The Big Problem - Real Life Requires Real Math

Solving real problems is messy.  Sometimes, we don’t even know what problem we are trying to solve, and it doesn’t become obvious until some investigation and discovery takes place.  We must decide what information is needed and attempt to get it, although it isn’t always available.  Sometimes there are so many variables that they distract or even confuse us from defining a course to follow.  And, frequently there may not be one absolute solution.  The solution that we reach may have corollaries or disclaimers, or it may simply be a best guess given all of our efforts.  I hope this is starting to sound like real life because it doesn’t make a lot of sense to devote a huge chunk of time in school to learning math that is not useful in real life.  And, if our students don’t get opportunities to use math in real life situations, then they will continue to see it as a boring, inert process that must be slogged through just to get to the next math course; or, even worse, as the way to a better score on the SAT.  Math is so much more than a way to get into college -- it is a way to view the world, and it gives us the ability to understand, seek, and find solutions to the world around us.

This week, we started working on one of what we call our Big Problems --  a real problem.  I told the students that I had been thinking about replacing the long, rectangular tables in our lunch room with circular tables.  Because our students are primed from years of practice as problem solvers, it took them all of ten minutes to come up with the following questions and comments in some small group discussions.  Although as a school administrator, I have thought of changing out the tables for a long time, I hadn’t considered several of their ideas as variables:

• Are round tables more ergonomical?  Forearms naturally form triangles when on the table.
• How big can a round table be to hold a conversation with someone across the table in our lunchroom?
• Does looking at someone when talking to them help conversation and relationships?
• Would there be more space to move between the tables?  
• What happens to aisle space?  Will it open the flow or restrict it?
• How would moving to round tables affect cleaning? How big can it be and still be easily cleaned?
• Storage? (We move our tables every day to clean the floor.)
• Will round tables hurt or help inclusivity?
• Will they fit in the lunchroom?
• What will be the cost?
• Will the cost be worth the benefit (if any)?
• Unintended consequences?
• Other stakeholders (the LS students who use the lunchroom also).

What kind of math tools will we need to pursue this problem?  Some things are obvious like measuring, performing simple arithmetic calculations, working with geometric shapes, and spatial reasoning.  However, we may look at hearing as a function of distance from speaker (this is an algebra class after all).  Or the number of seats available as a function of the circumference of a table.  We are going to have to figure out some way to apply a dollar amount to something that is not easily counted (building relationships) and this will definitely involve some statistical analysis.  We are going to have to do some data collection, analysis, and interpretation.  More statistics. Finally, we are going to have to reach beyond our collective knowledge base to get information and possibly even help.  

So, how does this assignment hold up to the teaching of skills that have become a fundamental element of our middle school:  collaboration, problem solving, communication  creativity, perseverance, grit.  We can check all of these off.

I told the students that if we decide that replacing the tables would be a good idea that we would present our findings to our Chief Financial Officer and other stakeholders.  We are not sure if the school will take our advice; this is the real world after all, and there are all sorts of other claims on school dollars than lunch room tables.  But, regardless of the outcome, the process of working through this problem will give the students and teachers some practice with the utility and function of math.   

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.

Building Relationships

Seventeen years ago, I was sitting in a sterile, public school administrator’s office being interviewed for a teaching position.  When asked about my best qualities as a teacher, the first thing out of my mouth was my ability to form positive relationships with my students.  I explained how I listened to students’ problems, took them to perform community service work on my own time, and went to important events in their lives outside of school.  I professed that because I worked to develop relationships with my students, they would behave better in class, work harder, and gain self-confidence.  Almost immediately I realized that the principal interviewing me didn’t hold the same beliefs.  She quickly directed the conversation back to curriculum and testing, and I left the office knowing that I didn’t get the job -- and feeling somewhat grateful that I wouldn’t be working for this person.

I am fortunate to find myself working in a school that puts a premium on relationships, and we have structured our middle school to reflect this belief.  We offer students and faculty opportunities to connect with each other throughout the daily schedule and the calendar year.

• Group work -- I can honestly say that not a day that goes by that a student does not have the opportunity to work with another student or group of students.  Learning to work together is our culture.

• Advisory -- our advisories are single gender and multigrade.  Advisories are small, six to eight students, and led by a faculty member of the same gender.  We meet first thing each morning for fifteen minutes and have casual chats, foster important discussions, or play games.  
• Breaks -- our students have two breaks during the day, one during the morning and one after lunch.  Students can choose to play or talk together.  Students are discouraged from doing academic work at this time.
• Advisory intramurals -- each day during morning break, two advisories compete against each other in fun games like handball, beach volleyball, and pinball.  It has become so popular that half of the school comes down to watch the games and cheer.
• Exploratory -- twice in our six-day cycle, our students attend a class called "Exploratory." Faculty members choose a pursuit that they enjoy such as photography, board games, knitting, Pinterest, Lego robotics, theater games, and coding; and students sign up for the class.  Exploratory classes change three times each year.  Students (and faculty) of different grades and genders spend time together in pursuit of mutual interest.
• Dances and activities -- we hold three dances per year for our middle-school students.  Nearly every student attends and they are highly anticipated.  There are also three after-school social activities per school year like bowling or roller skating.
• Buddies -- all of our middle-school students are buddies with lower-school students.  Buddies get together six to ten times per year to participate in fun activities centered on the younger of the buddy pair.
• Extracurricular activities -- In middle school all of our students are encouraged to participate in athletics or our musical theater production.  Nearly all of our students take advantage of these opportunities to play, compete, and perform together outside of the regular school day.
• Overnights -- All of our students participate in two separate overnight trips during the school year where an emphasis is placed on developing teamwork among the students and faculty in the grade.

As a faculty, we also talk about ways to continually develop relationships with students.  None of these require teachers to be charismatic "pied pipers;" they are simply good practice in establishing and growing relationships:

• ask questions and listen
• be genuine
• go to extracurricular activities and talk to students about them
• smile
• be patient and persistent in your attempts to connect
• be observant of students’ changes in mood and ask them about it
• share your own passions
• tell interesting stories from your past

Being a part of something, belonging to a community, is especially important during the middle-school years when adolescents and preteens start pushing away from family and trying to decide who they want to be.  It is sometimes a confusing time in a child’s life and a time of struggle with self-confidence.  We know that connecting with others helps middle-school students to find their own way and be happier, which is why we put so much effort into building our relationships with each other.