Adventures in Cheap Math: the $3 graphing calculator

So yesterday I popped into Staples to recycle a toner cartridge and walked past this:

Staples Graphing Scientific Calculator, aka Dirt-Cheap Graphing
Staples Graphing Scientific Calculator, aka Dirt-Cheap Graphing

The sign said it was on sale for $2.97.  Next to it was a rack of TI-83’s for ten million, I mean $125.00.

One could buy an entire class set of these Staples things and still have like thirty dollars left over, instead of buying a single TI-83.

So I decided to conduct a three-dollar experiment.  Can this thing actually do everything one would need to get through the BC pre-calculus stream?

The hardware

First thing I notice when I turn it on, in the parking lot before I drive away: the screen is glitching out.

I go back in, swap it for another, okay this one seems fine.  Well, that didn’t last either, as you’ll see in the rest of the photos.

Missing a few lines.
Missing a few lines.

I have no idea if this is indicative of all of these calcs, or if this was a batch of return-for-refund (which some of them looked to be) and that’s why they were on sale, or if I just had a bad stroke of luck, or if they act weird when the batteries are low.  Speaking of which!  They use annoying large watch batteries, the ones that run out faster and cost more money to replace than this calculator did in the first place!  So points against for the cheapo build and annoying battery choice.

The display itself is kind of a hybrid of normal scientific calculator LCD, and a full pixel-grid graphing calc display.  There’s one section on the left where graphs appear, a row along the bottom where text appears, and some other bits on the top right for random other LCD symbols or whatever.

The software

Assuming you get one of these with a working display, this is the important part.  Can it actually do everything you need it to do?

The short answer is, yes, except for one small thing, but it also does one new thing I’ve never seen in a graphing calc that’s kind of awesome.

All the stuff you’d expect from a scientific calculator is here.  Trig, inverse trig, exponents, a fraction button (that kids never seem to clue into the existence of unless you spell it out to them), logs, etc.  It seems to be able to do a couple of different kinds of storing numbers into memory, if you’re into that kind of thing.

It also has more than I expected in terms of statistical and data-analysis functionality.  You can enter data and get standard deviation, mean, sum of squares, that sort of thing.  Most surprisingly, it can do regressions!  Linear, logarithmic, exponential, power, inverse, and quadratic.  (I didn’t test these out, I’m just reading the manual here, but this is already above and beyond our province’s math curriculum anyway.  Still, neat.)

Apparently it can also do numerical integration.  So we’re entering “could complete high school calculus with this thing maybe” territory.


Now the meat of the question: does it really do graphing properly?

Pretty much, yeah.  You can’t graph as many simultaneous functions, but you can do two at a time.  The screen is a bit smaller than a TI-83’s but let’s face it, we’re comparing low-res to low-res and they both do the job about as lousy as the other.

Also sometimes it seems to forget to erase the previously graphed function.
Also sometimes it seems to forget to erase the previously graphed function.

There’s a graphical solver that is a separate button from the normal ‘Draw’ button, but which lets you enter whatever function and whatever you want to test for y being equal to.  In fact it’s sort of less annoying than the TI-83 since you don’t need to choose left and right bounds. It just finds all the solutions it can on-screen.

There’s some additional ‘sketch’ functionality that lets you do things like draw lines between two points, or more interestingly draw a tangent to a given function at a chosen point.

The only thing this is missing: you can’t find local max/min of a function such as a quadratic.  You can zoom in on the vertex and trace it manually until you’re close enough, I suppose, but it’d be a bit of a pain.

The surprise feature

The calculator has a ‘GRAPH LEARN’ button that was bewildering at first, until I read what was going on.  This thing is letting you explore function transformations visually.

Function transformations!
Function transformations!

You can choose one of a bunch of standard functions, such as x^2, square root of x, ln x, sin x, etc.  You pick whether you want to try “shift”, ie. translations, or “change”, ie. expansion / compression.  Then it graphs that function for you and you can alter the graph using the arrow keys.  As you move or change the function, it shows the updated function definition beside the graph.  So kids could practice moving a function around and seeing how it affects the equation for that function.


If I had my own class, which I don’t, and if I could get my hands on a whole set with working screens, which might be challenging, I would totally be happy with a class set of these things.  Not being able to find the vertex of a quadratic is a small disappointment, but the fact that it manages everything else for such a low price is crazy worth it.

Also keep in mind, I’m primarily thinking of BC’s PreCalc 11 and PreCalc 12 here.  We don’t have provincial exams.  If you decide to adopt this calc for your entire class, you can just assess the “with technology” version of everything that this calculator can do, and leave the “find a min/max” for problems done algebraically.  Or with Desmos on something that’s not an exam.

Now this isn’t to say the hardware issues aren’t a real concern.  If I were putting down a lot of money for calculators, I’d like to know that they’re going to last more than a year and won’t all glitch out on me.  I’d also much prefer to have something that uses AAA or AA batteries, and not this watch-battery nonsense that costs significantly more over time and is more annoying to replace.  (Although you sure can buy a lot of watch batteries for $122.)

It does make me wonder a lot harder about the other alternatives out there, though.  I’ve seen kids use Casio graphing calculators that are less than half the price of a TI.  If someone wants to send/loan me one maybe I’ll test out one of those next time.

A lot of teachers wonder why we even use TI’s when there are free apps like Desmos, Geogebra, and Wolfram Alpha out there.  I think that’s ignoring the unfortunate pressure of needing to have something that works during exams, and that it’s an extra pain to lock down iWhatevers from messaging during classroom tests.  But there’s no reason we need to keep handing TI a monopoly over the market.  This Staples cheapo is an extreme example of something low-balling and still managing to pretty much get the job done.  It might be too cheapo, but it should still serve as a wakeup call.  There’s no reason why we math teachers can’t support our students by doing the due diligence to test out and recommend alternatives to the TI regime.

Make, make, make, make makemakemakemake

(Read it enough times and you start wanting to pronounce it as Japanese)

Invent to Learn is free for a few days this week on Kindle again, and Dr. Gary Stager has another essay out just recently.

The paper gives Dr. Stager’s snapshot view of how the maker movement is doing, and how it plays into the virtues of progressive constructivist education.  It also mashes in a healthy dose of fear, citing trends of privatization, charter schools, the increased view of “bad teachers” in the public perception, more and more energy lost on standardized testing, etc.  Stager simultaneously sees more and more parents adopting a constructivist viewpoint, pushing for their kids to have access to maker spaces and hands-on learning.

Along the way, Stager also gives a more complete picture of how his position on “maker ed” stands in relation to corporate “Maker” movements.  He makes it clear that “learn to code” programs pushed by Silicon Valley corporations have dubious value at best; that saying learning to program makes you a superpower genius while also saying it’s incredibly easy are contradictory statements; that learning to code in an hour is silly.  These were reassuringly sane things to hear.

He also mentions some of the criticism towards the maker movement, or as he wants to differentiate, the Maker(tm) movement.  He refers to the criticisms by Leah Buechley regarding Make Magazine’s lack of diversity in gender and race representation.  (He cites something from a FabLearn conference, but you can also see her state the case rather well at her presentation at Eyeo 2014.)

It’s great that Dr. Stager seems to be taking these issues to heart, but I wonder.  I don’t know what Buechley covered at FabLearn, but Stager still seems to be falling into the same trap of what is and isn’t considered “making” that Buechley discusses near the end of her Eyeo presentation.  Electronics, Arduinos, Makey Makeys and Scratch are all in the club, but what about all the other things people make? Cars? Crafts? Knitting? Painting? Poetry? Woodworking?

Buechley’s presentation reminded me of a nagging question I’ve had about maker ed ever since reading Invent to Learn last summer.  If maker ed is really about teaching kids to design and create their own hands-on solutions to practical problems (and not just about shiny new high-tech toys), then why are we pretending that maker ed is anything new?  There are woodworking, metal shops, and home ec teachers who have done this for decades.  The level of self-directed, student-designed work will vary by teacher and by grade, I’m sure, but I’ve seen high school woodworking classes where students are not only choosing their own projects but designing fantastic solutions of their own.

This comes back to my biggest concerns I was left with in reading Invent to Learn.  The authors highlight their three “game changers”, new developments that they see as enabling creative learning better than all else.  Naturally, they are: fabrication (with an emphasis on 3D printing), physical computing (robotics and Arduinos), and programming.

Now, for the record: I love all three of those things.  I play with programming on a regular basis (and used to do it professionally), and I’ve recently started a line of digitally fabricated jewellery.  But I don’t see how they are inherently more creative than any of the traditional tools of art and craft.  And while designing something digitally is a great skill, which is more empowering: to teach someone how to craft their design using hand and power tools, or giving them an expensive fabrication machine that does the work for them?

And let’s be real: digital fabrication is expensive.  Even as 3D printers have come down in price, I could still realistically stock a reasonable set of power tools for the same amount.  And 3D printing is great if what you want to make is a whole lot of small plastic doodads that you have to keep buying spools of plastic to create.  If you’d rather manufacture out of wood or metal, you’re looking at laser cutters or CNC machines that quickly go up into multiple thousands of dollars.  (The one thing I do love about the maker movement – people opening up spaces where you can rent time on these otherwise out-of-budget tools.)

By the way, click that link I left in that last paragraph and read it, please.  It’s from The Architectural Review, and it goes into the danger that 3D printing is ignoring what they call ‘materiality’.  Printing plastic while ignoring the real cost of plastic. Ignoring the environmental impact of plastics.  Praising the potential efficiency, but the author has “yet to see a full supply chain analysis on the energy and resource requirements of 3-D printing – over and above a comparison with producing a specific object using subtractive processes.”

I think it’s telling that this critique comes from the realm of architecture.  Architects are no strangers to the skills that maker-ed claims to promote – digital design, creativity, and real-world solutions.  But the maker movement hasn’t risen out of architecture, or mechanics, or crafts.  It’s been born out of Silicon Valley, a place rising high on the perceived value of creating things with no materiality whatsoever.

My father in law creates things.  He makes things that wouldn’t be included in most ‘maker’ movements: designing and welding a set of stairs, turning old solid-wood chairs into really fantastic cutting boards, restoring old cars.  Some months ago we asked if he could help come up with some risers for our china cabinet so that our roomba could fit underneath it without getting stuck.  He looked at the existing feet on the cabinet, took some measurements, came up with a plan, and turned some chunks of leftover wood into a precise solution to our problem.  The actual fabrication took probably half an hour at most.  They match the cabinet enough that you don’t even notice them, and when you do you just think they look great anyway.

How would I have done that with the tools of the maker movement?  Maybe whipped up 3D models in AutoCAD and then printed it (if I wanted ugly chunks of plastic underneath the beautiful wood china cabinet someone gave us)?  Or gone out and found time on a CNC router?  Unless I had some incredibly privileged access, that would’ve taken twice as long and increased the cost by A Lot.

When it comes time to get something really made, I feel totally out to lunch next to his skills.

And you know what?  I’ll bet most programmers would feel the same way.  Most of us have been too busy playing with digital worlds to learn how to master hands-on skills the way the less “academic” minded students did as they signed up for automotive classes.

This is what bothers me when I see things like digital fabrication or robotics billed as the “game changer”, or when I hear Leah Buechley asking why it is that nearly all of the projects in Make Magazine feature electronics, or robots, or Arduinos, or something else that Make Media will sell to you.  These tools should be situated in a larger context of construction, architecture, mechanics, textiles, etc.  Instead, we see them elevated to a high status because, as best as I can tell, they let programmers who’ve been lost in a world of material-less abstractions actually apply their skills to something physical, something real.

Making shouldn’t be anything new, but the maker movement is pretending otherwise.  Even Dr. Stager has bought into this enough to write as fact that Maker Media “has fueled the explosive rise in making”.  (What the heck does he think that word means, exactly?)

The maker movement isn’t born out of a desire to say, “I made this!”, but rather from those immersed in the digital saying, “Look, I can make actual things! See? I’m not just playing pretend, this really is making something!”

This is the real reason we’re not including knitting, mechanics, ceramics, painting, etc in our “maker” movement.  The maker movement is born out of a uniquely digital insecurity, of those who’ve spent their lives making things that don’t physically exist and suddenly found a way out.

I almost want to end there for maximum impact, but I want to re-situate this back in my own context and also make it clear that this should be a call to action.

First: like I said, I am actively living out of this space, and I’m finding it liberating.  I’m making frickin’ wooden jewellery with a level of detail that would take me far too long to do by hand, with designs that are generated entirely by code I wrote.  There is nothing wrong with finding value in bringing digital work to physical form.  The problem is when we forget that what seems revolutionary to us – “I just conjured a design out of thin air!!!!!” – is an incremental step to those who have been working with physical materials all along.  (There are woodworking classrooms in my school district that have had CNC machines well before anyone here talked about makerspaces.)

Second, by ignoring or co-opting the work of those teaching shops / home ec / etc, we are completely shooting outselves in the foot.  Those who have gone before us in the work of teaching how to create things are the ones with expertise we need – expertise in working with materials and in leading students through designing and creating their own work.  Many of these programs are already nearly gone.  We should be finding a way to build support for those who’ve come first.  As it stands now, the maker ed movement seems just fine with letting sewing classes fade into nothingness while busily stocking up on Lilypad Arduinos.  (If you don’t think that’s a sign of insanity, consider my hands thrown up in the air from exasperation.)

I also need to add that a necessary follow-up read to this post is Deb Chachra’s writing on why our culture’s valuation of “making” vs non-stuff-making work should be questioned at the core.  Give it a read and apply that back to education, then ask yourselves why Stager and Martinez would suggest that makerspaces could be built using up space from the school library.

Edit: I was remembering the phrase “Designed in California” today.  Suspicious this is bigger than just programmers. Silicon Valley dissected the word “Made” into “Designed / Assembled” to try and retain pride in their work.  How does this insecurity of the immaterial affect product designers and their surrounding industry when their design is separated from the making by an entire ocean?

Teacher turnover

I am job hunting.

I haven’t been fired, laid off, or anything. Nothing has changed since the start of the school year. But something’s different than last year.  I’m on-call, no regular hours, and haven’t been getting phoned as regularly as I have on my on-call days in the last few years.  It also comes at a time when we were just thinking that my hours were regular enough that my wife didn’t have to go back to work this school year.  Now, she’s in her third trimester* and there’s no going back even if she wanted to.

There were next to no job postings this school year in my district, and none that I was even remotely likely to get.  This is despite me having taught in varying capacities here for over three years, despite having experience teaching both senior math and having a uniquely strong background for teaching computing.  All this in a time when we’re “expanding our use of technology”.

So I’ve taken phone calls day by day, going from school to school, watching our savings account get smaller and smaller as my pay checks fail to pay the bills.  Looking ahead to an unpaid two week Christmas break.

I’ve churned over in my head whether to write this post, how to write this post, what to say, what I shouldn’t say, what would be unfair or unnecessarily burn bridges.  Thinking all of these things just tended to make me think of everything that’s been unfair, getting me angry, not getting anywhere.

Today I’m just tired of it. Where would I even point fingers if I wanted to? Administration who are trying to wrestle the money they need out of a funding model that keeps them starved thin, playing chicken with budgets until the very last second? School boards making everything as “efficient” as possible to make ends meet? A Ministry of Education that underfunds, undermines, privatizes, blames teachers, hijacks their professional autonomy … and gets re-elected for it? Do I blame the majority vote in the province?

I don’t like how things went down.  But I believe in something greater than myself, greater than politics of any size, that has something better in store for me.  So I wait.

In the meantime, I wanted to tell a bit of my story because I’m tired of hearing excuses and victim-blaming around “teacher turnover”.  Some of us freaking love this job, are fighting hard to do the best we can, to innovate and empower and care.  But we also have a family of our own to take care of and bills to pay.  Sometimes all it takes is one bad year and sticking around just isn’t an option anymore.

I don’t know what’s coming next.  This isn’t a goodbye from teaching yet.  For all I know, someone’s mat leave is coming up next week that is exactly the right fit for what I can teach.  Or maybe one of those programming jobs I applied to will call me for an interview, and I won’t get to cross paths with my former students during class time any more.  I’m still considering a Masters program in Ed Tech and Learning Design, so maybe I’ll still be connected with education but from that side of the table someday.

That’s all for now.  Cover letter later.


* Baby on the way is a giant “YAAAAAY!” and not a downer, lest you think I’m being horrible. But it’s part of the reality of what we’re locked into now financially.

Fountain pens, prisms, trig integrals

(Note: I wrote this a month or more ago, it’s been lingering, I know it’s a bit too long but if I pull the ideas apart they’ll lose something. That or it’ll turn into a 4-part series, which is waaaaay too much. Enjoy!)

This past summer I decided to take on learning to draw. I had to make it a project, a goal, which will likely seem absurd to almost every artist who has devoted their life to the visual arts. So many kids who just love drawing, who grow up just loving drawing, struggling to find a way to make ends meet through drawing because it’s what they’ve wanted to do all along.

I was and wasn’t one of those kids.

Sure, I totally drew stuff all the time. In school when I’d finished my homework (with time to spare – yes I was *that* kid) it’d be time to draw absurd cartoons, swap them with my friends, create dumb jokes that were hilarious then and would probably just make me shake my head today. But I never, ever tried to draw anything real, anything serious, anything “good”.

Working with both large and small-scale game development had reminded me of this gap between my doodles and what “artists” can do. Without visual art, drawing, 3D modelling, and sound design, most games are impossible to make.

So I was often reminded that I can’t draw. Which is a lie.

Of COURSE I can draw. I can pick up a pencil and make marks. I can even compare those marks to the shape of what’s in front of me and try to make them resemble each other. But somewhere along the way I had decided, this is not what I do, this is not what I am good at. I didn’t have that many classmates who really loved to draw, and it seemed a distant thing.

The lie of “I CANNOT DO THIS” is pervasive, controlling, and debilitating. I know this because I’ve taught math. Kid after kid after kid who declare “I HATE MATH”, who describe themselves as incapable, powerless in the realm of numbers. Who fail to pick up the pencil and try because they know they won’t succeed. You can put up all the motivational posters you want, try to tell them that not trying is the only sure way to fail, toss up “First Attempt In Learning” acronyms (I really like that one, actually) but this is something deep inside, something a poster is likely never going to reach.

I’ve always been “good at math”.

I knew this about myself when I hit Calc 2 in my first year of Engineering, didn’t know how to self-regulate my effort spent on practice work and failed my first midterm exam. I was MAD. I KNEW I was good at this, had to be good at this, how dare you tell me that I should consider a voluntary withdrawl.  I was mad at myself for letting this happen. I was mad at trig integrals for not having a consistent, well-defined path to solve.  I studied more for that final than anything before, maybe anything since.  I walked away with a B.

The power of “I am good at this” saved me that year.  Although maybe without it, I would’ve seen that I really did need more practice along the way. Maybe those trig integrals would’ve stuck, instead of coming back to bite me in my third and fourth years as I struggled with Fourier transforms.

I’ve taught a lot of kids without the “good at”. I struggle to keep them engaged when curriculum guidelines tell me they should be able to factor a polynomial, solve for x, parse this obfuscated word problem.

So this summer I told myself, I am going to draw. I am going to draw whether I am good at it yet or not. I am not going to let the “not good at this” voice win, I am going to push past it and succeed despite it.

The NeoLucida Kickstarter was a nice boost in that direction. Learning that the great masters of old may in fact have been using technical aids in drawing felt like a playing field being levelled.  I dove onto the initial offering of the NeoLucida within the first 24hr blitz of pledges. (Not something I usually do, or recommend.)  I found a copy of Hockney’s “Secret Knowledge” in the library and read it cover-to-cover. I decided I would practice drawing now so that when the NeoLucida came, it would be an aid instead of a handicap. So I wouldn’t be cheating. (I knew it wasn’t cheating, and still worried about feeling like it was cheating.)

Reviving an old Processing sketch to try and publish something on Android was another boost to drawing. I had created one tool for digital drawing that looked neat, and drawing on a touch screen sounded like a natural fit, so I made it run on my new (and first) smartphone. Then I reworked it to incorporate ideas that had come up while teaching middle-school kids to use Scratch to create drawings. They created some crazy ideas, most of which looked like scribbles, and I realized that we were translating movement into line and computers are incredibly powerful at simulating and inventing new kinds of movement. So my radiating lines became a physics simulation, particles orbiting your touch and leaving traces.

Developing a drawing app while feeling incapable of drawing sounds crazy, but it was safe. I was comfortable with computing and with generative art. Giving a computer partial control over marks on the screen took away the pressure of precision. But the irony, the hypocrisy was still there.

So I started to draw.

I picked up “Keys to Drawing” by Bert Dobson from the local library, and loved it. It put concrete experience and immediate action first. It didn’t try to abstract reality into shapes. Dobson just told you, draw what you see. The hard part isn’t the drawing, it’s the seeing – letting yourself put to paper exactly what’s in front of you without letting your mind preprocess it into concepts and abstractions first. It had exercises. It was perfect for me, and when I had to return it I went out and bought a copy of that plus his later “Keys to Drawing with Imagination”.

I started working through the exercises. It was kind of safe – this was homework, I was supposed to draw this, it was okay if it was a weird thing to draw – and once I started, I kept drawing and drawing and suddenly I had something that looked GOOD. It worked. Next day I picked the next exercise and drew again.

It took me a while before I realized I could draw with my fountain pen.

I’ve been a bit of a pen geek for years now, lured into buying nice looking ballpoints and gel pens and whatnot. But when I got my Lamy Vista, I was done buying anything else.  It’s the affordable version of a Really Good Pen – clear plastic body, durable, made for everyday use, not too pretentious, but a for-real fountain pen with a high-quality nib.

Writing with a fountain pen took some getting used to. Fountain pens don’t require the kind of brute force that we’re used to with ballpoint pens.  When the tip touches the paper, ink starts to flow.  If the pen so much as thinks of touching the paper as you move from line to line, from letter to letter, it will leave a mark.  My writing, on the other hand, was shaped by the ballpoint pen.  Signing my name dozens of times at once when I worked as a courier turned my signature into a swift, violent scribble.  You just can’t do that with a fountain pen, it’ll slice things, it’ll tear paper, it’ll jam paper scraps into your nib and muck it up.

The world shifted away from the fountain pen before I was born, but not so long before that I wasn’t still raised in its legacy. I grew up learning cursive writing in elementary school as well as “printed” letters.  It wasn’t long into high school before I had dropped cursive entirely, resorting to a semi-connected mess of hastily printed letters that I still use today. When I first learned how to use my fountain pen, I remembered that legacy.  I remembered it every time I failed to lift the pen completely off the paper between lines, leaving connections where there were meant to be gaps.  I saw first-hand why cursive writing had persisted for generations despite it seeming like more work and more pretentiousness than simple printing.  The fountain pen is the hardware it was designed for.

The dominant writing hardware shifted decades ago, back in the 1950’s and 60’s, but in education we still see people struggling to choose what writing software to teach.  Cursive is fading, a writing style meant for pens we no longer use, and it’s neither good or bad that this is so.  It’s a natural consequence of a change of tools, of our shift in media (as Marshall McLuhan would think of it).

But it’s taken us this long to see the change caused by the ballpoint pen.  We mostly don’t even see why it happened.

Makes you wonder where we are in the shift caused by calculators – never mind the computer, LOGO and Papert, the freely-available computer algebra systems.  Maybe Wolfram Alpha will change how we teach in a few more decades.

So. One day I picked up my fountain pen and drew.

loved it. Somehow the results felt more real – not more realistic, but more “I AM REALLY DRAWING”. I wasted less effort with the insecurities of erasing. I was careful where I placed my pen, as I had been now trained to do when writing with a fountain pen, and when I did choose to leave a mark the ink and paper responded at my merest touch. No more faint, cautious layers of graphite as I try to define proportions correctly before wrestling darker shades of graphite into the image.  The fountain pen insists that where I draw, I DRAW.  Don’t pretend to put a mark there that you can’t really see.  Put it there for REAL.

I came up with some good drawings. Some getting-closer-to-great drawings.  I started getting brave enough to carry a drawing pad with me in public spaces, drawing during my son’s swimming lessons. (Maybe later I’ll be brave enough to put them online, but not today.)

Summer’s ended, and my mind has turned from my learn-to-draw project onto finding another classroom, trying to define for myself what I want to be teaching and what I want my teaching to be.  Starting to read Invent to Learn and understanding why I loved teaching middle-school kids how to make things in Scratch.

And now when I see my drawing pad beside my usual laptop parking spot, I hesitate. I feel like I can’t do it. I’m not patient enough. I don’t have time. I’m … not good at it.

Sometimes, change is slow.

And I need to remember that when I teach kids math who don’t believe, and I give them something they succeed in they still don’t believe, and when I give them another space to succeed in they still don’t believe, and when they walk out with a B they breathe a sigh of relief and are grateful to have survived because they still don’t believe.

And I need to remember that when I see the news that somewhere not far away, positive change is being clawed back in the name of tradition, of getting “back to the basics”, of holding on to old software because we’re still only a few decades into calculator use and we can’t remember why we valued cursive, we just know we did and still should, somehow.


A while back (when I first wrote this), a couple of articles related to Howard Gardner’s multiple intelligences (MI) theory floated through the Twitters.  First, we have Gardner himself trying to draw a line between his MI theory and “learning styles”.  For those who are reading this and haven’t heard of MI, here’s Gardner’s own summary:

The basic idea is simplicity itself. A belief in a single intelligence assumes that we have one central, all-purpose computer—and it determines how well we perform in every sector of life. In contrast, a belief in multiple intelligences assumes that we have a number of relatively autonomous computers—one that computes linguistic information, another spatial information, another musical information, another information about other people, and so on.

Gardner goes on to explain why MI does not in fact mean the same thing as “learning styles”, and points out that there is no evidence of the benefit of trying to teach to multiple learning styles.

Following that came a link to an actually older article by Daniel Willingham which discusses the problems with Gardner’s MI theory itself.  The biggest takeaway from the article (which matches what I learned studying intro Ed Psych a few years ago) is that the data on intelligences supports multiple, hierarchical intelligences.  There is evidence for separate mathematical and verbal intelligence, plus a controlling general intelligence “g” factor that influences them both.

It is important to bear in mind that the hierarchical model described in the previous section is not a theory, but a pattern of data. It is a description of how test scores are correlated. A theory of intelligence must be consistent with these data; the pattern of data is not itself a theory. For example, the data do not tell us what g is or how it works. The data tell us only that there is some factor that contributes to many intellectual tasks, and if your theory does not include such a factor, it is inconsistent with existing data. Gardner’s theory has that problem.

In other words, Gardner’s theory not only seems flawed, but Gardner is completely misrepresenting the discussion by only comparing his theory to a “one unified intelligence factor” theory.  He’s still trying to make his theory sound good by comparing it to a model that psychologists have rejected for something like half a century.

Okay, great. So with that summed up, here’s what I’d really like to explore: why do people fall in love with both MI and “learning styles” in the first place?

I know of fantastic, clever and thoughtful teachers who dislike having these theories shot down because they’ve seen something good in applying them.  I think we need to call out that good, maybe find a way to reframe it and hold it up as being valuable and defensible without needing MI or learning styles language.

Both Gardner and Willingham take a stab in this direction.  Gardner gives the following advice that highlights the appeal of a “learning styles” mentality:

1.       Individualize your teaching as much as possible. Instead of “one size fits all,” learn as much as you can about each student, and teach each person in ways that they find comfortable and learn effectively. …

2.        Pluralize your teaching. Teach important materials in several ways, not just one (e.g. through stories, works of art, diagrams, role play). In this way you can reach students who learn in different ways. Also, by presenting materials in various ways, you convey what it means to understand something well. If you can only teach in one way, your own understanding is likely to be thin.

To me this hits exactly what people want to hear when they’re taught about multiple learningstyleintellwhatevers. And the reason is it’s great advice. But it’s great for reasons that probably have nothing to do with intelligence models.  Is getting to know your students and connecting learning with their interests a good idea?  Heck yes of course!  Students learn more from a teacher who actually cares about them.  Students need mentors who invest in their lives.

Is presenting new material in multiple ways a good idea?  Heck yes of course!  Off the top of my head I am pretty sure this is evidence-based and everything.  If we really want to connect this to cognitive science somehow, we could point out that connecting new material to existing things-that-the-students-know helps them remember it, is how the brain wires thoughts together, and the more connections you make the more likely they will recall it.  (But notice that you could just cut the “brain wiring” bit out of that last sentence and it’d be just as clear and could still be verified.)

Willingham points out another reason that MI hits the “like this” trigger in our minds:

Great intelligence researchers–Cyril Burt, Raymond Cattell, Louis Thurstone–discussed many human abilities, including aesthetic, athletic, musical, and so on. The difference was that they called them talents or abilities, whereas Gardner has renamed them intelligences. Gardner has pointed out on several occasions that the success of his book turned, in part, on this new label: “I am quite confident that if I had written a book called ‘Seven Talents’ it would not have received the attention thatFrames of Mind received.” Educators who embraced the theory might well have been indifferent to a theory outlining different talents–who didn’t know that some kids are good musicians, some are good athletes, and they may not be the same kids?

When contrasting MI with a “unified intelligence” model, it’s not difficult to see why teachers would grab onto MI.  To say that all students contain a single variable that ranges from “smart” to “er, not smart” stings when you think of the wild variety of skills and talents that students have.  Kids who shine in one area may look incompetent in another – but they DO shine somewhere, and a psychology that seems to ignore that sounds heartless.

There are two things to extract here.  One is that those teachers were right about intelligence – the data supports them.  The problem was that Gardner’s MI went too far, creating vague “intelligences” that seem only to amount to prior knowledge and experience and strongly stating their independence even when the data does not support it.  The layered, hierarchical model that the data supports does show that some kids may be incredibly well-spoken and insightful but still struggle with mathematical reasoning.

The other question here is how much any of this has to do with overall “intelligence”, or whether it all boils down to past experience, domain-specific knowledge and self-efficacy.  Within any one of these intelligence models, it’s possible for someone to have significantly more botanical knowledge than the average.  Does this mean they have a uniquely high “intelligence” in that area, or does it just mean they’ve learned a lot of knowledge in the domain of botany?  I want to believe (although don’t know for certain) that psychologists working in the area of psychometrics try to take this into account as they test their models.  But for the teacher looking only at the bare structure of the theory, it may be easy to forget that neither model excludes the possibility of students who excel through past experience.


Let’s keep telling people to use multiple representations – preferably meaningful ones – to teach their subject.  Let’s keep telling teachers to get to know their students and individualize things where they can.  Let’s also stop promoting poor models of the mind.  We don’t need to hold onto flawed theories to be able to keep the good stuff that came from applying them.

Final infographic MOOC assignment: Poverty in India

For this final Infographics and Data Visualization assignment, we were given the freedom to research and produce an infographic on any topic we wanted.  I floundered on this for a few days, then decided to turn this into a chance to educate myself on India. My wife will be travelling there bringing medical aid to rural communities in a few months, and I realized that I have a very incomplete view of where India is at today.

So the target audience was … myself, mostly, to answer the question : how bad is poverty in India, and how has it changed in recent history?  The end result for me is that I feel like I still have a lot of gaps in my understanding of India’s poverty, but the big picture makes a lot more sense than it did a month ago.

However, not everything I learned found its way into the infographic.  I was running short on time – the assignment had a deadline of Sunday this past week, and while they gave us some extra time to submit I didn’t really want this running into my work week.

Click on the picture above to see the full infographic.

What I think turned out well:

  • It had a decent range of forms of representing data – a little heavy on line graphs, but they fit what’s being shown.
  • I made a choropleth map! Pretty much manually, actually, using Illustrator to color and using Excel to color-categorize. I also managed to wrangle Illustrator into converting a bitmap of the map into a vector graphic that it would let me color properly.
  • Hopefully the highlight of the message – that India has come a long way, but still has a long road ahead – shows up in the GNI graph, where you can see the dramatic improvement in the last decade but contrast that with how little that still adds up to per person.

What got left out:

I had found a decent resource showing the cost of various expenses in India vs other parts of the world, and wanted to incorporate that into the featured GNI graph.  My hope had been to replace the “$3.85/day” metric with a measure of what someone in India could actually buy with that amount of INR earned in a day.  (eg. a horizontal line across showing how much a loaf of bread or 1L of milk would cost.)  Comparing directly to US $ can be misleading, since spending $10 worth of rupees (based on currency conversion) will actually pay for something on the order of $50 worth of goods (based on costs in INR vs what that would cost in North America).  I’d experienced this weirdness before travelling in Uganda – currency valuation is just strange – but this was more extreme than I’d expected.

The biggest reason it got dropped is that I could not figure out whether the WorldBank data I was using for GNI had taken buying power into account or not.  I didn’t want to double-multiply the effects of this difference by accident, and I was low on time to hunt down the details.  If I’d wanted to commit more time to this, though, that would be high on my list of ways to make this more impacting (and meaningful).

Things that could use fixing based on feedback I got in the course:

  • Apparently I ought to pay more attention to how my monitor is color-calibrated, because I honestly thought those beige boxes (title, callouts) were more grey!  They were mentioned by a few people as being too strong, taking attention away from the rest of the page.  (Even as a grey that dark, they’d probably be too much though.)
  • One person mentioned that it looked a little too thin on content for a whole page.  This was interesting because while making it I often kept pushing things in closer than my original layout – but then still wondered what to do with empty space in a few spots (most notably around the slope graph).  Possibly should have rearranged things for a more natural layout for the slope graph, with text beside it instead of below.
  • Just say no to vertical text! I gotta admit, I had that in the back of my mind and ignored it because I was too hesitant to break my original grid layout to make room for titles. Which makes no sense because there was plenty of room.  I should pull those y-axis labels up above the graphs.
  • The infographic actually pulls data from two sources which use varying cutoffs for the poverty line – I originally messed up and mislabeled two of them as being $1.25 / day, when they weren’t.  I edited those off so I wasn’t lying – but since the per-state lines were created by the Planning Commission using a more complex metric (that gave a varying line per state) I couldn’t think of a good concise way to relabel it.

I’m tempted to take this feedback and create a v2 of the graphic, but that’ll have to wait until later.  I’ll post again if I get it done.

Week 4 Infographic Exercise: A decade of US unemployment

So this week’s infographics MOOC exercise was another draft for an interactive infographic, this time on the unemployment rate per state in the US.  The assignment was based on another DataBlog post from The Guardian which showed a choropleth map of unemployment using data over the time of Obama’s presidency.

The biggest problem was that the data during that time looks nearly meaningless.  It’s noisy, it has a vague downward trend, but you see this *blip* at the start where everything is jumping upwards.  Those who remember the last five years’ worth of economic history better than I did will remember why – the insane crash all kicked in about half a year prior to Obama’s election.

So step one, I hunted down a wider data set via  Using the last 8-10 years’ worth of data gave a much more interesting picture and set the context for what was actually going on in the last four.

Step two this week for me was playing with making the data work in Tableau Public.  I had spotted this tool a few weeks ago, and didn’t try it last week as it does have a bit of a learning curve and I really wanted to practice something in Illustrator.  But this time I decided, what the heck, if making something actually interactive isn’t that much more work than graphing and drawing it up in Illustrator, why not?

The end result was very close to what I wanted – my ideal needs just a couple more features (pop-up or overlay annotations on a line graph, a customized timeline control on the line graph) which may or may not ever show up in Tableau, so I guess I still have some motivation to learn a decent chart library in Processing.

You can see the published interactive at Tableau, but the line graph isn’t working, which is kind of lame since it was made using a technique they demonstrate in their own tutorial.  Hopefully that gets fixed, but in the meantime I just screencasted from the desktop version for the assignment hand-in.

Noisy motion – learning from Generative Design

I picked up a copy of the absolutely-beautiful book Generative Design recently and I am loving it.  It’s a perfect resource for where I’m at – exploring generative art, wanting to learn more but don’t need someone to teach me the basics of programming.

It’s been great to find out how many techniques are much simpler to code than I’d expected.  For example, I decided to code my own copy of this noisy motion sketch which creates fantastic wispy-smoke-like patterns.  I’d seen work like this before and assumed some amount of complex simulation was going on.  Turns out it’s just taking Perlin noise and using it as a sort of vector field, defining an angle for particles to move in from each spot.  (Which sounds fancy but it’s basically just a few lines of code.)  Huh!  Easy-peasy, tiny code, fun results.