Learn to Use Math

I frequently use math.  You probably do too, so I’d like to give you a math awareness challenge.  At the end of the day today, spend ten minutes or so making a list that describes when, where, and how you used math during your day along with the math skills that you used.  If you are kind of geeky like me, you may want to put it into a table:

when	where	how	why	math skill used
5:45 AM	bedroom	looked at clock when alarm went off	oriented me into the day	telling time
5:50 AM	bedroom	counted pushups	helped me to set and reach goals of physical fitness	counting
6:10 AM	kitchen	measured ingredients for pancakes	prepared food that tasted decent	measuring
6:30 AM	kitchen	read info from yearly physical from prior day,  (specifically my body mass index and how it related to averages)	helped me to understand my physical condition and enforced beliefs about eating and exercise	reading tables and comparing data

Perhaps you will be surprised by how often you actually use math.  We frequently use math for day-to-day tasks, and we never think about it.  We use math to help us make sense of the world around us and our place in that world.  One of the other things that becomes obvious from my table is that I was not born with any of the math skills that I used in the first forty-five minutes of my day.  I learned all of them.  

I’m not sure where I learned the skills listed above, but I’m pretty sure that I learned all of them before I was six or seven-years-old.  I carry all of those math skills (and a few more) around with me every day in what I like to call my math toolbox, a toolbox that was first opened soon after I was born. I am almost always unaware when I use my math tools.  However, every time that I use something in my toolbox, I get some practice with that skill.   I remember how to do all of this math because I do it on a regular basis.

I also know that folks can lose the computational math skills that most of us take for granted.  My father has lost most of his cognitive function due to Alzheimer's.  While he may recognize a number on a clock, he has no concept of what that number means.  He doesn’t know the difference between ten dollars and a hundred, and he couldn’t count twenty paper clips on a table.  While Alzheimer's has done other terrible things to his mind, it has also taken away his ability to make sense of the world by using math.  

The ability to use math in our lives is a skill that is frequently overlooked and taken for granted, but without it we could not function successfully.  It is no wonder that we teach math in school.  However, I do wonder about the math that we teach and the way that we teach it.

If the function of math is to help us make sense of the world around us and to solve problems in that world, then shouldn’t we spend some time practicing how to recognize problems, how to get the information we need to solve them, and then how to apply the math that we carry in our tool box (or that we can access from a resource)?  Unfortunately nearly everyone who attends school in the United States gets little practice at this, which I would argue, is a more important skill than memorizing algorithms.  

We need to present our students with situations and scenarios where they actually have to determine the problem, find the information that they think they need to solve it, and then reach into their toolbox of math algorithms to find a solution.  Students who are taught to recognize problems that others may not see, who are taught to seek multiple solutions, who are taught to appreciate the possibilities of alternate perspectives, and who are taught to synthesize other’s ideas into their own -- these are the students who are going to have control over their lives.

Yes, of course students still need to know the algorithms necessary to solve problems.  However, for math to be truly useful in their lives, students must develop the capabilities to know how and when to use the appropriate tool in the box. They can't do this without practice.

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.

Modeling: Another MOOC Course

I’ve been doing a little modeling on the side the last few weeks.  No photo shoots for Esquire or GQ, but modeling -- as in creating ways to represent the world by using math or graphics to gain understanding and find solutions to problems.  I enrolled in my second MOOC (Massive Online Open Course) through Coursera a couple of weeks ago and have gone through the first three weeks of Dr. Scott E. Page’s “Model Thinking” class at the University of Michigan.  It already has me thinking that modeling, along with probability and statistics, should be required at all schools.

If you have been listening to the news lately, you are probably aware of the growing demonstrations in Sao Paulo, where Brazilians are protesting against high taxes and low living standards.  Dr. Page’s lecture that I watched yesterday demonstated a simple model that explains how difficult it is to predict these huge public demonstrations that have occurred around the world the last three years.  It all has to do with thresholds and peer effects.  I’ll let him explain it in this six-minute video:

This simple model has some pretty big implications for seventh-graders.  We know that as children grow to be teens that most look to peers for cues on what they should wear, how they should act, what music to listen to, the type of social media to use, etc.  What is a particular thirteen-year-old's threshold for "trying on a new hat" and what if that new hat is not something harmless, but something that can have lasting ramifications.  I plan to show this video to my advisory next year in hopes that  understanding thresholds and the peer effect may give my boys enough knowledge to display courage and confidence in situations that could be harmful or dangerous.  

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.