Tag: creativity

Looking for the Teacher of Grit

I’m in the middle of working on organizing my courses for the Exeter conference in about a week and something I’m really struggling with is trying to articulate to teachers how they can impart to their students this idea of grit in the PBL classroom.  So I started doing a little research online (besides looking through all of the books I have read on the subject).  I took Angela Duckworth’s Grit Test at her lab’s website (got a 3.63 grit score- grittier than 60% of other U.S. citizen’s my age…hmmm).  Then I started reading some blog posts of other PBL teachers and writers like here on the MAA’s blog which is trying to encourage math students to tinker with problems or here which is more of an all-purpose index of resources to teaching grit. There was this wonderful video of a teacher in NH who created a neat grit curriculum for her 5th grade class (with Angela Duckworth too)

John Larmer of the Buck Institute wrote a really nice blog entry on how project-based learning fosters grit in students. I even found a nice video of Po Bronson, author of Nurture Shock (the book about how parents have failed kids because we don’t let them fail).  This is a short video of how Mr. Bronson believes we should be allowing kids to fail these days.

He says (in so many words) that if kids grow up without learning how to fail, they will become risk-averse.  This is what I am finding in my classroom at times.  The risk-averse kid combined with the fixed mindset kid, combined with the “I-have-to-get-into-college-and-make-my-parents-happy” kid makes the PBL classroom very difficult when you are trying to get them to take risks and be creative.  Add that to the classroom culture that they have been used to for the first 9 years of their education in the U.S. and sadly, it makes for a tough place to foster the teaching of grit.

In fact, on my most recent course evaluations I asked students what they found most challenging about the class and the two pieces that tied for first place were journal writing and

“having to be vulnerable and make mistakes in front of my peers.”

I so want to change that and I always thought that I created a classroom atmosphere where students were comfortable.  I did all of these things that the professionals are suggesting on these websites:

1. modeling risk-taking and making mistakes myself
2. talking about growth mindset regularly
3. ask them to write about positive experiences when they are proud of themselves
4. using class contribution feedback forms (self-report and analysis of class contribution sheets)
5. using strategies where students think of a wrong way before we talk about the correct solution method together.

But somehow, even at the end of the year, their fear of being wrong in front of each other (and me, some commented) is still predominantly what they say challenged them.  So I would say to Po Bronson, where is the teacher of Grit?  What is the secret?  How do I make it so?  Is there a time when it’s too late for some kids?  Most of what I’ve seen on the internet is teaching grit to elementary school children – does the fact that I am teaching high school kids make it any harder?

I finally found this great Prezi created by a teacher named Kristen Goulet which, I know, is geared towards elementary school kids, but I think I could find a way to direct it towards older students.  The idea of having them ask themselves whether their self-talk is “because of me” or “because of other” and whether it is “permanent (i.e. fixed mindset)” or “temporary (i.e. growth mindset)” definitely would help them realize how much of the way the deal with adversity is flexible.  It also helps with seeing how to have a more realistic and optimistic view of a certain situation (and is kind of hard to argue with).

So, I’m still in search for the best practices to teach grit (and apparently so is Angela Duckworth – she admits this in her TED talk), but now I know that it is way more complex than just following a certain number of steps – it has so much more to do with a student’s socio-emotional state of mind. Vicki Zakrzewski’s article “What’s wrong with Grit?” is probably the closest I got to agreeing with someone’s assessment of grit and how to teach it.  I know that I am really good at letting kids know what is important to me and doing that modeling that is important as well.  Undoing what has happened to them before they got to me is a tall order, but I’m not going to stop trying.

PBL & James and the Giant Peach: Try looking at it a different way

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James Henry Trotter: “When I had a problem, my mum and dad would tell me to look at it another way.” (Roald Dahl)

I’ve always thought that PBL fostered creative problem solving as opposed to memorization of pneumonic devices.  One of my students today proved me right when I gave a “quick quiz” on the use of the idea of tangent.  We had discussed tangent in class for only two days and in two ways – one as a slope of a line with a given angle and from that idea we discussed how it could be interpreted as the ratio of the sides of a right triangle (if you put a right triangle under the line).

Of course, during this conversation some student who had studies the ever popular SOHCAHTOA before mentioned this in class and told everyone that they had just memorized this and that’s how they knew it.  I said that’s fine but I’d like them to try to think about the context of the problems and see if this helps make any sense of it for them.

So today on the quiz one student was attempting this problem – very basic, very procedural, not at all something that I would call atypical of a textbook-like problem on tangent.

A bird is sitting on top of the Main School Building and looks down at the end of the baseball field with an angle of depression of 4 degrees.  If the MSB is 87 feet tall, how far away is the end of the baseball field?

So the student attempts to create a ratio with the sides of the triangle and even sets it up correctly.  However, because she does the algebra incorrectly, she gets an answer that is extremely small 8.037 x 10^-4.  In fact, during the quiz, she calls me over and asks what it means, she doesn’t remember scientific notation and starts getting all anxious because we didn’t do anything like this in the problems in the previous two days?  How can the answer be that small?  I said well, you better go back and think of something else.

In most classes, a student in this situation might stress out, try to do the problem over again with the limited perspective of “TOA” or of just viewing the right triangle in one way.  However, because this students had also learned other students’ perspectives of tangent as slope of a line what this girl did at this point was to see it from a different way.  Interestingly, this is what she did.  In an alternative, albeit confusing way of writing the equation of the x-axis, she wrote y=0x to represent the ground.  Then she found the tangent of 4 degrees and used that as the slope of a line.  She put the bird at the point (0,87)

She writes the equation y= – (tan4)x + 87 and explains that this is the equation of a line that makes a 4 degree angle with the x axis and has a y-intercept of 87.  Then she realizes that if she finds the intersection of that line and the x-axis, she would find how far the building is from the baseball field.  This is what she does and uses her graphing calculator to get the right answer.

When she hands in this quiz to me, I half expected that tiny little answer as her distance to the baseball field.  But what I got was an amazingly inventive solution and a correct answer.  With a problem that didn’t make sense, she looked at it a different way and ended up getting the right answer.  It was amazing what changing your perspective could do and this was great evidence that even under pressure, the habits of creativity and connection were paying off.

Experimentation, Creativity and Problems

Returning from vacation is always a tough time, but the other day in my honors geometry class, I decided to present them with a problem that had at its heart the Pythagorean Theorem – which we’ve been using since the beginning of the year – and I wanted to see what they would do with it.  So I showed them this video I found on line.  It poses an interesting question regarding buying android tablets and what size you might want.  Before we watched it, I had them search online to compare the prices of some well-known tablet brands and see if there was a major difference in their 7 inch size tablet vs. their 10 inch size tablet.  We came up with some prices that looked like this:

We talked about how, in most cases the price of the 10 inch tablet was about 1.5 or 1.6 times the price of the 7 inch tablet.  Was that reasonable?  Did it make sense?  10:7 was only about 1.4.  So then we watched the video:

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I posed the question to them, “Do you think what this guy is saying is true?  Is the 10 inch table really twice as big as the 7 inch? If so, what evidence can you give to say that it is and how can we justify whether or not any of these tablets really are?”

Great conversation ensued.  I was so excited.  One group of students started trying to find numbers that the dimensions of the two tablets could be.  Of course, the first thing they assumed was that the one with the 10-inch diagonal screen would have width of 6 and height of 8 (don’t we all just love those Pythagorean Triples?) but then they realized when they did that there could be so many other triangles that could have a hypotenuse that was 10 as well.

Another group started trying to compare the areas of the screens to see if they could find dimensions of two tablets that actually had one area that was twice as big as the other one (that kept the diagonals 7 and 10).  This was an interesting group because they had thought through the concept of “twice as big” but hadn’t made the jump to what it would mean for one to be that much bigger.

I was then called over to a group where a girl was trying to explain her idea of how to make two 7 inch tablets fit into the 10 inch tablet.  I’ll call her Tracy.  Tracy said something like this to me: “If ttwo small ones fit into one of the big one, that would mean that the height of the big one is twice as big as the width of the little one” and she proceeded to go up to the board and draw a picture like this:

This started everyone talking.  It actually became really cool for a while.  They soon realized that you could let the dimensions of the smaller tablet be w and 1/2h while the dimensions of the bigger one were h and w.  This combined with the Pythagorean Theorem allowed them to solve a quadratic system of equations to find the dimensions of both tablets, if it were true that the 10 inch tablet were truly “twice as big” as the 7 inch. (I believe the 10 inch tablet had to be 8.24 inches by 5.65 inches approx).

We were unable to confirm all of this by finding dimensions online so if anyone can do this, please let me know!  But what was the most amazing part of this problem solving exercise for me and my students was the engagement that I observed from their interest in the problem and their own motivation to come up with a way to justify or debunk the claim made in the video.  We are going to write up some paragraphs about their findings and present them to each other next time we meet.

I was very proud of the way they were not afraid to experiment with different ideas initially and how Tracy moved through her own ideas and took risks with the group and those around her, eventually getting her and others to the path that made sense to many of them.  It was really a group effort and worked well.  If anyone else tries this, please let me know how it goes.

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!

Minimizing Shame in the PBL Classroom…and maybe Daring Greatly?

I recently read a blogpost by one of my favorite authors, Brene Brown, of TED talk fame, and the author of a great book about vulnerability called Daring Greatly.  In her blogpost Brene wrote about some reactions to a comment she made on Oprah Winfrey’s Super Soul Sunday show where she talked about shame in schools about which she received a great deal of criticism in the blogosphere and on twitter.

I kept reading as I was shocked that anyone would be offended by anything that Brene Brown could say – especially teachers.  She has always been extremely inspiring and very supportive of teachers – as a teacher herself, her book, Daring Greatly, has a whole chapter on how schools can support a community to come together around vulnerability and become closer and foster creativity and innovation in this way.

However, she talks about the research that she has done about learning and teaching.  She says,

“As a researcher, I do believe that shame is present in every school and in every classroom. As long as people are hardwired for connection, the fear of disconnection (aka shame) will always be a reality. ..Based on my work, I do believe that shame is still one of the most popular classroom management tools.”

Think about it.  When you talk to adults about their memories of school, and specifically math classrooms, many people will tell stories of being embarrassed or humiliated about getting something wrong, about feeling less than adequate or unworthy of being in the class they were in.  Even if the teacher was not doing anything deliberate, if a student has the courage to answer a teacher initiated question and get it wrong, the response that is given can make or break their self-worth that day.

I’ve been giving this a lot of thought in the context of the PBL Classroom – How are we supposed to be teaching students how to take risks and not be afraid to be wrong and make mistakes in their learning if they have this fear of shame that is so deeply entrenched in our culture?  Especially in mathematics classrooms, how are we supposed to undo so many negative experiences that may have affected a student’s ability to allow themselves to be vulnerable and learn in this way?

PBL relies on the fact that a student is willing and able to make connections and conjecture regularly – numerous times in a class and on their own during “homework” time.  Being wrong and uncertain is really the norm and not the anomaly in this classroom.  As October rolls around and I hear more from students (and parents) about the discomfort they are feeling, I really do understand how different this is for everyone.  However, I do think we need to rely on the fact that students can be resilient and strong when pushed to try new things and to learn in a way that is good for them.  It is just that resilience that will make them better leaders, learners and more creative in the work force later on in life.

In talking to some students recently, I asked them where they thought they would learn more, in a classroom where it was laid out for them what they had to do or where they had to make choices about methods and sometimes it would be unclear.  I could tell that one girl was really struggling with that question.  She knew that it would be easier in the other classroom, but also knew that she would learn more and wanted to stay where her learning would be more effective.

What can I do to help this process go more smoothly?  Make sure that they know that I am working hard NOT to use shame as a classroom management tool.  That I am sincerely interested in the mistakes that they are making and how it is helping their learning.  I want them to grow from their errors and misconceptions and find ways to use those to their advantage.  I want to add to their self-worth not only as a math student, but as a problem solver in every way.

As Brene Brown says:

“I don’t believe shame-free exists but I do believe shame-resilience exists and that there are teachers creating worthiness-validating, daring classrooms every single today.”

I can be truly aware of the language that I use and the questions that I ask in order to make sure that everyone’s voice is heard and that my students know that I want to hear their ideas.  It’s really the only way to get them to Dare Greatly!

PS – Check out the wonderful quote by Teddy Roosevelt that I use in my PBL classes about Daring Greatly that Brene Brown used for the title of her book.

Get Comfortable with Uncertainty: A Short Dialogue

And so it begins.   The students are flustered. The emails are coming at night.  The faces stare at me, scared to death.  Although I repeat numerous times, “You do not have to come to class with each problem done and correct” students are totally freaking out about the fact that they can’t “do their homework” or they can’t “get” a certain problem on the homework.  No matter how many times I attempt to send the message the first few weeks about how unnecessary it is to come to class with a problem complete or an answer to show, students feel the need.

Tomorrow I am writing on my large post-it notes in HUGE capital letters, “Get comfortable with uncertainty because it’s not going anywhere.”  Every year about this time, I give the speech about how my homework is extremely different from any homework they have probably encountered in math class.  These are not problems that you are supposed to read, recognize and repeat.  They are there to motivate your thinking, stimulate your brain and trigger prior knowledge.  In other words,  you need to be patient with yourself and truly create mathematics.

Today I met with a young woman who I thought was about to cry.  She came and said, “I can’t do this problem that was assigned for tomorrow.”  Here’s how the conversation went:

Me: Why don’t you read the problem for me?

Girl:  Find points on the line y=2 that are 13 units from the point (2,14)

Me:  Ok, so show me what you did. (she takes out her graph paper notebook and shows that she graphed the line y=2, plotted the point (2,14)).  Great, that’s a great diagram.

Girl:  But it didn’t make sense because in order for it to be 13 units away, it had to be like, diagonal.

Me: Huh, what would that look like?

Girl: (drawing on her diagram) There’d be like two of them here and here.

Me; yeah?

Girl: But it can’t be like that….

Me: yeah? Why not?

Girl: Um…cause it wouldn’t be a straight distance.  I think..

Me: Is it 13 units away from (2,14)?

Girl: yeah, I think so…

Me: Hmmm….how far is (2,14) from the line y=2?

Girl:  Oh that’s easier – it’s like 12. ..Oh My gosh..it’s like a hypotenuse….and the other side that I don’t know is like the a and the 12 is like the b.  I can just find it.  Oh my gosh that’s so easy.  And the other one is on the other side.    Why didn’t I see that?

Me:  Well, you did…actually….

Girl: well, after you asked me that question…

Me: yeah, but eventually you’ll learn how to ask yourself those questions.

 

And they do….it’s just the beginning of the year.  We have to give them time – time to look into their prior knowledge as a habit, time to surprise themselves, time to have those moments, time to enjoy the moment and revel in the joy and courage and disappointment.  It’s all a part of the breakthrough that is needed to realize that they are creative and mathematics needs them to be.  It’s amazing and it’s worth it.

Teaching Students to Become Better “Dancers”

So the other day I read a tweet by Justin Lanier that really sparked my interest.

 We all know the scenario in classroom discourse where a student asks a question – a really great question – and you know the answer, but you hedge and you say something like, “That’s a great question! I wonder what would happen if…”  So you reflect it back to the students so that they have something to think about for a little while longer, or maybe even ask a question like “Why would it be that way?” or “Why did you think or it like that?”  to try to get the student to think a bit more.  But what Justin, and the person who coined the phrase “authentic unhelpfulness” Jasmine Walker (@jaz_math), I believe were talking about was hedging because you really don’t know the answer – sincere interest in the uniqueness of the question – not because you’re so excited that student has helped you move the conversation forward, but because of your own excitement about the possibilities of the problem solving or the extension of the mathematics.

I think what got me so excited about this idea was how it connected to something that I was discussing earlier this summer with a group of teachers in my scaffolding in PBL workshop in late June.  In a PBL curriculum, the need to make sure that students have the right balance of scaffolded problems and their own agency is part of what Jo Boaler called the “Dance of Agency” in a paper she wrote in 2005 (see reference).  My understanding of this balance goes something like this:

(c) Schettino 2013

So initially, the student is confused (or frustrated) that the teacher refuses to answer the question although you are giving lots of support, advice and encouragement to follow their instincts.  The student has no choice but to accept the agency for his or her learning at that point because the teacher is not moving forward with any information.  But at that point usually what happens is that a student doesn’t feel like she has the authority (mathematical or otherwise) to be the agent of her own learning, so she deflects the authority to some other place.  She looks around in the classroom and uses her resources to invoke some other form of authority in problem solving.  What are her choices?

She’s got the discipline of mathematics – all of her prior knowledge from past experiences, she’s got textbooks, the Internet, her peers who know some math, other problems that the class has just done perhaps that she might be able to connect to the question at hand with previous methods that she might or might know how they work or when they were relevant – that discipline has had ways in which it has worked for her in the past and lots of resources that can help even if it may not be immediately obvious.

But she’s also got her own human agency which is most often expressed in the form of asking questions, seeing connections, drawing conclusions, thinking of new ideas, finding similarities and differences between experiences and thinking about what is relevant and what is not.  These pieces of the puzzle are not only important but a truly necessary function of the “dance of agency” and imperative to problem solving.

Interweaving both of these types of agency (and teaching kids to do this) have become more important than ever.  Yes, being able to use mathematical procedures is still important, but more important is the skill for students to be able to apply their own human agency to problem and know how and when to use which mathematical procedure, right?  This “dance” is so much more important to have every day in the classroom and if what initiates it is that deflection of authority then by all means deflect away – but the more we can “dance” with them, with “authentic unhelpfulness” and sincere deflection because we need to practice our own human agency, the more we are creating a true community of practice.

Boaler, J. (2005). Studying and Capturing the complexity of practice – the Case of the ‘Dance of Agency’

So How Do We Shift Gears?

OK, OK, I get the idea – not everything on the Internet is true and, for sure, not everything on the Internet is meaningful or helpful.  Since April of this year I have started following a bunch of people on Twitter (before that I really didn’t even know what it was or care) and thought that there were so many people out there that I wanted to learn from.  I would read other people’s blogs and try my best to think about what I had to learn from others. Mind you, I know I am definitely not the god of teaching, that’s for sure, but many of the things that are written out there – should I guess – with the hope of being “inspirational” or meaningful to others, I find less than helpful.

One site that I have really enjoyed reading which often has some great links and blogposts is Mindshift.  But they just tweeted this blog entry that cited an article about creating a business that fosters creativity.  OK, I see the connection to education, but honestly, it is a very different machine.  Kids and adolescents have a very different mindset than adults who are out there making money.  Not to mention the consequences of risk-taking in the classroom vs. risk-taking in the office have the potential for being very different.  (Assessment for grades has a different meaning possibly for a 13-year-old mind than brainstorming on the job, vs. assessment for a salary raise, etc for an adult who we hope can handle the pressure a little more.)

Then the blogger writes two short paragraphs at the end about how schools are just “incurious and risk averse” places.  Basically stating that schools don’t ever allow students to practice risk-taking or mistake making at all:

“Too few schools are incubators of curious and creative learners given their cultures of standardization, fear, and tradition. No doubt, external pressures exist that drive that culture. But if there ever was a time to shift gears, this is it. “

No doubt…sadly, our blogger, Will Richardson doesn’t really give us any advice on what to do about it….except, to do something about it. (Admittedly, he may have written something someplace else that I missed.)  And I don’t want to single out Mr. Richardson – I find tweets and blogs like this all day long – “Exploration, inquiry & problem solving are powerful learning mechanisms…” or “asking good questions and promoting discourse is an integral part of teaching and learning”…. Hmmm, well let me think about ways in which we can talk to teachers  in terms of mistake making and risk-taking:

  • Blogpost on making mistakes and classroom activity tied to Kathryn Schultz’ TED talk On Being Wrong
  • Discussion about article “Wrong is not always bad” with teachers
  • Modeling risk-taking in Problem-Solving in my course at ASG conference in June
  • Discussion of Relational Pedagogy to foster Risk-taking
  • Using a PBL curriculum to foster mistake-making and communication

I found that many teachers that I work with and who contact me are entirely dedicated to changing the culture of the mathematics classroom in the U.S. and making it (as Mr. Richardson writes) an “incubator of curious and creative learners.”  We need to make changes to our curriculum, our classroom relationships, our classroom culture and the authoritarian hierarchy that traditionally is prevalent in our mathematics classroom.  Students need to be able to feel safe enough, from judgment, alienation and failure to make those mistakes while learning.  We, as teachers, need to begin the discussion with each other about how to move forward with these initiatives and make sure that student voice is heard in the mathematics classroom as they question each other and us, the teachers, with true questions – ones we may not be able to answer.  These are the important aspects of creating curious learners who make mistakes and learn from them.  But we, as the adults in the room have a responsibility to let them feel safe in doing that.

I think teachers are aware of the fact that it’s time to “shift gears” – to make the classroom more conducive to students working together and taking chances.  There are so many subtleties to making this shift, however.  Students who need to shift, parents who are not used to that, assessment changes to be made – the list goes on and on.  I am doing what I can to help people with this conversation.  The pedagogy of relation (I believe) is at the heart of all of this – keeping in mind that in order for people to be vulnerable and make mistakes, we need to consider the interhuman aspect of learning.  In a classroom where this connection has for too long been typically so acceptably removed, it will take a lot of work to make this big “gear shift” but I’m up to it – bring it on!

Be the Change You Want to See

I just finished listening to a great “blogcast” that Tony Wagner gave as an interview for Blogtalkradio about his new book “Creating Innovators:The Making of Young People Who Will Change the World.” Kind of a neat idea for a book in which he has done some great research looking into how some new ideas got started by young people, how their creativity was fostered in their childhood, parenting and education, etc.  Definitely worth taking a listen to.

Listen to internet radio with Steve and Mary Alice on BlogTalkRadio

One of the things that Prof. Wagner talks about in his interview is the idea of fostering the creativity that leads to innovation.  As he spoke to these great innovators that he interviewed, they could all name at least one teacher in their career who had a “significant impact” on their learning.  Interestingly, the characteristics of that teacher were often very similar, Wagner said.  They were known for encouraging collaboration and often assessing it, creating a classroom that was often interdisciplinary and problem-based (of course) and empowered his or her students to be creative in their problem-solving and make mistakes.  Why is this not surprising?  To all of us who strive to foster the practice of creativity and hope to allow our students to become innovative and original thinkers, we have known that these are the values that we should uphold in the classroom. I’m so glad that Wagner did this great research and wrote this wonderful book.

However, we also know the realities of the limitations that many of us teachers have that come with the system within which we teach.  I have spoken to so many teachers from around the country who, with all good intentions are striving to make their classrooms more problem-based and encourage creativity.  They are truly trying to be the change they want to see in mathematics education today.  But the fear of standardized testing that is not assessing these values, affecting their evaluations or public awareness of parental or administrative dissatisfaction or vocal disagreement with these goals, needs to be balanced with a teacher’s desire to move ahead.  Limitations of a teacher’s time, energy and their own creativity keep them from being able to proceed without support from like-minded colleagues and leaders in their district.

At the end of the interview, Prof. Wagner talks about his move from the Harvard GSE to his new position in the Technology and Entrepreneurship Center at Harvard.  He says something like he’s found that he doesn’t belong in a school of education because he’d like to be somewhere where the focus is “explicitly on innovation.”  My question is why can’t that be a school of education? or a school at all?  Why can’t learning be explicitly innovative and thought about as innovation in general? I believe all of us are capable of thinking of our schools as places of learning where students are being innovative as they learn.  Every day I ask my students in my classroom to attempt to think of something new to them.  It may not be innovative to me, but as long as it is in their eyes and their brain is attempting to see something in a new way on their own, I believe they are being innovative.

I would encourage us all to continue to be the change that we want to see in schools and not try to find other places where we think we belong.  It’s so important that we continue to make these changes no matter how small and I hope to continue to be a resource in your own classroom innovation!