Category: tech enthusiasm

Total 111 Posts

Must Read: Larry Berger’s Confession & Question About Personalized Learning

Larry Berger, CEO of Amplify, offers a fantastic distillation of the promises of digital personalized learning and how they are undone by the reality of learning:

We also don’t have the assessments to place kids with any precision on the map. The existing measures are not high enough resolution to detect the thing that a kid should learn tomorrow. Our current precision would be like Google Maps trying to steer you home tonight using a GPS system that knows only that your location correlates highly with either Maryland or Virginia.

If you’re anywhere adjacent to digital personalized learning – working at an edtech company, teaching in a personalized learning school, in a romantic relationship with anyone in those two categories – you should read this piece.

Berger closes with an excellent question to guide the next generation of personalized learning:

What did your best teachers and coaches do for you—without the benefit of maps, algorithms, or data—to personalize your learning?

My best teachers knew what I knew. They understood what I understood about whatever I was learning in a way that algorithms in 2018 cannot touch. And they used their knowledge not to suggest the next “learning object” in a sequence but to challenge me in whatever I was learning then.

“Okay you think you know this pretty well. Let me ask you this.”

What’s your answer to Berger’s question?

BTW. It’s always the right time to quote Begle’s Second Law:

Mathematics education is much more complicated than you expected even though you expected it to be more complicated than you expected.

Featured Comment

SueH:

I have come to believe that all learning is personalized not because of what the teacher does but because of what’s happening inside the learner’s brain. Whatever pedagogical choices a teacher makes, it’s the student’s work that causes new neural networks to be created and pre-existing ones to be augmented or strengthened or broken or pruned.

Scott Farrand:

I’ll accept the risk of stating the obvious: my best teachers cared about me, and I felt that. Teaching is an act of love. A teacher who cares about each student is much more likely to, in that instant after a student responds to a question, find the positive value in the response and communicate encouragement to the student, verbally and nonverbally. And students who feel cared for are more likely to have good things going on in their brains, as described by SueH.

Desmos + Two Truths and a Lie

I’m absolute junk in the kitchen but I’m trying to improve. I marvel at the folks who go off recipe, creating delicious dishes by sight and feel. That’s not me right now. But I’m also not content simply to chop vegetables for somebody else.

I love the processes in the middle – like seasoning and sautéing. I can use that process in lots of different recipes, extending it in lots of different ways. It’s the right level of technical challenge for me right now.

In the same way, I’m enamored lately of instructional routines. These routines are sized somewhere between the routine administrative work of taking attendance and the non-routine instructional work of facilitating an investigation or novel problem. Just like seasoning and sautéing, they’re broadly useful techniques, so every minute I spend learning them is a minute very well spent.

For example, Estimation 180 is an instructional routine that helps students develop their number sense in the world. Contemplate then Calculate helps students understand the structure of a pattern before calculating its quantities. Which One Doesn’t Belong helps students understand how to name and argue about the names of mathematical objects.

(Aside: it’s been one of greatest professional pleasures of my life to watch so many of these routines begin and develop online, in our weirdo tweeting and blogging communities, before leaping to more mainstream practice.)

I first encountered the routine “Two Truths and a Lie” in college when new, nervous freshmen would share two truths about themselves and one lie, and other freshmen would try to guess the lie.

Marian Small and Amy Lin adapted that icebreaker into an instructional routine in their book More Good Questions. I heard about it from Jon Orr and yesterday we adapted that routine into our Challenge Creator technology at Desmos.

We invite each student to create their own object – a circle graph design in primary; a parabola in secondary.

We ask the student to write three statements about their object – two that are true, and one that is a lie. They describe why it’s a lie.

Here are three interesting statements from David Petro’s circle graph design. Which is the lie?

  • The shaded part is the same area as the non shaded part.
  • If these were pizzas, there is a way for three people to get the same amount when divided.
  • If you double the image you could make a total of 5 shaded circles.

And three from Sharee Herbert’s interesting parabola. Which is the lie?

  • The axis of symmetry is y=-2.
  • The y-intercept is negative.
  • The roots are real.

Then we put that thinking in a box, tie a bow around it, and slide it into your class gallery.

The teacher encourages the students to use the rest of their time to check out their classmates’ parabolas and circle graphs, separate lies from truth, and see if everybody agrees.

Our experience with Challenge Creator is that the class gets noisy, that students react to one another’s challenges verbally, starting and settling mathematical arguments at will. It’s beautiful.

So feel free to create a class and use these with your own students:

2018 Feb 6. I added eight more Two Truths & a Lie activities on suggestions from y’all!

BTW. Unfortunately, Challenge Creator doesn’t have enough polish for us to release it publicly yet. But I’d be happy to make a few more TTL activities if y’all wanted to propose some in the comments.

Challenge Creator & the Desmos Classroom

Briefly

  • At Desmos, we’re now asking ourselves one question about everything we make: “Will this help teachers develop social and creative classrooms?” We’ve chosen those adjectives because they’re simultaneously qualities of effective learning and also interesting technology.
  • We’ve upgraded three activities (and many more to come) with our new Challenge Creator feature: Parabola Slalom, Laser Challenge, and Point Collector: Lines. Previously, students would only complete challenges we created. Now they’ll create challenges for each other.
  • The results from numerous classroom tests have been – I am not kidding you here – breathtaking. Near unanimous engagement. Interactions between students around mathematical ideas we haven’t seen in our activities before.

Read More

One question in edtech bothers us more than nearly any other:

Why are students so engaged by their tablets, phones, and laptops outside of class and so bored by them inside of class?

It’s the same device. But in one context, students are generally enthusiastic and focused. In the other, they’re often apathetic and distracted.

At Desmos, we notice that, outside of class, students use their devices in ways that are social and creative. They create all kinds of media – text messages, videos, photos, etc. – and they share that media with their peers via social networks.

You might think that comparison is unfair – that school could never stack up next to Instagram or Snapchat – but before we write it off, let’s ask ourselves, “How social and creative is math edtech?” What do students create and whom do they share those creations with?

In typical math edtech, students create number responses and multiple choice answers. And they typically share those creations with an algorithm, a few lines of code. In rarer cases, their teacher will see those creations, but more often the teacher will only see the grade the algorithm gave them.

For those reasons, we think that math edtech is generally anti-social and uncreative, which explains some of the apathy and distraction we see when students use technology inside of class.

Rather than write off the comparison to Instagram and Snapchat as unreasonable, it has motivated us to ask two more questions:

  1. How can we help students create mathematically in more diverse ways?

So we invite students to create parking lots, scale giants, mathematical arguments, tilings, sketches of relationships, laser configurations, drawings of polygons, tables, stacks of cards, Marbleslides, informal descriptions of mathematical abstractions, sequences of transformations, graphs of the world around them, and many more.

  1. How can we help teachers and students interact socially around those creations?

So we collect all of those creations on a teacher dashboard and we give teachers a toolkit and strategies to help them create conversations around those creations. It’s easier to ask your students, “How are these two sketches the same? How are they different?” when both sketches are right in front of you and you’re able to pause your class to direct their focus to that conversation.

Today, we’re releasing a new tool to help teachers develop social and creative math classrooms.

Challenge Creator

Previously in our activities, students would only complete challenges we created and answer questions we asked. With Challenge Creator, they create challenges for each other and ask each other questions.

We tried this in one of our first activities, Waterline, where, first, we asked students to create a graph based on three vases we gave them.

And then we asked them to create a vase themselves. If they could successfully graph the vase, it went into a gallery where other students would try to graph it also.

We began to see reports online of students’ impressive creativity and perseverance on that particular challenge. We started to suspect the following: that students care somewhat when they share their creations with an algorithm, and care somewhat more when they share their creations with their teacher.

But they care enormously when they share their creations with each other.

So we’ve added “Challenge Creators” to three more activities, and we now have the ability to add them to any activity in a matter of hours where it first took us a month.

In Parabola Slalom, we ask students to find equations of parabolas that slip in between the gates on a slalom course. And now we invite them to create slalom courses for each other. Those challenges can be as difficult as the authors want, but unless they can solve it, no one else will see it.

In Laser Challenge, we ask students to solve reflection challenges that we created. And now we invite them to create reflection challenges for each other.

In Point Collector, we ask students to use linear inequalities to capture blue points in the middle of a field of points. And now we invite them to create a field of points for each other.

We’ve tested each of these extensively with students. In those tests we saw:

  • Students calling out their successes to each other from across the room. “Javi, I got a perfect score on yours!”
  • Students calling out their frustrations to each other from across the room. “Cassie, how do you even do that?”
  • Students introducing themselves to each other through their challenges. “Who is Oscar?”
  • Students differentiating their work. “Let’s find an easy one. Oo – Jared’s.”
  • Students looking at solutions to challenges they’d already completed, and learning new mathematical techniques. “You can do that?!”
  • Students marveling at each others’ ingenuity. “Damn, Oscar. You hella smart.”
  • Proud creation. One student said, “We’re going to make our challenge as hard as possible,” to which his partner responded, “But we have to be able to solve it!”
  • Screams and high fives so enthusiastic you’d think we were paying them.

At the end of one test of Point Collector, we asked students, “What was your favorite part of the activity?” 25 out of 27 students said some version of “Solving other people’s challenges.”

I’m not saying what we saw was on the same level of enthusiasm and focus as Instagram or Snapchat.

But it wasn’t that far off, either.

Questions We Can Answer

How much does it cost?

As with everything else we make that’s free for you to use now, we will never charge you for it.

Will we be able to create our own Challenge Creators?

Eventually, yes. Currently, the Triple C (Challenge Creator Creator, obv.) has too many rough edges to release widely. Once those edges are sanded down, we’ll release it. We don’t have a timeline for that work, but just as we think student work is at its best when it’s social and creative, we think teacher work is at its best under those exact same conditions. We want to give teachers the best toolkit possible and enable them to share their creations with each other.

Questions We Can’t Answer

What effect does asking a student to create a challenge have on her learning and her interest in learning?

What sorts of challenges are most effective? Is this approach just as effective for arithmetic expressions as laser challenges?

Does posing your own problem help you understand the limits of a concept better than if you only complete someone else’s problems?

Researchers, grad students, or any other parties interested in those same questions: please get in touch.

Putting the “Use” in “Look for and Make Use of Structure.”

This is beautiful, right? Put enough straight lines in the right places and your eyes see a curve.

How many linear equations did the student use to create it? You might start counting lines and assume it required dozens. For some students, you’d be right. They typed 40 linear equations and corrected a handful of typos along the way.

But other students created it using only four linear equations and many fewer errors!

The seventh mathematical practice in the Common Core State Standards asks students to “look for and make use of structure.” The second half of that standard is a heavier lift than the first by several hundred pounds.

Because it’s easy enough for me to ask students, “What structures do you notice?” It’s much more difficult for me to put them in a situation where noticing a mathematical structure is more useful than not noticing that structure.

Enter Match My Picture, my favorite activity for illustrating my favorite feature in the entire Desmos Graphing Calculator and for helping students see the use in mathematical structures.

First, we ask students to write the linear equations for a couple of parallel lines.

Then four lines. Then nine lines.

It’s getting boring, but also easy, which are perfect conditions for this particular work. A boring, easy task gives students lots of mental room to notice structure.

Next we ask students, “If you could write them all at once – as one equation, in a form you made up – what would that look like?” Check out their mathematical invention!

Next we show students how Desmos uses lists to write those equations all at once, and then students put those lists to work, creating patterns much faster and with many fewer errors than they did before. With lists, you can create nine lines just as fast as ninety lines.

What are the four equations that created this graph? Personally, I find it almost impossible to discern by just looking at the graph. I have to write the equation of one of the lines. Then another. Then another. Then another, until that task becomes boring and easy. Only then am I able to notice and make use of the structure.

Pomegraphit & How Desmos Designs Activities

Eight years ago, this XKCD comic crossed my desk, then into my classes, onto my blog, and through my professional development workshops.

That single comic has put thousands of students in a position to encounter the power and delight of the coordinate plane. But I’ve never been happier with those experiences than I was when my team at Desmos partnered with the team at CPM to create a lesson we call Pomegraphit.

It’s yours to use.

Here is how Pomegraphit reflects some of the core design principles of the teaching team at Desmos.

Ask for informal analysis before formal analysis.

Flip open your textbook to the chapter that introduces the coordinate plane. I’ll wager $5 that the first coordinate plane students see includes a grid. Here’s the top Google result for “coordinate plane explanation” for example.

A gridded plane is the formal sibling of the gridless plane. The gridded plane allows for more power and precision, but a student’s earliest experience plotting two dimensions simultaneously shouldn’t involve precision or even numerical measurement. That can come later. Students should first ask themselves what it means when a point moves up, down, left, right, and, especially, diagonally.

So there isn’t a single numerical coordinate or gridline in Pomegraphit.

Delay feedback for reflection, especially during concept development activities.

It seemed impossible for us to offer students any automatic feedback here. After a student graphs her fruit, we have no way of telling her, “Your understanding of the coordinate plane is incomplete.” This is because there is no right way to place a fruit. Every answer could be correct. Maybe this student really thinks grapes are gross and difficult to eat. We can’t assume here.

So watch this! We first asked students to signal tastiness and difficulty using checkboxes, a more familiar representation.

Now we know the quadrants where we should find each student’s fruit. So when the student then graphs her fruit, on the next screen we don’t say, “Your opinions are wrong.” We say, “Your graph and your checkboxes disagree.”

Then it’s up to students to bring those two representations into alignment, bringing their understanding of both representations up to the same level.

Create objects that promote mathematical conversations between teachers and students.

Until now, it’s been impossible for me to have one particular conversation about the tasty-easy graph. It’s been impossible for me to ask one particular question about everyone’s graphs, because the answer has been scattered in pieces across everyone’s papers. But when all of your students are using networked devices using some of the best math edtech available, we can collect all of those answers and ask the question I’ve wanted to ask for years:

“What’s the most controversial fruit in the room? How can we find out?”

Is it the lemon?

Or is it the strawberry?

What will it be in your classes? Find out and let us know.

2017 Jun 16. Ben Orlin adds several different graphs of his own. Delete his objects and ask your students to choose and graph their own. Then show Ben’s.