Last week, I wrote about ‘The Web of Content’ metaphor. In short, schools should be wary of making the ‘industrial model’ of education, where products are passed in a linear arrangement through one checkpoint after another which ensure conformity to a narrow band of tolerances, the focus of modern curriculum. This includes 1) restricting the number of ‘outcomes’ through which a student can ‘display mastery’ to just pen-and-paper tests as well as it includes 2) teaching mathematics or history as a journey from point A to B with questions along the way that you have to answer and get ‘right.’
- After all, the key characteristic of a healthy ecosystem – like a school – is diversity. Students should of course be pushed to overcome their weaknesses, but even more so their strengths should be fostered. Why can’t a particular project have one student turning in a typed paper, one turning in a well-crafted podcast response, one turning in a YouTube video, one turning in a live presentation, and one turning in a ‘museum exhibit’? Obviously most students would choose the paper, because it seems easiest when you really get down to creating quality in each of those other modalities; however, I will now immediately go back on my statement because I would argue that really good writing should be just as challenging. But I seem to be a tougher grader on writing assignments than others…
- I had a new-to-me student this year that asked a question that almost knocked me off my feet, and not in a good way. I made a comment at some point (and I wish I could remember what it was now!) to another student in the class about how they had a good question – one that was so good, in fact, that “you could probably follow that rabbit-hole for a long ways – even write a book on it! It could be a new subject to study in math!” My new student, Mark, laughed out loud. A few of us looked at him, puzzled. “It’s a funny idea!” he said, “Because it’s like, where would you get all the questions from for this new class? What would you even study without having problems to do?”
I am very sad to say that I am serious right now. This is a ninth-grade student whose entire conception of a ‘subject’ is that someone wrote a textbook that you have to study on the subject. The idea that ‘subjects’ are actually ideas created by people who are curiously observing the world and begin to ask testable questions about it, create theories based on their observations, and then analyze/scrutinize the accuracy of those theories based on continued observation was completely beyond him. I need not say this, but I will anyways: SOMETHING WENT VERY, VERY WRONG IN THIS YOUNG MAN’S EDUCATION.
Well, here’s a story from ‘The Web’ that highlighted just how far I ‘stretch’ its silky threads sometimes. I think high school math educators everywhere can find ways to stretch the threads similarly.
My seniors are currently working on a unit called “Pollster’s Dilemma,” wherein they explore the statistics of Election Polling. It’s a super-fun unit, and obviously we talk a lot about topic related to voting and elections during the course of the unit. Well, last week was an election week in Denver, and we had a couple of interesting topics on the Ballot (as well as candidates). I wanted the students who were 18 to make sure they engaged in their first voting experience, but in the process of asking some of them if they were going to vote and what their research processes had been, I realized that there was an opportunity here (check out the footnotes of this post).
One of the major topics was “Proposition CC,” which despite the language it used, was essentially about TABOR. Now, talk about some funny use of language, TABOR itself is kind of hilarious. But I won’t comment to much on that – as I did with my students, I’ll leave that to you to do the research. The point, though, is that TABOR is a classic example of a bill that has real-world implications, but that it seems the majority of people out there don’t have either the intellectual capacities or the wills to actually take the time to understand. It’s difficult, certainly! But I wanted my students to experience a bit of that difficulty and come to understand that ‘difficult’ does not mean ‘impossible;’ that ‘complex’ does not mean ‘not worth it.’ Their assignment for the entire class was to research the propositions out there as well as the candidates, and to write me a description of who they would vote for and why. To preface the assignment, we talked about the challenge of trying to place quantitative value on various issues in order to make a decision that is black-or-white when you would prefer shades from each side, and I offered an alternative assignment to only describe the history of TABOR if students felt uncomfortable sharing voting ideas.
The resulting assignments and discussions were incredibly interesting. Without commenting on TABOR too much, one quick ‘did you ask this question or not?’ moment came from the idea of ‘how much does each taxpayer actually get back as a refund? Is that amount worth saying that education and transportation shouldn’t get the ~310 million dollars that they would have?’ It turns out that the amount most people would be getting back this year was about $39-150, and by even just next year people who make over a quarter-of-a-million dollars a year (the highest tax bracket) would be getting a $79 refund. These numbers began to change some students minds on whether or not they wanted their refund over education and transportation getting more tax dollars.
Students who really got into the trends within that hour were able to discover that a second bill was passed years after the original TABOR bill passed that turned out to be drastically affected by the economic situation of 07-08. Those students especially seemed to realize by the end of the session that we cannot rely on what we hear on the news or from our friends to give us good understandings of even the most localized politics. We have to learn to be astute observers and be able to analyze big data in order to understand situations on our own.
The point I want to make is this: don’t be afraid to deviate from curriculum in service of providing lifelong lessons that kids need to understand. Sometimes, these lessons become the most long-lasting. Obviously, you can’t do it every day. These moments are special only when they buck the trend on an otherwise fairly rigid devotion to ‘math.’ But when they happen, they will make those 1 or 6 days a year completely worth it.
Vena Cava 