Tuesday, October 30, 2012

IBL Instructor Self Assessment: How IBLish is your class?

Assessing your own teaching is significantly important.  A trait of an effective teacher is one, who is reflective and assessing oneself continuously.  While this is not easy to do, it can lead to continual, meaningful growth in the context of a larger teaching assessment program.  For IBL instruction there are at least a couple of ways to split this up.  The first level is to evaluate the course itself and measure how IBLish it is.  The second level is to self-assess one's methods or techniques, which will be posted in subsequent blog post.

How much of the course is IBL?
  • Level 0: All teaching is done by lecturing.
  • Level 1: In addition to lectures, other presentations modes are used such as videos and the use of worksheets for the purpose of practicing rote skills.  For example, the instructor shows students how to take a derivative of a trig function, and then provide some more problems similar to the shown example.
  • Level 2: The instructor lectures for most of the time, but intersperses some interactive engagement, where students are asked questions and given mathematical tasks that require thinking and making sense, such as "Think Pair Share".  Interactive engagement may take up a few minutes to anywhere up to approximately a third of class time, which may vary day-to-day or be based on weeks (e.g. lecture MW, problems on F). A key feature is that lectures remain a significant component of the teaching system.  The instructor is the primary mathematical authority and validator of correctness.
  • Level 3: The instructor lectures for roughly 1/3 to 1/2 of class time.  Students do a variety of activities that focus on understanding of core ideas, problem-solving, generating ideas, evaluating arguments.  The primary student-centered activities are higher-level tasks, such a problem-solving, categorizing, and understanding concepts.  The instructor is not the only authority on the subject matter, and students share responsibility in validating mathematical facts.
  • Level 4: All teaching is done via student-centered activities.  Students are either presenting proofs/solutions, working in groups on problem-solving tasks.   In this case, the instructor does talk for part of the time, often in the form of setting the stage for a new unit, facilitating discussions, or summarizing or pointing out important facets of a proof/solution after it has been approved by the class.  The instructor and students primarily work together to form a consensus about the validity of solutions. Logic, reason, and mathematics are used to validate solutions.
In the next post, I'll make a list of questions for the purpose of self-evaluation.  

Wednesday, October 24, 2012

The "Education Pendulum" is Really a Ball at the Bottom of a Hill

Angie Hodge sent a nice article to me a week ago.  (Thanks Angie!)  On October 11th, Marion Brady published in the Washington Post How long one teacher took to become great.

The article hits on several topics.  It hits on the notion of the dashing stereotype of "good teacher," how effective teaching is when the instruction is student-centered, open, and collaborative, and then onto the difficulty of quantifying what good teaching really is.

Also of note from the article, and the point of this post, is about changing the system:
Because, when it comes to change, you can’t do just one thing. Switching from passive to active learning — which is what that 1960s effort was all about — had, at the very least, implications for classroom furniture, textbook use, length of class period, student interaction, teacher understanding, learner-teacher relationships, methods of evaluation, administrator attitudes, parental and public expectations, bureaucratic forms and procedures. -- Marion Brady
I hear about the pendulum in education frequently from various teachers, parents, educators, random people.  Education goes in one direction, and then there's a switch back the other way.  It feels like that when you're in the middle of it and observe from behind the desk or podium.  From a broader perspective, we are actually NOT on an pendulum.  What I think is a more appropriate model for our failed attempts at changing the system is that we are trying to roll a ball up a hill.  Before we get the ball all the way to the top, however, we give up (one way or another) and the ball rolls back down to the bottom of the hill.  It's definitely a periodic phenomena just like a pendulum, but there's a difference.

We've been talking about education reform for a long, long time.  W. Colburn wrote in 1830
By the old system the learner was presented with a rule, which told [the student] how to perform certain operations on figures, and when they were done [the student] would have the proper result. But no reason was given for a single step... And when [the learner] had got through and obtained the result, [the student] understood neither what it was nor the use of it. Neither did [the student] know that it was the proper result, but was obliged to rely wholly on the book, or more frequently on the teacher. As [the student] began in the dark, so [the student] continued; and the results of [the student's] calculations seemed to be obtained by some magical operation rather than by the inductions of reason. -- W. Colburn, 1830
John Dewey in 1899:
"I may have exaggerated somewhat in order to make plain the typical points of the old education: its passivity of attitude, its mechanical massing of children, its uniformity of curriculum and method. It may be summed up by stating that the centre of gravity is outside the child. It is in the teacher, the textbook, anywhere and everywhere you please except in the immediate instincts and activities of the child himself. On that basis there is not much to be said about the life of the child.  A good deal might be said about the studying of the child, but the school is not the place where the child lives. Now the change which is coming into our education is the shifting of the centre of gravity. It is a change, a revolution, not unlike that introduced by Copernicus when the astronomical centre shifted from the earth to the sun.  In this case the child becomes the sun about which the appliances of education revolve; he is the centre about which they are organized."
Then there was the New Math, there's IMP, CMP, CPM, reform calculus, etc.  The curriculum out there is good, meaningful, and amendable to IBL or hybrid IBL.  We've tried to change the system, but have failed in the past, for the reasons that we try one or two changes, but not all the necessary changes.    So we try a few good ideas, but not enough and the ball rolls back down the hill.

Hope vs. Despair:  The pendulum also represents at least to some degree a sense of futility in the enterprise of systemic change.  For sure, if we continue the one-thing-at-a-time approach we keep going back and forth.  Roll the ball a bit, and it rolls back.  However, if we actually view the ball and the hill model for what it is, then perhaps there's a chance that we'll muster the courage to get enough force behind the ball and move it over the hill. It means tackling more than one thing at a time, and doing a lot of hard work on several fronts.  

Easy? No.
Doable? Yes.

Classroom: For instructors there are implications to your everyday life.  Just changing from lecture to students doing group work or presentations at the board isn't a full switch to IBL.  The interaction of IBL content, managing student interactions with each other and with the material, assessment, coverage, getting students to buy-in, etc.  There are several components that need to be addressed for effective IBL instruction.  While this may seem daunting, all the skills are learnable and doable.  Taking your time or taking small steps is a reasonable strategy, but if you change to little or only in minimal ways, the gains will also be minimal.

The upshot for the classroom instructor is to make teaching changes that are systemic changes.  Doing cute activities are nice and useful, but it's better of the course has at least some minor systemic changes.  If you structure your course so that you regularly incorporate inquiry, plan content and instruction for inquiry, and assess (at least minimally) inquiry practices, then those changes, even if small, add up to a lot.

Teaching is system.  Roll the personal ball up to the next level, and you change your the system.  That helps all of us change the big system.

Upward and onward!

Wednesday, October 17, 2012

Umami: Pleasant, Savory Taste

Umami is a loan word from Japanese, which means "pleasant, savory taste."  Examples of Umami are when you drink a soda on a hot, sweaty afternoon, and you say "Ahhh!"  Or perhaps you walking in nature and reach a favorite spot to breath in the fresh air, see the wonderful sights, and take it all in.  Ahhhhh!

The notion of umami applies to teaching.  Instead of Ahhhh that was savory, it's more like an Aha!  "That makes sense!"
"Beautiful idea!"
"Great solution -- I never would have thought of that!"

In math courses where students primarily memorize rote skills and learn procedures developed by someone else, it is hard to provide an opportunity for students to have an Aha moment.  The ideas are dull and foreign.  The emphasis is on getting to answers quickly, and there's little time for unpacking deep concepts and enjoying the experience of thinking about beautiful ideas.

Thinking about or discovering for oneself beautiful ideas can result in Umami.  This is another way to look at authenticity of teaching.  By authenticity I mean that students are doing "real mathematics" and are not just memorizing say Gauss-Jordan elimination.  When students do authentic mathematics that allows them to grow intellectually, that's a good thing.  And if the students buy-in and find the experience of discovery an aesthetically pleasing and fulfilling one, then I believe this is a highpoint in these students' intellectual development.  In IBL classes, the opportunity exists to provide regularly authentic math tasks that engage students in figuring out how things work and why things work.  Doing math, then becomes an enriching, pleasant, savory experience.


Monday, October 15, 2012

Jo Boaler on IBL

First, we're not switching the name of this blog to "The EBL Blog" -- I'd have to change the url, my business cards,...  :)   

But seriously, in this short clip, Jo Boaler and her students make the case for why inquiry.  Jo Boaler is a professor at Stanford University and has written the excellent book, "What's Math Got to Do With It?"

Tuesday, October 9, 2012

Ted Mahavier Talk: Legacy of R. L. Moore Conference, Washington DC, 2011

Ted Mahavier opens the 2011 Legacy of R. L. Moore Conference with this inspiring talk.  Ted Mahavier is a professor of Mathematics at Lamar University, and one of the most experienced and dedicated supports of Inquiry-Based Learning.