece, and fret about the human piece becoming too small, let’s examine ways to use computers to enhance human learning. If we keep thinking of computers as a threat rather than an aid to human interaction, computer-assisted instruction will continue to lack the human touch, the human touch will continue to lack the power and resources of computers and the internet, and student learning will suffer. But if we get creative, the college learning experience could be in for a renaissance.

Bound for New Orleans

Happy New Year, everyone. The blogging was light due to a nice holiday break with the family. Now we’re all back home… and I’m taking off again. This time, I’m headed to the Joint Mathematics Meetings in New Orleans from January 5 through January 8. I tend to do more with my Twitter account during conferences than I do with the blog, but hopefully I can give you some reporting along with some of the processing I usually do following good conference talks (and even some of the bad ones).

I’m giving two talks while in New Orleans:

• On Thursday at 3:55, I’m speaking on “A Brief Fly-Through of Cryptology for First-Semester Students using Active Learning and Common Technology” in the MAA Session on Cryptology for Undergraduates. That’s in the Great Ballroom E, 5th Floor Sheraton in case you’re there and want to come. This talk is about a 5-day minicourse I do as a guest lecturer in our Introduction to the Mathematical Sciences activity course for freshmen.
• On Friday at 11:20, I’m giving a talk called “Inverting the Linear Algebra Classroom” in the MAA Session on Innovative and Effective Ways to Teach Linear Algebra. Thats in Rhythms I, 2nd floor Sheraton. This talk is an outgrowth of this blog post I did back in the spring following the first non-MATLAB attempt at the inverted classroom approach I did and will touch on the inverted classroom model in general and how it can play out in Linear Algebra in particular.

Both sessions I’m speaking in are loaded with what look to be excellent talks, so I’m excited about participating. I’d be remiss if I didn’t mention that Gil Strang and David Lay are two of the organizers of the linear algebra setting, which is like a council of the linear algebra gods.

I’ll give Casting Out Nines readers a sneak peek at my two talks by telling you I’ve set up a web site that has the Prezis for both talks along with links to the materials I mention in the talks. And if you’re there in New Orleans, come by my talks if you have the slots free or just give me a ring on my Twitter and I’d love to meet up with you.

Coming up in January

Fall Semester 2010 is in the books, and I’m heading into an extended holiday break with the family. Rather than not blog at all for the next couple of weeks, I’ll be posting (possibly auto-posting) some short items that take a look back at the semester just ended — it was a very eventful one from a teaching standpoint — and a look ahead and what’s coming up in 2011.

I’ll start with the look head to January 2011. We have a January term at my school, and thanks to my membership on the Promotion and Tenure Committee — which does all its review work during January — I’ve been exempt from teaching during Winter Term since 2006 when I was elected to the committee. This year I am on a subcommittee with only three files to review, so I have a relatively luxurious amount of time before Spring semester gets cranked up in February. A time, that is, which is immediately gobbled up by the following:

• I’ll be at the Joint Mathematics Meetings in New Orleans from January 6–9. This will be my first trip to the Joint Meetings since 2002, and I’m pretty excited about it. I will be giving two talks, one in the MAA Session on Undergraduate Cryptology (PDF) about my five-day micro-unit on cryptology for freshmen and the other in the MAA Session on Innovative and Effective Ways to Teach Linear Algebra (PDF) on experimenting with the inverted classroom model in linear algebra. Both of those sessions are loaded with interesting-sounding talks, so I hope to attend the entire session. I also hope to catch up with friends I haven’t seen since, well, 2002 — and maybe connect with some new ones. If you’re attending, let me know!
• The second iteration of the MATLAB course is coming up in the spring as well, and I will be doing some significant redesign work on it based on experiences and data from the first iteration. I’m constantly humbled and gratified by the interest and positive responses that the course has generated in the MATLAB community and elsewhere — and by how much interest and attention the course has received. I’ve had a chance to observe and talk to the alumni from the first run of the course during their Calculus III course that used MATLAB significantly, and their usage habits and feedback have given me some ideas for what should be positive changes in the course. I’ll elaborate on that later.
• I am teaching Linear Algebra again in the spring, as I have done for the last 4-5 years, and this year I am targeting that course for a more robust implementation of inverted classroom techniques. A lot of the students in that course will be MATLAB course alumni, so they will be used to all that inversion. But I’ve had enough experience with peer instruction and classroom response system (“clicker”) use on the one hand from this past semester (which I never blogged about, and I’ll try to remedy that) and inverted classroom approaches in MATLAB on the other that Linear Algebra seems well-positioned to benefit from a combination of these approaches. I’ll be sketching out and planning the course in January.
• Like I said, I used a lot of peer instruction and clickers in calculus this semester with great success (I think; at least the students say so). I’m teaching two more sections of calculus in the spring and will be refining my teaching using these tools. But calculus in the spring has a different flavor than calculus in the fall, so we will see how it goes.
• What I’m reading this January: Teaching with Classroom Response Systems by Derek Bruff; Learning to Solve Problems by David Jonassen; The Craft of Research by Booth, Colomb, and Williams; and catching up on a mountain of articles that accumulated during the semester.
• I’m also reading Geometry and Symmetry by Kinsey, Moore, and Prassidis leading up to an MAA review of the book. The “Prassidis” in the author list is Stratos Prassidis, who was my Ph.D. dissertation advisor.

Throw a couple of consulting projects on top of all that, and you’ve got yourself a busy January!

What correlates with problem solving skill?

About a year ago, I started partitioning up my Calculus tests into three sections: Concepts, Mechanics, and Problem Solving. The point values for each are 25, 25, and 50 respectively. The Concepts items are intended to be ones where no calculations are to be performed; instead students answer questions, interpret meanings of results, and draw conclusions based only on graphs, tables, or verbal descriptions. The Mechanics items are just straight-up calculations with no context, like “take the derivative of “. The Problem-Solving items are a mix of conceptual and mechanical tasks and can be either instances of things the students have seen before (e.g. optimzation or related rates problems) or some novel situation that is related to, but not identical to, the things they’ve done on homework and so on.

I did this to stress to students that the main goal of taking a calculus class is to learn how to solve problems effectively, and that conceptual mastery and mechanical mastery, while different from and to some extent independent of each other, both flow into mastery of problem-solving like tributaries to a river. It also helps me identify specific areas of improvement; if the class’ Mechanics average is high but the Concepts average is low, it tells me we need to work more on Concepts.

I just gave my third (of four) tests to my two sections of Calculus, and for the first time I started paying attention to the relationships between the scores on each section, and it felt like there were some interesting relationships happening between the sections of the test. So I decided to do not only my usual boxplot analysis of the individual parts but to make three scatter plots, pairing off Mechanics vs. Concepts, Problem Solving vs. Concepts, and Mechanics vs. Problem Solving, and look for trends.

Here’s the plot for Mechanics vs. Concepts:

That r-value of 0.6155 is statistically significant at the 0.01 level. Likewise, here’s Problem Solving vs. Concepts:

The r-value here of 0.5570 is obviously less than the first one, but it’s still statistically significant at the 0.01 level.

But check out the Problem Solving vs. Mechanics plot:

There’s a slight upward trend, but it looks disarrayed; and in fact the r = 0.3911 is significant only at the 0.05 level.

What all this suggests is that there is a stronger relationship between conceptual knowledge and mechanics, and between conceptual knowledge and problem solving skill, than there is between mechanical mastery and problem solving skill. In other words, while there appears to be some positive relationship between the ability simply to calculate and the ability to solve problems that involve calculation (are we clear on the difference between those two things?), the relationship between the ability to answer calculus questions involving no calculation and the ability to solve problems that do involve calculation is stronger — and so is the relationship between no-calculation problems and the ability to calculate, which seems really counterintuitive.

If this relationship holds in general — and I think that it does, and I’m not the only one — then clearly the environment most likely to teach calculus students how to be effective problem solvers is not the classroom primarily focused on computation. A healthy, interacting mixture of conceptual and mechanical work — with a primary emphasis on conceptual understanding — would seem to be what we need instead. The fact that this kind of environment stands in stark contrast to the typical calculus experience (both in the way we run our classes and the pedagogy implied in the books we choose) is something well worth considering.

Pushing back

Seth Godin has a lot of good things to say in this short blog post, such as:

When a professor assigns you to send a blogger a list of vague and inane interview questions (“1. How did you get started in this field? 2. What type of training (education) does this field require? 3. What do you like best about your job? 4. what do you like least about your job?”) I think you have an obligation to say, “Sir, I’m going to be in debt for ten years because of this degree. Perhaps you could give us an assignment that actually pushes us to solve interesting problems, overcome our fear or learn something that I could learn in no other way…”

When a professor spends hours in class going over concepts that are clearly covered in the textbook, I think you have an obligation to repeat the part about the debt and say, “perhaps you could assign this as homework and we could have an actual conversation in class…”

As a professor, I love it when students make such demands of me. It’s how I want to teach anyway, and it makes it a lot easier when I know students are not only on board with but insisting that I not simply lecture from the book, repeat problems that are in the book, and expect them to learn only the things that are printed in the book.

So I would add one thing to Seth’s injunction: Students, if you feel this way about your professors, take a look at your peers who don’t feel this way. Do you have classmates who just want the professor to read from the book, give tests that are just like the book’s examples, and not expect more from them? Then push back there, as well. Demand from your peers that they not leave you out on an island demanding academic excellence and getting your money’s worth.

This week (and last) in screencasting: Functions!

So we started  back to classes this past week, and getting ready has demanded much of my time and blogging capabilities. But I did get some new screencasts done. I finished the series of screencasts I was making for our calculus students to prepare for Mastery Exams, a series of short untimed quizzes over precalculus material that students have to pass with a 100% score. But then I turned around and did some more for my two sections of calculus on functions. There were three of them. The first one covers what a function is, and how we can work with them as formulas:

The second one continues with functions as graphs, tables, and verbal descriptions:

And this third one is all on domain and range:

The reason I made these was because we were doing the first section of the Stewart calculus book in one day of class. If you know this book, you realize this is impossible because there is an enormous amount of stuff crammed into this one section. Two items covered in that section are how to calculate and reduce the difference quotient and doing word problems. Each of these topics alone can cover multiple class meetings, since many students are historically rusty or just plain bad at manipulating formulas correctly and suffer instantaneous brain-lock when put into the presence of a word problem. So, my thought was to go all Eric Mazur on them and farm out the material that is most likely to be easy review for them as an outside “reading” assignment, and spend the time in class on the stuff that on which they were most likely to need serious help.

Our first class was last Tuesday and the second class wasn’t until Thursday, so I assigned the three videos and three related exercises from the Stewart book for Thursday, along with instructions to email questions on any of this, or post to our Moodle discussion board. I made up some clicker questions that we used to assess their grasp of the material in these videos, and guess what? Many students didn’t have any problems at all with this material, and those who did got their issues straightened out through discussions with other students as part of the clicker activity.

They’ll be assessed in 2 or 3 other ways on this stuff this week to make sure they really have the material down and are not just being shy about not having it. But it looks like using screencasts to motivate student contact with the material outside of class worked fine, at least as effectively as me lecturing over it. And we had more time for the hard stuff that I wouldn’t expect students to be able to handle, not all of them anyway.