Never questioning the importance of questioning

The important thing is not to stop questioning. ~Albert Einstein

Last week Al Overwijk and I gave a one-day workshop entitled Everything we know . . . so far.  At one point Al was describing one of the lessons that came from our lesson study.  The main thrust of the lesson was to develop the criteria for asking good questions.  The impetus had come from an earlier lesson for my class where the students were given an assortment of materials and directed to ask a good question and then answer it.  The students floundered.  The questions were lousy.   As lousy as the disjointed irrelevant questions that we ask them too often.  So the lesson for Al's class was careful crafted to get at the heart of what makes a good question.  See Al's blog for more details.
 

After listening to Al's account of this lesson, a participant raised her hand and I smiled as she asked, "Why is it important for students to be able to ask good questions?"  Sure enough, Al responded with "That's a good question."  I jumped in.  I don't know exactly what I said. My words were sloppy but my passion was real.

The world is changing.  If this younger generation is to deal with problems that don't even exist yet in a rapidly changing world, then it is imperative that we help them develop the skills that they will need.  The first step in problem solving is problem-sensing and for that you need to ask questions - good questions - tough questions - good, tough questions.  Some days the toughest question I get is "Can I go to the washroom?"  We need to stop doing the heavy lifting for our students and let them do the bulk of the work and ask the questions.  We owe it to them.

 
A timely article concerning Jordan Ellenberg’s new book, How Not to Be Wrong: The Power of Mathematical Thinking appeared in Friday's Globe and Mail. To quote the article “Math is the science of not being wrong.” Ellenberg writes. In the real world, it doesn’t just find the right answers – it teaches us to ask the right question in the first place.  I couldn't agree more.

You Need to Change

Last week Al Overwijk and I had the opportunity to present at the Board's Leadership Conference.  To be fair, Al presented.  You see, our story is really Al's story.  There is no doubt that I changed my practice as a result of our collaboration but it was Al who really turned his practice on its ear.  In the presentation Al explained how after 3 semesters he was done teaching the grade 10 applied Math classes.  No matter what he tried it seemed that he couldn't engage the students and he was frustrated with the results.  He then said something in the presentation with which I took acceptation.  He reported that, as his department head, I told him he needed to change;  that he had nothing to lose because what he was doing wasn't working anyway.  He may have heard "You need to change" and maybe I did say it, but I like to think that what I did do was give him permission to take everything he knew about good teaching and put it aside.  To fill the void we went with two fundamental ideas.  First - let's just play - for the first month anyway, and teach everything through activities.  Second - we won't restrict and define our play within units of study, instead we will spiral back to all the big ideas again and again.  Al likes to say we had no idea what we were doing.  I like to believe that I knew exactly what we were doing.  We were casting off the moorings, pushing off from shore and slipping into uncharted waters.  We met almost every day to plan our next move.  The result of which fundamentally changed Al's approach.  He turned away from his rock solid chalk-and-talk and embraced an open-ended approach steeped in inquiry and observation.

We felt very good about our morning session and received great feedback.  With less time allotted for the afternoon session we knew that it was going to be a challenge.  With our principal and our superintendent and directors from other boards already in the room, our own director of education walked in with the keynote speakers Andy Hargreaves and Pasi Sahlberg.  The stakes increased along with Al's heart-rate.  It made me giggle to think that these accomplished educators whose work we have followed for years were now listening to us.  

In the end we both felt a little disappointed with the way the afternoon session rolled out because of time constraints.  As we were wrapping up we were offered a compensation prize of sorts.  A woman told the story of her friend's daughter who had been through three years of 'our program'.  At first I thought she said "You changed her life" but after consulting with Al and others I confirmed that she had indeed said "You saved her life." 

Slow Ed

Concerned with a population of increasing girth, Brazil recently came out with a new food guide.  Two of the basic principles are; cook from scratch and eat with others.  These are also basic principles in my classroom. 

Much of what we do in the classroom is the intellectual equivalent of fast food.  Relying on textbooks for example.  I would rather my students developed their understanding from scratch though activities.  Activities are the learning equivalent of slow food.  Research shows that eating alone can lead to unhealthy eating habits.  I believe that learning math in a group setting promotes healthier thinking.  The student desks in my class are arranged in pods of 4 to promote collaborative learning and encourage accountable talk.  (I do not want to discount the value of being alone with your thoughts when conceiving ideas but ultimately those ideas must be shared, tested and scrutinized by peers - hence this blog.)

Consider the number of questions in a textbook.  The 700 page Calculus and Vectors textbook that I have in front of me has over 2000 questions.  It is safe to say that most of these are not meaty problems; more like small bite-size snacks. Of course no one does every question in a textbook.  It is assumed that you will pick and choose or simply 'ace it'; "Do questions 1 to 25 odd only; a, c, e....".  Now, I know there are great and interesting problems in textbooks but most of the books tend to be filled with appetizers that are supposed to prepare your taste-buds for the main course.  Instead they tend to fill you up, leaving you bloated and sleepy.

I think that after reading The Man of Numbers by Keith Devlin, I have a better sense of our textbooks' pedigree.  It is an account of how Leonardo of Pisa, better known as Fibonacci,  published The Book of Calculation in 1202.  Early math textbooks were created to teach merchants commercial arithmetic skills. This pivotal textbook set the standard for years to come.  In fact, other than the addition of web links, textbooks haven't changed much since.   In an age where there are calculators in just about every kid's pocket, maybe it is time to start question what we value in Math class.

Historically the ability to do fast and accurate calculations has always been rewarded.  Students needed to know their "number  facts" to allow them to solve more complex questions without being  bogged down with basic calculations.  I get that.  But is it so bad to use a calculator for bigger numbers?  Unfortunately the value we place on snappy answers tends to permeate our work; question/answer wait times averaging less than a second; mad minutes; unconnected one-mark questions on evaluations; timed testing: rapid actions with limited capacity for nourishing deeper thought.

 

I know that calculation skills are important, but let's not be nostalgic for our glorious past of memorizing multiplication tables.  When someone in the back-to-basics movement complains that a young store clerk (a casualty of the 'new math') can't do simple arithmetic in an electrical blackout, I think of an old-school office administer who asked for my help with percentages.  How to best develop basic skills is not the main issue.  A bigger concern is our reluctance to even consider applying mathematics outside of the math classroom.  Even people with solid computation skills may never think of doing any math to see if an electronics store's extended service plan makes sense or if locking into a 5-year natural gas plan can actually save money.  Do our classrooms nurture or destroy math for most?

Another idea I have adopted from the slow food movement is 'eat local'.  If you close your textbook, you and your students may start to see mathematics as way to understand the world around us.  For example, when a local car drove into a sinkhole, I used the story in my grade 9 class to dig into concepts of area, volume, ratio and proportion.  One of the students knew the make and model of the car.  We found the car's dimensions online and calculated the volume of the hole.  We built scale models of the hole using linking cubes and built a life-size model with desks and plastic sheets. When the news reports stated that the hole had grown to the size of an Olympic-sized swimming pool, we used rope to outline a pool on the playing field.   What does two and half million litres look like?

But doesn't all that foolishness with ropes and cubes take time away from the hard math that these kids will need for the next grade?  There are so many curriculum expectations and so little time.  It seems we are always in such a rush to cover the curriculum.  To do that we need all the students to move along at the same pace.  It reminds me of the story about the man riding a bus in Moscow.  He watched as the driver failed to stop and pick up people waiting at each bus stop.  The man finally asked the driver why he didn't stop to pick up passengers.  The driver explained, "I am on a tight schedule and if I stopped I would no longer be on time".  We need to pick up all the passengers, even if it seems to slow us down.  But here is a trick.  We don't need to get every student to the same place at the same time.  Moving a group of toddlers down the street while they hold on to a rope is safe but it's not efficient. Some will be bored with the pace and others will be tripping over their shoe laces.  I say, let the faster students run ahead while we concentrate on helping the slower students. We will all be further along - in the long run.

Is getting everyone through the curriculum on schedule always effective?  I recall a colleague's account of an entire class of grade 11 academic students swearing that they had never seen the Cosine Law before.  They all were very adamant until one of the students found the Cosine Law on a test from the previous year; an evaluation on which she had done quite well.  We often introduce a concept with a concrete activity but quickly move to more abstract representations and concepts. Pushing into the abstract too quickly tends to lead to limited understanding and outright misconceptions.  Many students cope by desperately clinging to formulas.  My grade 9 students come to my class knowing that A = l x w but many need to count the squares one-by-one in a 5 by 4 grid.   They all know A = bh/2 but most never consider that a triangle has half the area of a rectangle.  Similarly, students can recite "a squared plus b squared equals c squared" and then tell me that 3 + 4 = 5, or 4² + 5² = 3².  I have had students tell me that they are quite positive that a positive times a positive is a negative.  And as every teacher knows that once something is 'learned' it is extremely difficult to 'unlearn' it.  Giving students a formula, rule or trick for the sake of expedience will ensure that we all get to 'teach' basic concepts over and over in grades 7, 8, 9,  10 and again in grade 11 and even 12.

Slow down.  Developing concepts takes time.  Making connections takes time.  Formulating good questions takes time. To solve complex problems without having the teacher slice everything into small chewable pieces takes time.  To reflect on the validity and reasonableness of a solution takes time.  To build an repertoire of complex skills takes time.  Slow down and in the end we will all be ahead.

The government of Brazil knows that fat-free, calorie-counting diets won't stem the rising tide of obesity.  Taking a page from the slow food movement, they are banking on a simple approach to save medical costs and ultimately people's lives. Fast food is not cheap.  It's nutritional value is minimal and the overall negative effects on our health and the environment is significant.  Thinking that you are saving yourself time and money with fast food is false economy.  Thinking that you are saving yourself time and effort in your classroom with snappy questions, tricks and shortcuts is also false economy.

 

I am not the first to use a food analogy for education.  Give a man a fish and he will eat for a day, teach him to fish and he will eat for a lifetime.  The word fish acts as a noun and a verb.  My attempt to rework it is not quite so nice;  give students some strategies and they will understand for test-time but teach students to strategize and they will create their own understandings for a lifetime. 

It's time to break from our diet of quick and easy questions, formulas and tricks, the cognitive equivalent of salt, sugar and fat. Time to construct mathematical concepts from scratch with the basic ingredients of investigation, questioning and accountable talk. 

Fast food is junk food.  Slow food is best.  Fast education is junk education.  Slow education is best.