Posts Tagged ‘Pedagogy’

Covid 19 Planning: Part 2

March 13, 2020

Well, we are moving to online only courses. Next week’s classes are canceled so that faculty can prep to move online, and then we have online classes at least through Easter. Students are (mostly) being sent home.

Here are a couple of great pages that were shared with me. The first is from the Chronicle. The second is from Stanford.

HOWEVER: I also read an article called Please do a bad job of putting your courses online. The title basically suggests that we should keep things extremely simple. My students are not going to be on campus, so I can’t expect them all to have high-quality internet (several have already told me that they won’t). I was planning on using Zoom a lot when I thought the students would be on campus, but now I am not going to use it as a main tool (although I will use it for office hours).

I get the luxury of having a week to plan, but here is what I am thinking about doing in my statistics classes:

  • My classes will be asynchronous. If students get sick, they are going to be missing scheduled meeting times. I am going to build the class so that they have maximum flexibility in how to do things.
  • I will have ample Zoom office hours (including during the time when we would have met synchronously).
  • Canvas, my LMS, will be the primary way of interacting with students.
  • I might do oral exams instead of written exams. Better yet, I may give the students the option of which they prefer.
  • I will try to cut exam content. If I am assessing it reasonably well with, say, homework, perhaps I do not need assess it in an examination environment, too.
  • I will extend grace to my students as much as I possibly can.

Here are some things that I still want to figure out.

  • What is a low-tech way of building community? Zoom Breakout Rooms seem awesome (and I will still use them for office hours), but I don’t want to assume all students would have access to this. Perhaps I could set up conference calls?
  • What should I do with team projects? Can I still do them? Likely, I won’t have them collect any data now, but could I still have them design the study in teams?
  • How do I maintain equity in an online environment generally?
  • What should I be thinking about that I am not?

Really, I am going to design the rest of the semester the way I always do:

  1. Figure out learning goals (these will largely be the same, but maybe I will jettison some of them).
  2. Re-figure out how to assess them, given the new constraints.
  3. Figure out how to best get the students there.

My final thought: this is going to be far from perfect. Obviously, I wish that Covid 19 would just go away and wouldn’t hurt anyone else. However, we might learn from this. One thing that I am excited about: we are working to figure out how to move our tutoring center online. This seems like something that we could do all the time; a student in his/her residence hall could just Zoom into the tutoring center for a quick question without having to go out in the snow. It seems like we should have already been doing this.

Let me know if you have ideas. Stay healthy!

Covid 19 Plan

March 6, 2020

I was inspired by Stan to come up with a plan for a campus closure due to Covid 19 (or anything else). Here is an initial outline, knowing that my plan will evolve as I learn more about how to work an online course that was designed to be a face-to-face course.

I have two classes, which are very different. Both will use Zoom as the main tool

I am teaching a Mathematics Capstone class, which is essentially a research seminar. We are already using an discussion board on Canvas, so I might lean on that a bit more. I think that we can replicate what we do in class pretty well, with some people breaking off and working together (using Breakout Rooms now) and coming together to share what they have learned (using a combination of screensharing, possible by taking a photo of their paper, and Zoom’s whiteboard). This is very doable.

My statistics class is tougher. However, I run a spiral classroom, and they have seen all of the material already. My plan in-class is to go deeper into the concepts by using clicker questions with Poll Everywhere. Poll Everywhere literally has “everywhere” in the title, so I can keep using that; I can display the clicker questions on Zoom via screensharing, and I can have students discuss via Breakout Rooms.

There will also be times when I think I might have mini-projects, where I might have students design statistical studies to answer certain questions. This can also be done in Breakout Rooms.

My statistics classes also have several quizzes now. I will likely just make Canvas quizzes. Students will be able to either type in their answer or take a picture and upload. I am concerned about cheating, since it would be really easy to text/email answers to friends (my students are generally pretty honest, but not 100% so). Either I will decide not to worry about it, or I might make up multiple quizzes and hand them out randomly.

I think that I might steal one of Stan’s ideas and have “mandatory” office hours via Zoom with teams for 10–15 minutes per week. This may be in place of class time. Also, Zoom will generally work for the usual office hours.

Finally, I will create/provide videos as needed.

Obviously, I am hoping it doesn’t come to this. But I wanted to take the opportunity to think ahead a bit. I think that this is very doable, if not ideal.

On Giving Examples

February 24, 2020

I am having my statistics classes do projects. Basically, they come up with a question, do a mini-IRB process, collect data, and perform a statistical test to try to learn about the answer to their question. They write up their work in a report.

We are on our section project of the semester. The first project reports were fine, but there was a lot of revision needed (this is not unexpected, even though I provided them with specifications). The second round of reports were excellent.

The difference? I provided them with a sample report for the second project but not the first.

I initially struggled with whether this is a good thing or not. I am now confident it is good. The alternative would be to expect them to fumble around to learn what a good report looks like. This seems inefficient and unnecessary. Providing the report was part of the way I was teaching them how to write a report. It is similar to the Benjamin Franklin process, which requires a starting piece of writing to mimic.

Let me know if you disagree that it is reasonable to give them an example copy, and let me know if it is completely obvious that I should have given them an example for the first project.

The Importance of Feedback

May 22, 2014

My semester is ended, and now is the time to write some post-mortem entries into this weblog. The first idea is something that is probably obvious, but I over-thought it. I have been been putting more of the course’s assessment at the end of the semester lately, thinking that that is when students are most prepared to do well.

And I am correct, but I took it too far. I did not give my students enough regular feedback during the first part of the semester this spring. My education students actually pointed this out to me—I realized that they were correct as soon as they said it (it also reinforced that they are pretty on top of education issues). Fortunately, I get to teach that course for education majors again this fall; I will make things right this time.

Additionally, I am working on ways of getting students immediate feedback. Clickers are one way of doing this, but I also might have students start grading their own quizzes (I would provide a couple of solution keys and a marker for them) and doing more computer-graded stuff.

Linear Algebra Class Structure

February 21, 2014

I was originally scheduled to teach abstract algebra this semester, but my section was cancelled due to low enrollment. Instead, I am teaching linear algebra, as we had higher-than-expected enrollment there.

The good news is that I can use the same basic course structure for linear algebra that I was planning to use for abstract algebra. The model is this:

  1. The semester is divided into two parts. The first part, from January 15th until March 31st, is where we learn the content. The second part is all review and assessment.
  2. For the first part, we do IBL-type presentations on Mondays and Fridays. Each day, we can do 4–6 presentations in 55 minutes. On Wednesdays, we review what we learned on the previous Monday and Friday. The reason why I chose Wednesday as the review day was so that students could have at least three nights to prepare for each presentation day.
  3. For the second half of the semester, we will alternate between assessment days and review days. Students will be able to choose what they want to review based on what they found most confusing from the first half of the semester AND from the recent assessments.

One advantage of having the Wednesdays saved for review is that I can use it for an emergency presentation day if a Monday or Friday class is cancelled; this has happened twice so far this semester, due to cold and snow (including today).

One problem that I have is that the course notes I wrote for linear algebra have 314 problems in them. Since I am compressing the presentation part into the first part of the semester AND only using Mondays and Fridays for presentations, I only have 20 presentations days for the 314 problems. This means that we need to average 16 problems per presentation day. I accomplish this by designating 6 problems as “Presentation Problems” (which will be presented, naturally), creating video solutions for another (roughly) 6 problems, and then leaving the remaining four-ish problems without solutions (these are mostly computational problems for which the students were given a video “template” on how to do the process).

It took a while to create the videos, but they are pretty much necessary for our course. This course serves as a very gentle “Introduction to Proofs” course, but the level of proof that is expected is of the “figure out how the proof follows directly from the definition” type. Since there are more complicated proofs that need to be done in the course, I would either need to lecture in class, have the students read the proofs from a textbook (which we don’t have), or create video lectures.

Also, given that we only have six Presentation Problems each day, I have developed a method of having the students volunteer for the problems that cuts down on the amount of work that I have assigning students to problems. My usual way of doing this is putting one essay quiz on Moodle that asks “Which problems would you like to present?” I still do this for my capstone course, in which we present 15 problems per day. For linear algebra, though, I put one quiz consisting of one multiple choice question for each problem that is to be presented. The students are given three choices: “I want to present this problem,” “I really want to present this problem,” and “I changed my mind—I no longer wish to present this problem” (a student who does not want to present does not need to complete the quiz for that particular question). I assign each question 10 points, 5 points, and 0 points, respectively. These points do not affect a student’s grade, but a there simply so I can look at the quiz summary to see each student’s preference quickly without much clicking. The drawback to this is that there is a lot more to do on Moodle (6 quizzes per day instead just one). However, I created all of the quizzes at the very beginning of the semester, and it didn’t actually take that long to do once I learned about the “duplicate” feature on Moodle.

We are just over halfway through the presentation days, and the class is going really well. I think that I have a remarkably good class, so I cannot really say how this class structure is working; I think that any class structure would work with this particular group of students. On the other hand, this shows that this class structure can work, given the right set of students.

Again, a new IBL-Peer Instruction Hybrid Model

December 24, 2013

I am continuing to try to figure out a way to effectively use both IBL and Peer Instruction (“clickers”) in my classes.

First, my main constraint: my favorite grading scheme requires students to be given many chances to get questions correct. Ideally, this means that we would finish with new content for the course 1/2 to 2/3 of the way through the semester.

Here is the approach I have been using up until now:

  1. First part of the semester: Students get the content from reading the textbook.
  2. First part of the semester: Students assimilate the content through Peer Instruction.
  3. Second part of the semester: Students do something that resembles (but isn’t actually) IBL.
  4. Second part of semester: Assess the students a lot.

Below is the same model I discussed last summer for my abstract algebra class. That abstract algebra class was closed due to low enrollment, and I was assigned linear algebra instead. I am keeping the same model, although I have a lot more exercises/theorems/conjectures in my linear algebra notes than I do for my abstract algebra notes.

Here is the new approach:

  1. Mondays and Fridays during first part of the semester: Use IBL and student presentations to introduce the content.
  2. Wednesdays during first part of the semester: use Peer Instruction to review and solidify ideas learned on the previous Friday and Monday.
  3. Second part of the semester: We review the most difficult material through Peer Instruction and in-class practice.
  4. Second part of semester: Assess the students a lot.

Here is the main problem that I am facing: I have 312 exercises in my IBL notes; I basically wrote the notes that I wanted—including many examples to build intuition—and I am now trying to figure out how to shoehorn all of the content into 1/2 to 2/3 of a semester. This works out to an average of about 7 exercises per day if we did IBL work every day of the entire semester, 10 exercises per day if we did IBL work on Mondays and Fridays (and review on Wednesdays) every day of the semester, and 20 exercises per day if we did IBL work on Mondays and Fridays (and review on Wednesdays) every day for half the semester. So I want to see if I can do between 10 to 20 exercises per class IBL class period, which is too much to do without some modifications. Here are the options I can think of to make this happen:

  1. Cut some of the content. I don’t want to do this.
  2. Provide screencasts of some of the exercises. I want to do this anyway, since part of the goal of our linear algebra class is to introduce students to proofs, and I believe that it is very useful for students to see worked examples. But I don’t want to have to provide 10–15 screencasts each class period.
  3. Simply do not cover many of the intuition-building exercises in class; Dana Ernst suggested this to me yesterday, and I think that it is brilliant. There is not reason why I have to do everything in class. Perhaps I could just take questions on any intuition-building exercises after we do the main theorems; I could provide screencasts for some of these if we run out of time.
  4. Other ideas?

Right now, my plan is to have students present and thoroughly discuss roughly 5 problems per IBL day, I would do screencasts for roughly 5 problems per day, leaving roughly 10 intuition problems to leave for the students to do.

Do any of you have ideas about how to improve this?

New IBL-Peer Instruction Hybrid Model

September 18, 2013

Here is my plan for my abstract algebra class in the spring semetser. This is probably a little early to post this, but it ties in with Stan’s post on coverage in IBL classes.

My plan for the spring is to run an IBL course. I wrote my own notes this summer (although they are based heavily off of Margaret Morrow’s notes). One problem that I have with most of the IBL notes for abstract algebra is that they do not do much with ring field and field theory. In creating my notes, I included just about everything that I would want to include in a first abstract algebra course (including a section on group actions). This, of course, is too much content to cover in a semester in an IBL class (I suspect, anyway).

Here are the details: I figure that I can expect the students to discuss 5 problems per class, I can assign 1 other problem as a special type of homework, so I have accounted for 6 problems per day. Since there are about 30 days of class, this means that I can expect them to do 180 problems on their own. But I created a set of notes with 234 problems, and I expect to add more throughout the semester. This is too many problems.

But my solution is similar to Stan’s: I have roughly 50 extra problems for 30 classes. I can simply do three of the problems for students via screencast for them each class period (then I get some extra days for exams, review, and snow days). This has a couple of advantages. First, it allows me to cover all of the material I want to cover over the course of the semester. Second, it gives students model proofs to help them learn how to write proofs.

A second feature that this course will have is a better integration of IBL and Peer Instruction. I am a fan of both pedagogies because of the learning gains reported in the research. I am a fan of IBL because of the level of independence it promotes; Peer Instruction does not do this (at least, the way I do it). I am a fan of Peer Instruction because of the way it stamps out misconceptions and helps students make sense of mathematics; IBL does not do this (at least, not the way I do it). So I am continually looking for ways to combine these pedagogies.

Peer Instruction (for me) works best when the students have already been exposed to the content. I have previously tried to merge the two pedagogies by splitting the semester into halves. This has its advantages, although I am trying something new out next semester: I am going to have IBL classes on Mondays and Fridays (30 classes), and I will have Peer Instruction classes on Wednesdays based on the material that was covered on the previous Monday and Friday.

The basic idea is this: students are introduced to an idea the first time in preparing for an IBL class. They see the material a second time in class. They see the material a third time on the next Wednesday’s Peer Instruction class. They see the material a fourth time on homework/tests/whatever I end up planning.

I am really looking forward to this. Please let me know of any potential problems or improvements that you can think of.

So you suddenly have 68 students enrolled?

August 11, 2013

Suppose you are an instructor who uses Inquiry-Based Learning. You are used to running a particular course with 30–35 students, and you are about to start teaching that course in two weeks. But then you find out that you have 68 students registered for your class. What do you do?

Peer Instruction, hands down. Here is how you do it.

Since I am assuming that you only have two weeks to prepare, this is the most basic way of implementing Peer Instruction. Robert Talbert’s Guided Practice idea would be better to include if you are able.

If it is too late to get “clickers,” use Poll Everywhere, Socrative, or Learning Catalytics. I would tend toward Poll Everywhere, since it is pretty cheap ($65 per month for 68 students—get someone else to pay for it), and students only need a texting plan to use it. But Learning Catalytics seems pretty awesome; I just don’t trust all of the students to have a tablet or smart phone.

Do you have a textbook for the course? If so, here is the recipe:

  1. On the first day of class, assign students to fixed teams of 2 or 3. This will help every student feel like they are part of a community in your class. Students should sit together with their team. You may want to change up teams later in the semester.
  2. Students read a section of the text the night before class. You prepare 5–10 multiple choice questions based on the section. These questions should cover the main points of the section. Some questions will only be to help students understand a definition/concept, other questions will force students to confront misconceptions. Peer Instruction is awesome for confronting misconceptions. Just make sure that you have good distractors for each question.
  3. Everyone comes to class.
  4. If you need to pass back papers, make administrative announcements, etc, you can do that at the beginning of class. But do not, under any circumstance, give an overview of the section; this will teach them that they do not need to read the section, and the result will be that your class will eventually morph into a standard lecture. Instead, simply start the first clicker question.
  5. Display the question on the screen. Have students silently think about the question themselves and “click” their favorite answer when they are ready. You may want to give them a fixed time limit here, although I usually do not; I can usually tell how much students need by the number of students who have already responded. But I usually do not have 68 students.
  6. Look at the results, but do not let them see the results (mute the projector if you need to). If the students overwhelmingly get the correct answer, display the results and give a very brief explanation about why the correct answer is correct AND why the other answers are incorrect. (Note: there is a high bar for “overwhelmingly correct.” For instance, on a True/False question, if half of the students know that the correct answer is True, say, and the other half guess blindly, then 75% of the students will answer correctly. This is bad, since half of the class does not understand. So you might want 90% correct answers on a True/False question, slightly lower for a question with three options, etc. This is an art and not a science, though).
  7. On the other hand, if the students do not overwhelmingly answer correctly, tell the students to discuss their answers with their team. The students should try to convince the other team members of their answer, but the students should be open to changing their mind. Once the team agrees on a single answer, have them re-vote. You should wander around the class as much as you can here, eavesdropping. Once most students have responded (or your time limit is up), display the results to the class.
  8. Now, explain why the correct answer(s) is (are) correct AND why the incorrect answers are incorrect. You can tell how long you should spend talking about this by how the teams did in the most recent round of voting. If they did well, do not talk for long. If they did not do well, give them a more thorough lecture (although you probably will not need to talk for more than 10 minutes).
  9. Repeat with the remainder of your questions until class ends.

This will get every single student involved, and my students have overwhelmingly loved the experience. There is also evidence that Peer Instruction will help students learn enough to increase grades by half of a grade.

If you do NOT have a textbook, you should do your best to find some sort of a free online text for them, write your own notes, create your own lecture videos for students to view before class, and/or use existing videos (e.g. Khan Academy) to use to “transfer” knowledge to the students before class. Then you can use class time to have the students make sense of the new knowledge.

Failing this, lecture. But build some number of clicker questions into your lecture. The process is the same as outlined above, but you will just have fewer questions.

IBL vs Presentations

August 9, 2013

Here is what I learned about Inquiry-Base Learning (IBL) this summer. This is something that I probably should have learned a couple of years ago, but I didn’t. Also, I have heard this misconception from several people, so I do not think I am the only one.

It seems that a lot of people (including me) incorrectly think that student presentations are the main point of IBL.

I figured out that this was a misconception when I heard some other people talk about how they do IBL in their courses. I spoke to several people this summer who said that, while they couldn’t do pure IBL in a class for whatever reason, they did IBL one day a week.

A common model has been: student read proofs out of the textbook, and they present on those proofs in class on that one IBL day.

This didn’t sit well with me. I want to have a “big tent,” but I also want to preserve the integrity of the term IBL (I do not object to this teaching practice—I think it could be very useful. But I don’t think I want it called “IBL”).

I compared this model to my favorite definitions of IBL. Dana Ernst thinks that the two essential elements of IBL are that students should be both primarily responsible for guiding the acquisition of knowledge and primarily responsible for validating the ideas presented. The model above fails on both of these elements: the students were not guiding the acquisition of knowledge (they were told what theorems to look at, and they did not do any of the work to prove the theorem) and they did not validate the idea; the fact that it was listed in a textbook is already a pretty good validation. (This practice does not do any better under TJ Hitchman‘s definition).

So I was feeling pretty smug about my realization. At least, I was feeling smug until I remembered the paper I had just submitted about my Fall 2012 Calculus I class. It described the way I blended Peer Instruction and IBL into the course, and it reported how students’ conceptual understanding improved during the semester.

The problem is that my “IBL” portion of the class was little more than student presentations—it did not meet the IBL criteria that Dana and TJ described. In fact, I recognized that there was a problem part way through my class, but I did not understand that the problem was that I was not even doing IBL.

Fortunately, my paper was deemed “off-topic” for the special issue, and I was invited to re-submit the paper to the regular journal. This gave me time to fix the claims that I was doing IBL.

One last embarrassing note: I am planning my 2013-2014 classes right now, and they are mostly IBL courses. However, I was having trouble finding the right IBL format; I was building my courses around student presentations, and that did not seem quite right. Fortunately, I spoke to my colleague Anne Sinko (who attended the IBL Workshop in June), and she said something that gave me permission to let go of the focus on presentations.

One final note: I think that student presentations can be an important part of a good IBL course, and they will definitely be used in my courses this year. But they will not necessarily be the focus of the course, and they are not sufficient to be IBL.

So I apparently have difficulty letting go of the idea that IBL is basically synonymous with “student presentations.” I hope that writing this post helps rid me of the misconception.

The Many Ways of IBL Conference

June 26, 2013

I attended the University of Chicago’s “Many Ways of IBL” conference last week. Here is a brief list of my thoughts for the week, in no particular order.

  1. It was utterly great to see a couple old friends. I have been blessed to have had good colleagues everywhere I have been, and I wish that I could have taken many of them with me to my current position.
  2. It was great to meet a bunch of new friends. I hope to stay in touch with many of them.
  3. Part of the conference was to watch John Boller teach an IBL class on real analysis to a bunch of super-motivated high school students. Both John and the students did a fantastic job. I told John that it was so enjoyable that he could charge admission.
  4. One big thing I was failing at with IBL last year: I did not discuss the statements and meanings of the theorems before students presented. Boller did this, and it must help students understand everything about the course better.
  5. Paul Sally continues to be amazing. He is also hilarious.
  6. In many classes, I have students read the textbook rather than lecture. I have no idea how to mesh this with IBL, but it is something I value. I realized from the conference that the reason why I value this is that it helps students learn how to learn on their own.
  7. Even though I have been calling my recent hybrid classes “a mix of Peer Instruction (PI) and IBL,” I no longer think that I have been doing IBL. At best, it is IBL-Lite, although it is probably just “students presenting problems.”
  8. This will lead me to alter a paper that I recently wrote on a PI/”IBL” calculus class; I will now qualify that my IBL is pretty weak.
  9. I am now fairly certain that my courses for pre-service elementary education majors are IBL.
  10. I might do IBL in my abstract algebra course this spring. If so, I might interweave IBL and PI differently: I might mainly do IBL, but then have some PI days to make sure students understand the ideas that have already been presented.
  11. In abstract algebra, I might also create a class journal, where students can submit homework problems to an editorial board (of students) for peer review.
  12. In IBL classes, have students take pictures of the board work. They can then upload the pictures to the course website as a record of what happened.
  13. Matthew Leingang gave me a nice way of communicating course rules. He has “The Vegas Rule” for his class: “What happens in Vegas, stays in Vegas” where “Vegas” is defined as “the world outside of this classroom.” This is a nice concise way of reminding students to not use previous knowledge and outside sources.
  14. Leingang also got me excited about paperless grading. Now I just need to find $1200 for an iPad and scanner.
  15. Ken Gross uses an “adjective-noun” metaphor for fractions, where the adjective is the number and the noun is the whole. That is, you can explain common denominators by doing something like: 2/3 “units” + 1/2 “units” equals 4/6 “units” + 3/6 “units,” which is equivalent to 4 “sixths of a unit” + 3 “sixths of a units” = 7 “sixths of a unit” = 7/6 “units.” Most of the work then is just changing the “noun” and finding the appropriate “adjective” for each of the new nouns.