Cupid Shuffle, Robots, Teamwork

To the right, to the right, to the right, to the right, 
to the left, to the left, to the left, to the left, 
now kick, now kick, now kick, now kick, 
now walk it by yourself . . ..”  

The music started jammin’; the dancers in their pastel tutus started groovin’; kids started clappin'.  No, this was not last month’s middle school dance, rather it was seventh-grade science class on Friday at 9:50 AM, rooms five and six.  The dancers involved, while directed by the seventh graders, were actually Lego Mindstorm robots.  The routines, expertly choreographed and programmed, were the culmination of a week’s worth or teamwork.  While programming is a valued skill that involves logical sequencing, problem solving, and some discreet knowledge about the language involved, the real value of last week’s “dance off” was in the work and lessons learned about collaboration and communication.  

About a week ago, I was touring the mother of a fifth-grade boy who was interested in how the middle school had changed in the short time that had passed since her daughter, a current ninth grader, first entered Stephens Hall.  We spent some time in my office talking about educational theory and then moved down the hall to see what was happening.  I love to give tours because it is a chance for me to show off what we do and who we are, something that is sometimes difficult to describe with words or numbers.  We entered Mr. McManus’s room at the end of the hall and found Meghan and Anna Kate standing in front of their seventh-grade classmates.  While the following is paraphrased, it is pretty close to what we heard:

Okay, everyone be quiet.  We've got to get rid of the chaos, so we decided to give everybody jobs.  If you don’t like your job, it doesn’t matter ‘cause you can switch.  We think Sydney should be leader.

As this was going on, Mr. McManus was sitting off to the side pretending to be disinterested.  The mom and I looked at each other, and I got a big smile on my face.  

Now I wasn’t in the classroom the previous day, but from what the girls told me, it was pretty ugly: people talking, no one listening, raised voices, frustration, nothing getting done -- sounds a little like Congress.  Mr. McManus, being a wise, experienced sage, let the situation play out. He trusted the process and didn’t jump in to fix things. This empowered the girls to take matters into their own hands and work it out.  Some girls became programmers, some costume designers, some DJ’s, some choreographers, and one a leader.  Some girls changed jobs as it became apparent that more work was needed in different areas.  They worked together.  They solved their own problems.

I spent a few minutes talking to Anna Kate and Meghan who had stood in front of their peers to attempt to make order out of chaos, and asked them what I thought was going to be a tough question:  “Why didn’t appoint yourselves leaders?”  They didn’t miss a beat and said that they chose Sydney because she is really good at being a leader.  They said that she listens well and can organize things.  Nice!  

The three other seventh-grade core groups also struggled through the process of how to get a large group to work together to reach a goal. Some were not particularly pleased with the outcome; however, if each groups' performance didn't come off perfectly, they all persevered and brought something worthwhile to the dance floor. So, as Cupid says, ". . . do your dance, do your dance."

Seeing Math in the World

People are sometimes described as having a poetic heart or the eye of an artist.  These folks have a different perspective than others when they view the world; they look at events, images, relationships, and the daily happenings of life through a particular filter or lens.  These lenses may allow people to feel more deeply or experience life more fully than others.  

I frequently talk to parents and students about developing a math lens.  To be able to see the world and know that it can be represented in mathematical ways gives our students another perspective, similar in ways to the artist’s eye, that adds meaning and perspective to life.  Anyone who develops a math lens is likely to envision solutions that are not obvious to others and may understand the workings and complexities of the world in greater depth.

I ran across the following video the other day, and it startled me that it could describe my thoughts so much more clearly than my words.  Please take a a couple of minutes to watch it.

BEAUTY OF MATHEMATICS from PARACHUTES.TV on Vimeo.

While some of us are born with a greater ability and propensity to view the world through a mathematical lens, this lens can be developed and honed by everyone with practice.  We practice this skill frequently in our math classes by offering students images and video of everyday life and asking them to address it through a mathematical lens.  While they may not all become brilliant mathematicians, our hope is that developing this mathematical lens will enrich their lives.

Using Minecraft and Plotz to Visualize Limits

At the start of class for the last two weeks, my algebra team teacher and I have been using a discussion on “area under a curve” to extend our students’ thinking.  Of course, our eighth-grade algebra I students do not have the calculus tools they need to solve this type of problem, and we are not trying to teach them the necessary algorithms.  We’re asking them to envision different ways that the problem might be solved.  One of our primary goals in this algebra class is to create divergent thinkers who realize that the process of solving a problem is often more important than the solution.  By offering them problems that are “unsolvable” given the math that they know, they are forced to think of the problems as abstractions, to ponder the same ideas that intrigued the likes of Archimedes, Descartes, Leibniz, and Newton.

Our students’ first attempts to best measure the area under a curve mirrored the earliest methods of the Greeks -- the exhaustion method.  The students quickly decided that they could fill the area using different size polygons and circles, and they would ultimately get pretty close to a solution.  While this was a good first step, and started them down the conceptual road to limits, we ultimately decided that it would be problematic to obtain the measurements of different sized shapes.  Some students wondered if using a single shape of the same area would simplify the process.  Then one of our students, Rion, said that every gamer knows that shapes on the computer screen are just made up of the same size pixel, and that the problem could be best addressed by filling the area under a curve with pixels that could be counted.  Extending this line of thought, Rion thought that he could use the Minecraft creating website, Plotz, to illustrate the idea that reducing the size of the squares, thus increasing the number of squares under the curve, would result in a more accurate answer.  Rion shared these images with the class:

After this, we discussed the idea of being able to reduce the error of the area measurement to a point where for all practical purposes it was accurate.  While the students certainly did not reinvent the concept of a limit, they did discover, in a general sense, the way a limit could be used to help solve this type of problem.  Our hope is that they will be able to apply this concept and type of thinking to other problems that we challenge them with in the future.

My team teacher and I believe that it is vital to continue to push the students’ ability to think of math in abstract terms.  This forces the students to see math as something different from memorizing steps in order to follow the predictable, worn-out path of textbook examples and problems.  It forces them to engage with math -- to wrestle with it in a way that builds engagement and deep conceptual understanding.

Google Sees Little Value in Test Scores and GPA

It must be reassuring to the folks who believe that school shouldn’t prepare students for the workplace to read the following written by Max Niesen from Business Insider:

In an interview with The New York Times' Adam Bryant, Google's Senior Vice President of People Operations Laszlo Bock explains that some of the biggest stalwarts of the hiring and recruiting world, the interview, GPA, and test scores, aren't nearly as important as people think.

Google doesn't even ask for GPA or test scores from candidates anymore, unless someone's a year or two out of school, because they don't correlate at all with success at the company. Even for new grads, the correlation is slight, the company has found.

Bock has an excellent explanation about why those metrics don't mean much.

" Academic environments are artificial environments. People who succeed there are sort of finely trained, they’re conditioned to succeed in that environment," he says.

While in school, people are trained to give specific answers, "it's much  more interesting to solve problems where there isn’t an obvious answer," Bock says. "You want people who like figuring out stuff where there is no obvious answer."

When I started teaching in the early 1990s, I had already worked for a bank, done some oil and gas properties management, and run different divisions of an automobile dealership.  My first teaching job at Robert E. Lee High School in San Antonio was a shock on many levels, but the biggest head-spinner was that it became clear to me that school had little to do with other workplaces or real life.  Some teachers were unmotivated and would have been fired in a week if school were anything like the working world.  I’ll never forget one seasoned teacher asking me why I worked so hard.  There was little focus on the customers, e.g. , the parents who paid our wages through taxes and the students who were the passive recipients of knowledge that was of little use in their lives.  A lot of time and energy was spent in managing the students’ days, making sure that everyone was accounted for and trying to limit the opportunities for students to engage in illicit or unsupervised activities.  Even amidst this mind-deadening, controlled world, there were many dedicated faculty and students who struggled to teach and learn in a system that really wasn’t conducive to helping students learn how to be successful in their lives outside of school.

The students who were successful at Robert E. Lee High School and most other high schools around the country, the students who learned how to “do school” and be successful in what Bock calls an “artificial environment,” went on to ply their school skills at college.  Then they faced what I and nearly everyone I knew faced when I graduated from college:  they faced a world of work that was quite different from high school and college.  While a college diploma may have given them a ticket into the workforce, it did little to prepare them for what they would be doing.

The most frustrating thing to me is that we know how to help students learn to be succesful outside of school.  We know how to teach students to examine and solve open-ended problems; we know how to instill grit in our students to give them long term perseverance; we know how to help students develop character strengths; we know how to create environments and methods that hone students’ communicative and collaborative skills; we know how to help internal motivation flourish within students; we know that we should limit curriculum to what is truly “lifeworthy.”  If you don’t believe me, pay attention to the experts who have spent the better part of their lives researching and reporting on these topics:  Check out Dan Meyer’s work in implementing problem solving, look at Angela Duckworth’s work on grit, read Martin Seligman on developing character, don’t forget Daniel Pink’s and Alfie Kohn’s books on motivation; listen to what Dave Perkins has to say about lifeworthy skills.

There are many things standing in the way of making school more relevant to life, but the primary obstacle is the collective mindset of institutions, parents, teachers, administrators, and students that we all think we know what school looks like.  In our minds, even though many of us know better, school should look like what it looked like last year, or ten years ago, or fifty years ago simply because that is school.  Unfortunately, the school that we are comfortable with, the school of our memory, grows in irrelevance as the rest of the world speeds toward the future while we remain firmly planted in the past.

Free Your Mind, Share a Run

They say that if you sleep on a problem that you will wake up with a solution.   I solve problems when I run.  Creativity happens because I am unencumbered by linear thought.  My mind floats and roams on a rocking sea, held afloat by the the constant rhythm of my feet, my breath, and my arms.  When running, I have true attention deficit, and my mind leaps and frolics in places that it normally doesn’t venture.  Because of this, I rarely run with others.  The conversation keeps my mind too focused to float.  However, on the last day of the faculty workweek, Andy Lammers and I hit a small portion of the Mountains to Sea Trail together, and something unusual happened -- at least for me.

After five minutes of panting up the Stuyvesant Road hill, we both fell into a comfortable rhythm of breath and legs.  The stressors of our work week started dripping off of us like the sweat that rolled down our backs.  After a few minutes, we began free associating childhood memories that were so close in spirit and emotion that our childhoods could have occurred in the same time and place instead of being separated by fifteen years and several thousand miles.  We talked about the risks that we took as boys:  throwing mudclods at our neighborhood friends, reading books soaked in the heroics of war, building forts, and pretty much being clueless to the world outside our neighborhoods.  Our memories fed off of each other, bouncing around from one thread to another.  It struck me much later that on this run, our minds worked together to do the same thing that happens to me when I run alone.  That is cool.  

Although I’ve known Andy for many years, that run brought me closer to him than any time we have spent together socially or professionally.  Long term memories have their neural grounding in deep emotion.  I’ll remember this run with Andy, and maybe in the future I’ll seek out running partners rather than shunning them.

Postive Psychology - A Summer Project

A few weeks ago, Missy Sullivan gave me an article to read about Positive Psychology written by Martin Seligman.  Missy has her headlights set on the completion of an advanced degree in School Psych, and during the summers we sometimes discuss ideas that apply to psychology and school.  I admit that I knew little to nothing about Positive Psychology, and although I found the article interesting, I was also a little skeptical.  In the meantime, I came across a large section in the book, How Children Succeed by Paul Tough, that described the theory and outcomes of Positive Psychology.  It seemed too much of a coincidence for me to be exposed to this theory twice in such a short period of time, so I’m following the serendipitous guidepost and delving into the theory, process, and outcomes.

The following is an excerpt from Martin Seligman’s Flourish: A Visionary New Understanding of Happiness and Well-Being

First, a quiz:

Question one: in one or two words, what do you most want for your children?

If you are like the thousands of parents I’ve polled you responded, “Happiness,” “Confidence,” “Contentment,” “Fulfillment,” “Balance,” “Good stuff,” “Kindness,” “Health,” “Satisfaction,” “Love,” “Being civilized,” “Meaning,” and the like. In short, well-being is your topmost priority for your children.

Question two: in one or two words, what do schools teach?

If you are like other parents, you responded, “Achievement,” “Thinking skills,” “Success,” “Conformity,” “Literacy,” “Math,” “Work,” “Test taking,” “Discipline,” and the like. In short, what schools teach is how to succeed in the workplace.

Can and should schools attempt to teach well-being?  The list of adjectives that Seligman describes as what parents “most want for their children” seems pretty squishy.  Is it really our job in school to teach kids to “love each other” or to “find meaning?”  Truthfully, great teachers have always taught these skills and attitudes.  It is one of the things that promotes such strong bonds between teachers and students.  However, what if schools adopted systematic and coordinated approaches to teaching well-being?  This has been done and, according to Seligman, done with success.  

I’ve got some research to do this summer.

Seeing the Unseen

photo by Elizabeth Douglas

This winter as we drove along the Blue Ridge Parkway on the way to school, my boys and I would sometimes attempt to spot wildlife.  Winter isn’t a very good time to see animals in the mountains of Western North Carolina, but we persisted and were occasionally rewarded with a glimpse of the odd squirrel or crow.  I wonder what we would have seen had we parked the car and walked that five mile stretch on the Mountains to Sea Trail that parallels the Parkway?  Or, what would we have seen if we just wandered through the woods, off the road and off the trail, through the leafless blackberry brambles and among the dark green rhododendron, peering around the gray trunks splotched with white?  Would we have seen more wildlife?  Would we have seen something unexpected that might have created some new synapses in our brains that would cause us to view the world in a slightly different manner?

Students need to get off the road and off the trail.  Most schools are all too predictable.  Our daily schedules with learning boxed up nicely into particular disciplines make it all too easy for students to pass through their education without really looking beyond three feet on either side of the road.  

We know that today’s students face an unpredictable future where they will bounce from job to job, perhaps holding as many as ten or fifteen different jobs during a lifetime.  Futurists claim that by 2025 over half the jobs that our current students will compete for don’t even exist today.  In order to thrive in this world, our students need to have an adventurous spirit; their thinking needs to be nimble and adaptable to new and changing conditions; their minds need to be trained in a way that frees them to take mental risks.   

We are creating a school that supports this type of learning and thinking.  The faculty in the Middle School at Carolina Day School is constantly working to provide experiences for our students to develop a mindset that forces them to see things that others don’t, not necessarily because they have better vision, but because our students relish the opportunity to walk off the trail and know how to seek and value the unseen.

Learn to Program - Starting with Scratch and Minecraft

Last week, my sixth-grade son and his classmates were asked by their science teacher to design a program in Scratch (a beginning programming language developed by MIT) that depicted the water cycle. When he was in the fourth grade, I introduced my son to Scratch, and he has played around with it occasionally over the past two years. He and his classmates had fun with the project, and even those who were totally unfamiliar with it learned some basics of programming.

Yesterday, my son downloaded a new "protocol" into Minecraft. Like many boys his age, Minecraft has become the first thing that he turns to on the weekends.  Along with playing on Minecraft with other folks, my son is in the process of creating his own city that is really pretty complex.  While he was engaged in his city planning, I asked him if he had been able to transfer any skills from his extensive Minecraft experience to Scratch.   Here is his off-the-top-of-his-head response, without looking up from his laptop:

• 3-D modeling
• coordinate grids 
• I can go in and change the code a little to make it do what I want. 

I don’t think anyone would consider my son a computer geek.  He plays sports after school; he practices piano; he has sleep-overs with friends, he reads the Sunday comics; he occasionally washes his mom's car; he eats constantly; and he programs a little.  In the future, my son may decide to study and learn more sophisticated programming, or he may not. The important thing is that he knows that he can, and coding is not some mysterious operation that only geniuses can accomplish. He can do it; anyone can do it; everyone should.

 

All Things Piratical

photo by Tanja Mamas

One of the best things about being a faculty member is that I sometimes get to learn from and with our students.  This occurred recently when I was asked to become a member of the pirate chorus in our middle school musical, The Pirates of Penzance, Jr.  As a student, I shunned any opportunities to be on stage.  Like many young people, I was terrified of appearing foolish to my peers.  Over the years, I conquered those fears and often relish the irony of being the assistant principal who does goofy things like disco dancing in the hallways, so I was excited to join the fun.  

I have had a couple of brief cameos in past plays, and I expected my pirate part to be a quick wave and laugh.  However, I attended my first practice a couple of weeks before the performance date and was startled to find that I actually had to sing and act in several numbers.  While I am egocentric enough to be in our middle school play, I’m not quite so needy as to have to recount my struggles learning lines or figuring out drama jargon.  I will simply say that I spent a lot of time working on the play over the past several weeks, and my wife and kids are grateful not to have to listen to “A Rollicking Band Of Pirates We” in the car anymore.

I had always known that working on the play was a special thing for the students involved, but I never really realized how special.  After a couple of weeks of practices, a dress rehearsal, and an actual performance, I felt like I was accepted as just another one of the actors.  The students and I joked together, chatted at times when we should have been listening to direction, sang the silly warm-up riffs, drank imaginary “pirate sherry,”  put on lipstick, and stood side-by-side on the stage.  A student and I got to take a few swings at each other in a fight scene, and he had a blast pretending to pummel me.  (I think he may have taken a little too much joy in this).  

From being a regular cast member, I got to understand the team spirit involved in the production.  I have heard all about egos and prima donnas in acting circles, but there was none of that happening on our set.  The tech crew, actors, directors, costumers, and make-up “moms” all supported the primary mission, and all worked together to put on the best play possible.  What is so amazing to me is that everyone knew their respective parts so well that the play would have been a success without any adults present during the performance.  This is not to discount the wonderful direction of Mandy Bean and Beth Heinberg, the costume work of Susan Mycroft, or the talents of tech master, Mike Congleton, but rather to extol their great leadership by bringing a group of middle school students and a bumbling administrator to a place of independence and competence.

This play is a brilliant microcosm of the skills we value in our middle school.  While there may be some external motivation like applause, the students’ participation as a member of the crew or cast is voluntary.  Most of the students like it because it involves them in something that is much bigger than themselves.  We challenge our students to get involved, to form relationships, to achieve something of value, and to gain confidence and strength of character.  It is difficult for me think of a better venue for them to practice and gain these attributes.

I received a professional and personal gift this year by being allowed to become a student in my own school.  If anything, my involvement with Pirates of Penzance, Jr. raised my respect for what we accomplish on a daily basis within our community.  And, yes, Elizabeth, I will shave off my scrubby beard!

Learning Math

I would bet that my middle school (junior high) math classes were quite similar to the way you were taught math.  I watched the teacher work problems on the board and then I was given problems to practice.  I frequently rushed through my homework in an attempt to get it done as fast as possible so I could head to the tennis courts or shoot baskets in the driveway.  After a couple of weeks, I was given a “unit test” which was supposed to assess whether or not I had learned the material.  Having some natural ability in math, I usually scored well on the tests.   

However, school is not where I really learned math.  I learned math on my summer car vacations adding up miles on creased, fold-up maps; and by figuring the amount of gasoline our lumbering Buick Estate Wagon gobbled up on trips to the Texas coast.  I got pretty good at predicting arrival times based on our average speed and distance left to travel.  I learned to compute with fractions by helping my dad and older brother refurbish a hulking wooden sailboat and build a two-story fort that protected our back yard from neighborhood rapscallions.  I learned probability by playing cards and dice games, which eventually led to me reading Scarnes New Complete Guide to Gambling when I was twelve-years-old.  It is a pretty heavy read for a seventh grader, but I made some pocket money in my teens because I knew the odds in blackjack.


So, where are our kids really learning math today?  At Carolina Day School, they are learning math in school.  Surprise.  They are learning math because they are using math.  

In eighth-grade, students play with motion by building and zooming balloon-jet cars across the floor.  They plot rates of change on graphs and understand that slope is more than just a line on a page in a book.  In seventh grade, students measure and cut popsicle sticks to form specific geometric shapes.  They create these from scale drawings, and, in addition to getting practice with angles, they learn that precision is sometimes critical.  Our sixth graders design and run their own experiments and determine what types of graphs and charts best display the generated data.  Analysis and use of data is crucial to our students’ understanding the world around them.

Learning has little use unless you can do something with the knowledge.  Doing something implies action, and CDS students do much more than sit in class absorbing facts and algorithms. They build, observe, compute, design, record, analyze, and judge -- and in doing these things, they actually learn math.

Charette - Learning Through Process

                                     -  video created by Julie Daughtry

As a part of the Future of Learning (FOL) Institute at Harvard’s Graduate School of Education, a small number of the 200-plus institute participants volunteered and were selected to participate in a charette.  When asked to volunteer for this experience, we were told little about the process other than the fact that it would involve designing an artifact to represent the learner of the future.

While others may define a charette to fit their own needs, our experience in charette could be defined as a small group working together over multiple, intense sessions to design and construct a product through collaboration.  The process was valued equally, or perhaps more, than the product.

The success of the charette was achieved by the intentional and thoughtful planning of our facilitators, Justin Reich and Arzu Mistry, along with several FOL Fellows.  The sessions were an outstanding example of excellent teaching and reinforced my belief that great teaching occurs as a result of great planning.  While what happens in a classroom has been referred to as art, that art only occurs when the teacher is constantly engaged in the creation of the experience.

This charette experience focused on the process of creation.  Daily elements of scaffolding were put into place before we began our design work.  The intention of the scaffolding was to prepare us for the process that we would undertake during that specific class period.  The best example of this scaffolding was prior to the session when we were asked to develop our design elements.  We were asked to create something in five minutes given a concept and a medium.  We all randomly chose slips of paper from two piles; my medium was a sculpture and my concept was “tension between old and new.”  I had five minutes to think of an idea and make something.  The limited time forced me just to do something without thinking.  Most of the time this is the exact opposite of what teachers try to get students to do, but in this case the purpose was for us to generate ideas.  It was freeing not to have to think about whether the idea was good or bad and just do something with it.

The other effect of this small exercise was that it lowered tension and stress for me.  Justin told us that we didn’t have time for good ideas, we just needed to jump in and do it.  This removed the expectation of judgement by others.  We were all in the same boat, individuals creating something under impossible constraints with little or no expectations.  Many of the products of this brief exercise were creative because the exercise forced us to get out of our normal analytical minds and access the creative parts of our mind.  One of my partners stated that before the charette she thought she was not an artist and after it she thought that she was an artist.  I had the same feeling as I accessed and employed my “creative mind.”

There were many other short scaffolding sessions before and during our work.  All of them were purposeful, and, for me, effective.

The other element that focused us on the process was forced reflection.  At different points of our work session, we were asked to reflect on how we felt or what we were doing in front of a camera.  This was done in two different ways, one was in the “confessional booth” where we responded in front of a camera to a written question without anyone else present.  The other method occurred when we were filmed responding to oral questions in the middle of our design work.  Perhaps Arzu and Justin were really interested in documenting the process, but the effect for me was that it forced me to look inside myself frequently throughout the process.  The filming was essential to this process as it made my reply spontaneous.  I didn’t have time to craft a response.  While I don’t remember specific revelations in design that occurred as a result of this process, I do remember feeling less stress and more focused afterwards.  I was never asked to look at my recorded reflections, and I don’t know if anyone ever looked at them.  This made and makes no difference to me as the value gained was in the moment.

The final essential element in process was getting outside input into our design.  There were a couple of formal review periods where people outside of the charette were invited to question us about our process and design.  There were also informal reviews done by Justin, Arzu, and the Fellows.  The reviews were always done by questioning:  Have you thought about this?  Why did you do it that way? What are you trying to express?  What about the use of color?  Why did you choose wood as a medium? Getting input was crucial to the process.  Nearly every time someone interacted with us it changed our design to some degree.  At the very least it forced us to think in deeper and broader ways about the design.


While I have believed in Constructivist learning for years, participating in this charette gave me a personal understanding of the process that I previously lacked. To be a student in a classroom where process was central to learning deepened my appreciation for this model and will give me a framework to build upon.