They Sure Can Slide Fingers on a Pane of Glass

Increasingly it seems to me that if, twenty years from now, we took the time to assess what the young folk of today got from their childhoods, the one thing we’ll be able to state with surety is that there was never a generation so adept at sliding their fingers along a small sheet of glass.

Thirty-five years ago I began (getting paid for) my teaching career. In those days I self-identified as a science – math teacher. I loved it, especially the lab activities. I was lucky because at the time–the early eighties–science curricula were designed to be very hands-on. It was great, but there was something else: I generally found that the activities jived very well with the students’ personal experiences. Students could, for example, relate to labs studying motion because the objects of study seemed so very familiar. For non-accelerated motion the students were used to gliding along ice, rolling along level ground on skateboards, bikes and rollerblades. For accelerated motion, they could similarly draw on tobogganing or biking downhill, playing ball and just throwing rocks in the ocean. For circular motion they had experience on playground merry-go-rounds, swings and even with twirling things on the end of string.

But then time passed. I noticed it first for circular motion, never an easy topic and one that you had to ensure that students had up-close-and-personal experience with before digging in through the lens of physics. Students could not relate anymore to any of the once-familiar events. Not even twirling stuff on strings! I just put it down to the increased time that the children were spending playing video games indoors, figured, “That’s sad, but I guess we’ll just have to redouble our efforts with the hands-on activities in school,” and thought no more of it.

…until the penny dropped.

Talking to the young people who attend the university at which I work it became increasingly obvious that, not only are the students not directly experiencing the physical world (aka playing outdoors) but neither are they doing that in school! Regardless of what happens in k-6, once they hit Intermediate and then High School, their days in science class are mostly spent with their bums in uncomfortable ancient school desks, all neatly arranged in rows, and listening to an adult talk, talk, talk about scientific knowledge or show off how well they can “solve a problem,” which, by the way, is not that at all but, rather, a boring run-through of some algorithm for dealing with some contrived situation or other.

And there’s shag all interaction with the physical world.

Once there was a thing called “core labs,” hands-on activities that HAD to be done. In the eighties they numbered 12 to 15 per course. These days the number is more like six and, guess what, less than that are actually done. Oh, they’re talked about and sometimes even simulated–you know, rubbing your fingers across the glass top of a tablet or whatever to simulate motion, or something equally banal–but rarely ever really done.

What a shame. It turns out that our remarkable, wonderful brains are ideally suited to experience the world in two different but complementary ways. One way is procedural, logical, even rules-based. It is dealt with mostly–but by NO MEANS EXCLUSIVELY–by the left side of the brain. Talking, reading and experiencing simulations feeds it nicely. The other was is more holistic, even probabilistic, and, similarly is mostly handled by the right side. It’s best fed through direct physical and / or sensory experience with the phenomenon in question. Two views, ideally nicely merged and coexisting, producing a complex and useful representation of whatever the senses encounter.

Too bad that the simulated and  talked about and PowerPointed-to-death world is mainly processed procedurally. It’s not real in the experiential sense and, as such, the processing that the (mostly) right brain is so good at never gets to happen. As a result, the young people can talk and diagram about the physical world, even “solve” paper-and-pencil problems but give ‘em something real like some electrical components or mechanical parts and they have no clue whatsoever what to do with them.

Because they’ve never had the chance to. Still, they have experienced glass displays and they are no doubt adept with that.

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The Sorcerer’s Apprentice, Again

A conversation with a former student, now abroad, who informed me of how all the teachers’ lesson plans need to be written in procedural form and pre-approved by the upper administration, reminded me of the old story of the sorcerer’s apprentice. Tired of fetching the water himself, the master sorcerer enlists the aid of his best apprentice to do the menial task. Thinking he knows more than the master, the apprentice enchants a broom to do it for him. Sadly, though, he does not know how to stop it and soon the place is flooded. Sometimes the “upper underlings” think they know more than they really do, to the detriment of us all.

The mysterious duality that brain physiology imposes upon our perceptions!  While the notion of the hard and inseparable divide between the left and right brain function has been debunked over the past ten years or so it remains that the brain is not symmetric. There are significant differences between the left and right halves–differences in weight, in shape, in appearance and even in the ratio of right to grey matter. And while neuroplasticity is a thing; yes, the brain can “rewire” itself in response to injury and to education, there is a decided selection on the left for processing things in a logical, procedural way and on the right for dealing with things that, frankly, seem to be decidedly quantum-mechanical, governed by things that can only be understood on a more holistic, probabilistic, even whimsical sense.

It’s painful, therefore, to observe, more and more, a growing emphasis, throughout society, on things that appear more left-brained, at the expense of things that best come from the right. Witness the increased de-skilling of the trades and the professions, a thing you see increasingly in my own field as, more and more, everything gets reduced to something “anybody could do.” Everything has to be reduced to an algorithm, a set of procedures or rules, with less and less room left for that wonderful, powerful thing we call “good judgement” or “art” depending on the context. It all makes you  wonder just how many of those apprentices are busy enchanting brooms as you read this. Let’s hope there’s at least a few wiser sorcerers who can undo it.

Save You All A Few Bucks on that Proposed Royal Commission

Contrary to the views of Dr. Wade Locke, widely distributed by the local media as alarm over out-of-control health care costs as well as the notion that NL’r’s live exceedingly unhealthy lives (some truth there, mind you), we don’t really need to spend oodles of dollars on a royal commission to try and get to the bottom of it. The answers or, rather, THE answer is already known.

We’re older than average; a province of increasingly older farts. Health care costs are higher for older people.

Check out the graph, prepared by StatsCan with your own tax dollars (the data has already been gathered at public expense). It shows the average age of Canadians broken down by province and territory.

age-canada

Notice two things:

  1. Blue Bars: In 1982 we had the youngest population in Canada.
  2. Yellow Bars: In 2012 we had the oldest one.

See—that’s the whole thing, innit?

Why did we get so old so fast? Is it something about the fog? The moose sausages? The toutons? Our crappy water supplies, perhaps? Blue Star beer? The awful weather?

Nope, we all know why, don’t we–our young people left.

In 1982 they were all here. Over the years, off they went, mostly to Alberta I suppose, leaving only the older ones behind. This did two things: 1—left us with fewer young people and 2—left the rest of Canada with more young people. In other words our Blue bar went up while this helped drive everyone else’s down.

And, now, more to the point, now that those who moved away are having kids of their own, somewhere else, this is again dropping the rest of the Blue elsewhere in Canada, while ours keeps climbing as we get older with each passing year..

Might I suggest that instead of wasting piles of money on a question that’s really been answered that, perhaps, we engage in a much harder, but more fruitful conversation around the topic of what should we do, as a people, in response to the fact that our young people really don’t want to stay in this place?

(Oh, and can I have the million$ the province was going to spend on the commission now? I need to pay off my MasterCard, Mortgage and Line of Credit. That would be almost enough to fix it so I can still stay here after Muskrat Falls comes online and the s**t really hits the fan.)

What do I Teach?

My friend Ed Wade was shocked to hear I planned to offer you advice.
Said, “They’ve heard enough of our old stuff. Some stories should suffice.”
Let’s do both, but be forewarned, you’re about to hear the pronoun “I” a lot.
It’s not about me, but about you, and maybe you’ll find some food for thought.

As this past year went by so fast many thoughts have came my way.
So I supposed I’d draw on those to frame out what to you I’d say.
I don’t want to ramble as I often do. I’ll try to be more concise
and gauge my speed against your need to check what’s on your mobile device.

This time each year I try to put a few words together for you
who are about to start; words from the heart; advice on what you might do.
In the past I made a list of things that seemed important at the time
and figured a way for me to say them in a way that rhymed.

But looking back I realized I’d made an error fundamental,
said too much, and so, as such, lacked an idea that was central.
Therefore, this time I took my own advice, and thought it through before I begun.
So now I’ll share one idea here, not a bunch as from a scatter gun.

“What do you teach?” I’ve often been asked by people I’ve just met.
That’ll be the thing to which I’ll cling in the few words you’re about to get.
But first let’s come around to it in a way that makes more sense
for you’re all from here, and you know, my dears that’s not how things commence.

You see around here, when you meet someone, first thing they will blurt out
is, “Hello me son, where are ya from?” They know people from there no doubt.
Next thing you’re asked is what you do—that’s the one that leaves me most concerned.
Are they following cues, or judging you, based on what they think you earn?

And so you answer them as you see fit; maybe ask about them too,
‘til finally they come around to the one about which I’m making all this ado.
“Oh! What do you teach?” they’ll ask, expecting you to answer in terms so short & plain.
Ah, it makes me squirm, I must affirm! Please sit and listen while I explain.

You’re thinking maybe I can’t commit, for many of you know why I have no tattoos.
You’ve heard my fears that after seven years, when our bodies are made anew,
the several things that once meant the most will likely have been replaced
as experience brings even more new things and the old stuff gets displaced.

But it’s more than that, sure I’ve changed. In first year MUN I’ve memories so clear.
Physics and Math, choosing, all the while musing teaching them as my career.
But my first job in a small rural school proved that wouldn’t be the case.
Eleven courses kinda forces subject teaching to an impossible pace.

I found it best to look at my students instead of the subjects that I taught.
It being a small school I found, as a rule, I’d have ‘em again more often than not.
Knowing their strengths & shortcomings let me get the most from those I’d been assigned.
Nine years came & went with me giving 100%, ‘til to move on I felt inclined.

I still recall that day twenty five years ago when I landed what was then my dream job.
Teaching Physics and Math online—ah the stars had aligned for this poor geeky bay-dwelling knob!
And to my delight I found that things hadn’t changed much. I still taught students from small rural schools.
Taught multiple subjects, and in many respects still able to use all my tried and tested teaching tools.

And so the time passed. Every few years brought more change: some good, some bad, some unexpected.
I got better, yup, yet I often screwed up, but each time I had more experience thus collected.
And so, over time, many things became clearer—that’s one gift that experience brings.
What I teach,” I now know, and I’ll tell you, although, first let me clarify several important things.

In the time you’ve been here many of you’ve come to know there’s some questions that I love to ask.
My favourite? This is it, “What’s love’s opposite?” If you say, “hate” I will take you to task.
For both love and hate coexist; you can feel both at one time, so opposites then they surely can’t be.
So take away love, yes, go give ‘er a shove, and what’s left is not hate but apathy.

So I caution you, then, when you’re put in clarge of a class and your priority is maintaining control,
keeping the sweet little dears all quiet—or in fear—really, that should never ever be your first goal.
Be mindful that when they’re unwilling to express what’s going on inside of their heads
you’re just flying blind, while they’re falling behind. All hands’d be better off at home in their beds!

But in all the time that I’ve asked of the opposite of love not one soul has shot back, “But what’s love?”
To me that seems weird, but perhaps you were “afeard” I’d keep babbling…I’m like that…sort of.
As you probably know, there’s many possible responses; the ancient Greeks spoke of no less than eight.
But it is this for me: “to want you become the best you can be.” So to teach is to love; ain’t it great!

So, then, as you practice your craft, and get on with your lives, you’ll let students in more and more.
And while their joys you will share, I bid you beware for then they can hurt you right down to the core.
And after several bouts of this you may feel jaded and wonder if it’s all really worth the price.
But let there be no doubt, once they’re “in” there’s no “out.” Been there, and on that I’ve advice.

At times you’ll get hurt, perhaps by students you love, or maybe because of the stunned things you’ll do.
Perhaps you’ll be too headstrong, at any rate there’ll be wrong that will leave you feeling broken too.
When you’re down you’ve three choices of what happens next. Here they are in the order of ease:
First: stay down, don’t get up, you poor sweet buttercup. If that’s you, you best quit now; do it please.

Second, you can get back on your feet and go on, displaying fortitude and resiliency.
But there’s a third choice: become stronger; it’s been voiced by sages with some brilliancy.
In order to get stronger, first you must get hurt but work carefully on that damage, I implore.
Because your strength it will grow and in time it will show, you’re far better than you were before.

After all there’s no sense expecting students and class to always be perfect and bright.
Rose-coloured glasses, are only for asses convinced their way is the only one that is right.
For once you get used to letting your students just be, even cranky and putting you to the test
they’ll trust you enough to share with you the stuff you need to help them be their best.

So I know you’re wondering, “Where’s the point in all this?” After all I promised an answer to you.
But you made a mistake, said my time I could take. To me that’s licence for some ballyhoo.
One last thing I will tell: back when I was in school, I was advised I should be an engineer.
At gadgets I liked to pick, I could fix ‘em right quick so ‘twas a good choice for me, they were clear.

But there was this thing, see there was something else that intrigued me far more than that stuff.
And so when I applied to MUN ‘twas cut and dried, choosing Education, for me, was not tough.
Yes, messing around in the lab is still fun, but a life in the classroom leaves me with no remorse.
And if you haven’t figured it out, what I teach, there’s no doubt: I teach students, of course!

The Bellislilunnel–Completely Unaffordable

Every so often you will hear talk about a proposed under-sea tunnel across the Strait of Belle Isle connecting mainland Canada—Labrador or Quebec—with the Island of Newfoundland. The benefits to the province as a whole are often pointed out—things like the possibility of increased tourism, more reliable transportation schedules and the potential for construction-related jobs—however the costs associated with the project are generally not discussed. That’s too bad because they are exceedingly high.

A study commissioned in 2004 indicated that the tunnel could be built at a cost of $1.7 Billion, however, for the life of me I cannot understand where the numbers came from. As I see it they are underestimated by an amount that can only be termed laughable.

Let’s assume that the proposed project—and let’s term it the Bellislunnel—can be to some degree compared to its much more famous elder sibling, namely the Channel Tunnel or Chunnel.

The Chunnel cost $21 Billion dollars and is 50.5 km. Since the Chunnel was completed in 1994 you need to adjust for inflation. According to the Bank of Canada that would be $31 Billion today. Dividing that by the length gives a cost of $600 Million /km.

To get across the Strait, the Bellislunnel will need to be 18 km long. Simple math gives an overall estimate of $10.8 Billion, a figure nowhere near the amount from the 2004 study.

As I see it my figure is a low-ball estimate since the Chunnel was built under ideal conditions, specifically:

  • Between two countries that each had a healthy industrial base right next to the endpoints;
  • With guaranteed sustained, heavy use that would defray the costs;
  • Through a region whose geology was well known and well-suited to tunnelling;
  • Through a no-ice, no-iceberg zone—a place where no ice impact and scouring would be a factor;
  • In an area that does not experience harsh weather effects.

In light of this, it would be reasonable to mark up the estimated cost by at least 40% giving a more realistic figure of $15.1 Billion but let’s leave it as is, for now.

The $10.8 Billion price tag needs to be mortgaged. Let’s assume a 40-year term and a 3.8% interest rate, which is about the same as the terms for the Muskrat Falls project. That gives an annual finance cost of $525 Million, a figure that does not include maintenance. Let’s put it on perspective: the Bellislunnel will cost every person in the province over $1000/year, not counting usage fees and maintenance.

The only current fund available to offset this is the budget allocated to Marine Atlantic, which operates the ferries between NL and NS. That is currently only $19 Million but has been more typically in the $150 Million range, which though sizeable in its own right is paltry compared with the debt payment needed to service the construction loan.

Using Marine Atlantic’s budget as an offset complicates things even more. It’s been done before, yes—he PEI Confederation Bridge’s main source for revenue is the Federal Government grant taken from the monies that used to pay for the ferry the bridge replaced. This complicates things moreso than they did in PEI.

Marine Atlantic is, in effect, the highway linking Newfoundland to the mainland. If you use its budget then you also have to account for a proper highway connection to the mainland. As it currently exists the Trans Labrador highway could not provide the connection that’s currently needed. Not only could it not handle the traffic volumes but, more importantly, the conditions that exist on it in winter would mean delivery schedules subject to frequent shut-downs owing to winter storms, making for a situation that would in all likelihood be even less reliable than the current state. That’s not to mention the added fuel and maintenance costs owing to the much longer route.

A new highway linking Blanc Sablon to Kegashka along the south shore of Quebec would be equally unrealistic. Not counting the bridges the 400-450 km road alone would likely cost around $2.5 Billion. A quick glance at a map of the region also shows the terrain to be particularly watery, marked by numerous lakes and rivers so the many bridges required would increase this base cost by a considerable amount, perhaps even doubling it.

Some may object to the numbers I’ve provided, noting, for example that the Chunnel is in fact three tunnels, two train tunnels and one for maintenance. They may say they we only need one so the cost needs only be one third as large. That’s not accurate. Certainly two train tunnels are not needed given the anticipated traffic volumes but the maintenance tunnel is still required so the best reduction would be by one-third, not two-thirds, bringing it down to a still unaffordable $350 Million per year.

Admittedly this simplistic essay has limitations. First you can’t really model things using simple proportions as I have here. There are start-up costs such as environmental impact studies that do not scale; they are what they are so reductions downward as I have done here are likely going to result in under-estimates. Second, most projects like this one tend to go way over budget so any figures you have seen are really rock-bottom estimates with the real costs—assuming the go-ahead was ever given—being possibly as much as twice the suggested amounts. There’s also the issue of ongoing maintenance.

In either case the status of the Bellislunnel project should remain, for now, as unaffordable.

 

Homework and Questions in Math: a Lob Scouse

I was discussing homework in mathematics with my friend and colleague Susan Ryan just the other day. Initially the topic of conversation was homework. Soon we realized we were pretty much of the same mind about it—specifically that it’s a good practice when given in the appropriate amount, thus implying that teachers need to be judicious regarding exactly what tasks they assign.

While there are no doubt many homes in which creative effective learning can take lace it’s been my experience that quite a few are not, and, in the interest of fairness to all, it’s vital to ensure that homework tasks are things that all students have a fair opportunity to get done well at home. I am therefore of the mind that it’s generally a good idea to assign some of the more routine tasks such as review drill and practice as homework. For example back when I taught grade ten math, before covering the factoring of trinomials I found it useful to assign a review of math facts (I am not kidding. That was grade ten and I am thinking of the 1980s. The whole problem about remembering math facts is truly nothing new) before getting started as a significant number of the students were rusty, especially regarding the multiplication facts bigger than 7×7. Since it was not worth taking class time with I’d just pass out a boring review worksheet. Similarly, the following year, just before we started the unit on quadratics I’d also assign review on factoring polynomials as homework, again for the same reason. These days if I was still doing it I’d certainly make use of a flipped classroom approach and provide a modern version of essentially the same thing.

———-

The talk then turned to things that do not work well for homework. Both of us, as parents, could easily recount numerous stories of especially frustrating experiences we’d had when our children asked for help with certain tasks that had been sent home. We then put on our cynical retired teachers’ hats and concluded that in many of these instances what had been sent home were items from the textbook that the teacher did not feel comfortable with handling in class.

My particular “favourites” were the ones that start with, “explain why…” such as “Explain why you chose the solution you did,” or “Explain why a polynomial function of degree n can have, at most, n  zeros.” I was particularly not fond of questions that started with “Write to explain…” Now, don’t get me wrong—I am very much in favour of students working on their mathematics communication skills. It’s just that sometimes the questions do not lend themselves to independent thought and are much better handled as a group or whole-class discussion when many ideas can be drawn out, thus forming something of a mosaic of shared understanding.

When tough questions like the ones above are posed to individuals, the students tend to find themselves totally stuck and most either totally give up or turn to the parents. In the absence of classroom context it’s not hard to see how those same parents would become equally confused, frustrated and absolutely angry at a mathematics program that would expect from young children to be able to respond to such open ended and difficult questions; questions that in the absence of context (after all they were not in class and can’t be expected to see how it fits in) seem pointless.

Me—I would never knowingly do that. I would have no problem taking up those “explain why…” questions but never for homework.

———-

And that’s where things got interesting. Susan then more-or-less agreed, but took the conversation in a different direction. She encouraged me to think about those questions and how, so very often, they form the stuff of angry, frustrated Facebook posts. You know what I’m talking about, don’t you? Some samples that I have seen at one time or another follow.

Regarding those posts, as is often the case, the extreme frustration is generally due to two errors. First, the teacher likely made an error in judgement and either selected a problem that was too difficult and, second, the parent assumed that the child know much more than they did. For example, in the above letter back to ‘Jack” the parent clearly has no idea of how difficult place value is for young children, and that the idea of ‘borrowing’ to do computation makes absolutely no sense until the child does have that firm grasp. Simply put, children and not small adults. Sure, the suggested parent solution seems obvious to someone with a university education but for a grade school child—no! That response–the letter to Jack–while venting pent-up frustration, just suggests the enormity of the gulf that exists between the child’s grasp of math and the adult’s grasp. As Susan would point out, the parent’s solution amounts to no more than “squiggles on a page” for most young children until a LOT of development work is done on number sense, place value and subtraction itself.

We don’t always acknowledge the simple fact that things that we know very well seem obvious to us. The better we know them the more obvious they are and, in fact, the less perceived need for any external learning strategy.

Just because things are obvious to us, doesn’t mean that are equally discernible for others, though. That’s a fundamental problem we all have as parents—we think that young children are just smaller versions of their adult selves and totally forget the fact that as the body develops physically so, too, does the brain. The mental capacities we have as adults are not necessarily developed to the same extent for kids.

———-

That, then led to Susan showing me one of the activities she has used with parents to help explain why teachers do what they do. She asked, “why is 2 + 3 = 5?”

I was caught unawares with the question and mumbled something. She laughed and said, “hang on. Let’s think what students might say instead of what you might say.” She got out a sheet of paper and wrote this:

5

“There will be some students in the class who just ‘get it’ intuitively and it will seem obvious to them. They see it as most adults do. It’s not that they can’t explain it—no it’s just that it’s so obvious to them they suspect you’re daft to even ask (just like most adults). They are where they need to be and are ready to move on.”

Then she wrote this:

3   4   5

“Some students know to start from 2 and just count up three more. They’ve also pretty much got it. They need a little help, perhaps, as they’re not thinking abstractly just yet, but it’s safe to say they probably understand what’s going on well enough to take it to the next level.”

Then she wrote:

1   2       3  4  5

“Some students need to write the whole thing out from the start. They are still pretty concrete as they have to have 5 ‘things’ before them in order to understand what’s happening. Perhaps they will even draw 2 dots and 3 dots. They have the essence of addition but are still heavily reliant on the concrete. Perhaps it’s a development thing, and you just have to allow them time for their brains to develop more, or perhaps they just need more help—a decent explanation of what addition is might be all that’s required for some. Either way, you know there’s a hump to be overcome before they have it nailed down.”

Then, finally she said, “and, finally there are the ones who have to look at what everyone else has done. You might call it cheating or copying, or whatever. At any rate they will be unable to complete the activity and are certainly not ready to do anything further unless more development is done. They can complete work and make it look good, but it’s not their own work. For these students it makes little sense to memorize addition facts as they have no idea what it’s all about anyway.”

“So people often wonder why teachers ask what seem to be silly, even stupidly obvious questions. The fact is, though, that they’re not necessarily silly. The answers the students give is tell an important part of the story regarding the degree to which they understand any given topic. In turn this informs our own practice.”

———-

Funny how one thing leads to another, isn’t it? Homework led to a discussion of questions and how what seems to be nonsense on the surface can be something quite useful when you consider it in context. Most things are like that, aren’t they?

Oh, and since this rambling disquisition seemed to start with homework it might as well end there. Any way you look at it homework is something that should be carefully considered. After all, while students’ time in the classroom is precious and needs to be spent wisely, so too, is their  time out of it. Many other things besides school subjects need attention—sports, the arts, learning social interactions, volunteer time, and just having fun, to name just a few. If a school subject needs to occupy that time then it seems to be the respectful and wise thing to choose carefully the when, the how much and, most importantly, the what.

Final Note: perhaps you don’t know what a lob scouse is? Click the link to find out.