math Archives - The Jose Vilson


This week, I’m supposed to teach my students how to solve a system of equations by elimination. It’s the hardest of the four ways  for solving systems (graphing, substitution, guess-and-checking), and I’m not entirely sure everyone in the class gets the first three. The main point of the unit is to determine exactly where two or more linear relationships meet, if they ever do. The situation could be realistic (two cars running a race, two trains on a schedule, cell phone pricing plans) or already abstracted (simultaneous equations), but I’m hoping they can find this meeting point because it’s really interesting. Is it relevant to their daily lives? Perhaps. Do I care? Not necessarily.

Really, I don’t always want the things that people learn to be within the realm of possibility, because I’m trying to prepare them for the improbable as well.

One missing piece of the Common Core State Standards debate is that, while I’m glad to teach students higher order math that puts them on the pathway to do well in high school algebra (and trickles into geometry, trig, and hopefully calculus / statistics), I can’t, and sometimes don’t want to, always do what the standards are asking me to do.

After nine years, I’m still trying to find ways to push my teaching – and their learning – further, and I believe I’ve earned the right to say what works and what doesn’t with any group of students. I often find it’s a waste to try and create a week’s worth of lesson plans when things are bound to change from day to day. I know what they have to learn and I have a given window of time I’d like to finish the learning by, but I’m also trying to maximize student learning if possible, meaning that I’ll have to come up with six ways of explaining something and hoping the students catch at least two of those.

That’s the thing with math generally. People are taught that we ought to teach math only one way, and, if not taught this way, they’ll never get it. I’m happy just knowing that, out of the hundreds of ways of doing a problem, they at least caught on to one. Because I really don’t have all the answers. I have mine. The next person might have a better way. I have no ego or qualms mentioning this all the time.

At some point, however, I’d like to get them confident enough to not have to depend on whether I know it or not, but that I gave them some tools for them to do it themselves. Because maybe the math we’re doing isn’t necessarily relevant, but it could be useful for the things we haven’t yet used, or necessary for the things we haven’t yet needed.



A few notes:

  • Hannah Nguyen bursts onto the scene with a comment at Michelle Rhee’s Teacher Town Hall last week. Check this out! [InspirEDucation]
  • Richard Rothstein just earned himself a new fan with his dissection of Secretary of Education Arne Duncan’s assertion that integration should be “voluntary.” [Economic Policy Institute]
  • Contrary to popular belief, the general public values math the most out of the general subjects taught. More on this soon, but please read this. [Gallup]
  • The New Republic makes the case for the wild child. No, really. [The New Republic]
  • Salome Thomas-El chimes in about the school year with a passionate post about passionate leadership. [ASCD Inservice]



Back to school time for us NYC folk (and a few others, surely). Let’s get this party started!


Grant Wiggins and How I View Math Curriculum

by Jose Vilson on August 22, 2013

in Mr. Vilson

Grant Wiggins, What issss UBD?

Grant Wiggins, What issss UBD?

This week, a few of us got into a discussion, and involved Grant Wiggins. He calls himself a troublemaker, but I don’t remember seeing him at the last few meetings, and I’m the treasurer. In any case, for his 100th blog, he wrote this:

Algebra is a dumb course.

It survives only by unthinking habit. It cannot be justified intellectually as a subject, really. It is just a set of tools, not an intellectual discipline with larger meaning and an ongoing scholarship.

Worse, it is an insidious dumb course because everyone must take it, and many people fail it – in part, because it is so dumb.

DO NOT MISUNDERSTAND ME! I said Algebra is a dumb course. I did not say the content called algebra is not worth learning. The distinction is critical.

Algebra, as we teach it, is a death march through endless disconnected technical tools and tips, out of context. It would be like signing up for carpentry and spending an entire year being taught all the tools that have ever existed in a toolbox, and being quizzed on their names – but without ever experiencing what you can craft with such tools or how to decide which tools to use when in the face of a design problem.

I see the logic here, but, like a few of us, I get annoyed at people who want to bring up math as the strawman in need of reform in high school curriculum. Naturally, after seeing people put @grantwiggins in my mentions, I said, “Wait, does this guy actually have a plan?”

Oh boy.

Sure enough, he responded a few minutes later, matter-of-factly, with, “I do have a plan and have written about it often. Design backward from big ideas and complex tasks.”

Of course, being the edu-heretic I am, I challenged him with, “With all due respect, we can’t UBD our way out of [reforming math education]!”

How dare I challenge Grant Wiggins, Andrew Hacker, and Nicholson Baker so deftly! What passes for “new” ideas often gets muddled in resentment from previous experiences with a certain subject without looking at the whole.

I respect Wiggins and the UBD model tremendously. With a few tweaks, I helped reconstruct the entire math department’s curriculum planning by learning how to think about what we want students to know. While still a challenge, I believe it made all of our jobs easier in the long term.

However, the UBD model is a planner. Nothing more, nothing less. We can call it a framework, a bunch of small boxes to fill out, or a separator between the have-professional-development-on-this-s and the have-nots. However, the UDB model isn’t a plan.

Unfortunately, I don’t think it gets better for high school math, either. After years of looking at the high school Common Core Math Standards, it doesn’t seem to truncate or synthesize much of anything for what high schools ought to teach besides the four major math groups (algebra, geometry, trigonometry, and calculus), at least not from New York State’s standpoint.

In other words, standards, scripted lessons, and unit plans may (or may not) help with reforming math, but we have to look at the whole ecosystem. It’s not just what we want students to know, but how they receive it, and what we have to make compulsory in order to actually measure “college and career-readiness.” Frankly, I’m not comfortable with that term, either.

The truth is, few of us actually know what we’re going to do with our lives until later in life. We should have a strong, compulsory curriculum that gives them options in case their preferred career of interest doesn’t work out for them. The more knowledge they acquire, the more options our students have. Most of us don’t have the privilege of knowing what we want right out the womb and achieving it.

That’s where the discussion about curriculum should have gone, but noooo. People had to pick on math. Come now.

Mr. Vilson


Math As A Merit Badge (And Other Comments)

August 20, 2013 Mr. Vilson
Don't Drink and Derive

The responses to my last post about math (who said I’m not a math blogger again?) ranged from the plauditory to the super-critical. Here’s a selection of some of my favorite comments to my last piece. First, Michael Doyle sets the record straight: Algebra II has become a badge, one of many, that pretends to separate middle […]

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No One Puts Algebra 2 In A Corner (Math For All Kids)

August 19, 2013 Mr. Vilson
No One Puts Baby In The Corner

First, let me say that this Nicholson Baker article already starts off wrong by not discussing al-Khwarizmi’s contributions to algebra, mainly NAMING it. Secondly, this conversation about math reminds me of the conversation we had about Andrew Hacker’s article last year. Here’s another guy who ostensibly doesn’t have a focus in any math-related subjects trying […]

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Short Notes: A Cautionary Tale for Edubloggers

June 9, 2013 Short Notes
Arundhati Roy

A few notes: The New York Daily News wants you to nominate teachers for their Hometown Heroes award. Start your engines, ladies and gentlemen. [NY Daily News] If you’re sick of the “disruption” talk surrounding technology, specifically education, then read this paper by Audrey Watters. Another hit. [Hack Education] Peter DeWitt writes an interview, and […]

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