## Monday, September 15, 2014

### Is Teaching = Art? Is Reform = New Curricula?

Founds this entertaining and well-written essay by Peter Taylor via my twitter feed recently.  I first want to say that I agree almost entirely with what Peter Taylor has to say, especially the call for doing more "artistic" math and letting go of doing it all for the students.  It's a good read and I recommend it.

There are two points in Peter Taylor's essay, however, that I find incomplete, which ultimately affects how we go about transforming our educational system.  I'd like to expand on those here and encourage others to think about these two points further.

Is teaching = art?  It's been debated, but in my opinion the answer is no.  Effective teaching has aspects of art (more artisan like) that require creativity, but teaching is teaching.  It is its own thing, and making analogies to other disciplines can help us make sense of it, but taken too far diminishes the unique activities and mindset required in the teaching profession. While teaching is a creative endeavor, it also requires mentoring, organization, managing young learners, learning outcomes, learning goals, assessment, etc.

Style matters to an extent in teaching, but learning outcomes matter more.  Much more.  I can't just teach my style and not think about the impact on my students.  I'm not saying Peter Taylor says this.  He doesn't.  But that's the way "teaching is art" gets interpreted by some people.  Artists have a freedom of expression and freedom of intention.  Their work can be interpreted in many ways by viewers, who see things through their own lenses and experiences.  Teaching on the other hand is very intentional work with real outcomes that matter to young people.

Math is beautiful to mathematicians, but math is not art, just because it is beautiful.  Yes it requires similar kinds of dedication, creativity, and expressing our ideas in clever ways.  But that doesn't make math an art form, unless we really relax the definition of art.

Teaching $\neq$ art.

Now this all sounds like academic banter.  I bring this issue up, because I think it matters in the real world.  The danger in thinking that teaching is art is that some people mistakenly take that to mean it's primarily about personal teaching style, which can disconnect the act of teaching from learning.

Teaching as a profession is more akin to medical practice.  Medicine uses science and problem solving in creative ways with the goal of improving health.  Likewise, teaching can be studied, it relies on knowledge of the academic disciplines, with the goal of improving learning and thinking.   We can study teaching, find better ways to teach through scientific research, and so on.   It's better to then to think of teaching as a unique profession.

Teaching is also fundamentally a system and a cultural activity, which brings us to the next point regarding curricula and reform.   Many reformers in the past have been tempted by the Sirens of "Reform = Curriculum Change."  Many reform efforts have crashed on the rocks of model courses and innovative curricula as complete solutions to reform.    I emphasize that good curricula is absolutely necessary for authentic reform.  Updated curricula alone, however, is not sufficient.   If all it took was good curricula to make our teaching system change, then reformed would have occurred already decades ago.   So why is curricula insufficient?

Math classes have their own distinct culture and history.  When students and teachers walk into math class, there is an expectation of what is going to happen and what math is.   The teacher shows.  Students mimic.  Students practice quietly to get the same answer as the teacher in the same way as the teacher.  Then it's on to the next topic.  That's the standard culture, where the assumptions for our (K-12) system have roots back in the industrial revolution, when the focus was on learning algorithms and facts for the factory workers, and a few elite would rise up to run the empire (by attending college).  The challenge is to shift this culture to a new model, and that has been a challenge that has resisted change for centuries.  The entire culture of teaching and learning that has to be shifted, and that is why changing curricula is insufficient.  Necessary, yes.  But insufficient.

What we somehow need to figure out is to change our teaching culture and teaching system.  It's a big, complex problem, where the core subproblem is implementation of active, student-centered teaching on a broad scale.

Do we have full answers to the big problem?  No, not yet.

Can we do this?  Yes.  But my guess is that it's going to take creative problem solving, coordinated efforts by large, organized groups of people, and about a generation of time.   Hopefully we can bet on exponential growth, and see changes sooner.

I have had the fortune of seeing Picasso's Guernica in person that Peter Taylor mentions. It's absolutely a great work of art with meaning and power that transcends time and culture.   All subjects should inspire people to equivalent stature.  Picasso once said that all children artists, and that the problem is to remain an artist when one grows up.  Likewise I believe all children are mathematicians.  The problem is to remain a mathematician when one grows up!

Upward and onward!

## Thursday, September 11, 2014

### Learning to Ride a Bike

More light-hearted posts here.  Thanks Paul Harper for starting this thread... Paul Harper recently posted this 7-minute video about active learning, using the context of his daughter learning to ride a bike.

In IBL land a central idea is creating a sequence of problems, and letting students experience the learning process through guided discovery.  The problems are spaced so that students have opportunities for authentic ownership of the mathematics and intellectual (and personal) growth.  In the spirit of showing our kids learning to ride, here's an image of my son, Hutch, working on a lemma (i.e. riding a balance bike with no pedals).  After he learned how to balance himself, he got on a bike and rode off.  All he needed to learn was how to use the brakes.  And you didn't need to tell him he got the right answer.  Q.E.D.

## Monday, August 18, 2014

### Julian Fleron, Phillip Hotchkiss "Inquiry-Based Learning to Engage and Empower the Disfranchised"

Julian Fleron and Phillip Hotchkiss, Westfield State University presented at the 17th Annual RLM and IBL Conference Co-Hosted by MAA, EAF and AIBL.  The conference was held in Denver Colorado, June 2014, and their talk has just been posted on the AIBL YouTube Channel.   This talk shows some practical ways to get going with students who typically have math anxiety and transform the course into a fun, engaging learning environment.

"Inquiry-Based Learning to Engage and Empower the Disfranchised"

I also recommend checking out their website on teaching courses for Liberal Arts Students at Discovering the Art of Mathematics.

## Friday, August 15, 2014

### IBL Poster Session at MathFest 2014

Some images from Portland.  The IBL poster session was held in the exhibit hall, and the turnout was steady and engaged.  Thank you Angie Hodge and Dana Ernst for organizing this session, and an especially big thank you to all those who presented posters!

Poster sessions are a great way to involve people in discussions on a particular theme.  Attendees can interact with presenters in a conversation.  I like both poster sessions and presentation, and perhaps there will be ways to mix the two strategies into a "mixed media" format in the future?  Just a thought.

Some images from the IBL Best Practices Poster Session, MathFest, Portland OR 2014.

## Sunday, August 10, 2014

### AIBL Booth at MathFest 2014

What is AIBL?  "AIBL is the organizational front to an existing community" says TJ Hitchman, University of Northern Iowa.   At MathFest 2014, the IBL community organized a booth in the  exhibit hall.

The co-organizers of the booth are Angie Hodge, University of Nebraska Omaha, and Dana Ernst, Northern Arizona University.  They asked IBLers to hold "IBL Office Hours."  These wonderful volunteers spent part of their busy conference schedule at the booth to talk to attendees interested in learning more about IBL.  A big thank you to...

• Angie and Dana,
• TJ Hitchman
• Victor Piercey
• Brian Katz
• Elizabeth Thoren
• Ron Taylor
• William Lindsey
• Melissa Lindsey
• Susan Crook
• Natalie La Rosa

In the age of top-down, centralized command-and-control reform efforts, based on model courses, external incentives, and penalties for non-compliance, we take a fundamentally different approach.  We take the bottom-up view, where working with individuals and supporting them to solve their own specific implementation challenges is the core.  Through intensive workshops, mentoring, small grants, and visiting speakers, we help individuals and small groups grow their IBL skills and practices, and cultivate a culture of learning at their institutions.  Over time we believe that this community will be more durable, more sustainable, and ultimately impact more students' lives.

One community. Infinite possibilities!

## Monday, June 30, 2014

### Productive Failure (#PF)

This spring quarter I taught Math 423, a course for future secondary math teachers.  This course is often called a "capstone" course and is intended as an advanced look into the secondary curriculum.  It's a hybrid course in that it is a math course, but it also has the goal of transitioning math majors from being a student to being ready to enter a credential program.  Put more simply, it's a transition course from being a math student to being a math teacher.

One of the main themes of the course was productive failure.  In an earlier post De-stigmatizing Mistakes, I wrote about how Ed Burger makes productive failure part of the course.  So I did the same for Math 423!  Five percent of the grade was based on sharing productive failure.  Students were required to share at least twice during the quarter a mistake that they learned from.  These mistakes could be natural or could be intentional (as in a strategy like trial and error).

The results were better than I had anticipated!  Students felt as future teachers they needed to learn this lesson about the value of productive failure.  They felt a sense that everyone makes mistakes and that we can all learn from them and others can learn from them, if we share our newfound insights.  We de-stigmatized mistakes in our little segment of society, and it felt right and good.

One student writes in an portfolio assignment:
One of the biggest themes that I will carry not only into my teaching career but in my life is the idea of productive failure. Failure is given the stigma of being negative and until I came to this class I believed that. After going through this class my thoughts on failure have completely changed. I never thought of failure as a device that can enhance learning and ideas. Every day, watching everyone present their productive failure I noticed how no matter how small the failure was someone learned something. It not only taught us how not to do something, but the right way to think about certain problems and common misconceptions that can help you better adjust your lessons as a teacher. Failure is a part of life and should be embraced and not chastised. By
giving failure in learning such a negative connotation you can inhibit students from good learning habits and for a love of school. I believe that failure should be considered productive and embraced in classrooms all around the world.  -- Jordy Adamski, Cal Poly Math Graduate
Experiences like this are some of the major reasons why I spent so much of my time thinking about improving teaching and improving the system.  When it works, it's wonderful!    When we say the classes are more fun to teach and students get more out of it, it's hard to communicate the impact.  Some might think that the C student moves up to a B, but that captures little of the real transformation that occurs in some the hearts and minds of our students.  Changing one's entire outlook on mistakes and how that might impact that student's math teaching practices in the future is a tremendous change!

An important point to mention is that productive failure fits naturally into an IBL framework.  Productive failure can easily be included in the course grade, since IBL courses already have the active, student-centered dynamic that can easily accommodate short student presentations on productive failure.  On the other hand, a lecture-based course normally does not have the comfort level and student buy-in that would allow students to open up and expose themselves by sharing their latest and greatest mistakes.   Hence, it is emphasized that the teaching system used is fundamental and that adding low-cost, high-impact strategies, like productive failure, should be done within a broader framework that supports it.

Throughout the term we used hashtags.  We labeled productive failure with #PF, which made class more fun and also elevated productive failure to it's rightful, dignified place in the learning process.  #PF showed up all over the place throughout the course, and I hope it finds it way into your classes, too.

#PF!

 The #PF Crew

## Sunday, June 22, 2014

### Legacy of R. L. Moore and IBL Conference 2014

Denver, CO hosted the 17th annual Legacy of R. L. Moore and IBL Conference, co-hosted by the Educational Advancement Foundation, The Mathematical Association of America, and the Academy of Inquiry Based Learning.  The theme: Engaging in IBL.  More than 80 presenters, over 200 participants over 2 days.

If you missed the conference or were not able to attend a parallel session for one reason or another, videos of all of the sessions will be available by the fall of 2014 on the AIBL YouTube Channel.

Many thanks to Harry Lucas, Jr., Norma Flores, Albert Lewis, Fain Brock, Judy Diaz and everyone else at EAF for their tireless efforts to setup the conference.    Thank you to Angie Hodge and TJ Hitchman and the conference organizing committee for putting together a wonderful program.

A big thank you to all participants!  Your contributions made it a special event!

Some images from the conference (more to follow)...