Wednesday, October 8, 2014

Other Blogs Strategies for Grouping Students, Student Resistance, Teaching Math Through Immersion,...


Some useful links from recent posts in the iBL blogosphere:

Strategies for Grouping Students by Chriss von Renesse is a great post on how to use grouping to develop an environment to increase student success.

Matthew Jones has a nice post on strategies for dealing with student resistance.  The shift from traditional, passive learning to active engagement can be hard.  Students can say, "I don't learn this way."  Matt has a nice post on how to handle these situations.

AMS blogs have really been interesting to follow.  Here's a nice post by Priscilla Bremser on Teaching Mathematics Through Immersion.



Sunday, September 28, 2014

Dynamics of Misinformation in Education

A post about a broader topic, not just about IBL...

Misconceptions about IBL (or CCSS or other education efforts in general) are in part due to what I call "selective reporting."  When there's news about evidence that points towards using active, student-centered methods of teaching, it rarely receives much fanfare, so most people miss it.  On the other hand, if school district or academic institution is struggling to implement effective teaching, then the story makes it to mainstream news, creating a bias.  Put another way, the problem is that the full picture isn't being reported in a reasonable way, so the takeaway message is distorted one.

Here's an analogy that gets across the depth of the difference.  In photography, cropping is a way to change or enhance an image.  What we exclude can significantly alter the impact of an image.  

Picture #1.  The subject is a boy who appears to be pensive or annoyed.  Presented by itself the image leaves the viewer with a very specific interpretation.  It's definitely not about playful, youthful themes.



Picture #2:  What was really going on?  The subject was engaged in a variety of silly poses and only pretended to be annoyed in the image above.  Taking a look at the frames below shows the broader story, and a completely different perspective of what is happening.


In a similar way, news is reported in bits and pieces about education that leaves the broader story out of the picture.  An oversimplification of education is presented below just to get the point across.  The diagram is not how I actually think about the education system, but I think it's good enough for these purposes for a "back-of-the-envelop calculation."  

Let's assume the main groups of topics in education reform are listed in the diagram below.




















What happens is that the media employs selective reporting, where the emphasis is on the problems with say implementation or highlighting a small subgroup's opinions disproportionately more than their earned merit (other stuff).  So to the non-expert it's easy to make incorrect/limited conclusions.

























For instance with respect to CCSS, the media emphasis has been on implementation struggles.  The public then could be swayed to think the entire CCSS idea is flawed, as opposed to seeing the problem for what it is -- early struggles with the transition.  Reporting rarely (if ever?) asks natural follow-up questions or provides a broader view to put the issues into context.  It's especially unfortunate, because education is a complex, long-term issue.  Therefore, context is fundamentally important to understanding what is going on in education, and context and framing is just what is being excluded by media reporting.

The math profession isn't entirely free of this.  The AMS published somewhat recently a Doceamus article in the AMS Notices http://www.ams.org/notices/201010/, where a narrow study on "worked examples" was extrapolated to imply that constructivist and minimally-guided approaches were invalid.   This article made the rounds, but the article by Freeman et al, based on a metaanalysis of 225 research articles from STEM disciplines appeared to get less fanfare, despite being categorically a vastly stronger body of work in scale, quality, and value to society.

The dynamics of misinformation is subtle, because it's hard to know about things you don't know about already.  Undoing misconceptions is harder than informing people right the first time, so it's a problem that can snowball and lead to unproductive or harmful resolution.

The misinformation gap is here and is real.



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!