## Free New Desmos Activity: Transformation Golf

[cross-posted to the Desmos blog]

We’re excited to release our latest activity into the world: Transformation Golf.

Transformation Golf is the result of a year’s worth of a) interviews with teachers and mathematicians, b) research into existing transformation work, c) ongoing collaboration between Desmos’s teaching, product, and engineering teams, d) classroom demos with students.

It’s pretty simple. There is a purple golf ball (a/k/a the pre-image) and the gray golf hole (a/k/a the image). Use transformations to get the golf ball in the hole. Avoid the obstacles.

Here’s why we’re excited to offer it to you and your students.

Teachers told us they need it. We interviewed a group of eighth grade teachers last year about their biggest challenges with their curriculum. Every single teacher mentioned independently the difficulty of teaching transformations – what they are, how some of them are equivalent, how they relate to congruency. Lots of digital transformation tools exist. None of them quite worked for this group.

It builds from informal language to formal transformation notation. As often as we ask students to define translation vectors and lines of reflection, we ask them just to describe those transformations using informal, personal language. For example, before we ask students to complete this challenge using our transformation tools, we ask them to describe how they’d complete the challenge using words and sketches.

The entire plane moves. When students reach high school, they learn that transformations don’t just act on a single object in the plane, they act on the entire plane. We set students up for later success by demonstrating, for example, that a translation vector can be anywhere in a plane and it transforms the entire plane.

Students receive delayed feedback on their transformations. Lots of applets exist that allow students to see immediately the effect of a transformation as they modify it. But that kind of immediate feedback often overwhelms a student and inhibits her ability to create a mental concept of the transformation. Here students create a transformation, conjecture about its effect, and then press a button to verify those conjectures. Elsewhere in the activity we remove the play button entirely so students are only able to verify their conjectures through argument and consensus.

Students manipulate the transformations directly. Even in some very strong transformation applets, we noticed that students had to program their transformations using notation that wasn’t particularly intuitive or transparent. In this activity, students directly manipulate the transformation, setting translation vectors, reflection lines, and rotation angles using intuitive control points.

It’s an incredibly effective conversation starter. We have used this activity internally with a bunch of very experienced university math graduates as well as externally with a bunch of very inexperienced eighth grade math students. In both groups, we observed an unusual amount of conversation and participation. On every screen, we could point to our dashboard and ask questions like, “Do you think this is possible in fewer transformations? With just rotations? If not, why not?”

Those questions and conversations fell naturally out of the activity for us. Now we’re excited to offer the same opportunity to you and your students. Try it out!

Mike Flynn, Zak Champagne, and I are very excited to bring you two month-long ShadowCon courses that each begin Tuesday, September 5, 2017. They’re both free.

First, Cathy Yenca will help you “Seek Students Who Hide,” describing her rationale for formative assessment and then the tools (both low-tech and high-tech) she uses to draw the best out of all of her students.

Check out her talk below for an introduction and then register for the free class.

Second, Anurupa Ganguly will examine the participation gap in STEM majors for historically disenfranchised students, asking, “Why don’t the humanities see the same attrition rate, and what can we do about it?”

Check out her talk below for an introduction and then register for the free class.

Both courses will feature lots of interaction with the speakers (including a live webinar halfway through), helpful readings, provocative discussions, and plenty of support from the teaching assistants, Mike, Zak, and I.

Third, in response to recent evidence that personalized learning is struggling to see positive results on important issues of belonging and engagement, I asked on Twitter for an invitation to the meeting where we question the core assumptions of the model.

One thing led to another and on Tuesday, September 5, 2017, at 4:00 PM Pacific, I’ll be having exactly that meeting with Mary Jo Madda of EdSurge, livestreamed on YouTube. I’m excited to examine those failures and, wherever the failures aren’t endemic to the model, brainstorm some solutions.

2017 Sep 5: Update – link changed for the EdSurge chat.

Welcome back to school! Do you remember how this felt?

If you feel anywhere close to how Nancy feels, click through for some great advice from your friends on Math Teacher Twitter. You’ll see very few people encouraging her not to smile until December and very many people encouraging her to do some math with your students on day one. Great advice. We crowdsourced loads of ideas for those math tasks last year. Please add more there.

As much as I’m curious what happens within the four walls of your classroom on day one, I’m also curious what happens on the four walls of your classroom.

This tweet caught my eye for a couple of reasons:

First, “… like Pinterest threw up in your room” is going to be a hard image to shake.

Second, I love the thought that our students would walk into rooms that aren’t fully authored by their teachers, that the space would be shared and awaiting their co-authorship.

Featured Tweets

## Let’s Retire #MTBoS [as an INTRODUCTION to Math Teacher Twitter]

2017 Jul 31. I have apologized directly to a number of people for aspects of this post. Among others, I apologized to the organizers of Twitter Math Camp (including Lisa Henry, Mary Bourassa, Tina Cardone, James Cleveland, Daniel Forrester, Megan Hayes-Golding, Cortni Muir, Jami Packer, Sam Shah, Glenn Waddell) for posting it during their camp weekend and distracting even a bit from their efforts. Loads of other people stepped up in unofficial, totally voluntary ways to make TMC an awesome, inviting time, and I regret however much I spoiled their efforts.

This community has also been built and nurtured by hundreds of people in thousands of big and small ways – from huge initiatives like Twitter Math Camp, ExploreMTBoS, and Global Math Department, down to folks who watch out for new Twitter users and say “howdy.” This post wasn’t and isn’t meant to critique any of those efforts, but I realize that it came across that way, and that was wrong of me. Precisely because there are thousands of those efforts, I can’t reach out and apologize to each of you individually for dismissing them, so please accept my apology here. Keep on making this place awesome.

Whatever else you think of this post, the people who have commented on it and whose tweets I’ve excerpted below are real people who have found our name alienating. (Not the community. The name itself.) That’s a problem that countless people in the last few days have told me isn’t worth tackling, or one that pales in comparison to other problems. I respect that opinion. I’d like to work on it anyway, and also work on the other problems. But rather than use my platform here to set a unilateral course, I should have found out who is already doing that work and found out how I could help. I’m generally skeptical of leaders and I’ve never been particularly eager to be one, but that isn’t any excuse for setting a bad example. If you’re doing that work, and if I can help or collaborate, please let me know in the comments or at dan@mrmeyer.com.

2017 Jul 28. Thanks to everyone who helped me think this through, especially the ones who did so in spite of being annoyed and hurt. Much love to you all, and to this place. My current plan is to introduce teachers to Math Teacher Twitter by inviting them to attach “#iteachmath” to a tweet, a tag that is intuitive, pronounceable, and importantly, a declarative statement. Meanwhile, “#MTBoS” has less certain pronunciation and, for newcomers, it has been unintuitive and felt a bit like you’re inviting yourself into a secret club. (Seriously, don’t trust me on this. Read the dozens of tweets and comments I’ve excerpted below.) I hope that the thousands of people who find community around “#MTBoS” will continue to enjoy it! But I’m hopeful that “#iteachmath” will be a better invitation for the hundreds of thousands of math teachers who don’t yet know how great we have it.

The original post follows.

——

I’m not asking us to retire the #MTBoS (unabbreviated: the Math Twitterblogosphere) the collection of people, ideas, and relationships that has provided the most satisfying professional development and community of my life.

I’m asking us to stop referring to it as “the MTBoS” and to stop using the hashtag “#MTBoS” in online conversations.

That’s because this community is only as good as the people we invite into it. We currently represent only the tiniest fraction of the math teachers in the world, which means we (and I’d like to believe they also) are missing out.

That fraction will stay tiny so long as our name alienates people. And it alienates people.

People don’t know how to pronounce our name. Whenever I use it, I get tweets back asking me what I’m talking about. Whenever I invite new teachers to get on Twitter and search for “#MTBoS,” their confusion is plain at that seemingly random assortment of vowels and consonants, capitalized in seemingly random ways.

This morning I read a tweet from a science teacher named Andrew Morrison. I learned from Andrew that the physics teaching community hashtags their work “#iteachphysics.” I felt such a sense of invitation when I read that hashtag – “This is who we are and what we do. You should join us.” And then I felt envy.

We should be so inviting.

This community of ours has no leader. It has no high council. Each one of us has to be the change we want to see in it. I want to see a more inviting community, a community that doesn’t shroud its entrance behind a hedge or protect its door with a password.

So I’m going to stop referring to my participation in “the MTBoS” and instead talk about how much I love “Math Teacher Twitter.” I’m going to stop tweeting using “#MTBoS” and instead tweet using “#iteachmath.”

No one has to join me, and I absolutely won’t be offended if you don’t, but I hope you will, and I hope you at least understand why I’m doing this. I think this change is necessary for our growth and this is how I’ll try to be that change.

“#iteachmath” is five more characters than “#MTBoS. That’s five fewer characters for my tweets!”

I accept that those five characters are the cost of a more inviting community.

Twitter users outside the United States will want to use “#iteachmaths.”

The MTBoS has a very, very tiny handful of community members outside the United States as it is. I think we can only improve from here. Me, I’m going to add both “#iteachmaths” and “#iteachmath” to the same column in Tweetdeck.

“MTBoS” includes blogs (the “B”) but “Math Teacher Twitter” just refers to Twitter.

“MTBoS” also fails to refer to Slack, Voxer, or any of the other ways teachers collaborate online. “Math Teacher Twitter” hints at all those ways. It doesn’t try to catalog them.

But I’m a coach / consultant / curriculum author / administrator. I don’t teach math so I’ll feel weird using “#iteachmath”.

Let’s not treat this hashtag like it’s a sworn statement in a court of law. It’s an invitation. It’s how we’ll gather community around a conversation. It doesn’t need to serve any higher purpose than that, and I think it’ll serve that purpose better than anything we have right now.

Featured Tweets

Justin’s tweet seems really, really important to me. Consider the perceived requirements for membership in the #MTBoS vs. #iteachmath.

#MTBoS: who knows, but a blood sample and credit verification is probably part of it.

#iteachmath: it’s right there in the hashtag. That’s it. No guessing. You’re invited.

Via direct message:

I always felt a little worried or unsure about joining the community and when it was ok to tweet #mtbos.

Also via direct message:

I actually had to look up the #MTBoS. I am not a member and not sure I am a blogger. I do have a question for the group. May I ask a question with the hashtag without the membership? Thank you!

I joined the community of online teachers this last year and attended the national conference. MTBoS felt like a secret society that I wished to be a part of but didn’t know how to get in.

… my honest-to-goodness first thought about being invited was, “Am I ‘in’ the #MTBoS ‘enough’ to speak about it with these other mathies who seem to be ‘in’ it ‘more’?

This makes me happy. For months when I first discovered #MTBoS, I had no idea what it stood for and felt so left out! And then I had no idea how to talk about it to others. (And usually resorted to “it’s basically math teacher twitter.”)

100% agree…I (found) find #MTBoS “clickish…and therefore offputting…even if/though that isn’t (wasn’t) the intent, it has (had) a mysterious and exclusive feel which made me, a 30 year teacher, feel “out of the loop”

Thank you, I’m on board! #MTBoS confuses me and I even know what it stands for.

2017 Jul 28.

This proposal made the rounds among the veterans of, let me try this out, Math Teacher Twitter, and they largely aren’t buying it. No hard feelings on my end. This project has become sharper with feedback from the community.

Here are the four most common responses.

We are inviting, in particular at Twitter Math Camp.

I have no doubt that everyone at Twitter Math Camp who comes within forty feet of Julie or the other organizers will feel warm and welcomed. But TMC hosts only a few hundred math teachers out of millions. What is the best way to invite people into this community who have never sent a tweet? Or who have only watched other people tweet? Too many people find our current approach alienating. Check the featured tweets and featured comments above for a sample. If they bother you, what solutions are you thinking about?

This is their problem, not ours.

If the alienated people in the featured tweets and comments above don’t burden you, or if you think their lack of comprehension at our hashtag and how to use it is their own problem, don’t let this proposal weigh on you for a second more. And don’t feel any guilt from me about it. This is my project, which doesn’t mean it has to be yours.

This won’t fix everything.

Using a different hashtag won’t make everything great. Totally true. I think it’s a necessary step, and an important one since it’s our figurative front door, but it’s insufficient. How can we sufficiently welcome teachers to professional community online? I don’t know, but I’m enjoying that conversation also.

I won’t use #iteachmath because I don’t teach math.

I’ve already addressed this above, but it’s possible that #iteachmath isn’t ever going to feel right for folks who aren’t practicing classroom teachers. That makes a lot of sense to me. I have may have chosen the wrong hashtag for these efforts, but that doesn’t change the reality of all the alienated teachers in the featured tweets and featured comments above. If they weigh on you as they do on me, let me know the solutions you’re thinking about.

I’m not sure if it’ll surprise you to find out that the people most enthusiastic about this proposal have been a) classroom teachers, and b) total strangers to me online. Very few people whose names I recognized. These are people whose ideas may nourish us, people who may need our nourishment also.

So here’s a new proposal: let’s treat “#iteachmath” as the welcoming lobby for new Twitter teachers. When I meet new teachers at conferences or in professional development, I want to recommend they post an idea or a question to a hashtag they’ll find intuitive and inviting. From there, perhaps a bit more emboldened, I hope they’ll venture out towards any number of our other hashtags and communities.

2017 Jul 29. Harry O’Malley has written up a really interesting proposal extending these ideas.

2017 Aug 7. Interesting to see medium-sized groups of educators with fewer than 30 combined tweets and followers popping up on the #iteachmath hashtag. See: Algebra for All; #NCLargeMath

## 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.

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.