Coaching vs. Cheerleading

I've had some nice, informative, and enlightening conversations with math instructors about the difference between coaching and cheerleading.   The discussions I had were generally about classroom management or the usual IBL questions like "How do you select presenters?" or "How do you get the quiet students engaged?"

The issue I want to bring up is somewhat subtle, and also an important one.   There are some people or personalities that react negatively or find that it is not in their nature to cheerlead.  I have no problems with this.  Cheerleading is not necessary.

On the other hand, coaching is necessary in effective IBL courses.  A problem a new (or even experienced) IBLer can run into is confusing coaching for cheerleading.  This takes on at least two forms.  Some don't coach since they are not inclined to be a cheerleader.  Others think they are coaching when they are really cheerleading.

Let's discuss some examples to sort out the differences.  Cheerleading examples:

• "Good job!"
• "High Five!"
• "You can do this!"
• Here's me showing how much I am excited about the subject!  Don't you just love this proof?!?!

Cheerleaders are supporters.  They give high fives and can positively affect the environment.  They root for the players.  Cheerleaders, however, do not affect the results of the play on the field directly by their actions, although they do contribute to a more positive environment.

Coaching examples:

• Noticing where students are struggling and creating a new task to bring out the issue so that students can engage in making sense of it.  "I noticed the following... Let's all now work on this new task..."
• Noticing if students have reached a high level of frustration, and makes an instructional decision to deflate the pressure, refocus the students, or whatever to keep students on the learning path.  This may be the instructor making a joke initially, and then talking about how being stuck is okay.  "I hope you all know that being stuck is okay.  I know problem 3 is challenging, and it is natural to be stuck.  Let's now focus on what you've come up with and share them out.  Then we can see if there's an idea we can work with..."
• Thanking students for their efforts and their work.  "Thank you Judy! You explained carefully using a proof by building a sequence that creates a contradiction..."

Coaching decisions affect the outcome of the game.  IBL instructor in-class teaching decisions (i.e. coaching) affects student learning outcomes.

Let's compare "Good job, Judy!" vs. "Judy explained carefully..."   Why is one cheerleading and the other coaching?  When we say "Good job!" it is praise and an evaluation (just as much as "Bad job!" is an evaluation).  Once uttered the discussion often stops there.   When we point out what Judy did and the strategies that she used, and then thank her, it highlights what Judy used to solve the problem, which other students can pick up on and learn from.  The focus is on the math and the thinking behind it.  The discussion could be extended with a follow-up task like "Explain what is important about this step of the proof to your neighbor."

Helping students get out of a rut by changing tasks, asking questions, and deflating a frustrating situation is effective coaching, because it keeps students in the learning zone.  Those who shy away from cheerleading should make it clear in their own minds the difference between coaching and cheerleading.  Adding some cheerleading on top doesn't hurt, and can create a more relaxed atmosphere, but it does not by itself create a fundamental shift in the learning environment.

In my experiences working with instructors who struggle with IBL, one of the common issues some of new IBL instructors struggle with is knowing the difference between coaching and cheerleading.  Often this is unacknowledged, and sounds like "I just don't know if I have that kind of personality."  So having the right personality then is conflated with a lack of effective observation and communication skills related to IBL teaching.  The danger here is that this means there's the assumption that nothing can be done about improving the skills and practice.  I hope that these examples help define where effective coaching lies, as well as point out that effective IBL coaching skills can be learned and employed by any math instructor.

How to get started if you're new to this?
Really, really listen to your students.  Ask students when they are working in groups basic questions like, "Can you show me what you're working on?"  Or "I would like to know how your are thinking about this problem.  Could you explain to me...?"  Then listen.  Ask follow-up questions and keep on listening.  The goal is to understand student thinking.

During or after class presentations, rather than say "Good job!"  Point out what the student did, the strategies they used, and so forth.  Next, ask the class to share what insights they gained from the student's work.  Finally thank the student for presenting as a gesture of appreciation for their effort and contribution.

Is cheerleading bad?  Well, there's some debate about this, especially in Child Development for early grades.  Generally Child Development experts agree that saying "Good job!" is counterproductive.

Effective teaching is about what we actually get students to do that is meaningful for their development.   Hence it is important that effective coaching and making good teaching decisions form the core of IBL teaching.  If you rely on cheerleading a lot, then it's time to upgrade to more coaching decisions.  If you've shied away from coaching due it feeling similar to cheerleading, then I encourage you to take a different view and try one instance of IBL coaching in your next class.

Efficiency in the Workplace

If you are the type that makes New Year's Resolutions, one thing I'd recommend you do is to spend time focusing on efficiency.  A few years ago I converted to using a to do list manager that syncs with all my iDevices.  This means that I can stay connected with the things that I need to do, I write everything down, and most importantly I no longer wake up in the middle of the night with thoughts of "Oh! I forgot to..."

1. Watch this video of David Allen ("Getting Things Done").

2. Do a "core dump" of all the things you need to do into an electronic todo list manager, such as OmniFocus.

3. When you get to your office open up your todo list manager AND do not check email.  Figure out your agenda, adjust, and (ideally) work for an hour on your stuff.  Then check email.

4. Figure out the specifics that work for you, and find the programs, apps, and system that gets you quickly and efficiently into you work mode. While I use OmniFocus, I know it's not for everyone.  It works for me, and I've made it work for me. You may prefer EverNote or some other system.

Why?  Time.  Time is the most precious resource we have, and if you are more efficient, you have more time to allocate to your teaching and research that is meaningful.  It helps you get better.  If you're always in catch-up mode, then your tasks are controlling you, and you have no margin for error. If you get sick or miss an appointment, you're way behind.

IBL Contributed Paper Session at MathFest 2013

Quick FYI -- If you are going to MAA MathFest (LINK), consider submitting an abstract and/or attending the IBL BEST Practices session.  MAA IBL MathFest Contributed Paper Session, Summer 2013

-SY

Inverse Pale Blue Dot

A departure from IBL topics for this post... 

I spent part of last week with my family taking a much needed break in Yosemite.  As we made our way back to civilization yesterday, we were rudely confronted with news of the massacre at an elementary school in CT.  My thoughts go out to those who have been affected by this terrible event.  

While in Yosemite, I made an image that I think is relevant.  I have always lived in urban areas so I rarely get to see the stars.  On this trip, one of the evenings was moonless and clear, so I took my camera and tripod to make a "wide field" night photo from Tunnel View.  At the time I was out there taking pictures, I thought of "A Pale Blue Dot" by Carl Sagan, and how this experience was the inverse of the Pale Blue Dot image.  Instead of the Voyager capturing an image of the earth as a single pixel, I was on the pale blue dot capturing a mass of stars and galaxies that make even a great national park infinitesimally small by comparison.

"There is perhaps no better demonstration of the folly of human conceits than this distant image of our tiny world. To me, it underscores our responsibility to deal more kindly with one another, and to preserve and cherish the pale blue dot, the only home we've ever known." -- Carl Sagan

Indeed it is all our responsibility to deal more kindly with one another.

Learning is Nonlinear

Learning is nonlinear.  

When a college student is learning to prove a sequence converges in Real Analysis or when a first grader is constructing the notion of grouping powers of ten, there is a period of mental construction that goes on where the ideas, language, problem solving, all that have to be put together coherently.  This process is highly nonlinear.  Certainly it isn't a matter of just transferring information from us to them.  Learning to do math is much more than say the simple act of memorizing your friend's phone number.  Learning a new idea takes time, energy, experimenting, mulling, messing around, all that.  Learning to creatively solve nonroutine problems requires even more of this kind of time.

What does knowing "learning is nonlinear" tell us about teaching?  One thing we can take away is that traditional courses tend to be set up linearly.  Section 1 on Monday, section 2 on Tuesday,... The factory model or industrial revolution genetics of our system become apparent here.  We line them up in rows, bolt on the parts one-by-one, and off they go.  Job well done, right?   

Linear teaching models are dangerously attractive, because they are easier to plan, follow the linearity of books, and institutions can be manufactured along these lines for less cost.  It's efficient on a cost basis, from the standpoint of human capital, because it requires little investment in faculty development and associated resources for teaching (e.g. technology, tools, materials, training, support).

Linear teaching is however inefficient in time allocation within class with regards to learning.  Students struggle on different things at different times.  Basic stuff is easily learned (even outside of class), and linear teaching may inadvertently allocate too much class time to basic material.

Further linear teaching may not allocate enough class time on harder material, which then conflicts with nonlinear learning.  When students need time and support to make it over the next tough section, the class moves on, ideas are half-baked, and misconceptions are formed or allowed to linger.  Students' foundation of thinking is not set upon bedrock, but rather a shifting, insecure base.

What is perhaps the most difficult part for a teacher regarding this linear vs. nonlinear issue (especially for traditional instructors) is the blind spot.  The blind spot I'm talking about is the not having a detailed understanding of student thinking.  If you don't know your students, you don't know where they are likely to struggle, other than through "inverse scattering theory," where in the past you've given quizzes or tests on a particular subject and students did poorly on certain items.  Of course it was too late for that batch of students, but at least the next batch will be slightly better off... Such issues are classic symptoms of traditional assessments, where your only learn about your students from tests (i.e. summative assessment).  Before you give an exam, you should be able to rank order your students (assuming a small enough class size), and then give a test that more or less confirms this.  If you can't do this, then you don't know your students well enough.

The ability to see the nonlinearity of learning is closely connected to student-centered teaching.  Giving students a chance to play and explore, gives us insight into their thinking.  (Just talk to them and ask them what they have tried on a particular problem.)   We use insights into their thinking to guide our instruction and do what is more likely to be useful as the next task.  If things are going well, students will just tell you, "I'm stuck on this..."  Great!  Now you know what the next move should be centered on.  

Linear assessment also takes the form of weighted averages used for grades.  If you rely solely on a weighted average of the hw, exams, final, and do not account for nonlinear learning, then this may be harmful to students.  If a student doesn't understand a topic in week 4, but figures it out by the end of the term, then how should the low score on first test be interpreted and used?  This is a topic of debate, and I am not going to say there is one right way to handle this.  But the point here is that you need to think about this issue and do something consistent with your values regarding education and what the point of education is.  Many faculty use a system where the final exam can make up for earlier lower scores at least to some degree.  This kind of policy is then an acknowledgement of nonlinear learning.  Let us now complete the circle by embracing nonlinear models for (student-centered) teaching!

Lecturing is linear.
Learning is nonlinear.
Teaching is nonlinear.

Online and Distance Learning: What We Should be Thinking About in Education

The wave of the future?  I'm not sure.  What is certain is the democratization of knowledge in the google era.  That's a good thing.  Below is a link to one look at a possible future.

Link to NYTimes Article on Massively Open Online Courses

I don't have a well-formed opinion of online courses today, and in a broader perspective of the role of technology in the math classroom.  It's okay for us to not know answers today as a profession, while at the same time it is NOT okay for us to ignore technological advances.

I would say that math classes today mostly look like they did decades ago.  Some of the differences are fashion, color textbooks, and demography.   That could have been said about brick-and-mortor bookstores just when Amazon, et al were getting started.

Another thing that is for sure is an increasingly rapid change in technology and its usefulness across society and in particular education.  Perhaps ironically for the scientific community the transition away from lecture will not be due to the data collected by education researchers.  Rather the changes might be the fact that we have to confront competing against the "best lecturer in the world in my profession."  Imagine the most dynamic, thoughtful, and articulate person in your field.  Then that person gets recorded by Hollywood caliber videographers giving the same lectures as you would.  At that point, then what does your class offer that can't be obtained for free or more conveniently?

I'm not sounding an alarm bell here or trying to stir up fear.  The point is that knowledge transfer is one generation of technological advance (or perhaps less) away from becoming trivial.  Add in improved interaction via video chat, and a few other features and then the experience of the classroom can be essentially recreated.

Coaching team sports, for example, doesn't seem threatened in the same way by technological advances.  This perhaps hints at what educators at the college level need to embrace.  What is it that we provide as an experience that cannot be learned from books or a set of online videos/classes?

IBL Self Check

Measuring yourself against your personal best is one of the best ways to evaluate yourself.  This is done in sports in particular, where the goal is to improve on one's best time or score.  IBL instructors can do this too!

How can we get better as instructors?  Focusing on the skills and practice of teaching is the way forward.  This list of self-assessment questions are meant as a guide or start. It is not definitive.  Ultimately your ability to improve rests upon being able to see what your students are doing and what you are doing that affects students.   If you can identify areas where you can improve, even if you are successful in that area, it gives you clear direction where you can exert your energy as a teacher.

Classroom Context and Teacher Moves:

1. Are student presenting/sharing ideas in class regularly? Can this be done more often in a way that benefits students?
2. What percent of time is devote to student-centered activities?
3. Are students deeply engaged in the tasks you have given them?  Can your problems/tasks be improved?
4. How many times per class period are you being supportive by giving encouragement, positive feedback, coaching, adjusting tasks to meet the needs of your students?
5. Can you give more positive feedback?
6. Can you improve the problems/tasks given to students?  Are the problems too procedural in nature? Are there good concept questions?  Are the problems too difficult?

Nature of student interaction:

1. How satisfied are you of students' solutions?
2. Do your students view you or a book as the mathematical authority? That is, do they frequently require an external (to them) authority to validate answers?
3. Are students able to understand and explain other students' solutions or strategies?
4. Are students mimmicking a book or model (i.e. "google search solution/proof") or are they generating solutions/proofs "from the ground up"?
5. Are a wide range of students regularly participating in class through presentations, questions, discussions?
6. Are there quiet students in class who do no participate very much?  If yes, then how many?
7. Are there any dominant personalities?  Are such personalities hindering the learning of some of the others sometimes?
8. What is the stress/anxiety level of your class on a scale from 1 to 10?

Keep it simple.  Here are some basic tools in a class that you have direct control over:

• Problems and tasks
• Questions/directions you say
• Basic strategies employed: groups, pairs, think-pair-share, class discussions

An example of how you can improve is if you identify that only 4 students answer your questions in class.  Then instead of asking "What is the answer to...?"  You can say, "Work on this, and I'll call on a person/group at random..."  Then you can get more students involved.

If every term you make a few meaningful improvements, then in a few years you can be brilliant!