Category: Books

Top 5 Recommended Readings for PBL Teachers Part 2

So, I finally got this done and I’ll continue with the top three readings that I just found extremely useful in my teaching last year.

3. The Innovators’ DNA: by J. Dyer, H. Gregersen and C. Christensen

I rarely recommend books that I have not read yet, but this one is actually on my list to read next so I am recommending it because everything about it just feels right to me.  Again, this is not an education book, but a book that is really for business people.  The research that was done in preparation for writing this book was looking to see what characteristics people who are viewed as transformative innovators in the business world all share.  The authors have come up with five major traits or behaviors that innovators share –

  1. associating
  2. questioning
  3. observing
  4. experimenting
  5. networking

You can read a wonderful summary of this book at this link, but I would highly recommend the book as well.  It is our job as progressive educators and teachers of PBL to teach these skills.  If it isn’t obvious to us already, as PBL teachers, I’ll say it again – that PBL is custom-made for teaching these types of skills which clearly is what this book is stating employers are now looking for.

One thing that I do not read enough of is how PBL encourages the skill of associating.  I write a lot about this in my blog and researched it in my dissertation.  In fact, connection is one of the main themes that came out in my research that students enjoyed about PBL.  The skill of associating is a major skill that is extremely important to innovation and in fact, Steve Jobs in quoted as saying, “Creativity is connecting things.”  Allowing students to practice making those connections themselves is key in order for students to practice their own creativity, especially in mathematics.

2. The Five Elements of Effective Thinking by Ed Burger and Michael Starbird

This little gem, published in 2012, was the focus of Ed Burger’s key note address at the 2012 NCTM Annual conference.  He actually didn’t try to sell the book too much, but focused on the idea of teaching effective thinking (so then, yeah, I went and bought the book – what can I say, he’s a great speaker).  As I was reading through it, all I could think about was how relevant it was to teaching mathematics with PBL.  If every student in a PBL classroom took to heart every one of the five elements that are put forth in this book, the classroom would be so much more effective (as would any classroom).

So Burger and Starbird but forth these five elements of effective thinking:

  1. Understand Deeply
  2. Make Mistakes
  3. Raise Questions
  4. Follow the Flow of Ideas
  5. Change (which they call the Quintessential Element)

So, you might ask – what’s so great about those?  I know this?  Well, it’s not those five that are so great – if you are a PBL teacher you probably are already telling your students these already.  What I think is so great about this book are the pieces of advice that Burger and Starbird give for each of these five elements.  In each chapter, these are not only examples from their own teaching but actual ways to promote each of these elements not only individually but in your classroom as well.  The anecdotes that are shared in the book are not only heart-warming but as a teacher you can see how you can make them useful in your own practice.

The combination of deliberately stating these five (and adding CHANGE as the most important) is really key for PBL.  Students may know that you want them to understand deeply and in order for them to do that they need to raise questions about their own understanding, but if you don’t constantly and deliberately create a culture for them and you in your classroom it is not a message they will receive seriously.

And the best book, that I would highly recommend reading:

  1. A New Culture of Learning, by Douglas Thomas and John Seely Brown

This book, in my opinion, is what PBL is all about.  Whether you teach in a school that uses a problem-based curriculum, uses text books and is trying projects, or if you are just trying to create a more student-centered approach to your teaching – this book is getting at the heart of what is creating a change in our schools nationwide.  It is why there is a huge movement going on with teachers in our nation trying to find something different to do in their classrooms.  Thomas and Brown describe this movement as a shift from a “teaching-centered culture” in our nation’s schools to a “learning-centered culture” which may be the most important shift in education since organized schooling began in the U.S. altogether.

This shift is based on the idea that knowledge is flexible (yes, the idea of Truth with the capital T does not exist – shhhh, don’t tell anyone).  Even in mathematics, the way that we solve problems and even the mathematics that we teach students – which topics are “most important” today- is changing rather regularly.  This has become so much more clear and visible because of not only the Internet itself, but our access to it.  Thomas and Brown suggest that we must be willing to admit that what is most important about education now is not what we teach in schools, but how students learn.  Can a student learn in the collective? Are they able to harness different modes of inquiry?  Do they experiment in their learning? This shift in the purpose of schooling is not really new to teachers but to our society it is major.  Teachers need to learn how to make this switch and articulate the deliberateness of what they are doing in their classroom in order to focus on the shift. (By the way, this also has major ramifications for teacher educators).

 I love the five dispositions that will help construct the new culture of learning (very applicable to a PBL environment!)

  1. Keep an eye on the bottom line (ultimate goal is to improve)
  2. Understand the power of diversity (strongest teams are rich mix of talents and abilities)
  3. Thrive on change (create, manage, seek out change)
  4. See learning as fun (reward is converting new knowledge into action)
  5. Live on the edge (explore radical alternatives and innovative strategies, discover insights)

All of this is so relatable to my own classroom and curriculum.  The more I create problems and experiences that allow my students do have these dispositions, the more I know that I am fostering the “culture of learning” instead of a traditional culture of “teaching.”

So that’s it.  My top 5 list of readings for PBL teachers – please let me know what you think and if you end up utilizing any of these authors’ ideas.  I know that I have been invigorated by these readings and hope that you will be as well!  Have a happy and fulfilling 2014!

Top 5 Recommended Readings for PBL Teachers of 2013 Part 1

Happy New Year!  It’s been a busy end of 2013 for me.  I’ve been doing a lot of reading and catching up with some writing.  So, the New York Times came out with their top 75 Best-Selling Education Books of 2013 and some of them are really great reads and some are just books that are commercially hyped education jargon.  I’ll let you read it for yourself and see which you think are which.  But this inspired me to think about what I would recommend as great reading for PBL teachers in terms of mathematics.  It’s not always easy to get inspired to continue with PBL so I am always on the look-out for good reads and things that might help me to find ways to motivate students in the classroom.  I also hate those lists from articles that seem to have all the answers but then when you read them nothing is ever really black and white like “To Flip or Not to Flip: that is the Question” or “5 Resolutions to Modernize Your Teaching For 2014” or “Top 100 Tools for Learning in 2014” – geez, does anyone just write about one thing anymore?  Or even give critical analysis of why these are the reasons to flip, or an argument as to the top 100 tools – anyone can make a list.

Including me!  So here goes nothing – well, I mean something.  I tried to put together some good reading that emphasizes the skills that are needed for working with students in a problem-based classroom.  One of the things I hear most from teachers is not necessarily how to work with the curriculum, but how to get students working with each other and how to foster the type of classroom community (curiosity, openness and risk-taking) that is needed in order for students to want to be engaged.

5. The Mistake Manifesto: How Making Mistakes Can Make Us Better by Alina Tugend, 2011.

I first came across Tugend’s writing when I read her Op-Ed piece in the NY Times while ago, but this essay on making mistakes says so much about Tugend’s great attitude towards how mistakes are not only helpful, but are a wiser and more powerful way of learning.  She says that “we do single-loop learning when we need to do double-loop learning.”  I love that and I believe that PBL’s  method of returning to ideas in its scaffolded and multi-topic approach often allows students to revisit ideas multiple times.  Tugend talks about how most of our society creates a fear of making mistakes because we have this idea that we aren’t supposed to make mistakes.  This is in turn makes us all risk-averse unfortunately and only allows the most unstructured students and learners to be creative innovators.  This is what we have to turn around.  Her manifesto doesn’t necessarily tell us how to do this, but it’s a wonderful argument for why we should.

4. Flow, by Mihaly Csikszentmihalyi, 1990

This book’s original intent was to investigate the psychological experience of happiness, however this past year it became connected for me to the process of problem-based learning.  OK, so this book is not from 2013 – or even from the past few years, but what happened in 2013, is that I read an article that sent me to this book.  The article was called “The Problem-Based Learning Process as finding and being in Flow” by Terry Barrett and it discussed the concept of ‘flow’ (from Csikszentmihalyi’s book) and compared the PBL process (the discourse that occurs, the exchange of ideas and that learning process itself) to the optimization of creativity that occurs in the ‘flow’ process.  In this book, Csikszentmihalyi defines ‘flow’ as “the state in which people are so involved in an activity that nothing else seems to matter.  The experience itself is so enjoyable that people will do it even at great cost, for the sheer sake of doing it.”(Csikszentmihalyi, p.4).  Wouldn’t that be great if that’s the way students viewed learning?  One way to see it is like this:

 

(Barrett, 2013)

The idea being that the state of flow in learning comes when the optimal problem or activity is presented to students such that the difficulty and time or skills given keeps their interest long enough to minimize anxiety and maximize love of learning and the return on their learning (reinforcement of confidence, efficacy, enjoyment, agency, etc.).   A lot of the book is based on the idea of the state of flow helping to create the optimal state of happiness so it might not relate directly to teaching, but I highly recommend the last two chapters which are entitled “Creating Chaos” and “The Making of Meaning” which can be directly translated to the PBL classroom and are highly useful for the PBL teacher looking to see how you can create the state of flow for your students.

Tomorrow I will catch up with numbers two and three! (hopefully get you #1 as well)

Why I disagree with Mr. Kahn

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I have to say that I am not usually a controversial blogger – I’ll just put that out there right away.  However, I am so frustrated with the conversations, blog posts and articles that are zipping around the blogosphere about online learning, MOOCs and Khan Academy that I have to say something about it as a teacher, teacher educator and responsible learner, myself, about education theory.  I have taught online classes, taken online classes, used open source materials for my classes and definitely promote the idea of equal “world-class education for anyone, anywhere.”  However, I have yet to see how that quality education occurs online and especially the way that it is promoted in Salman Khan’s book, The One World Schoolhouse: Education Reimagined.

Now let’s just put something else out there right away – it might be that I am frustrated by the fact that he has no background experience in education (which he admits – “I had no teacher training”) and I am offended that he is speaking out of turn speaking as if he does.  For example, he says “There’s an old saying that ‘life is school.’”  Hmmm, I wonder who said that? And I’m not sure that’s really the right saying.  Or it could be that he is attacking the very discipline that I am working so hard to change – mathematics.  I totally agree that there is a lot that is wrong with the way mathematics is taught in the U.S.  But NOT going all “rogue” and working against the people who have already done some research on the subject and know a little about which they talk, might be a good place to start.  There are many things that Mr. Kahn discusses in his book that he seems to purport as novel ideas like Mastery Learning, Flipping the Classroom, etc. that are not his ideas.  So let’s pretend that the fact that he wrote a book of concepts that seem to be a compilation of educational reform ideas that have been around for a while is not what really annoys me.

What really gets my goat, if I seem to have his idea right, is that he is advocating for “a free world-class education, for anyone anywhere” but I’m not really seeing how this is going to happen.  He advocates for the use of the Khan Academy for mastery learning in the classroom (in a school system) where the students watch the videos and then come to class and do “projects” with each other in the “one room schoolhouse.”  I actually agree that this is a wonderful learning scenario that promotes creativity, independence in learning and individualized lessons for students of all ability levels.  Besides the huge government and system-wide testing restrictions that are currently in place and teachers’ current use of assessment, it would be very difficult (but not impossible) to change this system.  Kahn very naively writes a 5-page chapter on Tests and Testing, which again is nothing new, on the evils of standardized testing and why they don’t really tell you anything about students’ knowledge.  His “one room schoolhouse” is an idealistic utopia of learning for someone who has never been in the classroom and dealt with classroom management, assessment, review or planning of these open-ended projects.  I do believe that a great deal of teacher training would need to be reformed and reviewed in order for something like this to happen and before any school thinks of moving to a model like this they should think wisely about the ways in which teachers are ready to handle the change of the classroom culture and how they are ready to deal with it.  Students will still have questions about the material and will all be at different places in the content and the projects, which will probably demand more planning from the teachers (which again, is not a reason not to flip the classroom, but a necessity of which to be aware). I found what he put forth as the ideal classroom short-sighted and with many limitations.

Secondly, what about the “anyone, anywhere” Idea? Even if children in third-world countries have access to internet-ready computer to watch these videos, where are the teachers and schools to have them do the “world-class” learning with these group projects?  Where is their utopian learning environment?  I am confused about how watching videos online is giving them a “world-class” education (although I could see how it was free if Mr. Gates donated a bunch of computers and Internet access, etc.).  Mr. Kahn also realized that “teaching is a …skill – in fact, an art that is creative, intuitive, and highly personal…[which] had the very real potential to empower someone I cared about.”  Yes, Mr. Kahn, that’s what teaching is all about.  Teaching is about, as you said, “genuinely [sharing  your] thinking and express[ing] it in a conversational style, as if I was speaking to an equal who was fundamentally smart but just didn’t fully understand the material at hand.”  How is that supposed to happen for someone sitting alone watching a video?

In the NY Times article, The Trouble with Online Learning, Mark Edmunson wrote:

“Learning at its best is a collective enterprise, something we’ve known since Socrates. You can get knowledge from an Internet course if you’re highly motivated to learn. But in real courses the students and teachers come together and create an immediate and vital community of learning. A real course creates intellectual joy, at least in some. I don’t think an Internet course ever will. Internet learning promises to make intellectual life more sterile and abstract than it already is — and also, for teachers and for students alike, far more lonely.”

This is the heart of Relational Pedagogy, that the interhuman connection between people is what constructs knowledge and the trust, authority, and value of perspective that is shared and given to each other is just as important as the content that is exchanged – most especially in mathematics, it’s just taking us a lot longer to figure this out, Mr. Kahn.

What’s the “P” in PBL?

One of the issues I talk about a lot with people who are interested in Problem-Based Learning is the “continuum” of integration that I use to tell people how they can implement it in their classroom. How do you want to incorporate the teaching with problems in your classroom? Magdalene Lampert wrote a wonderful book called Teaching Problems and the Problems with Teaching in which she chronicled her journey of teaching a fifth grade classroom for a year with problems (it’s an awesome book, BTW). The way in which you use the problems, the pedagogy you use, and the classroom community you set (the lack of hierarchy, the authority you allow the kids to have, the safety of the risk-taking, etc.) is all hugely important parts of the PBL environment. I found another “continuum” created by someone name Peter Skillen and a colleague named Brenda Sherry. Mr. Skillen, a lifelong educator from Toronto, Canada, doesn’t claim to be an expert in PBL, but has extensive experience in the world of education and has great ideas. Check out his blog if you have time.

He created a wonderful Continua to Consider for Effective PBL which I believe is definitely worth sharing. Although his “P” in PBL is Project, I believe his Continua (since there is more than one scale) is just as applicable to Problem-Based Learning. It reminds me a great deal of what I use in terms of implementation. He also has stated that anyone who would like to add categories should feel free, and I might actually work with that. His categories to consider are

Trust
Questioning
Collaboration
Content
Knowledge
Purpose

These are amazing to start off with and I would probably add a few more to those including authority (although, I think this is what he’s getting at with trust and locus of control) and perhaps also change the “collaboration” one a bit. It is pretty tricky – this idea of interdependent, independent or dependent learning – dependent on what? The teacher, other students, a textbook? Very complex ideas at stake here. Different types of PBL are being considered and in different frameworks. But what he and his colleague have put together is amazing start to an important discussion.

In fact, it’s really important to decide what you mean my “PBL” is? Even on the public shared website for the American Education Research Association Special Interest Group for PBL there is a “Statement on Nomenclature” about what PBL might be interpreted as meaning. There is an acceptance that there is more than one, and in fact many, meanings for the acronym “PBL” and what one person thinks it is may not be the same as another. I am very open to the understanding that when some contacts me about their own school’s interest in using PBL, I have many questions for them before we start talking about implementation.

Not to belabor the great article by David Jonassen that was published in the Interdiscipliary Journal of Problem-Based Learning, (see my other blogpost Worked Examples in PBL) but I really like the distinction he makes between Project-Based and Problem-Based Learning. What it comes down to for him really is the authenticity of the problem. It’s not really about how many, what kind, or how big the problems are that you have the students do. What it is about how did you plan (or not plan) the problems. He is calling it the difference between “emergent authenticity” and “preauthentication.” (definitions by Jonassen (2011). Supporting Problem Solving in PBL. Interdisciplinary Journal of Problem Based Learning 5 (2)).

Emergent Authenticity is when “problems occur during practice within a disciplinary field by engaging in activities germane to the field.” In other words, this is more like when you pose a problem to the students that is something that a mathematician might encounter in real life and an answer is truly unknown (like in real life!!) and they are engaging in that activity of not really knowing that answer and grappling with finding the tools and resources that they need to move forward to find a solution. That is when the authenticity of the problem (or project) is actually emerging as authentic.

Preauthentication is “analyzing activity systems and attempting to simulate an authentic problem in a learning environment.” In high school mathematics classes, this when the teacher knows they want their students to learn something specific from engaging in a specific type of problem or series of problems (mostly like what I do in my curriculum, honestly) and they “set up” a problem-solving situation, but make the kids think that it’s novel. The learning experience has already been analyzed by the teacher and the teacher is giving the students the authority to do the problem at their own pace and draw conclusions, struggle on their own. However, there is some control because it is really only a “simulation” and the teacher actually has more information that can be helpful in terms of learning outcomes, etc. The authenticity has already been “preauthenticated” so that it simulates the experiences of a mathematician as much as possible, but still has the learning outcomes, goals or desired content objectives that might need to be fulfilled.

Which is better? I don’t believe there is a “better”. I believe there is what works for your school, pedagogical beliefs, student audience, teaching style, etc. All of these wonderful categories are what must be considered when you and your department start on the journey towards incorporating PBL into your curriculum. There are many great choices to be made, but it is a long journey and cooperation with lots of reflection are definitely needed. So much to consider.

 

Being sterotyped?

My daughter is starting middle school this fall and is extremely anxious about so many things that new sixth graders worry about over the summer. She’s on of those kids, though, that go to extremes – you know the type – the ones who love to shop of school supplies the first week of August, have their planner written out the second week of August, etc. These attributes only endear her to me even more (in fact, she reminds me so much of myself), so to ease her worries we went out to our nearest bookstore and she bought a book entitled “A Smart Girl’s Guide to Starting Middle School”, which I thought would give her something to read and something to help ease her worries. This it definitely did – kudos to the authors and publishers for helping high-anxiety tweens across America ease their worries with some pretty good advice actually on handling the peer pressure, rough schedule and other worries that come with the onset of middle school.

However, as I was reading through this book, I came across a section called “Teacher Types” which I, of course, read with interest. The authors of this guidebook broke teachers down into four different types, but the one I was most struck by was the one entitled “The Freestyle.” The teacher-type was the quintessential “free-love” type teacher stereotyped to let the kids do whatever they want in the classroom. The style is described as this: “Loves to brainstorm. Teaches by asking questions and fielding answers from the class. Explores different ways of doing things.” I stopped reading as a muscle spasm hit my stomach. “Oh my god, that’s me,” I thought. “But I’m not freestyle?” I got very defensive as I read on…”Pros: Lets students work on their own. Gives lots of feedback and support.” Oh, OK, yeah I do that. (feeling a little better) “Cons: “Letting everyone have her say can eat up class time, leaving some material uncovered.”

Once again, my heart started pounding…this is me. My students have never described me this way, (at least to my face) as a “free for all” teacher that let’s the conversation go wherever it may, but I can remember times when students complained that we had to go back to cover something that we did not have time for. I became very defensive of this small book that I felt was stereotyping me in a way that I was not appreciating. However, thinking more about this, I realized that over time (and from observing many teachers that have chosen to either use discovery-based, discussion-based or problem-based learning in their classrooms) it is all too easy to become too “freestyle” and allow the students to have too much independence. From talking to one of the teachers that I have trained over the past 6 years, she said to me, in all honesty, I think it’s harder to teach with PBL than in a lecture classroom because you have to be prepared, but prepared in a very different way. You have to be prepared for the unexpected.

Being “freestyle” does not mean letting the students’ ideas take over. The teacher as the scaffolder of questions must know in their mind the direction in which to move the discussion and when and how to do this without pushing too hard as too ruin the delicate house of cards that is being construction team of students. It may appear “freestyle” because it is not what students are used to, however, the teacher is doing a great deal of work. The other way in which the teacher must do a great deal of work is in what this book does make note of and the teacher must:

1. give lots of feedback on student comments and ideas
2. encourage and value ideas and insights
3. make note of time use and if time is short, change assignments regularly (the internet is great for this)
4. create a safe classroom community for students to share (must be a priority)
5. make summaries of constructed knowledge or have students summarize

If all of this happens, it is difficult for students to take from the classroom that it is “free for all” and they can leave their class for the day feelings content for the moment – and if they don’t for one day, that’s OK too. What I’ve learned from all this is is that the advice in that book pointed out the truth about being “freestyle” in some ways, but that the preconceived notions about that stereotype (or any teacher stereotype) really needs to be viewed from different perspectives. I’d hope that a student in my PBL classroom would at least see it that way.