Westfield State is fortunate enough to have an amazing group of math faculty involved in IBL via their Discovering the Art of Mathematics project. Check out the latest blog post (HERE), with guest blogger Steven Strogatz, commenting as a new IBLer, and having a great time in class. Nice!

Kudos to Chrissi, Volker, Phil, Julian, Steven, and all the Cornell math faculty interested in IBL!

# The IBL Blog

The IBL Blog focuses on promoting the use of inquiry-based learning methods in the classroom at the college, secondary and elementary school levels. Learn more about IBL at ** The Academy of Inquiry Based Learning **

## Monday, July 6, 2015

## Thursday, July 2, 2015

### IBL SIGMAA: Be a Charter Member

The Mathematical Association of America has special interest groups for members to organize around a topic or area of mathematics or mathematics education. A special interest group of the MAA is called a SIGMAA. The IBL community has decided to apply to form an IBL in Mathematics SIGMA, or IBL SIGMAA for short. The purpose of the IBL SIGMAA is to have a group associated with the MAA to support the work of math instructors interested in developing, spreading, and supporting the use of IBL.

In order to create the IBL SIGMAA, charter members are needed. Today, I am asking you to sign up! Please use the link below to let MAA know that you are interested in being a part of the upcoming IBL SIGMAA.

Sign up to become a charter IBL SIGMAA member!

Many thanks to TJ Hitchman, Victor Piercey for spearheading this effort!

In order to create the IBL SIGMAA, charter members are needed. Today, I am asking you to sign up! Please use the link below to let MAA know that you are interested in being a part of the upcoming IBL SIGMAA.

Sign up to become a charter IBL SIGMAA member!

Many thanks to TJ Hitchman, Victor Piercey for spearheading this effort!

## Tuesday, June 16, 2015

### The Problems of "Good" Teaching and the Problem of "Excellent" Being the Enemy of Good

This post is about two dual problems. A significant percentage of faculty or institutions are satisfied with "good" teaching, and a separate and overlapping group of faculty or institutions are paralyzed by perceptions that a high degree of "excellence" is needed to switch to active learning methods, such as IBL. The purpose of this post is to offer a perspective on the dual problems in an attempt to minimize them and ultimately make change easier.

"Good" teaching comes in many forms, and I'll highlight just one prototypical case. By "good" teaching I mean an instructor who gives clear lectures, gets good student evaluations, and students get the expected grades. In 1988, Schoenfeld published an article "When Good Teaching Leads to Bad Results: The Disasters of `Well-Taught' Mathematics Courses," highlighting that beneath the surface things are quite the different than they appear. Good teaching evals and within-spec grade distributions make things appear like their are going well. Researchers have revealed since the 1980s that beneath the veneer of success are fundamental problems, such as strong negative beliefs associated to learning math. These beliefs include statements like

- Students perceive that the form of the solution is what counts (not the content)
- All problems can be solved in just a few minutes
- Students view themselves as passive consumers of mathematics
- Students separate deductive and constructive geometry (as in they are unrelated)

Further studies show that the problem is in fact more widespread and deeper than what Schoenfeld revealed in his article. There exists a long list of negative beliefs from the math education literature, highlighted in a post I wrote previously. Deep negative beliefs affect how students learn mathematics, and even if they do well on the usual timed-tests, they come away with crippled learning mindsets, which damages their future learning potential. One can go on and on, looking at pass-fail rates in Calculus, lack of improvement in problem-solving ability, how US students lag international peers, and much of this is traced (at least in part) to how we teach (See Stigler and Hiebert).

One factor in perpetuating "good" teaching is over reliance on student evaluations as a measure for teaching effectiveness. While student evaluations are somewhat useful, they are a highly limited and possibly misleading for assessing teaching effectiveness. One reason is that a strategy to get high teaching evaluations is to (a) give easy tests and (b) tell jokes or be friendly and entertaining. Studies also show there are gender effects (males get better ratings), and how the instructor looks (attractiveness) has an influence on student evaluations. Students are also not able to measure items such as the precision and quality of using scientifically-validated pedagogies, and in fact students may be more interested in keeping things the way they are, even if they would learn more and better with an active-learning classroom.

“I do not think I would get on very well in my ideal school because I am too used to being told what to do.”-- Frances, fifteen, (Claxton)

In addition to the problems of student evaluations as primary measure of teaching effectiveness, there are other facets of the math teaching culture that inhibit change. Teaching is a cultural activity. Students, parents, teachers, and administrators have default expectations for what "good" teaching is. These expectations are not tied directly to deeper learning outcomes, and so there are forces that make it more difficult to change the status quo.

If all the signals are "good," then why change? Consequently, societal, systemic, and cultural forces help to keep "good" teaching in place.

If all the signals are "good," then why change? Consequently, societal, systemic, and cultural forces help to keep "good" teaching in place.

*Excellent Being the Enemy of Good*

A dual issue is a particular notion of excellence. Let me explain. Even if one does the required homework and decides to try IBL, a factor that holds back instructors is the notion that one needs to be "excellent" at IBL before it can make a difference. Another form of this is that a department chair may want an "excellent proof" that IBL. I'm not saying we shouldn't strive for excellence. Nothing could be further from the truth. The point is that waiting until things are perfect and pristine is a mistake in terms of implementation timing.

Contributing to the problem of excellence being the enemy of good is the tacit assumption that there exists a safe neutral choice. It goes like this. If I am a "good" math teacher and my students like me, then I am taking a risk to try IBL. Hence, I had better be excellent at IBL to make the switch.

The reality is that there isn't really a safe, neutral choice in the current education climate. The recent work by Freeman, et al published work in the Proceedings of the National Academy of Sciences, essentially states that if active learning vs. lecture was a medical study, then with the preponderance of evidence available today

*it would be unethical to continue using the lecture method*.
Further, studies like the Force Concept Inventory sheds light on the excellence issue. In Physics education, we have learned the active learning group of instructors outperformed the traditional instructors, AND it did not truly matter if the active learning instructor was a novice and the traditional instructor was the award winning, inspirational figure. In terms of learning outcomes on conceptual understanding

*teaching methodology*won out as the most important factor. You don't have to be an expert active-learning teacher to get solid outcomes. All one needs is to be proficient enough at using specific active-learning strategies. Some of the active learning strategies employed in Force Concept Inventory study are relatively easy to implement, such as peer instruction (Think-Pair-Share). It's doable!
In summary, "good" teaching has an effect of lulling one into a false sense of success and security, which ultimately slows progress. Further, waiting for things to be excellent also slows progress and makes change seem larger than it actually is. Our teaching system and teaching culture unfortunately support these things (inadvertently), making it more difficult for change. On a more basic level, just having productive discussions about these issues are difficult, because of the fact that many of the assumptions and cultural norms about teaching are embedded deep within us. "It's the way it has been for long, long time. That's all I know..." is a commonly sung refrain.

Rather than basing our profession on labels, like "good" or "excellent," a more productive approach is to focus on implementing research-validated teaching practices (i.e. apply scientific knowledge). Instructors can learn to use one or more specific active-learning methods (think-pair-share!) and start on the path towards deeper, more meaningful student engagement. Workshops, IBL-specific conferences, mentoring programs, and regional or national math conferences offer opportunities for faculty to engage in discussions and find solutions for their particular situations.

Getting started with implementing active learning is a first step towards transformative experiences. I encourage instructors to set their aim high in the long run, because full IBL courses have the potential to be transformative. IBL instructors have repeatedly reported over decades stories of students, who initially did not see themselves as successful math students, go on to graduate school or careers that they did not think they could do.

Alfred discusses (~7:55 into the video) how he was about to drop out of college, but then buckled down and decided to go to graduate school in mathematics.

Getting started with implementing active learning is a first step towards transformative experiences. I encourage instructors to set their aim high in the long run, because full IBL courses have the potential to be transformative. IBL instructors have repeatedly reported over decades stories of students, who initially did not see themselves as successful math students, go on to graduate school or careers that they did not think they could do.

Alfred discusses (~7:55 into the video) how he was about to drop out of college, but then buckled down and decided to go to graduate school in mathematics.

It's worth the effort!

## Saturday, May 16, 2015

### David Bressoud Discusses Calculus At Crisis

David Bressoud is weighing in on the Calculus crisis, which I think many may not see as a crisis. This series will be interesting, and I'm looking forward to Bressoud has to say. This month Bressoud started a several part series on his blog Calculus At Crisis: The Pressures, with the first post focusing on the larger, societal forces affecting enrollments at the "macro" level. Bressoud has written often about Calculus, and it's worthwhile reading for math educators.

The quick version of Bressoud's latest post is that more students (often inadequately prepared) are taking calculus, while math departments are seeing resources and support dwindle. Simultaneously, a call has been made to increase the number of STEM graduates, yet resources, human capital, pedagogy, professional development infrastructure, and general education infrastructure upgrades have not been made.

Calculus has long been a hotly debated issue in undergraduate education. Much has been said, and can still be said. My hope is that discourse will pivot towards using data and science. One major positive aspect of the MAA Calculus Study is that we can now discuss issues with better data and deeper insights. MAA plans to produce an MAA Notes guide to share what successful programs do, and how other institutions can make changes that make material impact on student success in Calculus. Hence, there exists the opportunity to make data-driven or data-influenced decisions and upgrades, as opposed to merely relying on intuition and anecdotes (AKA anecdata or conventional wisdom).

I am reminded of a mental experiment regarding Calculus that expresses the issues on a human level. How many of our students say, "That was the best idea ever!" after finishing a Calculus course? The vast majority of us would say zero. This is an utter shame. Let's think about this. Calculus is one of the greatest human inventions of all time. In the absence of Calculus entire fields in science and technology cease to exist, and modern life as we know it would also not exist. Yet, few students walk away from Calculus with a deep appreciation and rich understanding of it. It's as if Calculus has become a standardized test.

It doesn't have to be this way, and there's reason to be optimistic. The MAA Calculus study provides a framework for how to think about the issues and how to make improvements to our classes or programs from a "system" perspective. Teaching is a system (and a cultural activity), and we have knowledge and insights, based on the hard work of many creative individuals, pointing the way towards solutions and specific areas where efforts will be productive.

Link: MAA Calculus Study

The quick version of Bressoud's latest post is that more students (often inadequately prepared) are taking calculus, while math departments are seeing resources and support dwindle. Simultaneously, a call has been made to increase the number of STEM graduates, yet resources, human capital, pedagogy, professional development infrastructure, and general education infrastructure upgrades have not been made.

Calculus has long been a hotly debated issue in undergraduate education. Much has been said, and can still be said. My hope is that discourse will pivot towards using data and science. One major positive aspect of the MAA Calculus Study is that we can now discuss issues with better data and deeper insights. MAA plans to produce an MAA Notes guide to share what successful programs do, and how other institutions can make changes that make material impact on student success in Calculus. Hence, there exists the opportunity to make data-driven or data-influenced decisions and upgrades, as opposed to merely relying on intuition and anecdotes (AKA anecdata or conventional wisdom).

I am reminded of a mental experiment regarding Calculus that expresses the issues on a human level. How many of our students say, "That was the best idea ever!" after finishing a Calculus course? The vast majority of us would say zero. This is an utter shame. Let's think about this. Calculus is one of the greatest human inventions of all time. In the absence of Calculus entire fields in science and technology cease to exist, and modern life as we know it would also not exist. Yet, few students walk away from Calculus with a deep appreciation and rich understanding of it. It's as if Calculus has become a standardized test.

It doesn't have to be this way, and there's reason to be optimistic. The MAA Calculus study provides a framework for how to think about the issues and how to make improvements to our classes or programs from a "system" perspective. Teaching is a system (and a cultural activity), and we have knowledge and insights, based on the hard work of many creative individuals, pointing the way towards solutions and specific areas where efforts will be productive.

Link: MAA Calculus Study

## Tuesday, April 14, 2015

### "Activation Energy" and IBL Uptake

Here's a basic question.

In Chemistry, activation energy is a term that means the minimum energy that must be input to a chemical system with potential reactants to cause a chemical reaction. Implementing IBL is analogous in that there is a substantial initial investment by an instructor to learn the necessary skills and practices to be successful in the classroom. What is the activation energy required for an instructor to switch to IBL teaching?

Instructors of course vary greatly, due to experiences and teaching environments. For our purposes a "back of the envelope" computation is all that's necessary to illustrate the main points. Let's take as an example an assistant professor who attends an IBL workshop. In this case, we have an instructor who elects to attend a workshop, is motivated to learn to use IBL, is invested in her job and institution, and wants students to learn authentic mathematics.

So here it is. The activation energy required is 100+ hours, plus resources to travel to a workshop, prepare for a course, and engage with the IBL community. The breakdown is as follows.

*What does it take to switch from traditional to IBL teaching?*This question can be answered in many ways. I'm going to come at this from an education system reform angle. Essentially the general problem is the implementation challenge in education. Perhaps the biggest challenge for the education community now is implementing what works in the classrooms on a broad scale, and open questions remain about what it takes in time and investments to make the necessary changes. In this post the notion of**activation energy**is used to shed light on what it might take to make reform stick.In Chemistry, activation energy is a term that means the minimum energy that must be input to a chemical system with potential reactants to cause a chemical reaction. Implementing IBL is analogous in that there is a substantial initial investment by an instructor to learn the necessary skills and practices to be successful in the classroom. What is the activation energy required for an instructor to switch to IBL teaching?

Instructors of course vary greatly, due to experiences and teaching environments. For our purposes a "back of the envelope" computation is all that's necessary to illustrate the main points. Let's take as an example an assistant professor who attends an IBL workshop. In this case, we have an instructor who elects to attend a workshop, is motivated to learn to use IBL, is invested in her job and institution, and wants students to learn authentic mathematics.

So here it is. The activation energy required is 100+ hours, plus resources to travel to a workshop, prepare for a course, and engage with the IBL community. The breakdown is as follows.

- 10 hours pre-workshop preparation
- 40 hours of workshop time
- 50+ weeks to prepare for a target course (begin course materials adaptation, plan activities for the first few weeks, syllabus, other course management.)
- Plus hundreds of hours more through the first few terms of using IBL.

The aggregate investment per faculty is roughly between $5,000-10,000 to attend a workshop, materials, mentoring, and so forth. Most of this cost is imbedded in the professional development infrastructure. Experts need to be hired to develop the materials and run the workshops. My initial estimate of the the IBL activation energy is approximately

It's noted that this investment level can go down with economies of scale, but we are nowhere near that level of uptake or infrastructure today. The infrastructure across the nation is not yet established to offer lower-cost options. In fact, at this point in history a focus on efficiency is likely a major strategic mistake. The infrastructure needs to be built up first, and then in the future as uptake increases, one can economize. It's called economies of scale for a reason.

**100hrs + $10K**(or 100+10 for short). This is the base investment to get started. Becoming an expert IBLer is a much, much longer effort that takes years.It's noted that this investment level can go down with economies of scale, but we are nowhere near that level of uptake or infrastructure today. The infrastructure across the nation is not yet established to offer lower-cost options. In fact, at this point in history a focus on efficiency is likely a major strategic mistake. The infrastructure needs to be built up first, and then in the future as uptake increases, one can economize. It's called economies of scale for a reason.

The situation quickly gets more complicated. Colleges, CTLs, professional development groups likely do not have good estimates of the activation energy required for uptake of student-centered pedagogies (or are even aware to think about it this way). Further, as we develop more sophisticated teaching frameworks, the complexity of professional development and the specific supports needed by faculty become more technical and discipline specific. The activation energy is dependent on the PD available, the subject matter, and the varies by instructor, course, and institutional environment. Teaching Calculus isn't the same as teaching Math for Elementary Teaching or Topology.

Further, an echo from the past that continues to be felt today that inhibits progress on implementation is the factory model mindset. Lingering to this day is the sense that instructors are delivery devices for information. With the factory mindset is the belief that fixes to the system are in the form of tweaking courses, chipping away at the margins, and changing textbooks. This is one reason why I am presenting the activation energy concept for education reform. When we view instructors as delivery devices and/or underestimate for whatever reason the real effort necessary to become an effective IBL instructor, then the level of support and resources allocated to the problem is too low. Invariably some new IBLers will struggle (due to inadequate preparation), and then the next, linked fallacy that results is something like, "I can't teach via IBL" or "IBL doesn't work at my institution."

The Pendulum. There exists a defeatist belief among some in education that there is an education pendulum, and that's just the way it is. Things repeat like a sinusoidal function, over and over again. I've written about this before here. Those weary of repeated efforts to make changes have a reason to be this way, and I am sympathetic to a degree. They've seen things swing one way and then another, and those with hopes for a brighter future have seen their efforts crash and and burn, which is highly demoralizing. The activation energy idea sheds some light on the matter. Let's think of it as an absurdly flawed road trip implementation. If we put in only half the gasoline needed for the trip, and each time we get towed back home, then one interpretation of these events is that this is what vacations are about. We go, don't make it to your destination, because we run out of gas. Then get towed home. Hence the pendulum.

But it doesn't have to be this way. Education is a human construction. It's not like the stars and the moon, where we have no way to affect the universe outside our planet in significant ways (as of today). We built it. We can change it. If we follow our own teaching philosophy, then we should ask good questions. Why is there a pendulum? What are the causes? Is there a better way?

Let's the put 100+10 estimate into context relative to current institutional practices. Faculty training programs often have 1-2 days of "new faculty orientation" or a weekly seminar that meets for 1 hours. More or less this is an

On a personal teacher level, getting started with IBL is hard. IBL, however is a "sticky" idea in the sense that once instructors use it well, they stick with it. Indeed, once you see your students think creatively and transform how they think and think of themselves as learners, there's no going back. And that's easily a worthwhile 100+10 investment!

Let's the put 100+10 estimate into context relative to current institutional practices. Faculty training programs often have 1-2 days of "new faculty orientation" or a weekly seminar that meets for 1 hours. More or less this is an

*order of magnitude below*what I am seeing as necessary, without considering the nature and quality of the programs. It is fairly well known that current practices of TA training or new instructor training are not sufficient to address the broader uptake problem, where low percentages of faculty in STEM actually use proven, student-centered teaching methods. With the activation energy perspective, we can start to quantify how much more effort is needed and what it would cost. While we are below the mark that I estimate is necessary with current practices, on the positive side we know ways to get people past the activation energy. Solutions exist!On a personal teacher level, getting started with IBL is hard. IBL, however is a "sticky" idea in the sense that once instructors use it well, they stick with it. Indeed, once you see your students think creatively and transform how they think and think of themselves as learners, there's no going back. And that's easily a worthwhile 100+10 investment!

## Friday, April 3, 2015

### IBL Workshop 2015, July 7-10, San Luis Obispo

One of the best ways to learn how to successfully implement IBL is to attend a weeklong workshop. The IBL Workshops hosted by AIBL are specifically designed for college math faculty. These hands-on workshops address the practical obstacles that faculty face in the transition from tradition to IBL teaching. Participants of the workshop adapt or develop IBL course materials, work collaboratively on IBL specific teaching skills, engage in discussions about IBL video lesson study, learn specific nuts and bolts issues in smoothly running an IBL course, and participate in a yearlong mentoring program.

A handful of spots remain for the NSF funded workshop this July. If you are thinking about making the transition to IBL teaching, please go to www.iblworkshop.org to learn more.

A handful of spots remain for the NSF funded workshop this July. If you are thinking about making the transition to IBL teaching, please go to www.iblworkshop.org to learn more.

## Tuesday, March 31, 2015

### Quiet Classes: Using Pairs to Generate More Discussion

Here's post on a common theme, but it's worth revisiting this topic. Quiet classes (or students) are ones we need to work harder at, and efforts can make a significant difference.

Quiet, low-energy classes are the ones that make me the most nervous as a teacher. As a long-time IBL instructor I have become accustomed to loud, boisterous classes, where students are engaged, communicate, work together, and ask questions to me and to each other.

At the start of the term some of my classes have a quiet or passive personality. Students may not have had an IBL class yet, and hence are likely to expect to sit, take notes, and generally not interact with others during class time. A potential problem with quiet students is that they give you little to no information about what they are thinking (and not thinking). Student thinking is critical in day-to-day IBL teaching. An IBL instructor doesn't know exactly the lesson plan for tomorrow, until today's class is over. Using what is known about what students are doing well and what they need to work on, is bread and butter in IBL teaching.

There are several options. My main goal is to reset classroom norms so that students understand that making their ideas and questions known to others is the default. Reseting norms can be accomplished via tasks that require students to engage verbally. My most preferred setup is to use

In a full IBL course, pairs can do a range of activities, from working on problems, reviewing a presented solution, getting started on a new problem set,... Asking students to share what they did in pairs is a safe, easy way to open discussions. The stress of having to be right isn't a factor, and students are more likely to offer thoughts, questions, or ideas that can generate a productive discussion.

Making a

In "hybrid" IBL courses, where the course has a larger percentage of instructor talk time, then the implementation of pairs becomes more specific. What I'm envisioning in this situation is an instructor just getting started with IBL, or an instructor in a situation where significant IBL time is not feasible. In this case, the instructor may be using some Think-Pair-Share or group work as components to their teaching. Here are some examples:

Quiet, low-energy classes are the ones that make me the most nervous as a teacher. As a long-time IBL instructor I have become accustomed to loud, boisterous classes, where students are engaged, communicate, work together, and ask questions to me and to each other.

At the start of the term some of my classes have a quiet or passive personality. Students may not have had an IBL class yet, and hence are likely to expect to sit, take notes, and generally not interact with others during class time. A potential problem with quiet students is that they give you little to no information about what they are thinking (and not thinking). Student thinking is critical in day-to-day IBL teaching. An IBL instructor doesn't know exactly the lesson plan for tomorrow, until today's class is over. Using what is known about what students are doing well and what they need to work on, is bread and butter in IBL teaching.

*What can an instructor do to liven things up, when students are (initially) reticent?*There are several options. My main goal is to reset classroom norms so that students understand that making their ideas and questions known to others is the default. Reseting norms can be accomplished via tasks that require students to engage verbally. My most preferred setup is to use

*pairs*. When you are talking to one person, it's awfully difficult to hide in the conversation. In contrast, within a group of 4 students, one or two students could sit back and let the others talk. Hence, I like pairs (while simultaneously admitting that personal preference is a part of the decision). I also use other sizes, but pairs are the default, especially for quiet classes.In a full IBL course, pairs can do a range of activities, from working on problems, reviewing a presented solution, getting started on a new problem set,... Asking students to share what they did in pairs is a safe, easy way to open discussions. The stress of having to be right isn't a factor, and students are more likely to offer thoughts, questions, or ideas that can generate a productive discussion.

Making a

*pairs seating chart*and ensuring all pairs are called on regularly ensures that all students are regularly involved. In a full IBL course, the requirements to present and comment are built into the course. Getting quieter students to offer comments, can be done via the pairs structure. For example, ask students to review and discuss a solution or proof in pairs (after a proof is presented) will generate more and better comments and questions. I normally phrase the task as, "Please review the proof and come up with 2 questions or comments." Then I call on pairs rather than ask for volunteers, and spread the work around to ensure all pairs get called on regularly.In "hybrid" IBL courses, where the course has a larger percentage of instructor talk time, then the implementation of pairs becomes more specific. What I'm envisioning in this situation is an instructor just getting started with IBL, or an instructor in a situation where significant IBL time is not feasible. In this case, the instructor may be using some Think-Pair-Share or group work as components to their teaching. Here are some examples:

- Let pairs discuss a concept or strategy: "In pairs, discuss for a minute a strategy you might use for this problem." Listen in on a few conversations, and choose one or two to share to the whole class.
- Check for understanding even when building skills: "Please work in pairs to apply the techniques discussed to the following cases." As you walk around, you can ask students how they are doing with the exercise.
- Pause for moment to let students try something on their own first. This could be the next step of a problem or proof. Or it could be that you ask students to justify a statement or review what just happened. After the pause, ask students to check in with
*one*neighbor. As students talk, you can visit a few pairs and ask a pair to chime in. (Be sure to visit different people each time you do this to spread the work around.)

The above are just examples. An infinite variety of ways to get students to talk more exist, and the main point I want to get across is the

*framework*. Use clear, specific mathematical tasks and pairs to get students to think and then talk. Once they start talking, they can open up.
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