## Sometimes, the Door Is Down the Hall

Today my blog is about one of the most important things I’ve learned as a teacher, and specifically as a teacher of math. I’m going to start with a story about a kid I tutored for a while, many years ago.

When I was younger and just starting to realize I had a passion for math and for teaching, I firmly believed that anyone could understand math and be good at it. Some people took to it more readily than others, but I was certain that given enough time and effort, every single person could excel.

Then I met Lief (not his real name).

Lief came to me when he was in grade 6, and our first tutoring session was about math questions involving time. The question we worked on was something like “Harry leaves home at 12:05 pm and arrives at his destination at 1:30 pm the same day. How long did the trip take?”. Lief was really struggling with the question, but I knew that I could explain it in such a way that he would not only be able to determine the correct answer he would fully understand how we did it and be able to answer many more similar questions. As my students would say, I have mad skillz when it comes to explaining math.

Boy was I wrong. I spent an hour with Lief and I used all my powers of teaching and explaining to no avail. Strewn about us were diagrams, pictures of clocks, number lines, a watch and even part of a model Volkswagen Beetle (don’t ask me why, I don’t remember). Lief just could not understand what the question was asking and why the answer was 1 hour 25 minutes (see how I threw that in there so you’d know if you got it right? ðŸ˜‰ ). I learned a valuable lesson that day.

Some people just aren’t wired for math. And that’s totally OK of course. Contrary to popular opinion, math is not a critical life skill. Aside from people like me I can’t think of a single person that needs to be able to complete the square of a quadratic function given in standard form in order to determine the coordinates of the vertex of the parabola. Proof? You most likely have no idea what in the world I was talking about there and I bet you do just fine. I know at least that you own some sort of electronic device capable of connecting you to the internet. That says something.

So why is this blog titled “Sometimes, the Door Is Down the Hall”?Â What am I talking about, you ask? Well you wouldn’t be the first to ask that. Allow me to explain.

Where I live in Ontario, Canada, students attend high school for four years — grades 9 through 12. During that time, in order to be awarded their high school diploma, they must successfully earn three credits in math. For most students, that means a grade 9, grade 10 and grade 11 credit, though some do grade 9, grade 10 and grade 12. It means that math is optional in grade 12, if all you want is a high school diploma. If you want a post-secondary education however, like college or university, you will most often need to take math in all four years of high school, and also be sure to choose the right math courses for your intended post-secondary program.

Phew! So that was kind of boring to read, right? But if you read it you may have noticed the glaring flaw in the system.Â A student must decide on a career path in grade 9. When they are 14 years old. Actually they have to pick their grade 9 courses when they are still in grade 8, so they and their parents have to make the call when the student is 13 years old. Who the heck knows what they want to do with their lives at the age of 13? When I was 13 I wanted to look at girls, play video games, eat steak as an afternoon snack and look at girls. And then look at girls. I had absolutely no idea what I wanted to do with my life. As a matter of fact now, at 43, I still don’t know what I want to do with my life (except for the looking at women part — I still do that and am lucky to have a wife that is exceptionally fun to look at). But I do know that I am happy with what I’m doing right now. Maybe that will change, maybe it won’t. But the key to my happiness is that I am doing something I am good at and that in turn makes me good at it. Read that last sentence a few times. It seems confusing but it isn’t. Try doing something you suck at for a long time. Keep telling yourself that you’ll get better if that makes it seem worthwhile. But I think you’ll find out that when you’re not good at something you are miserable doing it and then you are not good at it.

So how does this manifest in high school? Well it may seem obvious that since very few 13 year old kids have any clear idea about what they want to do when they finish high school — let alone as a career — that they choose the option that keeps all the doors open. In Ontario, that means that they will usually choose grade 9 academic math, because if they don’t they are closing the door to a post-secondary program that requires math. They do it again in grade 10, 11 and even in grade 12. I can not begin to count the number of students I have taught who have struggled mightily in math who then sign up for the hardest math course the following year because they don’t want to close doors. I’ll illustrate with an example. Good ol’ Hanz.

You might remember Hanz from “Steer With the Skid”. Hanz is a hard-working kid who does not have a lot of natural ability in math. By not a lot I mean he’s terrible at it. And please, before you object and say nobody who works hard can be terrible at something, look around. Some people are wired to be awesome at certain things and terrible at others. Some kids are born athletes, some are born artists, some are born mathematicians and some are born poets. You can improve your abilities in almost anything but that doesn’t mean you can excel in almost anything. Personally, as hard as I might have trained, I would never have been an Olympic sprinter. My legs are too short and I don’t have the reflexes. I’ve made peace with it.

So back to Hanz. Hanz doesn’t want to close doors, so he takes Calculus in grade 12. Currently in Ontario the course is actually called Calculus and Vectors. It’s the two hardest math topics in high school grouped together in one spectacular ride. Hanz has been miserable in math class ever since grade 9. He works hard, and puts in the time, but the most he can muster are grades in the 60’s, and it eats him up. His hard work is constantly rewarded with what he considers to be mediocre grades. He’s miserable because he’s convinced that he can’t be successful in life unless he’s successful in math and his definition of successful in math is marks in the 90’s, something he’s never been able to do. In trying so hard to keep a door open, Hanz has missed the fact that for him, there is no door marked “math”. He can’t see that if a program requires Calculus and he takes it and earns a 51% he won’t get in anyway. It’s a fruitless exercise. Yet every time I talk about this with Hanz or his dad Franz, they both insist that Hanz has to stay in Calculus so that he can keep his doors open. That’s when I shake my head and say “Sometimes, there is no door. Walk down the hall.”

See, if Hanz could recognize that there is no “math” door for him, he would be compelled to walk down the hall and see what other doors there are. If Hanz would spend more time in situations where he has natural strength, he’d know what those doors are and what lies beyond them, and he’d be so much happier. Unfortunately it’s extremely difficult to convince Hanz of this, and he spends all his energy working at something he was not wired for, spiraling further and further into self-loathing and often depression. I’ve seen it many times. I’m not exaggerating.

Now please, before you go off wondering how I can call myself a math teacher and be so willing to write kids off, understand that’s not what I am saying. I teach all levels of math. I am just as happy teaching someone like Hanz how to plan a family budget and the evils of credit card interest as I am teaching him how to take the derivative of a sinusoidal function that has been composed with the square of a logarithmic function in order to determine the instantaneous rate of change on the curve at the place where it intersects with a given exponential function. I work just as hard either way, and my reward is always Hanz’s success. It just pains me to see kids like Hanz convinced that they will end up “homeless under a bridge” (this is a saying my students have when they decide they are going nowhere in life) if they can’t do the derivative question. Honestly though, how many people can? And why on earth would most people need to? The derivative question is an exercise in abstract thought that is beautiful in its way, and critical for people going into a field where they have to solve high level math or science problems all the time, but it’s not the definition of intelligence or success.

Students like Hanz often ask me what courses they should choose when they are picking for the following year. I always say the same thing.

Me: “What are you good at?”

Student: “Well I’m good at <insert non-math or science discipline here> but that doesn’t get you anywhere so I need to take <insert completely inappropriate math or science course here>.”

Me: “Why would you take something that makes you so miserable?”

Student: “Because I need it to be successful. I need to keep my doors open.”

At that point I generally ask them how they intend to become successful in a field that requires them to be good at something that makes them miserable. They really never have an answer for that. Except for the door thing. My advice then is for them to take courses they enjoy, and that they excel in. Happy people who excel at what they do are always successful. Find one and ask them. You’ll see what I mean.

Rich

## On Being an Introvert

Hey how’s it going? My name is Rich and I’m what people call an introvert. I’ve been one for 43 years so I’m an expert at it. I decided that today’s blog should be about how that works. I’ll tell you what it means, and what it doesn’t mean, and how I’ve learned to embrace it. I’ll also tell you what you should and should not do with the introverts in your life. I will do so by writing about myself, but the truth is I am writing about all introverts. Maybe it will help, maybe it won’t. But I hope you’ll read and think about it.

First, I think I’ll start with what it doesn’t mean, and thus dispel a common misconception. I’m not shy. Far from it in fact. I make my living presenting to groups of 20-30 adolescents multiple times per day. I have presented to groups of 200 people and up. I have performed in musicals in front of theatres full of people. I played Jesus in Jesus Christ Superstar. I competed in a bodybuilding competition wearing nothing but a tiny speedo type thing in front of hundreds of strangers.

None of these things make me nervous. In fact, I thrive on it. The more people there are for me to present to, the happier I am. When I meet people for the first time I always look them in the eye and extend my hand readily. I am happy to have a meaningful conversation with a stranger and I don’t feel insecure in new situations. These things may make you want to conclude that I am wrong about myself. That in fact I am not an introvert. But I can assure you I am. Card carrying and proud, as they say!

What’s funny is that there are a lot of people who know me who are legitimately surprised when I tell them I am an introvert. That’s usually because they have only ever seen me in small group social settings, or because they have seen me perform or present. It means they don’t know what it means.

So then what does it mean? Well it means that I am happy to spend time thinking. A lot of time. I think and reflect and observe and then I do it all again. When I’m in a large group in a social setting I don’t say much. It’s not because I’m shy — it’s because I don’t have anything to say, and in any case I don’t want to compete for attention because I find it draining. I don’t feel the need to engage in conversation simply because it is a social requirement. I don’t like loud rooms because I can’t hear myself or others talk. I don’t understand why they play loud music in many restaurants when all that does it make it difficult to hear what your companions have to say. I like going to parties but I don’t like staying — I find it’s nice to see everyone but after a while I get overloaded with sensory inputs and I have to leave. Don’t take it personally. The fact that I came means I care about you. If you see me at a party you’ll find me in a quiet corner. You may think I am being stand-offish but nothing is further from the truth. Sit down and let’s have a nice conversation about something interesting. I will listen more than I talk, but I will talk plenty. You’ll probably find that refreshing because I am an active listener. I don’t just listen waiting until there’s a break in what you are saying so I can continue to talk about me — I really listen. And when I talk you’ll find out just how closely I was listening. When I leave I may not say goodbye. That’s only because there was so much going on and I didn’t want to interrupt. I know it comes off as rude sometimes but honestly I’ve found it’s easier to seem rude in one instance than to try and break into an activity to say goodbye.

I also like to be fully prepared before I try something new, and I constantly check my progress to make sure things are going as they should. I ask a lot of clarifying questions before I proceed into the unknown. I’m not afraid to try new things, but I like to understand what I’m getting into as much as possible before they happen. When I was a baby my parents laughed at me because when I would turn around to crawl off a chair I would check the floor 10-15 times as I slowly lowered myself to make sure it was still where I thought it was. When I behave this way with you, just answer my questions patiently and we’ll both be happier for it.

Being introverted means I spend a lot of time observing people. I don’t judge quickly because I’ve learned that the longer you pay attention to someone the more you learn and the more layers you see through. This means I understand most people better than most people. It also means that a lot of people think I’m a snob. I can’t tell you how many times I have been called that. My lack of talking comes off as snobby and disinterested. It simply isn’t true. My lack of talking has everything to do with me thinking about what is worth saying. The truth is there’s not much that is. Most people talk because silence makes them uncomfortable. I love silence — it lets me think.

I’ve also had a lot of extroverts try to “cure” me. That’s one of the most uncomfortable things an introvert learns to deal with. Please don’t get me wrong though. I love extroverts. I enjoy watching how much fun they have doing things that would give me no pleasure at all. I love how they can come into a new situation and within minutes be best friends with everyone in the room. It’s cool. Super-cool. But it’s not me and never will be, and I don’t care because I’ve tried it and it did nothing but make me uncomfortable. One of my favourite examples of extroverts’ deep need to cure me is during the Hora dance, which my Jewish readers will be intimately familiar with. For the non-Jews who don’t know, it’s a kind of dance that an entire room gets involved in. The step is very simple and involves everyone holding hands in a big circle, although very often there will be concentric circles when the number of people in the Hora results in a circumference that exceeds the dimensions of the dance floor. When the Hora music starts up, all the extroverts get a fire in their eyes. They leap from their table and charge to the dance floor, grabbing the hands of everyone they pass on the way. It’s like ecstasy in a dance beat. If you watch the introverts though, you’ll see them deliberately not making eye contact with anyone and keeping their arms firmly at their sides. We are not interested in dancing the Hora. It’s not because we’re not happy, it’s because it does nothing to enhance our enjoyment of life and actually makes us uncomfortable. The problem is our lack of participation makes the extroverts uncomfortable. How can someone not want to dance the Hora, they ask? There can be only one explanation for them — we never tried it. If only we’d try we’d find out just what a blast it is. So they leave the Hora, seek us out, and physically haul us onto the dance floor. The Hora is a perfect metaphor for extroversion. If only we knew how much fun it was, we’d want to do it all the time!

Now when I was younger, I was actually convinced that something was wrong with me. I also was way too polite to refuse. So I would let myself be pulled in by these well-meaning Hora Pullers. And then it was always a nightmare. I would freeze a somewhat horrified smile on my face and move around with the others, always wondering when it was going to start being fun. I looked awkward. I was embarrassed. Being in the Hora only emphasized my introverted nature — it did not even come close to changing it. As I got older I realized I was much better off simply politely refusing. I say things like “Nah, the Hora isn’t my thing” and I smile. It’s much better for everyone this way and I am completely happy and comfortable with it.

So my message to the Hora Pullers, Spirit Leaders and Party Planners is this — I don’t need curing. There is nothing wrong with me, and when I don’t participate in your fun it doesn’t mean there’s anything wrong with you either. IÂ like not participating in those crazy socializers. I like watching — it’s how I learn about people and how I experience large group activities. If you want to find out about me, ask me. If you want someone to talk to who will listen, talk to me. If you want someone to help you reflect, I’m your man.

And if you need a speaker for a conference you’re planning, look me up!

Rich

## Steer With the Skid

The physics behind why it works are fairly straightforward. When you enter into a skid your car has momentum which is carrying it in a direction that is usually not conducive to healthy living, and there’s nothing you can do about it because the friction between your wheels and the road has suddenly been reduced significantly by ice, water, gravel or some other non frictiony substance. This means that gross corrections where your wheels are pointed at an extreme angle to the skid won’t work, because the momentum of the car is overcoming the minimal friction at the wheels. So by pointing the wheels in the direction of the skid you force the momentum to cooperate with your goal of non-disaster, and then make relative small corrections which work because the little bit of friction you do still have is only slightly off from the massive momentum. Baby steps of correction eventually get you out of trouble. And it happens pretty quickly, as anyone who has ever done it can attest to. When you don’t understand the physics, it almost seems like magic.

The reason it has to be taught though, is because it’s so counter-intuitive. Aiming in the wrong direction so that you can go the right way feels like slowing down so that you can speed up. As it turns out, this driving lesson is actually an incredibly important life lesson as well. It shows up in so many ways. I’ll illustrate with a few examples of skids.

Skid 1: The Determined Daughter

Skid 2: The Quadratic Quandary

Here’s another scenario that I often encounter at school. Let’s say I’m helping a student solve a quadratic equation (apologies for this if you don’t know what that is — feel free to skip this part). Take this one for example:

xÂ² âˆ’ 5xÂ âˆ’Â 14 = 0

If you’re a math teacher you know that a goodly portion of students unused to solving quadratics are going to try and isolate the variable the nice old fashioned way. You also know that it won’t work – totally destined to fail. You might be tempted to intervene before they try, and suggest a different method, but if you do then in the back of their mind they’ll always be wondering why not just isolate.

The best strategy pedagogically is to let the student try it. Agree that isolating the variable is a good plan. Help them with the operations – steer with the skid. As you work with them to isolate the variable generally this will happen:

xÂ² âˆ’ 5x =Â 14

At which point you can have a very valuable discussion about why we are stuck. The student may try some fancy footwork here, but thanks to you being on their side, you can navigate it with them and they’ll see that there’s nowhere to go. Then you can gently steer them toward other options. What do we know we can do with quadratic expressions? Factor them. So what? Let’s find out. I won’t get into the actual solution here, because it’s not important right now and in any case if you were following until now I’m fairly confident you can finish up. But for those who need to know, the solution is x = 7 or x = âˆ’2.

Skid 3: The Perturbed Parent

Once more this scenario is one I encounter as a teacher, but in fact it generalizes to any customer service industry. I actually really learned this well in my previous life as a software engineer when I would spend quite a bit of time on the phone with our users who would call when they were struggling with our software. Readers who are teachers will understand this situation pretty well. It goes like this:

Hanz is a student in your class who has written a math test for you and earned a fairly low grade – say, 54%. Hanz has plans to go to university (or college if you’re American – here in Canada college doesn’t mean quite what it does in the States) to become a doctor. Hanz needs a high school average of 91% to get into medical school. Thus the 54% on your test is a somewhat sub-optimal result. The next day you get a call from Hanz’s father, Franz. Franz opens the conversation by informing you that he is a lawyer, and that he has a real issue with the mark you gave Hanz on the test. Franz tells you that Hanz is extremely gifted in math and has always earned grades in the 90’s until your class. Hanz worked extremely hard preparing for the test and his tutor guaranteed that he was ready to ace it. Franz concludes that the whole mess is therefore your fault, because you are an unfair marker, a bad teacher, a horrible human being and quite possibly a chronic hater of children. Franz insists that you raise Hanz’s mark so that it is consistent with Hanz’s abilities and also consistent with his goal to become a neurosurgeon.

At this point it is incredibly tempting to get defensive, or be offensive. After all, Attorney Franz has attacked your professionalism (unfair marker, bad teacher) and your motivation for being a teacher (child-hater). Furthermore, if you know Hanz you know that “gifted” and “math” are not two words that you would put together in a sentence describing him, unless you could liberally sprinkle said sentence with the words “extremely” and “not”. However there is nothing to be gained by this response. All it will do is exacerbate the situation.

Instead, steer with the skid.

First, tell Franz that you understand why he’s upset. In fact you are upset by the grade as well – who wouldn’t be? Ask him about the hard work Hanz put in to prepare. Commiserate with Franz about the difficulties of watching young people work so hard and then not have it pay off. I am not being facetious here, and neither should you be in a situation like this. Put yourself in Franz’s shoes. Hanz worked hard, and hard work is supposed to equate with success. So why didn’t it? You and Franz can discuss this question. You can provide Franz with some questions to ask the tutor about the work he does with Hanz. You can recommend that Hanz come and see you to go over the test to see where the disconnect was. After all, since Hanz is so talented in math, there must have been a disconnect. When Franz sees that you have no intention of fighting him, his momentum joins yours and you can then steer him in the direction he needs to go, which is ultimately to realize that you did not “give” Hanz his mark – Hanz earned it. And getting to the bottom of why he earned a mark as low as he did is what you both want so that you can both help Hanz. This will ultimately help Franz see that it is Hanz who was at fault, and will also eliminate the need to address some of the more insulting parts of Franz’s opening tirade. It is entirely possible that during the conversation Franz will admit that the “marks in the 90’s” comment was not completely true, and referred to 2 quizzes Hanz wrote when he was in the 3rd grade. By the end of the conversation, Franz will know that you are on his and Hanz’s side, and that the energy of all three people is channeled in the same direction – not the direction of the skid anymore!

There are countless other scenarios I can come up with, all of which I have experienced personally (no, I never taught anyone named Hanz …), but the theme is always the same. A situation arises and the temptation is to fight against it, but fighting only escalates the problem. The solution is counter-instinctive and often requires strong self-control but pays huge dividends. Leverage the momentum of the skid for a quick and successful course correction.

Works in cars, works in life. Steer with the skid.

Rich

## Dare To Be Exceptional

I’m kind of a strange guy, in that most of my favourite movie quotes come from animated films or sci-fi, or both. Yoda, Master Oogway, Jean-Luc Picard, Optimus Prime … all have wisdom to share. But today’s blog is about one of my very favourites, from Mr. Incredible himself, when he found out his son was going to be part of a graduation ceremony at the end of grade 4.

“It is not a graduation. He will be moving from the 4th grade to the 5th grade. It’s psychotic! They keep inventing new ways to celebrate mediocrity, but when someone is genuinely exceptional…”
–Bob Parr, aka Mr. Incredible

How sadly appropriate in today’s society. Our children are bedecked with meaningless medals, they stare at shelves lined with trophies for participation, and they are celebrated in ceremonies commemorating inevitability. Society has decided that recognition of excellence must not come at the expense of the runners-up. So everyone wins. Every moment is a photo opportunity. When my son finished Kindergarten the photographer at the school put him in a cap and gown and handed him a fake diploma for the portrait! How proud we were meant to be, I wonder, that through hard work and dedication he had earned his Kindergarten diploma? I mean truly, how many parents can say their kids have managed that milestone?

We manufacture their success and then we celebrate it.Â Then we lament the fact that this new generation comes off as underachieving, entitled, and uninspired.

Thankfully we are wrong about them. But sadly the reason young people often come off this way is because we give them little choice. How is a child who is constantly rewarded in the wake of mediocre performance to learn the benefit of striving for excellence? What will inspire them if, having put forth little to no effort, they are lauded as champions? Because that is what we do. And for those children who truly shine, what is their reward, when all the others are painted with the same glorious brush? How long should we expect those kids to put in all their effort when they watch their peers work half as hard, accomplish half as much, and get praised twice as often? Because the other sad truth is that for fear of hurting those who under-perform, we under-reward those who excel. Are we doing anybody any favours with this?

Of course, it’s not always like this. Happily younger generations still have the human condition, and still want to truly excel. TheyÂ are inspiring, theyÂ don’t all think life is a free ride, and many of them achieve their potential. And I know many teachers – myself included – who still push for excellence and reward it when we see it, and who do not praise mediocrity or manufacture success. That may sound harsh, but it is not. Kids know when they have put forth their best effort. They know when they have broken past old boundaries. In short, they know the difference between success and failure. And when they feel that nothing special has occurred, but the world around them still celebrates their “achievement”, it is confusing for them and makes them feel like a fraud. In other words, in trying to build self-esteem by making sure everyone gets a trophy, we really reduce it significantly. By recognizing true excellence, we foster it. We dare kids to be exceptional.

There is another quote I love, this time from a real-life person. It’s actually often mistakenly attributed to Nelson Mandela, because he quoted it in a speech, but the original author of the quote is Marianne Williamson:

“Our deepest fear is not that we are inadequate. Our deepest fear is that we are powerful beyond measure. It is our light, not our darkness that most frightens us. We ask ourselves, Who am I to be brilliant, gorgeous, talented, fabulous? Actually, who are you not to be? You are a child of God. Your playing small does not serve the world. There is nothing enlightened about shrinking so that other people won’t feel insecure around you. We are all meant to shine, as children do. We were born to make manifest the glory of God that is within us. It’s not just in some of us; it’s in everyone. And as we let our own light shine, we unconsciously give other people permission to do the same. As we are liberated from our own fear, our presence automatically liberates others.”
–Marianne Williamson