My Champagne Anniversary

So today is my 19th anniversary. December 19th. I never knew this was called the Champagne Anniversary but my wife told me the other day. Pretty cool. I’ve been married to my best friend for 19 years and we’ve been together for 26. I am so blessed I can’t even begin to express it. But I thought in honour of my wife and our anniversary I’d do a blog about marriage. Here it is.

A lot of people these days ask me how we’ve stayed married for so long. I usually tell them they should ask someone who’s been married for 40-50 years, since we are just babies in the marriage department really, but the other day someone asked and I took the question seriously. I think it boils down to three things really, Compatibility, Commitment and Communication.

(Side note: I actually just this moment thought of a way to say it using three things that start with the same letter — gosh darn I’m clever. Of course now I’ll Google it and find out it’s the oldest thing ever and feel suitably humbled again. Then again, maybe I won’t Google it just yet, and live under the impression I’m all that for a just a little while longer …)

So where were we? Oh yeah, “The Three C’s of Success” … wait … success actually only has to c’s … ah crap. This needs work … oh but wait, I was talking about my marriage. Allow me to continue then.

My wife Marla and I met in high school. She was my first real girlfriend and so she is the only girlfriend I’ve ever had. I therefore don’t have a ton of experience with women or with relationships. For this reason I generally feel unqualified to give relationship advice or judge the relationships of others, and that’s probably why I usually have a hard time talking about what makes a relationship or marriage successful. But then again, maybe that makes me uniquely qualified. I’ll let you be the judge.

First, let me tell you about why I fell in love with Marla. It’s simple. She saved me. I was an awkward, quiet, socially invisible teen. Marla didn’t care. She saw something in me and she wanted to be my friend. We spent hours and days talking about anything and everything, getting to know each other and she was never put off by my nerdy awkwardness. To this day I am not entirely sure why she was interested in me or why she still is, but I am eternally grateful. We learned through that early friendship that we are compatible (check it out – that’s the first “C”!) and the friendship grew into love. I was 17 and she was 16.

Laugh now, because what couple that age can have any clue about compatibility? And yet we were never presented with any reason to think we weren’t right for each other. It never occurred to either of us that there might be something better out there, or that we needed to play the field, even though I will say many of my friends believed their adolescence and early twenties were designed for nothing else, and never entered into any relationship believing it would last. I never understood that. What’s the point of starting a relationship you are convinced will end? Never got it, never will. So Marla and I were always committed to our relationship (the second “C” — are you keeping count?). Another thing that Marla taught me was that things need to be discussed. I grew up keeping quiet about feelings. I learned to deal with my emotions internally, and developed very strong rationalization skills. I wouldn’t say I swallowed my feelings, just that I always found ways to resolve issues by myself without really talking too much about it. Marla taught me to talk. It was like she opened a floodgate. I couldn’t believe there would be someone interested and caring enough to listen and absorb and respond. We talked about everything, and still do. Communication. The third “C”.

But so far all I’ve talked about is the beginning of our relationship, and that was 26 years ago. A lot has happened since then (2 kids and a mortgage to name a couple) and we are still together. How is that? Well … it’s the three “C”‘s. We never forget them.

Compatibility. We are immensely compatible. It doesn’t mean we like all the same things, or have similar personalities. In fact we are very different. But we fill the spaces for each other. I’m a big picture thinker – she’s a detail specialist. I am introverted – she loves to socialize at parties. When I go to the fridge to get milk for my cereal, I open the door and then forget why I’m standing there – she remembers every single person’s birthday. I love to make speeches in front of a large group – she hates presenting to more than one person at a time. The list goes on. At our core though, we share the same values about family, friendship and finances (Hey! The three “F”‘s … and don’t you go telling me there’s a fourth “F” … this is a family blog). Some people believe that there is one special person out there for you. Marla and I have never thought so. For me, the mathematics just don’t pan out. If there is only one right person out there, what are the chances you would meet them? What if the right person for you is a Nepalese goat herder? Nah. What I DO believe is that you have to be the right person. Find someone you are compatible with, someone you fall in love with, and then make yourself right — not by changing who you are but by being committed to the relationship. And there it is, the second “C”.

Commitment. Be committed to the relationship. There will be hard times. Some extremely so. Marla and I have had some fights let me tell you. But never … never during any one of those fights, has either of us considered that the fight wouldn’t end. We always know that we will work it out. It’s very hard sometimes to get there, and I won’t lie and say we always make up before the day is done, but I will say that we always make up. We know that we will even when the fight is at its worst. We are committed. And we know that even though it’s not always the best, as long as we are arguing we are communicating. See how I did that? The third “C”, and maybe the most important one.

Communication. Communicate always. I have learned that when one of us is feeling that there is something to keep to ourselves then that is probably the most important thing to talk about. Sometimes the reason you don’t want to bring something up is because you know there will be huge backlash. But I feel as though there is already backlash when you swallow what you want to say, because resentment builds. And then what happens is your partner senses the resentment but can’t pinpoint the cause, and the resentment is returned in a spiral of unproductive silence. So we always talk, even when it seems hard, and even when we know it will lead to an argument, because the argument can be resolved but only when both sides know there is an issue. Now of course communicating problems is not the only kind of communication, nor is it the most common. Not by a long shot. Marla and I spend a lot of time just talking. She tells me about her day and I tell her about mine. We listen actively — not just waiting until the other finishes talking so you can have a turn but respecting them by listening to what they are saying and digesting it. At any given moment Marla is the person I most want to be around, and she feels the same way. So we spend a lot of time just being together, enjoying each other’s company. And we communicate our love too. I tell her at least 70 times a day (OK, maybe less than 70 … but not much!) and so does she. I know some people feel they don’t have to say it because they show it, but it’s not true. You have to say it and show it. Say it when it occurs to you. I often just look at her, get happy because she exists, and then tell her that just happened. Communication. It’s the key “C”.

So that’s it. A blog dedicated to my wife, the love of my life, on our 19th anniversary. She is my best friend, she is my love, and she is my partner. I love her.

Thanks for reading,

Rich

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? 😉 ). 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”? 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.

At each grade, there are choices of which math course to take. There are different paths and they don’t all lead to the same place. For example, a student who intends to study math or science at university will take what’s called “Academic” math in grades 9 and 10, then “University prep” math in grades 11 and 12. Conversely a student who intends to go to college to learn a trade will likely take “Applied” math in grades 9 and 10, then “College prep” math in grade 11 and maybe also in grade 12, depending on the requirements of the college program. Some students take what’s called “Essentials” math in grades 9 and 10, then “Workplace” math in either grade 11 or grade 12. These students are either not planning to attend a post-secondary institution or else are planning to go into a field that has nothing at all to do with math.

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. 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.

Thanks for reading,

Rich

Steer With the Skid

When you learn to drive in Canada, one of the most important lessons is what to do when your car enters into a skid. It’s not a question of “if” really. In Canada, it’s definitely “when”. Usually it will happen in your first winter of driving, so you’d better be prepared. The technique is to steer with the skid. It means that you have to fight your natural urge to steer in the direction you’d like for your car to go, and instead actually aim your wheels right at that concrete median your car has suddenly decided to crash into. Then, once you and your car agree on the direction you want to go, you gently steer the car away from disaster. It works, and in fact it’s the only way to handle the situation, except perhaps throwing open your car door and launching yourself out onto the pavement.

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

Imagine this scenario. It’s 5 minutes before you have to leave the house to walk your daughter to school, and she is insisting that she does not want to wear a jacket. The problem though, is that you happen to know it’s 3° Celsius outside. If your daughter is anything like mine and she has her heart set on not wearing a jacket then you have 5 minutes to fight and win World War III. Good luck. This, ladies and gentlemen, is a bona fide skid. Your car is careening into two kinds of barriers. Frostbitten Child and Late Slip. Solution? Steer with the skid. Instead of fighting the momentum, agree that she does not need a jacket, but bring it with you and leave. If you really want to be fancy, don’t wear yours either. You carry hers and she can carry yours. Or you carry them both — it’s not really important. Once again if your daughter is anything like mine she will have a true aversion to discomfort, which is something she’ll start to feel within about 20 steps. She’ll ask for the jacket. If you didn’t wear yours, you can ask her for yours before she asks for hers. That will make it okay for her to ask for her own and still save face. Skid averted. No frostbite and no late slip.

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:

x² − 5x − 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:

x² − 5x = 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 = −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.

Thanks for reading,

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. 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. They are inspiring, they 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

I have read and reread this quote to many of my students, and often just to myself. If you’ve never heard it or read it, spend some time reading it over a few times right now. If you have read it or heard it before, read it again now. Think about what she’s saying. I think about it all the time. Every time I am tempted to, say, dumb down a sentence because I think maybe the audience won’t understand it. Or every time I am singing in public and catch myself deliberately about to use my “I don’t really think I’m a singer” voice so people won’t think I’m showing off. Every time a student asks me about how I did in math when I was in high school, and I almost lie because I don’t want them to feel bad about the mark they are getting. Every time these things come up, I remember that I should dare to be exceptional, so that others will too. So I use my full vocabulary and let my students use context to figure out what I mean, I sing with intent every time, and I tell them that I was very good at math and that I had an average of 97% in my last year of high school, which was only as low as that because my English mark brought it down.

So my advice is this:

  • Parents – love your kids but please don’t confuse love with empty praise. Challenge them to be better and praise/reward them for true excellence. Don’t be afraid for them to try something and fail, because failure feeds desire.
  • Teachers – let’s continue to raise our expectations and celebrate when the students achieve at these higher levels, rather than lower them (as current culture would have us do) so that everyone can “succeed”. Let’s breed true success.
  • All of us – don’t shrink from your own brilliance. Go all out every time, and watch how everyone around you starts to do the same thing. We can be so impressive when we want to.

Let’s want to.

Thanks for reading,

Rich

Switch the Side, Switch the Sign?!!?

You can always judge my level of incredulity by my combination of punctuation. Two exclamation marks bookended by two question marks is a high level indeed. It’s the DEFCON 1 of incredulity. It comes from the way I’ve seen a lot of my students conditioned in algebra. It’s extremely sad. I’ll explain, but I have to start with a story about something that happened last week.

Thursday night I came home from play rehearsal and got the debrief about the household goings-on from my wife. Turns out my daughter, my 11-year old angel of happiness, was crying for something like 2 hours while I was gone. Dads out there with daughters (and I guess daughters with dads?) will know that there’s a special thing going on between dads and their girls. I think the best quote I ever read to describe it was this one:

Certain is it that there is no kind of affection so purely angelic as of a father to a daughter. In love to our wives there is desire; to our sons, ambition; but to our daughters there is something which there are no words to express.
– Joseph Addison

So when I find out that my daughter was so miserable, a part of me curls up in the fetal position and cries too. But you want to know what made it worse? What made it even more upsetting? The source of her pain was … algebra. Algebra! Her first algebra. A person’s first exposure to algebra should be special. It should be life-defining. It should be a cherished memory that warms you on command. A polished jewel of contentment forever residing at the center of your soul. And yet here’s my daughter, crying for 2 hours, and it was because of algebra. And I wasn’t home.

Talk about two ways to break my heart. Unacceptable!

So I dug a little deeper. My wife told me that my daughter was doing question after question, getting them right, and crying that she didn’t get it. My wife, no slouch in the math department for sure, was explaining the process, but for some reason it wasn’t getting through. My daughter just kept insisting she didn’t get it, all the while getting questions correct. How does this make sense? In what universe can a child keep getting questions right and through tears insist she doesn’t understand? The answer is because she was just following orders. The old “Switch the side, switch the sign” gambit. Consider this question she was working on:

x + 3 = 7

x = 7 – 3

x = 4

Correct, right? And easy too? So why was she so miserable?

It’s because she had no idea why she was doing what she was doing, or what any of it meant, and certainly no way to tell if her answer was right. She was right by accident, and because she was following a bunch of rules. In short, she wasn’t doing any math at all. She was, for all intents and purposes (or for all “intensive purposes” if you’re one of those people who hears sayings but never sees them written down) a trained monkey repeating a task. And nobody wants that … except for maybe the monkey because they get a lot of rewards for stuff like that … but no human wants that. And my daughter is exceedingly human.

You see, here’s what she was taught (or at the very least, to give her teacher the benefit of the doubt, it’s what she thought she was taught): To get the variable alone you have to move the number to the other side. If it’s plus you do minus and if it’s times you do divide. If it’s minus you do plus and if it’s divide you do times. Ouch. So much wrong with this I don’t even know how to start. But I do know that it’s taught this way so often that I have students who think that’s what algebra is. And I know of one teacher who used to have her students repeat the mantra “Switch the side, switch the sign.” I used to ask those students what they do if it’s multiplication or division. They said that’s when you don’t switch the sign. Ooooookay then.

So here’s the thing. When students are taught “rules” for solving equations they are not learning math. They are learning algorithms. An algorithm is a sequence of steps you follow to complete a specific task. You don’t need to know why, and in fact the reason algorithms are so powerful and so common is because you don’t need to know why. Long division is an excellent example. Many of us remember how to use long division to get the answer to 97654 divided by 7. But how many of us know why it works? The algorithm was designed to turn humans into calculators so that mathematicians didn’t have to do the tedious work. In WW1 there were literally rooms full of people – called calculators – who would do repetitive tedious calculations assigned to them by codebreakers. The codebreakers knew why the calculations were required, but the volume of work to do it was so vast that if the breakers themselves were to do the work they’d never decode a single message. So calculators were invented. They were people. A lot of them. And they were good at algorithms. But they didn’t know any math. Of course nowadays we have little computers that do the same job, but the concept is the same. A computer doesn’t think – it only follows instructions. It is excellent at executing algorithms. BUT THAT ISN’T MATH!!!

Ok. Back to the algebra, and my daughter. Saturday morning we were sitting in the family room, still in our pajamas, and Phineas and Ferb had just ended. The time was right. I told her I was going to help her with algebra but first she needed to forget everything she’d learned thus far. She happily agreed and put the misery in some invisible incinerator. Ahhh. Square one. Then we had this conversation:

Me: “Imagine I split your class up into groups of 2. Pick a partner.”
Her: “Alyssa!” (this was meant to be obvious to me)
Me: “Ok, now every pair has to pick one person for the blue team and one for the red.” (blue is her favourite colour – I’m not a rookie)
Her: “Blue!”
Me: “Ok, we’re going to play a game. Blue team goes first. Here’s the game. Pick a number but not a hard one. Don’t tell red team what it is. Now your job is to give Alyssa one hint, and if she gets it right you both get a point. Otherwise nobody scores.” (yeah, lame game, I know – but there are points and a blue team so she’s right on board)
Her: “Ok. My hint is it’s my favourite number.” (I saw this coming a mile away, and had a plan)
Me: “Right, Ok. But here’s the thing. You want to be SURE Alyssa will get it right. What if she can’t remember what your favourite number is? You want to give her a clue that will work for sure. And no using your number in the clue!”
Her: “It’s my birthday.” (Ha! I saw that coming too)
Me: “What if Alyssa forgot your birthday?”
Her: “How could she? She’s coming to my party!”
Me: “Good point. But what if she thinks your birthday is on a different day than the party? After all it is. You want to be sure she’ll guess your number, so make the hint foolproof.”
Her: “Ok, I get it. My hint is my number is 5 less than 10.”
Me: “Awesome! Ok, I’m Alyssa. Is it 5?”
Her: “You knew that already because you know my favourite number.”
Me: “Good point. Ok, here, it’s red team’s turn. If you increase my number by 7 you get 12.”
Her: “Hey you can’t pick the same number as me!” (Success!!!!)
Me: “Yes I can I can pick any number I want. Ok your turn.”
Her: “If you cut my number in half you get 10” (ooooh, nice one)
Me: “20?”
Her: “Yes! Ok, give me one now!”
Me: “If you multiply my number by 2 and then add 1, you get 13.”
Her: “6?”
Me: “6? Why 6?”
Her: “Because 6 x 2 is 12 and 12 + 1 is 13.”
Me: “Nice! Ok, you go.”
Her: “If you add 67354 to my number you get 90543.”
Me: “Ummm, are you going to know if I got it right?”
Her: “No. But you always get it right so I want to know the answer.” (Love her – I always get it right? She needs to talk to my wife!)
Me: “How am I supposed to get it? Those numbers are huge!”
Her: “Just do 90543 minus 67354!”
Me: “Right. I knew that. Ok it’s 23189.” (I rock at doing subtraction in my head – blows her away every time – she checked with a calculator)
Her: “Yes. Nice one Daddy.”

This went on for a long time. She really liked the game. At some point she realized that I was not keeping score and she got mad at me. Then she realized that it would always be a tie so she said it was not a good points system. We spent some time coming up with a better points system. She came up with something. It was fairly convoluted and had to do with blue team’s ability to do an aerial cartwheel so I lost, but I’m comfortable with that.

Then I told her a story about a dude from a long time ago named al-Khwarizmi, who wrote a book called “Al-Kitāb al-mukhtaṣar fī ḥisāb al-jabr wa-l-muqābala (no, I don’t have the name of the book memorized – I always have to look it up – but I always know the al-Jabr part). I said the name of the book is a pain to say so a lot of people just called it al-Jabr. I told her that al-Khwarizmi’s book was all about ways to answer questions like the one in the game if you were not good enough to do it in your head. Take for example the clue

“If you increase my number by 7 you get 12”

al-K (that’s what his peeps called him I bet) would have said the clue slightly differently. He would have said

“Suppose thing, increased by 7 ducats, results in 12 ducats.” (take a moment to explain that ducats are kind of like dollars)

Then he would have said that you can solve it by reversing the increase, and conclude

“Therefore thing is 12 ducats reduced by 7 ducats, which is to say 5 ducats”

Then we did a few that way. I’d write “Thing, multiplied by 6, results in 18 ducats” and she’d write “Therefore thing is 18 divided by 6, which is to say 3 ducats.”

Now some people might not believe that you can ask and expect an 11-year old to use language like this, but I’ve never understood why people would think that. Speak to them this way and they will listen, understand, and respond in kind. It’s what we’re wired to do. It’s how we learn to communicate.

I should mention that at one point she asked me if al-K called his book al-Jabr because it sounds like algebra. I told her that algebra sounds like al-Jabr because of that book! That al-K invented algebra. She thought that was super cool but also wanted to know how I could know such a thing. She was amazed to find out that I studied some history in my life. Daddy points scored.

Ok. So this gets tedious right? My daughter agreed. It’s too much writing. So then I told her about a dude named Rene Descartes who really liked al-K’s methods, but was too lazy to write it all out that way. So he’d look at the sentence

“Suppose thing, increased by 7 ducats, results in 12 ducats.”

And he’d say for example that “thing” is too many letters to write, but it’s important since it’s the number we’re trying to get people to guess. So Descartes chose the minimum number of letters possible. One. I let her choose the letter. She chose “m”. She always chooses “m” when letter-choosing is the task at hand. Then I told her that “increased by” is a pain to write out also, and asked her what she thought Descartes would say instead. She wrote down “+”. Then I said what’s “results in”? She wrote “=”. And Voila! She had written

m + 7 = 12

Then without me saying anything else, she said “Oh, so then Descartes would write m = 12 – 7! Which is 5!”.

And honestly, with that the lesson was done. I gave her about 8 more equations to solve in the Descartes style, and she got them all. We never once discussed rules, and we never once switched a bloody sign.

And there were no tears.

Maybe I’ve rescued the algebra memory.

Thanks for reading,

Rich