You Didn't Prepare Me for Post-Secondary

Over the past several years I've been contacted by graduates or their parents with a similar complaint:  why didn't you prepare me/my child for post secondary math?

A few years ago it was a college bound student with learning challenges.  His mom was... outspoken (that's being very charitable) while he was in school, but I was able to work well with him and he eventually went into information technology at a local college.  He dropped out in his first semester with failing maths grades.  Mom emailed me in a rage blaming me for this.  I pointed out that I teach computer technology and asked how he was doing in those classes (he was getting 90s).  That ended that particular interaction, but it wasn't the first and it won't be the last.

I've also had students who I worked closely with both in class and on school teams, students who know me well enough to be straight up, get in touch while in post-secondary to say that they too are struggling with maths.  It's a familiar refrain; a student who got high 90s in high school maths suddenly finds themselves dysfunctional in post secondary.  A recent multi-award winning graduate put it well: "when we're given a problem, other students apply their maths skills like taking tools out of a toolbox.  They assess the problem and then apply the right mathematical approach to solve it.  I feel like we spent all our time learning mechanics on worksheets but spent no time contextualizing what we were doing."  This would be like trying to learn how to play hockey by drilling yourself independently on stick handling, skating and shooting, but never contextualizing those skills as a whole in a game.

When some of our most academically decorated students come back to me with this kind of feedback, I'm left wondering how to address it.  I don't think it's fair that the blame falls entirely on teachers.  Thanks to our community's everyone-can-go-to-university-if-they-want-to sense of privilege, many of our academic classes are populated by students without the background or interest in using what we're trying to teach them.  This means teachers have to simplify and compartmentalize their content to such a degree that the students who actually need it aren't getting it.  I frequently see students with weeks of absences who are still expected to earn a credit (you got auto-dropped at 10 absences when I was in high school).  When you've got students who barely attend, compartmentalizing the learning becomes a survival technique.  It also makes it nearly impossible to contextualize learning beyond single period lessons.

Last year my son was told, "don't worry, everyone fails that unit" in his grade eleven maths class.  If I had a unit that everyone failed, my first assumption would be that I'm teaching it wrong and I'd change my approach, but one of the ways we appear to drag students to the end of the Ontario maths curriculum is to just keep pushing through it, regardless of comprehension, context or mastery of previous concepts.  This isn't a new phenomenon, it happened to me in the 1980s too.

I'd quote statistics to you about how successful our graduates are once they leave the building, but no one in Ontario public education keeps those statistics.  Instead of quoting EQAO scores, what we should be doing is collecting data on the success rates of our graduates in post-secondary.  If we all claim to be about backward design, this kind of data would make that possible on a meta-level, but it's better to fly blind, then we don't have to take responsibility for those failures or change anything.

There is a lot of talk around destreaming as a cure-all to systemic prejudice, but the people framing it that way are usually the ones happy to see larger class sizes for everyone at a lower cost.  Streaming wasn't designed to denigrate anyone, it was instituted to let classes focus on learner needs with higher needs students having smaller classes and students aiming at advanced post-secondary programs working in a room where everyone is driving for the same goals.  The unfortunate truth is the destreaming has already occurred thanks in large part to parents and guidance ignoring it.  When I last taught university level classes I found that less than half the class was university bound and a number of those directionless students were put into university stream to 'keep their options open'.  In keeping their options open these students were knocking others out of contention.  In curriculums like English and mathematics, where skills development is vital in order for students to operate at the senior end of the program, this kind of watering down of intent hurts many of our graduates.

Even in my technology courses I see this.  My 'M' level courses are supposed to be for post-secondary bound students but I typically see 10-20% of the class coming out of credit poor essential and applied situations who have no intention of going into post-secondary.  I then spend an inordinate amount of my time catering to these high-needs children instead of helping the students who selected the right stream get to where they want to go.

I'm not sure why, with the pressure to reduce costs, we're not offering alternate pathways that allow the students who don't need senior classes to take alternate pathways.  An early graduation workplace/apprenticeship pathways option for students should be available for anyone who has passed the literacy and maths testing in grades 9 and 10.  If those students who would rather be out working were, we could refocus our classrooms on preparing the students in them for post-secondary success instead of watering everything down in order to babysit those who don't want to be there.  Instead we're all handcuffed by Ontario's learning until eighteen law.  If we're all really advocates for life-long learning, then it should be obvious that this doesn't just happen in schools.  There would be many benefits to stepping away from this mandatory restriction and refocusing our classrooms on developing rich, contextualized learning opportunities for students who show up and want to be there in order to go on and tackle post-secondary specialities.

This issue goes well beyond maths, but the structured development of skills over many years in mathematics exacerbates the problem in ways that make it much more visible.

Framing Mathematics

We had a numeracy PD day a few weeks ago.  This filled me with trepidation having barely survived high school mathematics.  It began with a warning about how we frame the subject:

Fair enough.  Evidently I'm not the only one who treats mathematics with caution, but I can see the point about how negatively framing maths with students can cause problems.  If you don't think maths are a useful tool that can help you solve real world problems then you've been living under a rock.  Everyone should develop basic numeracy.  I'll try and do better with how I'm framing it, but that doesn't mean maths gets a free pass on how it's delivered.

We then did a maths based online escape room exercise with Edtechteam.  This was an engaging process, but it cast a bright light on what was for me one of the problems with trying to learn maths: parsing poorly written word problems.

When one of our group (a published playwright with a Masters in English) suggested that the questions were vague to the point of being misleading the math teacher in our group said, "yeah, but any language based question is going to be somewhat unclear."  The English teacher looked at her quizzically and said, "no it isn't."

Therein lies the problem.  If a teacher who has never focused on developing strong language skills gets lost in creating nuanced word problems to get at complex mathematics, you can see where this might go wrong for everyone.

From the point of view of someone who doesn't pick up maths easily, confusing language doesn't engage me, it does the opposite.  I'd rather (and I speak as an English major) have the maths served straight up without any confusing or misleading language in the mix, but maths teachers seem determined to lean on language skills they don't have in order to confuse the numeracy they do have.

This problem appeared again when we got out to an exercise where we (again, in groups) were supposed to find factors in an array of numbers, but rather than simply explaining the logic involved, the activity was dressed up in a tax avoidance theme that made no sense to me or the science and history teachers I was working on it with.  So far this morning both maths activities had demanded that we embrace confusing and contradictory language in order to get at the logic below.

In this activity, if you selected a number to get paid the 'tax man' got all the factors of that choice.  So if you picked twelve, the tax man got 1  2, 3, 4 and 6 dollars.  When I asked how I was being taxed $16 on the $12 I made I was told that the taxes don't actually come out of the money I was making, which isn't helpful.  When I suggested that people should pay taxes in order to support all the  benefits of society they enjoy and shouldn't be trying to dodge paying them, I was told that I was putting too much thought into this.  At least someone is.  This has always been the way with me and mathematics, especially when it dresses itself up in confusing language in a desperate attempt to appear more interesting.

I think I'm a pretty sharp fellow.  I've been able to calculate binary subnets in order to build networks and I've never had trouble doing the maths needed to be a mechanic or a technician.  When the maths are immediate and real I'm able to get a handle on it, but the bubble gum world of high school mathematics has always alienated and confused me.  It seems arbitrary and nonsensical because it often is.

Maybe the best way we can frame mathematics is to stop trying to make it into something it isn't.  If we treated it like the tool it can be instead of trying to turn it into some kind of spy based action adventure or libertarian tax dodging daydream, we wouldn't have so many people feeling alienated by it.

Of course, the solution is obvious but how we solve it is prevented by how we organize education into departments.  If we collaborated on word problems with the English department, we'd remove a lot of that confusion.  If we applied our mathematics through science, business and technology we wouldn't get lost in the confusion of maths for maths' sake.  We could be applying mathematics in the statistics we use in social sciences or  the ratios we use in art, but we separate numeracy off in high school and let it atrophy in a maths classroom that struggles to connect to the real. 

Ironically, our PD followed these two engaging but ultimately confusing activities up with two teachers telling us about their experimental manufacturing technology-mathematics combined course which encourages applied maths students to work through manufacturing technology in solving real-world problems.  No imaginary tax schemes.  No escape rooms.  Just applying maths to real world problems in an unobstructed and meaningful way that leads to outcomes that are transparent and obvious.

This would mean combining mathematics with other courses and then working to integrate numeracy into those subjects in a constructive and transparent way.  There could still be an academic/abstracted mathematics stream for the tiny percentage of students who would need it, but for those of us who aren't aiming to be theoretical physicists or academic mathematicians, we need our math served up without the garnishes.  Knowing what we're doing it and why we're doing it would go a long way to alleviating the maths anxiety so many of us have.

Tyranny of Numbers

I’ve always found a strange disconnect between my experience in coding and how it is taught in school.  Back in the ‘80s, matheletes owned computer science, and still do today.  More interested in the theoretical number games they could play on computers than in actually building programs, I quickly failed out of it.

My self-taught experience was one of hacking and building.  Tweaking pieces of code and refining them until I got the desired result.  I could see the logical construction, but it was never numerical for me, it was mechanical.  Later in life I worked as a millwright and an auto mechanic before coming back to computers as a technician.  I’ve always had a love of machines and computers have always been included in that mechanical empathy.  That mathematics stole coding from me is something I've always regretted.

That tyranny of numbers still holds sway in coding no matter what attempts are made to pry it free.  I’m previewing a video for my computer studies class and came across this bit:

The Machine That Changed The World

So there you have it.  Had we developed computers with different intent, our analytic engines wouldn't have been confused with calculators.

One of the perilous moments I experienced while getting my philosophy degree was trying to get the mandatory symbolic logic credit.  My first attempt had me in a classroom full of science majors all taking symbolic logic because it was being delivered as a math course.  I fled the scene and worried that I'd never get this credit, the math-bullying in that class was something else.  I ended up taking symbolic logic the next semester and getting an A in it.  Why?  Because it wasn't taught by a math major.  I can appreciate logic, I have trouble with it when it gets abstracted in numbers.

The term ‘computer’ is prejudicial.  Computers were originally people who did tedious math problems, mechanical computers supplanted them, but modern computers aren't number crunchers.  Modern code on a modern computer is a construction of complex logic that produces results well beyond mere calculation, to reduce that process to mathematics is absurdly simplistic.  

The whole thing makes me want to change my department from "Computer Studies" to "Universal Engines" and escape from the confusion of a historically inaccurate name, and that tyranny of numbers.