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!

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.  

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!

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.

Umami.

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?"

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.