Tag: desmos

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Don’t Teach Math the “Smart Way”

Smartness and mathematics have an unhealthy relationship.

If you have been successful in math, by public consensus, you must be smart. If you have been successful in the humanities, you may also be smart but we cannot really be sure about that now can we, says public consensus.

In a world where our finest mathematical minds ruined the global economy and perpetuate unequal social outcomes, outcomes most ably critiqued by people trained in the humanities, public consensus is wrong.

A worksheet that asks students to use the 'smart way' to tell time.

This worksheet is worse.

This worksheet associates smartness with a certain way of doing math, diminishing other ways your students might develop to do the same math. Because there are lots of possible ways to tell time – some new, some old, and some not-yet-invented!

Worse, this worksheet associates smartness with a certain way of doing math that is culturally defined, diminishing entire cultures. For example, depending on your location in the world, “2/5/19” and “5/2/19” can refer to the same calendar date. Neither of those ways are “smart” or “dumb.” They work for communication or they don’t.

Try This Instead

If I’d like students to learn a certain way of doing math – whether that’s adding numbers a certain way or solving equations a certain way – I need to understand the reasons why we invented those ways of doing math and put students in a position to experience those reasons. I also need to be excited – thrilled even! – if students create or adapt their own ways of doing math when they’re having those experiences. Anything less is to diminish their creativity.

If I want students to learn how to communicate mathematically, I need to ask them to communicate.

So in this Desmos activity, one student will choose a clock and another student will ask questions to narrow 16 clocks down to 1.

I have no idea what ways students will use, create, or adapt in order to tell time. I will be excited about all of them.

I will also be excited to share with them the ways that lots of cultures use to tell time. When I share those ways, I will be honest that those ways aren’t “smart” any more than they are “moral.” They are merely what one group of people agreed upon to help them get through their day.

So I’d also offer students this Desmos activity, which tells students the time using several different cultural conventions, including the one the worksheet calls “smart” above.

Students set the clock and then they see how easy or hard it was for the class to come to consensus using that convention.

Later, we invite students to set the clock themselves and name the time using three different conventions. They make two of them true, one of them a lie, and submit the whole package to the Class Gallery where their classmates try to determine the lie.

The words we use matter. “Real world” matters. “Mistakes” matter. “Smart” matters. Those words have the power to shape student experiences, to extend or withdraw opportunities to learn, to denigrate or elevate students, their cultures, and the ideas they bring to our classes.

Defining smartness narrowly is to define “dumbness” broadly. Instead, we should seek to find smartness as often as possible in as many students as possible.

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[Updated] Will It Hit The Hoop?

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Six years ago, I released a lesson called Will It Hit The Hoop? that broke the math education Internet. (Not a big brag. It was a much smaller Internet back then.)

I think the core concept still works. First, students predict whether or not a shot goes in the hoop based on an image and intuition alone. Then they analyze the shot using quadratic modeling and update their prediction. Then they see the answer. For most students, quadratic modeling beats their intuition.

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The technology was a chore, though. Teachers had to juggle two dozen different files and distribute some of them to students. I remember loading seven Geogebra files onto student laptops using a thumb drive. That was 2010, a more innocent time.

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So here’s a version I made for the Desmos Activity Builder which you’re welcome to use. It preserves the core concept and streamlines the technology. All students need is a browser and a class code.

Six year older and maybe a couple of years wiser, I decided to add a new element. I wanted students to understand that linears are a powerful model but that power has limits. I wanted students to understand that the context dictates the model.

So I now ask students to model this data with a linear equation.

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Then I show students where the data came from and ask them to describe the implications of their linear model. (A: Their linear ball goes onwards and upwards forever.)

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And then we introduce parabolas.

Marbleslides Is Here

Marbleslides is the latest activity from my team at Desmos. It’s simple. We set up some stars. You press a “launch” button and marbles drop.

But here you have collected zero stars. No success.

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That’s because your students need to set up parabolic, linear, exponential, sinusoidal, or rational functions to send the marbles on a trip through those stars.

Success!

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That’s Marbleslides and you and your students should play it this week and let us all know how it goes. If you want a preview, head to student.desmos.com LINK and type “eht8”.

If you want to set up your own class, head to the Marbleslides activities listing, choose a function family, and get a classcode of your own.

Here are some quick, below-the-fold notes about what we’re trying to do here and why we’re trying to do it.

Delight. Whenever possible we want students to experience the same sense of delight about math that all of us at Desmos feel. Students can experience that delight both in pure and applied contexts and Marbleslides is that latter experience. Seriously, try not to grin.

Purposeful Practice. Picture two students, both graphing dozens of rational functions. One finds the experience dreary and the other finds it purposeful. The difference is the wrapper around that graphing task. If the wrapper is no more purposeful than a worksheet of graphing tasks, your student may fatigue after the first few graphs. In our Marbleslides classroom tests, we watched students transform the same function dozens of times – stretching it, shrinking it, nudging it up, down, left, and right by tiny amounts. That’s the Marbleslides wrapper. Students have a goal. Their pursuit of that goal will put you in a position to have some interesting conversations about these functions and their transformations.

BTW. Here’s the announcement post on the Desblog.