Wednesday, March 13, 2019

Momentum Building

This post is about reaching the broadest group of students in a class. The example or framing is based on classes where students present frequently, but the ideas can be generally applied. In every course that I have taught, the speed at which students move through the course is highly varied, and different students move quickly or slowly through different parts or segments of the course. One of the things I try and avoid is the scenario where some students are so far behind that they give up trying and defer to others to move the course forward. Even if we use active learning methods, students who are deferring are not fully benefiting from the experience as much as they can be. All students should be engaged and feel they can be successful.  Collaborative learning works best, when all are on board and contributing.

One strategy I use is something I call momentum building. Let’s say it’s a Tuesday and either the class is done presenting or no one has signed up to present a problem.  In either case, the focus could be on the next set of problems and having students leaving the class feeling they have a good start and can accomplish the work. To set this up, I focus on a problems, one-by-one, and use a variation of Think-Pair-Share.

First, I ask students to read the problem statement, and then think to themselves about it (Think).  This initial part is to ensure they understand the statement of the problem. 

Next, I asks students to think about how they might approach this problem. At this point I might give a leading hint, such as suggesting a proof by contradiction or drawing a diagram or picture that has some key piece without reducing the challenging. I think about this part as taking students to the trailhead and giving them a heads up about the terrain.

After this longer, more involved think phase, I ask students to work with their partner on their ideas (Pair). This is the “Pair” stage, and I often roam the class to listen in or check in with groups.  This part might also go on for several minutes, depending on the nature of the material they are working on. Working on the proof of a Intermediate Value Theorem takes more thinking and discussion time compared to unpacking a basic definition. I adjust the time based on the context.

Once I have a sense that students have had a good chat, then it’s time to call on groups to make public their ideas and come up with a strategy or ask questions. (Share) I write the word “strategy” on the board, and preface the discussion that we don’t want solutions or answers shared out. We want only strategies or approaches.  In this phase, I preselect groups I've checked in with, and I also ensure I am calling on different people over time. A typical opening is “[Name of Student] could you share what you discussed with your partner?” and move through groups until we have a decent outline of the problem.  Alternative strategies are often suggested, and then students have a good sense for multiple ways to move forward on the problem. Students can also ask questions. Perhaps they have questions about a concept or definition or are wondering if a certain technique works.

This whole process can be repeated, and then students leave with momentum for several problems. This catches people up, uses the whole class as a resource (AKA hive mind), and still leaves vital individual tasks outside of class for students to complete problems and find their own proofs.

Another way to think about momentum building is that it is a strategy for reducing variance. It employs a team effort towards getting the whole class on the same page. Class discussion is vital in momentum building, because discussion makes public the strategies needed to solve a problem. All students have access to this information and time to ask questions about them.

A fine line between making the gaps too small and leaving excessively large gaps exists here. This is one of the instructor “dials” in IBL teaching, and how much to turn this dial is student dependent and time dependent. Towards the beginning of the term, an instructor may want to error on the side of smaller gaps to build class norms and broad engagement, and then increase the size of the gaps later in the term on some tasks.  Too easy of course is not useful and too much frustration also something to be avoided. Additionally, having a range of problems from easier to harder can also keep students appropriately challenged for their specific development at that moment in time. 

Momentum building can be a positive feedback loop, which can lead to a highly successful course. Authentic, repeated successes can lead to amazing things. If you find your students are not engaged at the level you want and some are straggling behind, consider using momentum building strategies to get your class on the same page.

Wednesday, January 30, 2019

Ongoing Student Buy-In Strategies

"I learned how to face my problems, not run away from them; although it can be frustrating at times, if I persevere I can solve problems." - Calculus Student

"The most impactful thing... is the idea of productive failure. The idea that you learn more when you don’t get things right the first time has been beneficial because I can just relax and try things. I tend to get over worried with just getting the right answered rather than trying to deepen my understanding of concepts so the ability to fail gives me a lot of freedom." - Calculus Student

In a previous post, I wrote about a way to open a course. In this follow-up post, I share a few strategies to keep students going through the term on the path of growth mindset, productive failure, and dedicated practice. Mindsets are at the core causes student buy-in issues. When students don't buy it, it's often because they don't like being stuck or that being stuck implies there is something wrong with the problem, them, or the teacher or all of the above and more.

Math anxiety as something connected to student buy-in is one of the issues I feel math instructors ought to consider carefully. One reason for this is that math anxiety and other non-availing beliefs (i.e. beliefs that inhibit learning) are factors that affect how students engage on a daily basis. For example having the beliefs that "only geniuses can understand math" puts a person in a frame of mind when doing math of purposely not trying to understand what is going on and only memorizing. So even if the activity you designed is superbly crafted in every possible way, a student's beliefs could neutralize all that. "So, what do I need to memorize for the test?"

Further, mentioning some good advice on day 1 has some impact, but normally fades. Existing habits of mind and beliefs have inertia and durability. These take time to process. Hence, there exists a need for an integrated, long-term plan. Below are some ideas that might help you build your plan after day one.

Have students write a math autobiography early in the term. The idea is to get to know where your students are coming from, what kinds of experiences they have had, and see if they have had positive or negative experiences in Math. These assignments ought to be graded for completeness only, and instructions should indicate that the point is to be honest so you, the instructor, can understand where students are coming from. Math autobiographies also offer students an opportunity to look back and reflect, and it's an opportunity for instructors to affirm and appreciate what students have had to go through prior to arriving in their class.

Productive failure and growth mindset videos are another useful source for activities. In an earlier blog post, more than 10 videos are compiled around the theme of growth mindset and productive failure. One way these can be used is to assign 2 or 3 at a time, and ask students to write about what they learned and some personal reflections about their mindsets. These videos can be spread out over time, and students can be asked to do several assignments. Having videos of different people from different walks of life say the same sort of this adds credibility and weight to your messaging. It's one thing if you say it. It's another when you say it, and also John Legend says it, and Michael Jordan, and Carol Dweck, and Jo Boaler...  A chorus of voices is stronger than one, and offers a variety of perspectives.

Including productive failure presentations or written work as part of class and the course grade is another way. Students can present instances when the have been stuck, and share what they gained or learned from it. If presentation time is not something you can do in class, then students can be asked to submit something in writing about a mistake or something they were stuck on and what they learned and discovered from the process.

Lastly, instructors can chime in regularly, say once a week or so. There's plenty to highlight. The videos and student work are great opportunities to add further insights and affirmation. The instructor can also share personal stories about how they handled being stuck, and the value of practicing with intent and persistence.

And there's more instructors can add in. There's also reminding students to be good communicators, to be patient with being stuck, to be good listeners, to be sure that they are inviting their group mates into the discussion, and to practice hard and with focus like when they are doing their hobbies.

There are caveats of course. Not all students like this topic or put in an honest effort. Some write what they think you want to hear. What these assignments are for is to provide an opportunity for students to take the next step. Instructors can't force students to learn anything, whether it's Math or productive failure. But we can invite students in to a larger, more meaning view of learning, and many realize that they can do Math.

In the aggregate, students are exposed to a variety of positive messages throughout the term, while also reflecting on their own experiences and thinking. They have plenty of chances to adopt a different mindset. When students learn that there's no such thing as a math gene, and they have the capability to do something to make themselves successful, it's empowering!  And that's one of the best things you can teach to anyone.







Monday, January 21, 2019

Equity and Teaching Math

A student once remarked that Math is black and white. There's always one correct answer. There is no grey zone.  One of the facets of Math is that we have proofs, and facts like the Pythagorean Theorem are true. That's something to be celebrated! Math is special, and there are things we do in Math that you do not get to do or experience in other subjects. Of course, Math isn't black and white, and there are grey zones just like in every other subject.

Further, there exists a perception that since math is 100% objective, then people who are mathematicians are 100% objective in all facets of their lives. One hundred percent. I wish...  But just because Math is founded on logic and proof, doesn't mean that the human system of math education is immune to the human condition. Teaching is a cultural activity. Schools are designed and run by people, and inequities exist today. The content we teach and how we teach it are not designed via an axiomatic or scientific method, and not every instructor reads the education literature.  I'm not saying that this work is "bad" or done without careful thought. People think hard about this stuff, and do lots of good work. Much of what we teach is done, because it's important and valuable. So don't get me wrong. The point is that math instructors are not immune to blindspots and bias, and more importantly there exist feasible, doable pedagogies that can positively contribute. The focus of this post is what we can do to make things more equitable.

Using IBL methods does not guarantee equity, but it's a framework that has room for instructors to make choices that levels the playing field and provides opportunities for all students to have equitable opportunities to learn. Giving all students a fair number of chances, visiting student groups in an equitable way, affirming and valuing student input, and making all students feel welcome and respected, are some of the ways we can move the needle in the right direction.

Let's get to a specific strategy. A doable strategy can be applied to small group discussions and Think-Pair-Share. Generally when groups are used, the instructor can visit each students (over time) the same number of times.  The instructor can raise softer voices and redirect the louder voices for greater benefit to others and themselves. Rather than asking for volunteers (where the usual suspects raise their hands the fastest), assign the first one or two chimers and ask them to talk to their group first. Then ask the assigned chimers to share what they discussed with their group. If you keep track of who has chimed in, you can be sure to spread the chances around, and follow up each comment with an appropriate compliment ("Thank you for the insightful question/comment!"). It's the instructors job to provide an equitable set of opportunities. The common, "Are there any questions...?" teacher move focuses by default on the louder voices and not on the softer ones.

Also asking, "What did your group discuss..." is more inviting than questions like, "What's the right answer?"  The reason is that you can ask people to share their thoughts and not put them in a right/wrong answer scenario, which is higher stakes. It also invites asking questions without judgment, and gets more questions and ultimately solutions out in the open. The instructor or the class can't answer a question that isn't asked. The instructor can, however, create conditions where students feel comfortable asking questions.

In summary, spread the chances, keep track using a seating chart or roster, use prompts that invite people in, and give appropriate, positive affirmation.  Instructors don't have to revamp their entire teaching system to work on equity in the classroom. Every instructor out there has the opportunity to do something in their next class, by incorporating the strategies described here. These strategies raise softer voices and encourage those who get things faster to spend some of their time helping others via the group discussions, which in turn helps them learn math even better.

We are better when we all learn together!



Monday, January 14, 2019

Opening a Course (and Launching Winter Term 2019)

It's early January, and that means for those of us on the quarter system that we're already up and running!  Classes started on January 7th, and we're off and away starting another academic term. This term I am teaching Calculus 1 and Advanced Analysis. Two courses at very different ends of the college math spectrum.  This post focuses on opening a Calculus 1 course. I'll save Advanced Analysis for future posts.

One thing that I focus on in my classes at the start of the term is student buy-in. Student buy-in is important, because math anxiety and problem solving don't mix well. Problem solving requires being stuck as part of the learning process, but the math anxiety filter paints being stuck as a really bad thing. Therefore, student buy-in is part of my plan on day 1 for classes like Calculus.

There are many ways to open a class. Dana Ernst, Northern Arizona University, has a great take on setting the stage. I take a simpler approach in my classes, which I think can be a good starting point, especially for those new to IBL. For the past several years, I have asked two simple questions.

1. What is one of your hobbies?
2. How did you get good/better at it?

Students are asked to talk to one another about this, and then go to the board and write their responses. Then we have a chat about the amazing range of hobbies and interests in the class.



Every class I have done this with generates a huge range of interests and hobbies! I love it!

And then we get to how they got good/better at it. In every instance I have done this activity, the big theme is practice. Practice. No matter the hobby or interest, how one gets better is through practice.



From that starting point, I pivot to share with my students what it takes to succeed in math. I share my insights as their instructor. Getting good/better at math is no different from what they did to get good or better at their hobbies. Getting better takes practice and focus. There is no math gene, and that anyone who puts in enough time and focused practice can be successful. That's the main message on day one.

After that opening, we are off to look at the course logistics (briefly) and doing some math for the remainder of the class period. That's day one in a nutshell.

Opening is necessary, but not sufficient to get students to take ownership of their learning. It's analogous to a race and getting out to an early lead. The race isn't over yet, so you gotta keep on going. What a good opening does accomplish is set things up to go on a path that squashes math anxiety. We may not all get there, but at least that's an explicit goal. The next consideration is to help students stay on that path, and I have another post coming up on ongoing student buy-in ideas.

That's how I open a course. What have you done or what have you thought about?


Thursday, January 10, 2019

The NSF PRODUCT 2019 Teams!

It's time again to share who is on the teams for the NSF PRODUCT project I've been working on with others. I think this list shows the depth and breadth of the movement, the amazing people (of course) on the teams, and also the size and scale of our project.

NSF PRODUCT info is available HERE, and the NSF page is HERE.

A massive thanks to the team members! They have taken on with passion and dignity the task of providing professional development to college math instructors. We have a big year planned, and I look forward to doing the work and sharing what we have done here on this blog.

Team MN IBL Workshop (jointly hosted with MAA NCS)
Kyle Petersen, Depaul University
TJ Hitchman, Northern Iowa University
Xiao Xiao, Utica College
Nina White, University of Michigan
Rebecca Glover, St. Thomas University

Team Portland IBL Workshop
Gulden Karakok, Northern Colorado University
Amy Ksir, Naval Academy
Phil Hotchkiss, Westfield State University
Stephanie Salomone, Portland University
Dana Ernst, Northern Arizona University

Team LA IBL Workshop
Elizabeth Thoren, Pepperdine University
Robin Wilson, Cal Poly Pomona
Danielle Champney, Cal Poly San Luis Obispo
Rachel Weir, Allegheny College
Matt Jones, Cal State Dominguez Hills

Westfield Team
Chrissi von Renesse, Westfield State University
Volker Ecke, Westfield State University
Phil Hotchkiss, Westfield State University

Equity Team
Jess Ellis, Colorado State University
Briank Katz, Augustana College
Angie Hodge, Northern Arizona University

Regional Communities Team
Patrick Rault, University of Nebraska Omaha
Ryan Gantner, St. John Fisher College
Jane Cushman, Buffalo State University
Yousuf George, Nazareth College

Virtual Workshop Team, with a focus on Math for Elementary Teachers
Danielle Champney, Cal Poly San Luis Obispo
Todd Grunmeier, Cal Poly San Luis Obispo

Evaluation Team
Sandra Laursen, University of Colorado, Boulder
Chuck Hayward, University of Colorado, Boulder
Tim Archie, University of Colorado, Boulder
Devan Daly, University of Colorado, Boulder

AIBL Team
Katie Kahle, Cal Poly San Luis Obispo
Winston Chang, Cal Poly San Luis Obispo
SY, PI, Cal Poly San Luis Obispo


Thursday, January 3, 2019

Does Instructor Personality Matter?

"To be yourself in a world that is constantly trying to make you something else is the greatest accomplishment" -Ralph Waldo Emerson

I've been asked by many in one form or another about instructor personality. The basic question is, "Does personality matter?"

Let me get this out of the way first. Any professional instructor can teach effectively and can get students to buy-in and learn effectively, no matter what a person's personality is. Teaching, like being a craftsman or artisan, is a profession and as such can be learned by hard-working, thoughtful teachers. My belief is that personality does not really matter in terms of whether one can be successful at teaching via IBL. What matters are skills, vision, professionalism, effort, and passion.

With that out of the way, let's get to where the question, "Does personality matter?" comes from. There is a conjecture that certain personality types are better suited to IBL compared to others. For example, Mike Starbird, University of Texas, has been a strong proponent of IBL. He has a big personality, and he's an accomplished scholar and speaker. Some think he's the type of personality that can do IBL. But there are other personality types, other forms of learning, and the value of diversity of experiences, which combine to imply that there are range of ways to be successful as a teacher.  You'd don't have to be like Mike.

Mike is *an* example of a highly effective IBL instructor, and every instructor, who cares and puts in their time and focused energy, can be highly successful, while being true to their personality. You can be you, and carefully and effectively implement IBL methods. I really believe that. I'll also note that while Mike Starbird has a certain persona when he gives talks, I have been in his classroom as an observer, and he knows to pull back and let students do the talking and work on the material. It's learning first and foremost, and the teaching techniques that make that happen.

Let's refine the question. We could ask instead, "How do instructors use their personality as a strength?" Excellent teachers come in many forms. Math class is not a narrow, tall, and immutable monolith of a single, specific experience. It's a diverse landscape, drawing upon the varied experiences of instructors and students. Just as there exists a variety of music teachers and soccer coaches, math teachers are also a varied, diverse bunch (despite stereotypes trying to put us into a neat little box).

Here are a couple of oversimplified examples to get across a basic point. Assume say you're a more introverted, and not an animated speaker. You like to be thoughtful, and cracking jokes is not your style. But you are good at collaborating and understanding what students are saying. Then your strengths lie in the area of 1-1 interactions with students. It then makes sense to design your course using groups more. Groups can put you in a mode where you ask and listen to students, and build learning experiences from the small group interactions.

Now suppose a you are the type that does better with writing (versus speaking). Many of us prefer to write.  Then consider making more class handouts, supplemental handouts (recaps), and use email communication or LMS features like blogging or message boards. This might even be paired with flipped learning to further enhance what you can do in class. Then class time can be more focused on student-centered activities.

Hence, a basic point is that the IBL framework can be adapted to your strengths. Instructors can tune the course structure to take advantage their strengths. Personal strengths are not the only factor, but they can be factored in.

Another essential piece is communicating your strengths to your students. Informing students that "I'm not the type personality that gets in front of the class and does the big speeches... my strengths are in other areas, and I setup my courses so that I can better help you succeed in ways that utilize my strengths. Here's how I am setting things up so you get the best possible learning experience..." A core part of the message is letting students know you care and that you are thinking about how best you can help them.

Lastly, I'll also note that identity and culture are real factors. I won't get deep into this, but it needs to be mentioned. We know that gender and race influences perceptions and expectations. This is where advice gets tricky. I know what works for me, and what works for people I know. But what works for me may not work for you. Underrepresented faculty have added challenges compared to those who are more privileged. Yet, despite the fact that the terrain is not yet a level playing field and that some have to deal with more obstacles, there exists practical solutions that can allow you to be true to yourself.

In summary, instead of thinking of whether personality is good/bad for certain types of teaching, I believe it's more useful to start with your strengths and see where that puts you in Big Tent IBL. Every teacher is good at some aspects of teaching, and brings value to the classroom. Building off of these strengths, then is a key area to focus on. We can design our classes so that we take advantage of our strengths, and inform (repeatedly) to our students how and why class it setup in order to maximize their learning.

So what are your strengths? How do you use your strengths to shape your classes, while being your authentic self?

Happy New Year! It's 2019, and I wish you all the best!