Archives For inquiry-based learning

The fall semester starts in a couple days and I’ll be teaching Calculus 1 (for like the 15th time) and our undergraduate Abstract Algebra course. Despite my relatively low teaching load, I’ll also be advising 3 undergraduate research students (on two different projects) and 2 masters thesis students. Combined with the fact that I’m still frantically trying to prepare brand new IBL materials for my Abstract Algebra class, I expect a very busy semester. For this reason, I decided not to mess with the format of my calculus class very much. I think it has room for improvement—namely ramping up the IBL aspect of the course—but this will have to wait until a later semester. I feel a little guilty about this, but I’m no use to anyone if I’m trying to do too much.

Notice that I said that I wouldn’t mess with the format “very much.” I am going to make some small changes. In previous semesters, I always devoted one class period a week to students presenting problems at the board. This has always worked well for me, but last semester I tried something else that I don’t think was as successful. So, I’ve decided that I’ll return to presentation days. In the past, I had a fairly nebulous way of assessing student presentations. I want to encourage students to present, so I make it worth something. But on the other hand, I don’t want it to be a high stakes thing. A class typically benefits more from the discussion surrounding a less than perfect solution to a problem than they do from a presentation that is flawless. So, I encourage students to share what they have. Of course, I don’t want students putting crap up on the board on a regular basis either. In a small class, this isn’t very hard to manage, but in a class with 45 students (which is what I currently have enrolled in my calculus class), it gets a little trickier. I’ve been thinking about how to manage this for a few weeks.

The latest version of WeBWorK—which we use for our online homework platform—has a new feature called “Achievements.” You can read more about this here. This basic idea is this:

Instructors now have the ability to create and award “Math Achievements” and “Math Levels” to students for solving homework problems and for practicing good WeBWorK behavior. In a nutshell, students can earn achievements by meeting preset goals. For example, they might earn an achievement for solving 3 homework problems in a row without any incorrect submissions, or for solving a problem after taking an 8 hour break. Earning achievements and solving problems earns students points and after a student gets enough points they will be given a new “Math Level”.

I have zero experience with the WeBWorK Achievements, but I thought I would give it a try. I don’t want to make earning them mandatory and I don’t want to offer extra credit either. So, I’ve been passively brainstorming how to handle them.

Northern Arizona University now requires faculty to take daily attendance in all freshman-level courses. However, how we take this data into account is up the instructor. It just has to count for something. The past couple semesters, I’ve been diligent about taking attendance, but I’ve always been a little bit vague about how it does or does not impact a student’s grade. Policies like, “you’ll lose a letter grade if you miss X number of classes,” drive me nuts.

Yesterday, I decided it was time to sort out what the plan should be for presentations, WeBWorK Achievements, and attendance. I had read a short article about gamification in education (I can’t remember which article) recently and I thought, “hey, why don’t I just gamify this stuff that I’m not sure what to do with.” In general, I’m not a fan of offering points for things that students should naturally do (and I’m also sure I have tons of counterexamples to what I just said), but I’m going for it anyway. Maybe this is a horrible idea. Here is what I currently have on their syllabus.


Attendance

As per university policy, attendance is mandatory in all 100-level courses, and in particular, I am required to record attendance each class session. Daily attendance is vital to success in this course! You are responsible for all material covered in class, regardless of whether it is in the textbook. Repeated absences may impact your grade (see the section on Achievements). You can find more information about NAU’s attendance policy on the Academic Policies page.

Presentations and Participation

Throughout the semester, class time will be devoted to students presenting problems to the rest of the class. In addition, we will occasionally make use of in-class activities whose purpose is to either reinforce/synthesize previously introduced concepts or to introduce new concepts via student-driven inquiry. If necessary, these activities will be explicitly graded.

I expect each student to participate and engage in class discussion. Moreover, I will occasionally ask for volunteers (or call on students) to present problems at the board. No one should have anxiety about being able to present a perfect solution to a problem. In fact, we can gain so much more from the discussion surrounding a slightly flawed solution. However, you should not volunteer to present a problem that you have not spent time thinking about. Your overall participation includes your willingness to present, engagement in and out of class, and consistent attendance record. Your grade for this category will be worth 8% of your overall grade and will be based on Achievements (see below).

Achievements

This semester I’ve decided to “gamify” good student behavior. Here is the gist. I’ve generated a list of items that I deem good student behavior. Every time you achieve one of the items on the list, you earn some points. The more points you earn, the higher your Presentation and Participation grade (worth 8% of your overall grade in the course). So, how do you earn achievement points? Here’s a list.

Points Description
5 Stop by my office sometime during the first two weeks of classes. This is a one time offer and stopping by to just say hello is fine.
2 Stop by my office hours to get help. This goes into effect after the first visit and you can earn points for this up to 4 times.
1 Attend class, arrive on time, and stay the whole class meeting.
1/2 Attend class but arrive late.
1/2 Attend class but leave early.
2 Attend a review session offered by our Peer TA. You can earn points for this multiple times.
4 Stop by the Math Achievement Program to get help. This is a one time offer and you must get a “prescription” form from me in advance for a tutor to sign.
2 Find a typo anywhere on the course webpage, homework, exam, etc. These points are first come, first earned, but there is no limit to the number of times you can earn points for this.
5 Volunteer to present a problem to the class on presentation days.
3 Agree to present a problem to the class on presentation days after I’ve called on you.
2 Earn a non-secret Achievement in WeBWork. You can see list of possible non-secret Achievements by clicking on the appropriate link in the sidebar after logging in to WeBWorK.
3 Earn a secret Achievement in WeBWork. These shall remain a mystery.
2 Post a useful resource such as a video or link to a math-related website on our course forum.
2 Post a relevant question on our course forum.
2 Post a useful response to a question on the course forum that does not just give an answer away.
5 Earn at least an 8/10 on your highest score for a Gateway Quiz.

Important: Any time I feel you are taking advantage of the spirit of this, I reserve the right to take away an achievement point.

To calculate your grade for the Presentation and Participation category, I will divide your Achievement points by the maximum number of Achievement points earned by a student and then convert to a percent.


Feedback is extremely welcome. I’ll let y’all know how it goes.

Edit: One thing that I forgot to add is that I have a Peer TA for 10 hours per week. She attends class and has access to the course forum, etc. So, I’ll let her do most of the point tracking. Otherwise, I’d have trouble with the bookkeeping. Also, I decided to use the highest number of Achievement points earned by a student to calculate a percentage for each student. In the comments below, Strider suggested that I use the average of the top 3 instead. I like this idea, but I think I’ll use the top 5.

On Thursday, August 22, I was one of four speakers that gave a 20 minute talk during the Department of Mathematics and Statistics Teaching Showcase at Northern Arizona University. My talk was titled “An Introduction to Inquiry-Based Learning” and was intended to be a “high altitude” view of IBL and to inspire dialogue. I was impressed with the turn out. I think there were roughly 40 people in attendance, from graduate students to tenured faculty and even some administrators. Here are the slides for my talk.

If you take a look at the slides, you’ll see that I mention some recent research about the effectiveness of IBL by Sandra Laursen, et. al. During my talk, I provided a two-page summary of this research, which you can grab here (PDF).

After about 15 minutes, I transitioned into an exercise whose purpose was to get the audience thinking about appropriate ways to engage in dialogue with students in an IBL class. I provided the participants with the handout located here that contains a dialogue between three students that are working together on exploring the notions of convergence and divergence of series. After the dialogue, five possible responses for the instructor are provided. I invited the participants to discuss the advantages and disadvantages of each possible response. It is clear that some responses are better than others, but all of the responses listed intentionally have some weaknesses. We were able to spend a couple of minutes having audience members share their thoughts. It would have been better to spend more time on this exercise. I wish I could take credit for the exercise, but I borrowed it from the folks over at Discovering the Art of Mathematics.

If you want to know more about IBL, check out my What the Heck is IBL? blog post over on Math Ed Matters.

During Susan Ruff’s talk in the IBL Best Practices Session that Angie Hodge, Stan Yoshinobu, and I organized at MathFest, she made reference to an article by Kirschner, Sweller, and Clark. The paper is titled “Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching” (PDF) [1]. As a practitioner and serious proponent of inquiry-based learning (IBL), I am extremely interested in what this article has to say. Here is the abstract:

Evidence for the superiority of guided instruction is explained in the context of our knowledge of human cognitive architecture, expert–novice differences, and cognitive load. Although unguided or minimally guided instructional approaches are very popular and intuitively appealing, the point is made that these approaches ignore both the structures that constitute human cognitive architecture and evidence from empirical studies over the past half-century that consistently indicate that minimally guided instruction is less effective and less efficient than instructional approaches that place a strong emphasis on guidance of the student learning process. The advantage of guidance begins to recede only when learners have sufficiently high prior knowledge to provide “internal” guidance. Recent developments in instructional research and instructional design models that support guidance during instruction are briefly described.

I intend to read the whole article, but haven’t read much more than the abstract. Here are few thoughts before I dive in.

When discussing the advantages of an IBL approach with people, I’ll often cite academic work that supports the claim that it is beneficial for students. For example, see the work of Sandra Laursen et al. located here. However, to be honest, despite my interest in seeing data that validates my own opinions, the reality is that I don’t do IBL because the research told me to. I do it because I’ve seen it work! My students tell me it works. Alright, to be fair, my students told me that my lecturing worked, too. But the types of comments I get now from my IBL students make it clear to me that something really good is happening. For example, read this. IBL may not work for everyone in all situations and I’m okay with that. If it stops working for me, I’ll try something different.

The first thought I had when I saw the title and abstract was, “what does ‘minimal guidance’ mean?” I certainly provide a lot less direct guidance in my IBL classes than I do than when I lectured, but is it “minimal”? I do my best to provide scaffolded guidance to my students and to set up a support network in a safe learning environment. This is crucial in my opinion. I’ll have to digest the whole paper to see what their take is.

It appears that there are several reflections and discussions of this paper online already. For example, go here, here, and here. In addition, Kirschner, Sweller, and Clark have written a response to criticism that they have received in their “Why Minimally Guided Teaching Techniques Do Not Work: A Reply to Commentaries” (PDF) [2]. I’ll try to read this paper, as well.

Bibliography

[1] P. A. Kirschner, J. Sweller, and R. E. Clark, “Why Minimal Guidance During Instruction Does Not Work: An Analysis of the Failure of Constructivist, Discovery, Problem-Based, Experiential, and Inquiry-Based Teaching,” Educational Psychologist, vol. 41, no. 2, pp. 75–86, 2006.

[2] J. Sweller, P. A. Kirschner, and R. E. Clark, “Why Minimally Guided Teaching Techniques Do Not Work: A Reply to Commentaries,” Educational Psychologist, vol. 42, no. 2, pp. 115–121, Apr. 2007.

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When I was preparing my talk for the Legacy of R.L. Moore Conference a couple weeks ago, I reread the student evaluations for my introduction to proof course from Spring 2013. I was really pleased with all the comments, but two of them stood out because they capture the essence of what I want an inquiry-based learning (IBL) experience to be.

Here’s the first comment.

[…] he has found the perfect way to teach this course. […] The way Professor Ernst had us struggle through homework and then come together as a group and discuss the topics was very beneficial. I personally struggled through most of the material and when I finally got to the right concept I felt like I fully understood it because I personally came to that conclusion. Also, when I didn’t fully understand a topic, coming together and discussing it connected all the gaps I was missing. […] As a future educator, I would love to mimic his style of teaching so I can share with my students the same satisfaction that I got out of this style of teaching.

I stripped out a couple complimentary sentences that addressed me rather than the course. Of course, I’m thrilled about this student’s desire to incorporate IBL in their future teaching, but what I really appreciate about this comment is how the student reflects on both his/her independence and collaboration.

Here is the second, very short comment.

Try, fail, understand, win.

Four words of awesomeness. I couldn’t hope for more. This second comment inspired a recent post that Angie Hodge and I recently wrote for Math Ed Matters.

On Friday, June 14 I gave a 15 minute talk in one of the parallel session at the Legacy of R.L. Moore Conference in Austin, TX. The Legacy Conference is the inquiry-based learning (IBL) conference. In fact, it’s the only conference that is completely devoted to the discussion and dissemination of IBL. It’s also my favorite conference of the year. It’s amazing to be around so many people who are passionate about student-centered learning.
This was my fourth time attending the conference and I plan on attending for years to come.

Here is the abstract for the talk that I gave.

In this talk, the speaker will relay his approach to inquiry-based learning (IBL) in an introduction to proof course. In particular, we will discuss various nuts and bolts aspects of the course including general structure, content, theorem sequence, marketing to students, grading/assessment, and student presentations. Despite the theme being centered around an introduction to proof course, this talk will be relevant to any proof-based course.

The target audience was new IBL users. I often get questions about the nuts and bolts of running an IBL class and my talk was intended to address some of the concerns that new users have. I could talk for days and days about this, but being limited to 15 minutes meant that I could only provide the “movie trailer” version.

Below are the slides from my talk.

One of my goals was to get people thinking about the structure they need to put in place for their own classes. When I wrote my slides, I had a feeling that I couldn’t get through everything. I ended up skipping the slide on marketing, but in hindsight, I wish I would have skipped something else instead. Two necessary components of a successful IBL class are student buy-in and having a safe environment where students are willing to take risks. Both of these require good marketing and I never had a chance to make this point. Maybe next year, I will just give a talk about marketing IBL to students.

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On Saturday, May 5, 2013, I was joined by TJ Hitchman (University of Northern Iowa) for the Michigan Project NExT Panel Discussion on Teaching Strategies for Improving Student Learning, which was part of the 2013 Spring MAA Michigan Section Meeting at Lake Superior State University. The title of the session was “Teaching Strategies for Improving Student Learning” and was organized by Robert Talbert (Grand Valley State University). The dynamic looking guy in the photo above is TJ.

Here is the abstract for the session.

Are you interested in helping your students learn mathematics more effectively? Are you thinking about branching out in the way you teach your courses? If so, you should attend this panel discussion featuring short talks from leaders in higher education in employing innovative and effective instructional strategies in their mathematics classes. After speaking, our panelists will lead breakout discussions in small groups to answer questions and share advice about effective instructional strategies for college mathematics. Panelists will include Dana Ernst (Northern Arizona University) and Theron Hitchman (University of Northern Iowa), both noted for their effective use of the flipped classroom and inquiry-based learning.

Sweet, I guess running my mouth often enough about inquiry-based learning (IBL) gets me “noted.”

Each of TJ and I took about 10-15 minutes to discuss our respective topics and then we took the remaining time to chat and brainstorm as a group. The focus of my portion of the panel was on “Inquiry-Based Learning: What, Why, and How?” My talk was a variation on several similar talks that I’ve given over the past year. For TJ’s portion, he discussed his Big “Unteaching” Experiment that he implemented in his Spring 2013 differential geometry course.

Here are the slides for my portion of the panel.

Despite low attendance at the panel, I think it went well. Thanks to Robert for inviting TJ and me!

Montessori Observations

April 30, 2013 — 3 Comments

This morning I spent an hour observing my boys’ classrooms at Haven Montessori. Wow. My wife and I sat in the corner and just watched for 30 minutes in each classroom. My younger son (age 5) is in a Primary Classroom, which is for children 3 years to 6 years (including Kindergarten). My older son (age 7) is in Lower Elementary, which is for 1st–3rd grades. Both of our boys started Montessori in January of this year and we have been thrilled with the outcome. We were hesitant to move them mid-school year, especially after having moved to Arizona less than a year ago, but we have no regrets about our decision.

This wasn’t my first observation of a Montessori classroom, but each time I do it, I am blown away. Here are a few quick observations:

  • All of the students were working quietly and respectfully.
  • Students were either working independently or collaboratively with another student or two.
  • There were a variety of different things going on at the same time.
  • Students were freely moving about the room, but always focused on their respective task.
  • Students were smiling and enjoying themselves, but not goofing off.
  • Students appeared to be working on stuff because they genuinely seemed interested.
  • There were no incentives and no grades!

I could go on and on, but you get the idea. It seems like a Utopia. If you’ve never seen a Montessori classroom, go check it out. I’m sure the success of each classroom has a lot to do with the teacher, so we are tremendously grateful that our boys ended up with great teachers.

There are a lot of similarities between Montessori and inquiry-based learning (IBL), which is the approach that I try to take (to various degrees) in the classes that I teach. All of the wonderful things that I witnessed this morning are exactly the kinds of things that I strive for in my own classrooms. Sometimes it works and sometimes it doesn’t. But I keep trying.

While I was observing, I kept daydreaming; “What if students were provided with this type of experience throughout their entire education?” In particular, I spent quite a bit of time pondering my last observation above about grades and incentives. As a teacher, I try to de-emphasize grades as much as possible, but our educational system is so entrenched in their use. Is it possible to eliminate the need for incentives? Is there something that happens in our development that diminishes our curiosity flame?

Math Ed Matters is Live!

April 12, 2013 — 2 Comments

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Angie Hodge and I are excited to announce that Math Ed Matters went live earlier today. Math Ed Matters is a (roughly) monthly column sponsored by the Mathematical Association of America and authored by me and Angie. The column will explore topics and current events related to undergraduate mathematics education. Posts will aim to inspire, provoke deep thought, and provide ideas for the mathematics—and mathematics education—classroom. Our interest in and engagement with inquiry-based learning (IBL) will color the column’s content.

Our first post is isn’t terribly exciting; it’s just an introduction to who we are. Here’s a sample of what we hope to discuss in future posts:

  • How did Angie and I meet and how did we end up collaborating on this blog?
  • History and impact of Project NExT
  • Inquiry-Based Learning: What, Why, and How?
  • How and why did Angie and Dana start implementing an IBL approach?
  • What’s the Buzz? (Calculus Bee)
  • A recap of the 16th Annual Legacy of R.L. Moore Conference (June 13-15, 2013 in Austin, TX)
  • A recap of MathFest 2013 (July 31-August 3, 2013 in Hartford, CT)
  • Pivotal Moments: How did Dana and Angie get to where they are now?
  • Utilizing open-source technologies and text-books

We’d love for you to follow along and join in the conversation. What other topics would you like for us to discuss?

Thanks to the MAA for giving us the opportunity to share our musings with you!

The best teachers are those who show you where to look, but don’t tell you what to see.

Quote by Alexandra K. Trenfor

Several weeks ago I was asked to take part in the Project NExT Alternative Assessment Techniques panel discussion at the 2013 Joint Mathematics Meetings, which recently took place in San Diego, CA. I was extremely honored to be considered for the panel, but at the time I was not planning on attending the JMM, so I declined the invitation. A couple weeks later, it turned out that I was going to make it to the JMM after all. At about 11PM the night before I was going to fly to San Diego, I received an email from the organizers of the panel discussion indicating that one of the panelists was unable to make it and that they heard was going to be there. They asked if I could fill in at the last minute and I accepted.

Here is the abstract for the panel.

Since classroom assessment is used to determine a student’s level of mastery, how can we vary our methods of assessment to accurately reflect the diversity of ways that students learn and understand the material? Traditional methods of assessment, such as exams, quizzes, and homework, may not accurately and robustly measure some students’ understanding. In this panel, we will propose alternative methods and discuss the following questions:
– What assessments exist besides the traditional ones and how can I use them for my course?
– How can I determine the validity of an alternative assessment?
– How can I develop my own alternative assessments?
– How can alternative assessments help me evaluate the effectiveness of a non-traditional classroom?

It is worth pointing out that I’m not an assessment expert by any stretch of the imagination. Also, given that I had less than 48 hours to prepare amidst a pretty full schedule, I didn’t have a lot of time to come up with something new and creative for my talk. Inquiry-based learning (IBL) is one of my passions and I’ve given quite a few IBL-related talks in the past few months, so I decided to “twist” the ideas from some of my recent talks into a talk about assessment. In my talk, I propose implementing IBL not only as a pedagogical approach but also as an assessment strategy. This isn’t really a stretch since in my view, an effective IBL class is all assessment, all the time.

My fellow panelists included Theron Hitchman (University of Northern Iowa), Bonnie Gold (Monmouth University), and Victor Odafe (Bowling Green State University). Theron gave a talk on using Standards Based Assessment (you can find his slides here), Bonnie spoke on a variety of summative assessment techniques, and Victor shared his experience with oral assessment. It turns out that the person that I was filling for is mathematics education superstar Jo Boaler. Me filling in for her is ridiculous.

Here are the slides for my portion of the panel.

Thanks to the organizers of the panel (Cassie Williams (James Madison University), Jane Butterfield (University of Minnesota), John Peter (Utica College), and Robert Campbell (College of Saint Benedict and Saint John’s University)) for providing me with the opportunity to speak on the panel.