Sunday, June 28, 2015

Problematizing grit, II

How hard you work on something isn’t the only effort (or grit)-related variable. Also key—and what Angela Duckworth’s questionnaire doesn’t probe—is how you direct that effort within the project. I realized that recently when, for the first time in over a decade, I decided to learn a new piano piece. Having allocated myself a mere 15-20 minute window on weekday mornings (a rare stretch of quiet solitude), I was determined to practice as efficiently as possible.

And this meant resisting all sorts of temptations that as a student I often succumbed to: the temptation not to bother working out fingerings and using them consistently; the temptation to interrupt my work on the sections I knew the least well, or found the most difficult, for the satisfaction of breezing through easier or more familiar sections; the temptation to play the piece too fast, too soon. It’s not just the distracting temptations outside a project, I realized, but also the distracting temptations within a project, that need resisting.

Directing your efforts appropriately involves brains as well as brawn. In learning a piano piece, for example, it helps to realize that muscle memory is essential, and that muscle memory will develop fastest if (1) you use consistent fingering and (2) you play slowly enough to minimize errors.

Teachers, too, can be smarter about grit. Neither should they try, vaguely, to "teach" it (e.g., by spending lots of class time on "growth mindsets"); nor should they simply give students tons of work or make them "grapple" indefinitely without guidance. Rather they should give students frequent advice and feedback about performance--and about how best to allocate their efforts.

Friday, June 26, 2015

Math problems of the week: Common Core-inspired "algebra" test problem

A problem from the "calculator section" of Algebra II  Performance Based Assessment Practice Test from PARCC (a consortium of 23 states that are devising Common Core-aligned tests).





Extra Credit:

Based on the given information, determine the ratio of algebraic to verbal challenges in this problem. Describe the steps used and explain any assumptions made. Create a model and describe the steps used to create it. Enter your answer, model, explanation, and assumptions in the space provided.

Wednesday, June 24, 2015

Problematizing grit

In her Ted Talk on “grit,” Angela Duckworth offers the following definition:

Grit is passion and perseverance for very long-term goals. Grit is having stamina. Grit is sticking with your future, day in, day out, not just for the week, not just for the month, but for years, and working really hard to make that future a reality. Grit is living life like it's a marathon, not a sprint.
All this, Duckworth finds, predicts long term success. So far so good—but (dare I say it?) hardly surprising.

What’s a lot less obvious is whether grit can be taught. Of course, this hasn’t stopped the education establishment, ever eager to focus on something other than academic instruction, from jumping to conclusions. Here, on the other hand, is Duckworth:
Every day, parents and teachers ask me, "How do I build grit in kids? What do I do to teach kids a solid work ethic? How do I keep them motivated for the long run?" The honest answer is, I don't know.
Duckworth says the best idea she’s heard is Carol Dweck’s “growth mindset”: “the belief that the ability to learn is not fixed, that it can change with your effort.” Duckworth cites Dweck’s finding that:
when kids read and learn about the brain and how it changes and grows in response to challenge, they're much more likely to persevere when they fail, because they don't believe that failure is a permanent condition.
Again, so far so good—but (dare I say it?) hardly surprising.

Plus, there’s only so far mere beliefs can get you. Indeed, the questionnaire that Duckworth uses to measure grit (and predict success) addresses how distractible you are, how fickle vs. sustained your interests are, and how hard and how diligently you work on things; not what you think about failure.

Given this, perhaps a better way to raise students’ perseverance is to provide extra incentives for hard, concentrated work. Ideally these incentives would be built into the work itself. You make sure that it’s interesting; that students get timely feedback about their progress through it; that completing it results in a satisfying final product, set of revelations, set of new skills, and/or sense of accomplishment. As far as these things go, much school work (whether because it’s busywork, easy work, group work, vaguely defined, and/or lacking in timely feedback) comes up short.

But even with some of the best types of assignments, and/or with certain types of students, there may be insufficient incentives for perseverance. In that case, as we’ve seen with J, why not resort to extrinsic incentives? For those who fail the marshmallow test, why not incentive them with marshmallows?

Monday, June 22, 2015

All about meteors or all about MEteors?

According to Michael Tscholl, a researcher at the University of Wisconsin (as reported in a recent article in Edweek):

Most students harbor fundamental misunderstandings about how forces such as gravity and acceleration operate in outer space. That's because their beliefs about physics tend to be based on their experiences in their own bodies.
Bodies on earth, Tscholl explains, need energy to keep moving; objects in space don't.

How to overcome these fundamental misunderstandings? Guess what Edweek/Tscholl propose? Is it:

1. Enhance students understanding of the concepts of friction and inertia.

2. Give students "embodied cognition" exercises in which they move their bodies around through earthly friction?

Hint: the solution proposed by Edweek/Tscholl is MEteor,
a room-size "simulation environment" that calls to mind a space-age version of the popular space-age version of the popular arcade video game Dance Dance Revolution.
Still stumped? Here's more:
In MEteor, planets and other space objects are projected on the floor and walls. The students must predict the trajectory of an object moving through space by physically moving along the path they think a meteor (projected on the floor) will travel. Laser scanning technology tracks their movements, offering real-time feedback on whether their predictions are correct. Based on that feedback, students adapt their beliefs about scientific principles, then adjust their movements to reflect what they are learning.
Final hint: it's probably reasonable to assume that these MEteor-facilitated embodied cognition exercises don't take place in outer space.

Another problem reported by Tscholl: "students are scared of symbolic representations." Given this, what do you think his solution is?

1. Give students more practice with symbolic representations and their relation to physical phenomena.

2. De-emphasize symbolic representations.

Stumped? Consider: (a) how facility with symbolic representations, and with manipulating these mathematically, is essential to doing physics, and (b) how little sense there is in anything in this article.

Saturday, June 20, 2015

You need to do some graphics to make it look like they’re flying, when they’re not really flying

I recently came across this un-facilitated, unedited, in-class assignment that J wrote for his graphic design class. Somehow, with its earnest attempt to cope with whatever the prompt was, and with his years in high school now weeks away from their conclusion, I found it quite endearing. I reproduce it here with permission from the author.

Given what I’ve written recently about Facilitated Communication, I should note that, in a sense, the author’s in-class communication is facilitated. J’s handwriting being so bad that often even he can’t read it, he regularly uses an AlphaSmart keyboard. But the keyboard remains stationary, sitting on his desk rather than on the palm of someone else’s hand; it offers no text-completion software with pop-up windows of likely next words and grammatical corrections; and no one would even consider hovering over J and supporting his wrist while he types. This is an author who feels strongly about being left alone while the creative juices flow:

There are some people who becomes a graphic designer. Like making a fictional movie, you’ll have to do some graphics on some objects. Like when Violet turned into a blueberry, people had to do some graphics since you obviously can’t inflate people into a ball. 
You have to be good at programming. Graphics require some programming. When you make a movie, you’ll want it to look real, and not make it look like it’s edited. Like when we see Violet turning to a blueberry, it looks real, and has not been edited.
You have to be good at painting to make some cartoon movies. In cars, Lightning McQueen and other cars look like they’re real, but they were actually painted. You would want to make it look real, and not look like they have been painted.  
You have to have a software to do some graphics. Photoshop is one of the software. It can edit some things out, and put some new things in. Like if you want to change some of the words, you’ll want to remove the words, and put new words in, and you’ll want to make it look like real, and has not been edited.  
So if you want a graphic designer, you need to be prepared. You want to make a movie look real, and not been edited. Like in Harry Potter movie, quidditch is obviously not real. You’ll have to make some graphics to make it look like they’re flying, when they’re not really flying.

Thursday, June 18, 2015

Math problems of the week: Common Core inspired 8th grade functions problems

From the Smarter Balanced Assessments, a Common Core-inspired, standardized test consortium now consisting of about 12 states.


The Common Core goal in question?

Grade 8 » Functions » Use functions to model relationships between quantities. » 5

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.


Extra Credit:

Labels vs. Concepts

If you factor out the hurdle of knowing the meanings of the various labels ("linear", "non-linear," "positive slope," "negative slope"), how much mathematical challenge is left, and at approximately what grade level would you put it?

Tuesday, June 16, 2015

What we forget about history textbooks

It’s fashionable these days to decry traditional history as all about names and dates and powerful people, and history textbooks as inferior to primary sources. But our collective historical memories are short.

People forget that there are textbooks, and then there are textbooks. Some of them are written by committee, are dumbed down for a very general audience, and, written to offend no one, are dull as doorknobs. Others are written in the single voice of a learned historian and raconteur: someone who knows how to make even the driest facts as interesting to you as they are to him or her.

People forget that to really appreciate primary sources, you need historical context; that survey courses are the best way to acquire and retain this; and that there are some really good survey-based textbooks out there written by learned historians/raconteurs who know how to make even the driest facts interesting—particularly if you go back in time.

Because, finally, people forget—or probably never knew—that there are all sorts of really good history textbooks that were published ages ago, and that aren’t all about names and dates and powerful people.

Here’s how one of them opens:

Could Louis XIV now see the France he once ruled, how startling the revolution in politics and industry would seem to him! The railroads, the steel steamships, the great towns with well-lighted, smoothly paved, and carefully drained streets; the innumerable newspapers and the beautifully illustrated periodicals, the government schools, the popular elections, and his deserted palaces; the vast factories full of machinery, working with a precision and rapidity far surpassing those of an army of skilled workmen; and most astonishing of all, the mysterious and manifold applications of electricity which he knew only in the form of lightning playing among the storm clouds: all these marvels would combine to convince him that he died on the eve of the greatest revolution in industry, government, and science that the world has ever seen. It is the purpose of this volume, after describing the conditions in Europe before the French Revolution, to show as clearly as possible the changes which have made the world what we find it today.  
If a peasant who had lived on a manor in the time of the Crusades had been permitted to return to earth and travel about Europe at the opening of the eighteenth century, he would have found much to remind him of the conditions under which, seven centuries earlier, he had extracted a scanty living from the soil…  
The houses occupied by the country people differed greatly from Sicily to Pomerania, and from Ireland to Poland, but, in general, they were small, with little light or ventilation, and often they were nothing but wretched hovels with dirt floors and neglected thatch roofs. The pigs and the cows were frequently better housed than the people, with whom they associated upon very familiar terms, since the barn and the house were commonly in the same building…

Even in the towns there was much to remind one of the Middle Ages. The narrow, crooked streets, darkened by the overhanging buildings and scarcely lighted at all by night, the rough cobblestones, the disgusting odors even in the best quarters—all offered a marked contrast to the European cities of today, which have grown tremendously in the last hundred years in size, beauty, and comfort.
(From James Harvey Robinson’s Outlines of European History, which my daughter and I started reading a couple of months ago.)