Author: Carmel

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!

A Total Win…with lots of understanding

Before I left for the Anjs S. Greer Math Conference last week, I read an amazing blog entry at the Math Ed Matters website by Dana Ernst and Angie Hodge that was talking about Inquiry-Based Learning and the mantra “Try, Fail, Understand, Win.”  The idea came from one of Prof. Ernst’s student course evaluations this past spring as his student summed up his learning experience in such an IBL course.  This blog post was so meaningful to me because for each of these four words, the authors wrote how we as teachers (and teacher educators) can take this student’s perspective towards our own work.  I decided to attempt to take this attitude going off to my own conference with two courses to give and three smaller talks.  It was sure to be a busy week.

And in fact, it really was.  I had very little time to sit and listen to others’ work, which I really was quite sad about.  However, in my own classes I was so impressed with the amount of enthusiasm and excitement my participants had for PBL and their own learning.  As I sat in front of my computer this morning reading the course evaluations and their tremendously helpful input, it finally occurred to me how truly powerful the experience had been for my participants.  Many of them became independent thinkers and knowers about PBL and feel so much more knowledgeable and prepared for the fall.    Part of the class time is spent in “mock PBL class” where I am the teacher/facilitator and they are the students doing problem presentations.  We then sit and talk about specific pedagogical questions and distinctions in classroom practice.  Some of the class time is spent in challenging problem solving which is where I also learn so much from the participant’s different perspectives. “We win when we realize there’s always something we can do better in the classroom” – as Ernst and Hodge write.

The now Infamous ‘French Garden’ Problem

I want to give a huge shout out to all of my participants from last week and encourage them to keep in touch with me.  Many of you wrote in your evaluations that you still have many questions about your practice and how to integrate your vision of PBL in your classroom.  I will always be only an email away and hope that you continue to question your practice throughout the year.

My plan is to try to write some blog posts at the end of the summer/beginning of the year in order to respond to some of the remaining questioning while you plan for the beginning of the school year such as:

  1. How to plan for week one – writing up a syllabus, creating acceptable rules
  2. Helping students who are new to PBL transition to it
  3. Assessment options – when to do what?
  4. Working hard to engage students who might not have the natural curiosity we assume

If you can think of anything else that you might find helpful, please post a comment or send me a message and I’d be happy to write about it too!  Thanks again for all of your feedback from the week and I look forward to further intellectual conversation about teaching and PBL.

Anja S. Greer Conference 2013

What a great time we had this week in my courses!  I am so excited by all of the folks that I met and the CwiC sessions of other leaders that I went to.  Pretty awesome stuff presented by Maria Hernandez from NCSSM, my great colleague Nils Ahbel, Tom Reardon, Ian Winokur, Dan Teague, Ken Collins and many others.  I was so busy that I didn’t get to see many other people’s sessions so I feel somewhat “out of it” unfortunately.

I want to thank everyone that came to my CwiC’s and remind them to be sure to go and pick up my materials on the server before they leave.

For my participants – here are the links to the course evaluations:

Moving Forward with PBL: Course Evaluation

Scaffolding and Developing a PBL Course:  Course Evaluation

Linking Theory to Practice: A Shout-Out to ‘savedabol’

This past January, I gave a key-note address at the ISOMA conference in Toronto and posted my slides from that talk on my academia.edu site that I thought would be a good place for me to easily give other people access to my work. (along with my website).  Academia.edu is great because it gives you lots of information about the stats of surfers who come and look at your information.  All of a sudden I saw that this powerpoint had more than something like 400 views and I couldn’t believe it.  I had to see who was searching and looking at this slideshow.

I quickly realized that someone had seen it, liked it and posted something about it on reddit.  There were only a few comments but one of them went something like this:

“I think the single worst part of being a teacher is sitting through PowerPoints like this, while some earnest non-classroom pedagogue tells us the bleeding obvious.”

Whooo – that one stung…my first instinct was to try and find out who that person was and defend myself to the ends of the earth.  Anyone who calls me a non-classroom pedagogue deserves to be righted…but then I kept reading…and someone with the alias ‘savedabol’ wrote this:

‘Carmel Schettino (the author) led a seminar I took at the Exeter math conference last summer. She is incredible. I can assure you that she is not a non-classroom pedagogue. She has been in the classroom nonstop for at least 20 years (that I know of). She is particularly scholarly when it comes to PBL and other ed topics, but that doesn’t make her irrelevant to what we do every day. Near the end she gives some great resources.’

I can’t tell you how affirmed I felt by ‘savedabol’ and I want to just let them know how nice that was of them to share their thoughts about my work with them.  I have been in the classroom non-stop since 1990 (except for two terms of maternity leave and one term of a sabbatical when I was a full-time student myself) and I pride myself in researching as much as possible about what I do.

I do wish that the first poster had had the chance to hear me speak instead of jumping to the conclusions they had – and it definitely got me thinking about something that was discussed last year at the PME-NA conference in October 2012.  I was one of maybe just a few people in the special category of math teacher/educator/researcher/doctoral students at this research conference where many of the math research folks were talking about ways in which they could breach the great divide of the theory people (them) and the practice people (us).

For many years I have lived this double life of both theory and practice and I have to say, I love it.  Having just finished up my Ph.D. and teaching full time was probably one of the toughest things I’ve had to do in my life, but having my mind constantly in both arenas has only helped me be a better teacher and a better researcher.

Jo Boaler is a great researcher at Stanford University who is doing great work in outreach between theory and practice this summer by offering a free online course called “How to Learn Math.”  It’s a course for k-12 teachers that is grounded in the most recent research in math education.  What a great idea!  She is sharing some of her wisdom freely online with k-12 teachers who want to spend some time learning about new ideas themselves.  I know I’m in.

In August 2008, the NCTM put together a special Research Agenda Project to work on recommendations for just this cause and you can see their report here.  One of the major recommendations that came out of their work was to not only emphasize the need for communication between researchers and practitioners, but in my view to help them realize that this communication would benefit both parties equally.  We all have something to share with each other and I know that I appreciate every classroom practitioners’ experiences.  I learn something from every teacher that ends up in my workshop every summer and often end up using many of their ideas as they do mine.

So let’s keep supporting each other both in real life and virtually, and realize that often times, the “bleeding obvious” is something that needs to be stated and discussed over and over again to be sure that we are still talking about it with the right people.

PBL – Students making Mathematical Connections

As someone who has used Problem-Based Learning for almost 20 years and sad to say has never been part of a full-fledged Project-Based Learning curriculum, what I know best is what I call PBL (Problem-Based Learning).  I know there is a lot of confusion out there is the blogosphere about what is what, and with which acronyms people use for each type of curriculum.  I did see that some people have been trying to use PrBL for one and PBL for the other, but I guess I don’t see how that clarifies – sorry.

So when I use the acronym PBL in my writing I mean Problem-Based Learning and my definition of Problem-Based Learning is very specific because it not only implies a type of curriculum but an intentional relational pedagogy that I believe is needed to support learning:

Problem-Based Learning (Schettino, 2011) – An approach to curriculum and pedagogy where student learning and content material are (co)-constructed by students and teachers through mostly contextually-based problems in a discussion-based classroom where student voice, experience, and prior knowledge are valued in a non-hierarchical environment utilizing a relational pedagogy.

Educational Psychologist and Cognitive Psychologists like Hmelo-Silver at Rutgers University have done a lot of research on how students learn through this type of scaffolded problem-based curriculum dependent on tapping into and accessing prior knowledge in order to move on and construct new knowledge.  There was a great pair of articles back in 2006/2007 where Kirschner, Sweller & Clark spoke out against problem- and inquiry-based methods of instruction and Hmelo, Duncan and Chinn responded in favor.  I highly recommend reading these research reports for anyone who is thinking of using PBL or any type of inquiry-based instruction (in math or any discipline).  It really helps you to understand the pros and cons and parent and administrator concerns.

However, after you are prepared and know the score, teachers always go back to their gut and know what works for their intuitive feeling on student learning as well.  For me, in PBL, I look at how their prior knowledge connects with how, why and what they are currently learning.  One of the best examples of this for me is a sequence of problems in the curriculum that I use which is an adaption from the Phillips Exeter Academy Math 2 materials.  I’ve added a few more scaffolding problems (see revised materials) in there in order to make some of the topics a bit fuller, but they did a wonderful job (which I was lucky enough to help with)and keep adding and editing every year. The sequence starts with a problem that could be any circumcenter problem in any textbook where students use their prior knowledge of how to find a circumcenter using perpendicular bisectors.

“Find the center of the circumscribed circle of the triangle with vertices (3,1), (1,3) and (-1,-3).”

Students can actually use any method they like – they can use the old reliable algebra by finding midpoints, opposite reciprocal slopes and write equations of lines and find the intersection points.  However, I’ve had some students just plot the points on GeoGebra and use the circumcenter tool.  The point of this problem is for them to just review the idea and recall what makes it the circumcenter.  In the discussion of this problem at least one students (usually more than one) notices that the triangle is a right triangle and says something like “oh yeah, when we did this before we said that when it’s an acute triangle the circumcenter is inside and when it’s an obtuse triangle the circumcenter is outside.  But when it’s a right triangle, the circumcenter is on the hypotenuse.”

Of course then the kid of did the problem on geogebra will say something like, “well it’s not just on the hypotenuse it’s at the midpoint.”

 

Dicussion will ensue about how we proved that the circumcenter of a right triangle has to be at the midpoint of the hypotenuse.

A day or so later, maybe on the next page there will be a problem that says something like

“Find the radius of the smallest circle that surrounds a 5 by 12 rectangle?”

Here the kids are puzzled because there is no mention of a circumcenter or triangle or coordinates, but many kids start by drawing a picture and thinking out loud about putting a circle around the rectangle and seeing they can find out how small a circle they can make and where the radius would be.  When working together oftentimes a student see a right triangle in the rectangle and makes the connection with the circumcenter.

A further scaffolded problem then follows:

“The line y=x+2 intersects the circle  in two points.  Call the third quadrant point R and the first quadrant point E and find their coordinates.  Let D be the point where the line through R and the center of the circle intersects the circle again.  The chord DR is an example of a diameter.   Show that RED is a right triangle.”

Inevitably students use their prior knowledge of opposite reciprocal slope or the Pythagorean theorem.  However, there may be one or two students who remember the circumcenter concept and say, “Hey the center of the circle is on one of the sides of the triangle.  Doesn’t that mean that it has to be a right triangle?”  and the creates quite a stir (and an awesome “light bulb” affect if I may say so myself).

A few pages later, we discuss what I like to call the “Star Trek Theorem” a.k.a. the Inscribed angle theorem (I have a little extra affection for those kids who know right away why I call it the Star Trek Theorem…)

I will always attempt to revisit the “RED” triangle problem after we discuss this theorem.  If I’m lucky a student will notice and say, “Hey that’s another reason it’s a right triangle – that angle opens up to a 180 degree arc, so it has to be 90.”  and then some kid will say “whoa, there’s so many reasons why that triangle has to be a right triangle”  and I will usually ask something like, “yeah, which one do you like the best?” and we’ll have a great debate about which of the justifications of why a triangle inscribed in a circle with a side that’s a diameter has to be right.  So who are the bigger geeks, their teacher who names a theorem after Star Trek or them?

References:

Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential and inquiry-based teaching. Educational Psychologist, 41(2), 75-86.

 

Hmelo, C. E., Duncan., R.G., & Chinn, C. A. (2007). Scaffolding and achievement in problem-based and inquiry learning: A response to Kirschner, Sweller and Clark (2006). Educational Psychologist, 42(2), 99-107.

 

Affirming the “Un-fixing” of the roles in Mathematics

So after nine, long hard years, I am finally at a point where I am proud to say, “I’m finished!”  Woo-hoo and hurrah, tonight I will submit my dissertation electronically and you can call me Dr.  Reading over my work has been probably one of the most fulfilling acts of my professional life, as was defending my dissertation last week.  I can’t believe how fun it actually was – too true.  When you are passionate about a topic, it never gets old. Then, just today my advisor sends me an article that was published in the Harvard Education Letter titled, “Changing the Face of Math”which strangely sounds so much like what I’ve been working on for so long.  It talks about the current state of the way students create identities in mathematics in the U.S. and how this is detrimental to their beliefs about what they can do and be in the mathematics classroom and beyond.  Sadly, as high school teachers, half of our job is undoing the mathematical identity that the system has put in place all the years before they have come to us. In my dissertation, I wrote about not only this identity question but the difficulty in how American society has such a gendered, dichotomous view of mathematics that even those of us who attempt to move past the stereotypes because of our love of mathematics end up with difficult situations to work against.  For some, it is so difficult that we end up giving up and choosing the easier path – the girl who loves physics but choose biological engineering because she feels like she belongs there.  Or the young woman who goes to college to be a math major, but ends up in International communications because the classes were not taught in a way that worked for her learning style.  Or the weak female mathematics student who doesn’t even consider taking another math class in college because of the negative view of her abilities years ago. In this article they say,

“Math education experts say we’re in crisis and that traditional approaches of treating math like a cold-blooded subject amid the warm and engaging world of K–12 schooling are a big part of the problem. Narrow cultural beliefs about what math success looks like, who can be good at it, and what it’s used for are driving students to approach the subject with timidity—or not at all.”

Which was so affirming because it was the major educational research question that motivated my dissertation!  I love it.  Allowing all underrepresented students, not just girls to find ways to change the way they view themselves as math students by changing the way we teach mathematics would be revolutionary, and so many people are doing it.  I am proud to be a part of this movement to “unfix” the gendered, dominant, presumed ways of mathematics learning and open it up to more subjective, creative and collaborative thinking processes. It’s a great time to be a revolutionary!

Creating a Conspiracy in the PBL Classroom

Any Mad Men fans out there?  I just love some of the characters and the struggles they put themselves through.  In one episode from season 5, called “Signal 30,” Lane Pryce needs to take some clients out to dinner and Roger Sterling is giving him some advice on how to woo them to sign a contract with Sterling Cooper Draper Pryce.  Since he is not an account man, Lane is nervous about landing the account.

Roger:  And then it’s kind of like being on a date.

Lane:  Flattery, I suppose…

Roger:  Within reason, but I find it best to smile and sit there like you’ve got no place to go and just let ‘em talk.  Somewhere in the middle of the entrée, they’ll throw out something revealing and you want to wait ‘til dessert to pounce on it. You know, let him know you’ve got the same problem he has.  Whatever it is, and then you’re in a conspiracy – the basis of a quote “friendship”.  Then you whip out the form.

Lane:  What if I don’t have the same problem?

Roger:  It’ll probably be something like he drinks too much, he gambles…I once went on a five minute tear about how my mother loved my father more than me and I can assure you, that’s impossible.

Lane:  Very good then, and if for some reason he’s more reserved?

Roger:  You just reverse it – feed him your own personal morsel.

Lane:  Oh I see.

Roger: (getting up to leave) That’s it, get your answers, be nice to the waiter and don’t let him near the check.

My husband and I watched this episode about the same time I was having a great deal of resistance in my class to PBL.  I was talking to my husband about how to get students to buy into the notion of learning for the sake of learning where everywhere else in their lives what measures their learning are their grades.  Why would I expect anything different from them if this is the culture they were brought up in?  They depend on their grades to get them into a good college and if their grades are not up to a certain standard, they will not “measure up.”

I get this question all the time from other teachers – about  how to motivate students to find the love of learning and the interest in problems when they do not necessary know the solution methods to find them.  I usually tell them the same things – talking about the values of the class, grading class contribution with a viewable rubric,  grading their metacognitive journal writing, rewarding them with an interesting relationship with a great teacher…OK that might be pushing it.

However, this year is different.  I am having the hardest time trying to let them know what I want from them.  They do the homework, try their best, write down notes, but for some reason it feels different.  It’s almost as if there’s this wall between them and me and I don’t know how to get them to see my side.  I have had this problem with students in the past, but usually with a whole class.  Some of them blatantly are interrupting each other and others are obviously ignoring each other.

Then my husband says, “Maybe it’s like the conspiracy.”  I said, “What?” He said,” You know, what Roger was talking about on Mad Men.  Now, Roger Sterling is no saint (those of you who watch the show know this all too well) and I usually take what he says with a grain of salt.  I also would not ever consider taking advice from him, especially about teaching, but I allowed my husband to continue.  He said maybe what I had to do was build up the conspiracy that Roger was talking about.  I had a real problem with that because I am so committed to relational pedagogy that there’s no way I could lie to or mislead a student about their learning.  But that’s not what he really meant.

I suddenly realized that what had happened was I was teaching a curriculum that I didn’t even buy into.  I had just finished teaching them matrices and matrix operations with some problems that I had written, and it went very well.  However, in the end I did have to do Cramer’s Rule and determinants.  I tried motivating the problems about determinants with the area of a parallelogram, which kept them interested for a while, but in the end, with a 3×3 it was just here’s the way to do it.  I’m not sure that I could’ve expected them to have enough prior knowledge to derive the formula for finding a determinant of a 3×3.  As much as I tried to cover it up with problem-based learning, it was still a curriculum that is antiquated and not necessarily what I felt they should be doing and learning.  I couldn’t hide it any longer.

But we’re caught aren’t we?  Do we change the whole system – college prep curriculum, SAT required math, college expectations – and if so how do we do that? (see ahbel.com for a great article on this and a keynote address called Reflections on a 119 year old curricullum!)  Do we move beyond the required standardized testing material and allow our students to see mathematics the way we see it?  Yes, that’s the conspiracy – that’s what my husband was talking about.  When kids complain to me, I will “smile and sit there while they talk” knowing that I’m going to try to get something that we have in common.  “Do you hate solving a system of three equations with three unknowns with a determinant? Oh yeah, I did too in high school.  Wouldn’t it be great if we could do something else?  What else should we do?  Let me find some other problems that might be interesting.”  We have the same problem (literally and figuratively), now we’re on the same playing field having similar motivating factors.

And you know what?  I don’t think it would be the end of the world if they’re not revealing and you reversed it.  We are allowed to say to them that we don’t understand why we are still teaching this and these would be my reasons for taking it out of the curriculum – part of your own personal morsel.  It might actually bring you closer as a class and have you talking about how your hands are tied and we have to get through this “together.”

Yeah, there are little tricks that can be learned and carrots that can be used to get students to do what you want them to do, but in PBL, that’s not the point.  There is very little for them to mimic because it is based on their prior knowledge.  They are the ones who need to move the curriculum forward.  So in a nutshell,

  1. Take action – Get to problems in order for students to start feeling empowered and active in class.  Once they see that they are capable of a great deal on their own, it is amazing what they can accomplish.
  2. Create relationships – be sure that you are being reciprocal in your attempts at problems and valuing theirs.  The concept of Relational Trust and Authority are huge parts of a PBL pedagogy (Boaler, Bingham)
  3. But make sure that you are at least somewhat in control in the end because we are, at least for now, still responsible for making sure that some understanding of what we might consider unnecessary skills, for their next courses or future use.

As Roger said, “Get your answers, be nice to the waiter and don’t let ‘em near the check.”  Create that conspiracy.

 

 

 

Defying Gravity as a Means to Learning from Mistakes

There’s a lot of blogging, writing and research (and anecdotal stories) out there these days about trying to foster the value in students for the appreciation in failing.   I even wrote a blog entry two years ago entitled “modeling proper mistake-making” way before I read anything or watched any videos on the Internet.  From teaching with PBL for over 17 years, I am a pro at making mistakes and watching students struggle with the concept of accepting the idea of learning from their mistakes.  This is so much easier said than done, but it is clearly something that grow to love even if only for a short time.

Last April, I had the pleasure of hearing Ed Burger at the NCTM national conference where he spoke about having students in his college-level classes required to fail before they could earn an A in his class.  In his August 2012 essay “Teaching to Fail” from Inside Higher Ed (posted at 3:00 am, which I thought was kind of funny), he talks about attempting to make a rubric for the “quality of failure” on how well a student had failed at a task.  I thought this was an interesting concept.  I mean, in order to fail well, can’t you just really screw up, like not do it at all?  Prof. Burger states that allowing students to freely reflect on their “false starts and fruitful iterations” as well as how their understanding “evolved through the failures” can be extremely beneficial.  He also states:

“To my skeptical colleagues who wonder if this grading scheme can be exploited as a loophole to reward unprepared students, I remind them that we should not create policies in the academy that police students, instead we should create policies that add pedagogical value and create educational opportunity.”

Last year for the first time, I tried a similar experiment wherein I gave students an assignment to write a paper in my honors geometry class.  They had to choose from three theorems that we were not going to prove in class.  However, it was clear that they could obviously just look up the proof on the Internet or in a textbook or somewhere, since they clearly have been proven before.  The proof was only 10 or 20% of their grade.  The majority of the paper’s grade was writing up the trials and failures in writing the proof themselves.  This proved to be one of the most exciting projects of the year and the students ate it up.  I even told them that I didn’t care if they looked up the proof as long as they cited it, but I still had kids coming to me to show my how they were failing because they wanted a hint in order to figure it out themselves.  It was amazing.

This past week I showed my classes Kathryn Schultz’ TED talk entitled “On Being Wrong” in which she talked about the ever popular dilemma of the Coyote who chases the Road Runner, usually off a cliff.

My students loved her analogy of the “feeling of being wrong” to when the Coyote runs off the cliff and then looks down and of course, has to fall in order to be in agreement with the laws of gravity.  However, I proposed a different imaginary circumstance.  Wouldn’t it be great if we could run off the cliff, i.e. take that risk, and before looking down and realizing that vulnerability and scariness, just run right back on and do something else?  No falling, no one gets hurt, no one looks stupid because you get flattened when you hit the ground?  Maybe that’s not the “feeling of being wrong” but it’s the “feeling of learning.”

Next blog entry on creating the classroom culture for “defying gravity.”

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.

The Role of Technology in Relational Pedagogy?

So I’ve been thinking a lot lately about technology and learning.  There’s so much in the news about MOOCs, using iPads, schools using technology, etc.  I am even part of a pilot program at my school right now where all of my students have iPads in my honors geometry class and we are trying to communicate at night using Voicethread and the iPads.  My hope was that having a way to share ideas during the evening would lessen the stress of homework problems that students are asked to grapple with in the PBL curriculum would give them more opportunities to throw out problem-solving ideas with each other before class starts so that we would spend less time in class debating different methods of solving the problem (although that’s what I love about class, right?).

But I’m asked as a teacher to find ways to integrate technology into my classroom – but to what end?  I want to find ways to use technology to solve problems, to explore ideas and to help improve students’ understanding of the mathematics.  Not necessarily help them communicate with each other, which is what I’m finding most of the apps out there are for right now – which I am open to – but they are removing a huge part of the learning triangle.  In fact, David Hawkins (1974) wrote about the I-thou-it reciprocal relationships in learning that simply must exist between the learner, the teacher and the subject matter.  He said that if one of the relationships is hindered or dysfunctional in some way, that learning is not optimal.

Hawkins (1974)

So if I interrupt that relational triangle between the students’ communication with the material (and with each other) and with me, using technology instead of discussion and the connection with all three, my fear is that learning is not optimal.  Perhaps the technology could enhance it, but for now I see that it is not truly happening.  My guess is that it has to take time for the students maybe to want for that to happen.

I also just read an article on Edutopia by a guy named Matt Levinson that was entitled “Where MOOCs Miss the Mark: The Student-Teacher Relationship” where it was stated that a lack of mentorship, close guidance or meaningful relationship between teachers and students is what is really lacking in these online courses. Even students who use Khan Academy lectures for “learning” sometimes comment that even though they don’t like sitting and listening to lectures in math class, they would “much [prefer] listening to her math teacher explain the same concepts because she likes this teacher and feels comfortable asking questions and going for extra help outside of class.”

Carol Rodgers (one of my most favorite people on earth) writes about teacher presence and the importance of it in the classroom.  I believe in mathematics class and especially the problem-based mathematics class it is truly essential because in order for students to take a risk with a method, they need to feel supported and safe in order to be open to new ideas and to discuss them with others.  With the open presence of a teacher and mentor, students are not “receiving knowledge” but creating it with others – creating it within those relationships that Hawkins was talking about – maybe with technology or without it.  But  for someone who just spent two years writing about the importance of relational pedagogy in PBL, I find it extremely difficult to assume that without those relationship the same exceptional amount of learning would go on.