# Tag Archives: homework

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

## How do you manage ungraded student assignments?

Some questions for you in the “vlog” below:

Update: I’ve put the video “below the fold” because there is apparently no way to prevent Ustream embedded videos in WordPress.com blogs from autoplaying when you load the main page. Just click “Keep reading” and you’ll see it.

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Filed under Education, Teaching

## One more thought on working in groups

In my upper-level courses — especially the two senior-level math majors courses I teach, Modern Algebra and Topics in Geometry — traditionally I’ve seen timed tests and so forth as being ineffective in assessing the kinds of advanced problem-solving that students in those classes have to do. Mainly the problems are ones in which they have to prove a theorem. It’s hard to do that under a time pressure because it’s a creative endeavor.

So typically I’ve given such problems out as homework, with the instructions that students may work together on understanding the problem and drafting up a sketch of the solution (Polya’s stages 1 and 2) but the main solution itself, as well as any reality-checking, has to be done individually.

This article from the Harvard Crimson from a year ago captures exactly what I wish this process would look like on the students’ level. The article is about Math 55, called “probably the most difficult undergraduate math class in the country”. How do these students handle the homework in this class, which is assigned frequently and hits like a ton of bricks?

Georges Bizet’s Carmen blares from the computer of Menyoung Lee ’10. The boys sit scattered around their gray worktable, their eyes telltale red and fingers sore from countless hours at their laptops, dutifully LaTeXing problem sets. They have been here since 2 p.m. and will work for almost 12 straight hours to complete the problem set due the following day.

As the hours pass, they discuss the problem set. They formalize and write the solutions on their own for academic integrity. Despite the class’s cutthroat stereotype, this session is about community, not competition. [emph. added]

They work hard as a group — they have to — but when it comes time to actually write the solution, they voluntarily break off to work the solution out on their own, because they have a sense of academic integrity. It’s a community, but not a commune. Nobody is taking anybody else’s work and turning it in as their own, because I suppose they have pride in their work and in their abilities. As far as I can tell there are no timed assessments in Math 55 to hold them individually accountable.

I wouldn’t want my Geometry and Algebra classes to be as hard as Math 55, but I’d love it if students would have a solid sense of the correct point when working together on problems needs to stop and individual work needs to begin, and then make that switch from group to individual work as a matter of personal ethics and an understanding of what it means to learn a subject.  And I’d love not to have to shift assessment of problem-solving over to timed tests as a result.

Do students in high school and certain college courses where group work is stressed more and more frequently understand that this point exists?

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Filed under Education, Higher ed

## P.S. to the previous post about group work

Another thing about group work and assessment. In some courses, particularly upper-division courses with small enrollments, the same kind of individual accountability I’m looking for can be found through oral presentations, not just timed assessments.

I found this out in the textbook-free quasi-Moore Method abstract algebra course I did this past semester. Students were free to work with each other and consult outside sources on any course task they wished to, but at the end of the day their grade depended on their ability to get up in front of the class (and me) and present their work — answering questions on the particulars, being able to explain the overall strategy of a proof, and defending their work against potential holes. Students who could do this on a regular basis scored highly. Students who couldn’t scored poorly. It worked out.

And I know that the students learned a valuable lesson: You don’t present something unless you know it’s right, otherwise you’ll end up embarrassed. And don’t discount the educational value of potential embarrassment.

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Filed under Education, Math, Student culture, Teaching

## A resolution about group work

One of the things I have learned this semester (which is now officially over, having turned in my last batch of grades this morning) is the following lesson which I am convinced I must implement immediately: Group work has been playing far too great of a role in my student’s grades. From this point forward, assignments which could conceivably be done in groups — not just those that are designated for group work — will count for no more than 10-15% of the grade in my courses.

I like collaborative learning. I think, in fact, that working with other people on math can be not only a highly effective way of doing so but also carries with it a powerful pro-math socialization effect. The best personal friendships that I had during my college + grad school years were those that I formed with my classmates in my various math classes, as we struggled through material that, to us at the time, was really hard. Not only did those friends help me learn, I also associated good times and shared victories over math problems with learning math.

But here’s the deal: At the end of the day, the grade that an individual earns in a class, mine or anybody else’s, has to be an accurate reflection of that individual’s mastery of the material and that individual‘s ability to solve problems and think effectively. If were reasonably confident that group effort on problems was translating into individual mastery, I’d be perfectly willing to admit as much group work as students want. But the fact is that this has not been the case.

Case in point: In a recent course, I gave out some pretty difficult advanced problems and instructed students on the usual academic honesty procedures, which boil down to “collaborate if you want but not to the point where you’re no longer doing your own work”. I got back solutions which were eerily similar and all basically correct, and in many cases way out of character for the students handing them in. It was enough to make me suspect a breach of my academic honesty policy, but not enough to make a case. So I simply reproduced the exact same problem on a timed test. And guess what? Whereas before, nearly everybody had a really nice solution — the same really nice solution — this time only one or two people had an idea where to start or even how to correctly parse out the terminology in the problem.

And this has been happening all over, not just in that class — a sort of soft academic dishonesty that nominally stays within bounds. Students work together and hand in work that earns points but does not reflect their understanding of the material. I understand earning good grades is important, but equally important is my ability to identify problem areas and help students grow through them.

So I know what all the digital nativists say about how in the modern workplace, people work collaboratively and it’s a 19th century anachronism to give out timed tests and all that. But you know what? You can’t contribute to a group if you yourself have used the group to feign your own competence. So from here on out, the majority — if not all — of my assessments of students will be done in a timed setting, under conditions that I can set and monitor. For example, in calculus next semester, I’ll assign homework problems and let students work on it all they want in any size group they want. But the grade is going to come from timed quizzes, tests, a midterm, and a final. Some variation on that will also be in place for my two sophomore level courses as well. If you do group work properly, contributing where you can and really working to understand things where you can’t, then it will be no problem to do well on a quiz or test. If not, then the quiz or test will show that up as well.

If that makes me an anachronism, or unhip, or whatnot, then so be it. I’m tired of students not learning the material because they have easy workarounds for doing their own work, and one way or another they will get a good grade in the course if and only if they can show me that they know what they are doing.

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Filed under Academic honesty, Education, Higher ed, Math, Problem Solving, Teaching