The Weekend Collection

A small collection of good things to read, and hear (no watch) when time allows this week.

Read: This past Tuesday, March 14, was Pi day. 3/14 = 3.14, the approximation of this classic irrational number. From two years ago, a writer for the New Yorker goes beyond the trivia to briefly explain in relatively simple terms Why Pi Matters. A little math for all you non-mathematical types. (about 3 minutes)

Listen: If you’re not between the ages of 18 and 34, you’re not in the target demographic for SnapChat. You may not even know how the service works, or why so many young people check in and use it over, and over, and over every day. A recent episode of the Note to Self podcast tries to explain why this app is worth more than $10 billion, as well as “how far Silicon Valley will go to capture and control your eyeballs”. (18 minutes)

Read: Rolling Stone celebrates the 20th anniversary of Buffy, the Vampire Slayer with a nice essay that summarizes what made the series both fun and meaningful. I actually like the very flawed movie on which it was based and the series hooked me from episode 1. (about 6 minutes)

Listen: I’m late to Jenn Binis’ very informative podcast, Ed History 101, in which she discusses the background to our profession that you probably missed in college (or which they got wrong). A good starting point is the segment on summer vacation, a topic that generally falls into that got-it-wrong category. (23:11)

Read: Although I disagree with the central premise that Google is making us dumber, this interview with the author of a new book about how adults learn is still interesting. I do believe that many of the techniques we were taught in high school (and that are probably still taught) are not particularly effective. (about 6 minutes)

The “Right” Way to Learn Math

In a short essay for a Canadian newspaper, a high school math teacher reflects on his work and wonders if it’s pointless.

I also don’t feel the time I spent helping students (mostly freshmen and sophomores) understand math was “pointless”. I do disagree with with his idea of “math as a gym for the mind”, that doing math regularly “keeps the mind active” and improves abstract thinking.

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Certainly there are aspects of studying mathematics that can help students develop their analytical skills, but most of what we teach in K12 classes is largely focused on memorizing and recreating canned procedures.

However, the writer of this particular piece is exactly on target with this assessment of what math education should be.

The “right” way to do mathematics is not to learn many techniques, but to solve many problems using the learned techniques.

The problem must come first. Then we discover what tools, mathematical or otherwise, are needed to solve it.

That’s how math is really used, so why not help students learn that process? Instead of the very artificial one that embodies the math curriculum in most high schools.

3-2-1 For 2017

For the final 3-2-1 of 2016, here are three books, two audio books, and one movie you may want to consider enjoying during the coming year.

Three books worth a space on your reading list.

The Innovator’s Mindset by George Couros.  George is very much an advocate for empowering students and this book is a wonderfully positive collection of ideas for making that happen. It include many great suggestions that could and should be used immediately. This is one book that should be read with a group of other educators. (about 4 hours, 16 minutes)

Weapons of Math Destruction by Cathy O’Neil. Many decisions made by corporations and governments, such as who gets a loan or who is paroled from prison, are based on mathematical models that are poorly understood, even by the people who create them. This book is especially for those who are not “math people” and I’ll have more posts about it later. (about 5 hours, 26 minutes)

Education Outrage by Roger Schank. Few people do outrage better than Schank but, as you’ll find in this book, there is much to be upset about in the American system of education. This is a collection of Schank’s essays that will challenge some (maybe many) of your beliefs about what school is and could be. Share the book with your local school leaders. (about 5 hours, 57 minutes)

Two audiobooks for your commute.

Medium Raw written and read by Anthony Bourdain. Although he’s a chef by training, Bourdain’s television is all about travel and exploring other cultures as wide ranging as Vietnam and New Jersey. This is the story of those travels, mixed with a strong critique of restaurant trends and food television. Be warned, he occasionally uses bad language. (9 hours)

Me of Little Faith written and read by Lewis Black. If you have seen or heard Black’s stand-up work, you might think this is just his very caustic humor applied to religion. You would be wrong. This is a very thoughtful, and very funny, philosophical treatise in which he asks many good questions, and arrives at at least some good answers. Be warned, Black also uses some bad language. (5 hours, 50 minutes)

One movie to watch when you have time

The Big Short. This film was released at the end of 2015 and probably didn’t get a big audience. However, it’s a very thoughtful, surprisingly entertaining story about the housing crash of 2008, and bitingly very funny as well. Based on the book by Michael Lewis and featuring great performances by Steve Carell and Christian Bale. (2 hours, 10 minutes; on Netflix)

The Usefulness of Math

Catching up on items in my Instapaper queue we find a writer who says we should stop trying to sell math for it’s usefulness.1

One of the fall outs of children not understanding mathematics and the associated failure which often follows at some point in their 500 hour tour of the salt mines of mathematics?—?aka math education?—?is that teachers, through no fault of their own, start to sell/hawk mathematics like its some discontinued K-Tel kitchen product at a Saturday Flea Market.

Kids struggle with the number and symbolic manipulation we present as math for a variety of reasons, but the lack of context that necessitates that selling process is probably right up there. They are not dumb. Students understand that adults sometimes do use some math in their lives. But they also realize that there is likely an app for that.

Dozens of calculators to do the basic work, laser pointers that measure more accurately than a simple ruler, even software to produce each step of a process just as the teacher asked for. There may be a lot of trig involved with kite flying but learning from the mistakes of throwing it into the wind is more fun.

However, marketing math based on “its sometimes messy and intricate fun” and the intrinsic mystery of “symmetrical curvature” is also a dead end. And it won’t be especially beneficial to students in the long run.

Certainly playing with math can be both entertaining and lead to interesting discoveries. But even traveling that path, we will still arrive at the inevitable question: “when are we ever going use this?”, not to mention “is this going to be on the test?”.

I think there’s a middle ground between trying to sell kids on the need for our current formal mathematics program, most of which they will never use, and encouraging students to embrace the beauty and poetry of math.

How about using math to solve actual problems, other than those in books with mathematical titles? Like validating a survey in social studies. Gathering and analyzing data in science. Applying Geometric patterns to make art.

Maybe it’s time to eliminate the subject area silo called “mathematics” altogether in K12 (except for those few students in high school interested in that field), and instead incorporate those tools into the overall problem solving process. It would be a wonderful first step to tearing down all the artificial walls between subject areas.

I’m pretty sure someone can tell me why this is idea is impractical, unrealistic, or just plain looney. But there’s got to be something between “useful” math that really isn’t and “beautiful” math that few can appreciate (or even want to).

School Math is Void of Common Sense

A research mathematician turned teacher has a word problem for you: “There are 125 sheep and 5 dogs in a flock. How old is the shepherd?”

Most adults would quickly come to the conclusion that there is not enough information to find an answer. Not most students.

Now consider that, according to researchers, three quarters of schoolchildren offer a numerical answer to the shepherd problem. In Kurt Reusser’s 1986 study, he describes the typical student response:

125 + 5 = 130 …this is too big, and 125–5 = 120 is still too big … while … 125/5 = 25 … that works … I think the shepherd is 25 years old.

Remarkable. In their itch to combine the numbers presented to them, students negotiate three solutions. They show some awareness of context in dismissing the first two candidates. But a 25-year-old farmer is plausible enough for students to offer it up as their answer. The calculations are correct, but they are also irrelevant. Common sense has deserted these students in their pursuit of a definitive answer.

He says those findings are the direct result of the type of problems we ask students to solve during their travels through school math.

Students believe that all math problems are well-defined, usually with a single right answer. They strongly associate mathematics with numbers, to the extent that they will instinctively derive numerical answers to problems regardless of the context. They are subservient to computational procedure and trust that accurate calculations will always lead them to relevant truths. They accept that confusion and ambiguity is a staple fixture of mathematics, willingly offering up solutions that are void of context, meaning or even common sense.

So, what’s the alternative to our current standard math curriculum, featuring repetitive pages of calculations and ambiguous word problems with one right answer? The writer has some excellent ideas. However, they would require completely reimagining the way we teach math.

At the core of those changes is an emphasis on understanding process rather than finding answers.

Mathematics is a journey; it is defined by process, not rigid outcomes. That process can not be reduced to a series of discrete computation steps. It is governed by a flow of reasoning that guides the thinker towards a solution. Problem-solving often an unstructured, messy affair that requires several iterations of developing and testing assumptions. Error and ill-judgement are the most natural components of problem solving; they should be embraced. All mathematicians need pause to reflect on their problem solving strategies; to step back and retain full view of the big picture. Students must be afforded the same opportunities; their development as mathematical thinkers depends on this sense-making.