Posts Tagged ‘IBL’

Inquiry-Oriented Instruction

February 15, 2017

I was part of a grant last semester to implement a set of teaching materials that has been refined over the last decade. The materials use a teaching method called inquiry-oriented instruction, which I would say is a subset of inquiry-based learning (IBL). I used these materials in my abstract algebra class, although there are materials for both linear algebra and differential equations, too.

A very brief description is “intuition comes before definitions.” The materials introduce quotient groups by discussing Even and Odd integers, which students could easily see is a group at that point (using rules like “Even + Odd = Odd”). Once they got familiar with the idea that we could have sets of elements make up a group, we slowly backed our way into the definition of coset. It was pretty impressive to see students very naturally come up with definitions—having the right prompts helped a lot.

As part of the grant, I went to training at North Carolina State to use the materials. I also had funds to have student video my class, which will be used to analyze how well instructors who were not involved with the development of these materials can implement them.

We also used the class video as part of a weekly online working group. The purpose of this group was to prepare us, both in terms of pedagogy and course materials (not everyone was an algebraist), to teach the class. We discussed the purposes of the prompts, talked about what was going well and poorly, and watched video of each others’ classes. I found this immensely helpful.

I would use these materials again (in fact, I am planning on using the linear algebra materials next year). My sense is that my students had an abnormally good grasp of the definitions; previous students have struggled to understand what a coset means, for instance. My focus for the next time I use the abstract algebra materials is to work harder on the technical proofs—I think that my students did better on writing proofs than the previous time I taught the course, but not by a lot. Still, I think that the gains in intuition were worth it.

Links to the abstract algebra, linear algebra, and differential equation materials can be found here in the middle of the page.

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.

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.

New Grading Scheme: Presentations Fail

December 15, 2012

Last week, I talked about how determine my students’ grades up to a C (by the way—the students are doing much better on the quizzes than I expected. Most students should finish up on Monday, the last day of grading. I expected many, many more students to be struggling to meet the requirements). This week, I will discuss how they earn a B or an A.

There are two components in determining grades above a C: presentations and a take-home final exam.

The exam was pretty standard. The one comment here is that I could make it fairly difficult, since it is really aimed at differentiating the C-students from the B-students from the A-students.

For the presentations, I essentially made a list of 100-200 homework problems for the semester, and doled them out to the students. I assigned 15 problems to be presented per class period for the second half of the semester, and I told the students to spend at least 10 minutes trying each problem before they are due. The purpose of this was so that the non-presenting students would get more out of the class (spoiler: I don’t think that students actually looked at the problems they were not planning on presenting).

The night before class, students request (via Moodle, our classroom management system) to present as many or as few of the assigned problems as they like. The next morning, I assemble an “itinerary” of presentations. The presenting student comes to class with the substance of the presentation written out on notebook paper, and then presents the problem with a document camera (I receive no money for linking to this camera. It is simply inexpensive and I have been happy with it).

Here is how the presentation grades were determined (I heavily borrowed from Ted Mahavier for this, who has a lot of experience doing this):

• D – You attended every class, paid attention, and tried (mostly unsuccessfully) to present at least a few times.
• C – You fulfilled the requirements for a D, and you had a few successful presentations.
• B – You fulfilled the requirements for a C, and you had many successful presentations.
• A – You fulfilled the requirements for a B, and you had many successful presentations of difficult problems.

My goal for the presentations was to create a Modified Moore Method-type atmosphere in the course. The problem is that the audience for each presentation zoned out after 2-3 weeks. Thus, I think that the presentations were probably very helpful to the students, but not very helpful to the students in the audience. I did a pre-test and a post-test using the Calculus Concept Inventory, so we will see if the data confirm my skepticism about this teaching method.

I like the overall structure of the course (Peer Instruction for the first half to give a good conceptual foundation, and then some sort of IBL thing in the second half for reinforcement and details), but I will likely not be using this presentation style again. The best format I have so far is to return to my <a href="http://en.wikipedia.org/wiki/Cooperative_learning"Cooperative Learning roots and do something like this:

1. Do maybe 4-7 problems per day as homework.
2. Have the students work in teams on one assigned problem at the beginning of class so that everyone really understands it (after getting a head-start on it from the homework).
3. Randomly call on a team member to present the problem.
4. That random team member’s presentation grade is the grade for everyone in the team.

This will help the students teach each other. I would love to hear feedback and other suggestions (and I apologize for typing and weird formatting; my son just woke up, and I probably won’t have time to proofread until Monday. Since I want this off of my to-do list, I decided to publish without proofreading).

(Image “A Plus” by flickr user s_falkow)

Matching Students to Presentations

November 2, 2012

The presentation portion of my classes is now the focus. I now have the task of figuring out which students should present which problem.

Here is my system for my calculus I and calculus III classes:

1. I tell all students to try 12-15 problems the night before. The students do not need to successfully do the problems, but I want them to at least know what the problems are asking.
2. Students submit presentation preferences to our online course management system (Moodle). They can submit as many or as few problems as they want to present, and they order them according to their preference in presenting.
3. The morning of the presentations, I look at their preferences.
4. I maintain a list of problems that each student has presented, which also lets me know how many problems each student has presented. I start by ranking the students by the number of presentations they have already done; the students with the fewest presentations get the highest priority. In case of ties, I go alphabetically by last name.
5. I then give a number code to each student based on the student’s priority (“1” is the top priority).
6. I copy the list of problem numbers that will be presented. In order of priority, I go through the students’ preferences, writing down the student number and the priority next to each of the problem numbers. So if the 3rd student wants to do problem 21 as her 4th choice, I would write “(3,4)” next to 21 (in practice, I write “34,” since I am lazy).
7. When I have completed this, I do a greedy algorithm-thing. I start with Student 1, and assign her her top choice (which will be her first choice, of course). I continue with Student 2, giving him his top available priority, and so on. This ensures that as many students as possible present that day.
8. I then try to shuffle things in an ad hoc way to make people as happy as possible.

This is nothing too impressive, but it actually took me a little while to come to this. I am envious of Andy Rundquist, who has the motivation to create a similar computer program for his students. There are a couple of reasons why I have not coded this up yet:

1. This is still a pretty new system for me, and I think I might be able to improve it (or radically change how I do presentations).
2. I like doing this by hand.

Do any of you have suggestions on how to improve this? Better yet: just explain how you choose to assign students to problems.

An Inverted IBL Frankenstein

January 19, 2012

I am teaching complex analysis this semester, and I have decided to merge the inverted classroom approach that I used last semester with an Inquiry-Based Learning (IBL) approach.

The inverted approach will follow this flow: the students read the textbook and watch videos before class. In class, we answer clicker questions (to get a conceptual understanding) and get practice on the basic skills (taking derivatives, doing contour integrals, etc).

The IBL approach is this: I give the students a list of problems (created by Richard Spindler). The students do the problems at home (they can work together), and present them in class. One of the main benefits (as articulated by Dana Ernst) is that students are more skeptical of other students’ work than they are of the professor’s work. So the students will need to wrestle with the presentations, since some of them will contain errors (much like my presentations, but students will care more).

The basic idea is this: the inverted classroom approach will be used to quickly give the students the basic skills required for the course AND an overview of the course. The IBL approach will give students a deeper understanding of the course material.

The first half of the semester will be 2/3 inverted and 1/3 IBL. We will be able to get through the entire textbook in this half, although the understand will not be as deep as I would like.

The second half of the semester will be about 2/3 IBL and 1/3 review of the textbook. This is where the deep learning will take place.

I am not thrilled with the course policies—in particular the homework policy—but I will post about this later.