Here’s a case in that beautiful point.

Points, Lines, and Inequalities

Earlier this week I created an activity designed to help students make connections between individual points and graphs of linear equations and inequalities.

Here’s the first screen:

On its own, pretty simple. But imagine a class full of students doing this. And then imagine directing their attention to a graphical overlay of every student response.

Now we’re talking. Literally. At this point, I’m asking students:

1. What do you notice?
2. What do you wonder?
3. What do these points have in common?
4. What do they not have in common?
5. Is there a way we could summarize all of these points algebraically?

And then… Turn them loose on this:

My hope is that the previous discussion laid the groundwork for the idea that these are all points where x equals 3, so x = 3 is an (obvious?) way to summarize them algebraically. That’s how it plays out in my head, anyway. More on that in a moment.

Students then move on to the next (rather similar) prompt:

(And the activity continues in a similar fashion for a total of six scenarios—four lines, two inequalities. For a closer look, check out the links at the end of the post.)

Room for Improvement

Let’s circle back to Twitter. Yesterday I shared a link to the activity, invited folks to give it a test run, and hoped a few might offer some feedback.

I made a new Desmos activity: “Points, Lines, and Inequalities” Can you help me by giving it a try? https://t.co/ogMZydVViA #MTBoS #mathchat

— Michael Fenton (@mjfenton) March 9, 2016

The response proved incredibly helpful. In particular, Bowen Kerins offered not one or two, but nearly a dozen comments about what works, what doesn’t, and how I could make this activity even better.

I have a few takeaways from that conversation about how to make this activity better. I’ll share them here in order to clarify (for myself) and share (with others) some design principles that I think may prove helpful the next time we fire up the old Activity Builder.

I’ll share the first takeaway here, and a couple more in the next few days.

Takeaway #1

The cycle in screens 1-3 (place a point, imagine all the points, summarize algebraically) is missing a crucial step. It begins simply and somewhat informally, which is helpful. And then it invites students to imagine/predict, which I also think is helpful. But then it jumps straight to the summary, without pausing long enough on the “discussion” that I described above.

My current fix. Insert this between screens 1 and 2:

By asking students to name these points (note: not just their own, but also several others), I think they’ll be more likely to see (or “hear”) the repetition that leads to our algebraic summary later on:

• “x is 3, y is mumble-mumble…”
• “x is 3, y is something-something…”
• “x is 3, y is whatever…”
• “Hey, x is always 3! So then, x = 3!”

My future fix. This activity uses an existing (and lovely) feature called copy previous, where whatever a student did on one graph screen can be pushed ahead to (or “served up” on) a later one. You’ll see this in action between the screens 1 and 2 in my original activity.

What I would love here is another feature (even more lovely?) where the graphical responses from every student are served up to kiddos on a later screen. In other words, bring the graphical overlay feature that we have in the teacher dashboard into Activity Builder itself. Apply that to my original screen 3, and I think we’re in much better shape.

And the good news? Something like this is already in development. (Side note: I continue to be amazed at the engineering skill—wizardry?—of my colleagues.)

Closing Thoughts (For Now)

I think these proposed changes will prove helpful. But I also think they stretch the activity out a bit. So maybe it’s not realistic (or even helpful) to work through vertical lines, horizontal lines, linear functions, and linear inequalities all in the same activity. Maybe this is two separate activities. Or even three.

I take some comfort knowing I’m not the only one who thinks a narrower focus here could be helpful.

Like the way eq of vertical & horizontal lines are addressed here – I can see making an activity solely about that. https://t.co/MJiK15att4

— Cathy Yenca  (@mathycathy) March 10, 2016

With that in mind, here is my new-and-hopefully-improved activity. Give it a whirl, and let me know what you think in the comments.

Next Time

I’ll share some thoughts on making the middle section (linear functions) stronger.

Links

I almost forgot! You can get the original activity here. Or try it out as a student here.

@mjfenton from blog posts to new resources to shoulders to lean on, the #MTBoS has done more for my career than any course, PD, or training.

— John Stevens (@Jstevens009) July 13, 2015

I’ve learned a ton from John. I’m a huge fan of his work at wouldyourathermath.com and with La Cucina Matematica, and if memory serves, he’s the one who introduced me to the idea of a Twitter chat. John and some other outstanding folks run the #caedchat which drops every Sunday evening at 8 pm (PT). I joined in once, and it was great. (Side note: If Twitter is like drinking too much awesome from a firehose, then #caedchat is that to the extreme.)

I enjoyed the conversations and connections, but the whole synchronous chat thing didn’t work for me. Most chats are in the evening, and in my house that time is dinner time/bath time/story time/bedtime/put-the-house-back-together time. (My wife and I have four little ones, and the oldest just turned six. Yep. Intense is the way to describe it.)

#slowmathchat is Born

Anyway, a year ago I thought of a way that I could engage in Twitter chats without locking in to a specific time: #slowmathchat

I wrote about it here and with the help of Cole Gailus even archived some of the chats here.

#slowmathchat was a blast. I learned a lot in dreaming up topics and writing questions, and also through engaging in conversation. Sometimes I just learned by watching other folks’ responses. Either way, it was fantastic.

Time for a Shift

But it’s time for me to make a shift. I have some other projects I’d like to explore with the small pockets of discretionary time that I currently have. So I won’t be writing any more “This week’s #slowmathchat topic…” tweets, and I won’t be tweeting out #slowmathchat questions every Monday through Friday.

Several of you have shared that #slowmathchat helped you enter into this crazy online community, that the structure of these chats was helpful, even inviting. I still think the asynchronous chat format is really appealing, as is the focus on questions and discussions.

Call To Action

So if you have a math education question you’d love others to weigh in on, I’d love it if you kept using #slowmathchat. And if this thing keeps on ticking for a few more months, or even years, great! And if not, you know you can always find a great group of passionate math educators over on the #MTBoS hashtag.

So long, #slowmathchat! It’s been fun.

Instead of writing a full-blown recap (bedtime approaches) I’ll simply share a question that’s been on my mind since my return flight touched down in Fresno late Friday night. Okay, it’s not really a question, but a series of questions. Here goes:

1. What makes a conference like NCTM Nashville (or conferences in general) special?
2. What can you get at a conference that you can’t get on Twitter/blogs?
3. What can you get on Twitter/blogs that you can’t get at a conference?
4. Is there anything these two formats could learn from one another that would make each one even better?

I’m still formulating my own answers to these questions. I suspect I’ll write another post in a few days with my thoughts. In the meantime, I’d love to hear what you think. Drop a comment below, or give me a holler on Twitter.

P.S. I’ve really enjoyed Cathy Yenca’s and Tracy Zager’s recap posts.

P.P.S. The #MTBoS booth was so much fun!

Huge fun @ #MTBoS booth! #NCTMregionals @Trianglemancsd @mjfenton @mathinyourfeet @mpershan @MikeFlynn55 @talita624 pic.twitter.com/5bTzUtzr1R

— Tracy Johnston Zager (@TracyZager) November 19, 2015

That may sound strange, considering the following:

• I generally hate social media.
• I joined that Facebook thing all you kids talk about all the time, then decided it was a waste and deleted my account.
• When I first heard about Twitter, I thought, “Who cares what Bieber had for breakfast?!”
• I didn’t start texting until 2009. When I was 27. I know, I know! Crazy, right?
• I like complete sentences, decent grammar, and punctuation.

But literally, Twitter changed my life.

Somewhere around the beginning of 2013, I started using Twitter to connect with other math teachers. I ended up in this crazy-wonderful community that calls itself the mathtwitterblogosphere (MTBoS, for short). I’ve always had amazing colleagues at my small school, but usually on the order or one or (if I was lucky) two other math teachers across the entire JH and HS staff.

When I hopped on Twitter, I suddenly found myself in a community of dozens (rather, hundreds) of folks who were as nerdy and weird and interested in getting better at this teaching thing as I was. I loved it. I still do.

In fact, I’m pretty well convinced that jumping into this community (whether by starting a blog, getting more active on Twitter, or both) is among the best ways to supercharge your teaching, whether we’re talking skills or passion or enjoyment.

Anyway, that’s my rambling attempt to convince you that you should consider jumping into this mix of mathy folks.

And thanks to some amazing MTBoS folks, there’s a pretty sweet guide to getting started right here:

https://exploremtbos.wordpress.com/2015/10/18/a-new-exploration/

So whether you’re brand new to the MTBoS, a dabbler who wants to dive a bit deeper, or a grizzled veteran looking to help others with their first steps, give that link a try. I promise you won’t be disappointed.

Hey #MTBoS, can you give me 140 characters on how Twitter impacts your teaching life? Gathering responses to share with teachers tomorrow.

— Michael Fenton (@mjfenton) July 13, 2015

I found the responses both inspiring, and a refreshing reminder of why I love spending time in this space. I thought I’d share the responses here, either to encourage you with a reminder of why you spend time here as well, or in an effort to draw you into the fun.

Enjoy:

@mjfenton makes me feel like I’m not alone in the frustrating times. Allows me to share success in the good times. Always someone to help me

— casey (@cmmteach) July 13, 2015

@mjfenton When you can’t get that satisfying collaborative/supportive vibe from your face-to-face colleagues, then #MTBoS.

— Chris Robinson (@absvalteaching) July 13, 2015

@mjfenton gives me new ideas and connects me with other great educators

— Mike Bosma (@mbosma8) July 13, 2015

@mjfenton The #MTBoS community is great way to find resources & activities as well as positive, creative, engaged & reflective teachers 1/2

— Ann Arden (@annarden) July 13, 2015

@mjfenton In addition, the cross-jurisdictional conversations can be eye-opening, inspiring and affirming. 2/2

— Ann Arden (@annarden) July 13, 2015

@mjfenton from blog posts to new resources to shoulders to lean on, the #MTBoS has done more for my career than any course, PD, or training.

— John Stevens (@Jstevens009) July 13, 2015

@mjfenton reminds me the humanity we all have and allows us to connect thru shared experiences

— Megan Schmidt (@Veganmathbeagle) July 13, 2015

@mjfenton I hear about new practices before they become “research-based best practices.” #MTBoS

— Lane Walker (@LaneWalker2) July 13, 2015

@mjfenton I can always find someone who has the same questions (and possibly answers) that I do! #mtbos

— Jessica Borah (@JessicaBorah) July 13, 2015

@mjfenton collaboration w/ people in same mind set, ideas for enhancing current teaching, suggestions for taking teaching to the next level

— Katie Reneau (@klreneau) July 13, 2015

@mjfenton Creates a community which is not only professional & encourages best practice but is inclusive, warm, & welcoming. Keeps me sane.

— Wendy Menard (@wmukluk) July 13, 2015

@mjfenton nothing has accelerated my teaching faster than finding a group of people dedicated to the cause of math classes that don’t suck

— Jonathan (@rawrdimus) July 13, 2015

@mjfenton I can come to the #MTBoS any time that works for me, & I’ll find provocative questions & ideas about teaching, great puzzles, fun.

— Julie Wright (@msjwright2) July 13, 2015

@mjfenton Twitter serves as a source of ideas, encouragement, and feedback on teaching that spans virtually every time zone. #MTBoS

— Evan Weinberg (@emwdx) July 13, 2015

@mjfenton keeps me connected to current lessons, websites, activities, pd, books, blogs, learning opportunities

— Jennifer Fairbanks (@HHSmath) July 13, 2015

@mjfenton Twitter teachers give me ideas or flesh out my own that make my classes amazing. Most enjoy diving into a question.

— Megan Hayes-Golding (@mgolding) July 13, 2015

@mjfenton Lesson/activity ideas. PLN beyond my school. Discussion & conversation. Questions & answers. PD. https://t.co/cs2cc8zM1C

— Laura Wheeler (@wheeler_laura) July 13, 2015

@mjfenton helps me realize: it’s OK not to know all the answers, priceless convos, collaboration at its best, challenges me to keep growing

— pam j wilson (@pamjwilson) July 13, 2015

@mjfenton My PLN on Twitter makes me want to be a better teacher. There are resources and support when I need them and the best people.

— Mary Bourassa (@MaryBourassa) July 13, 2015

@mjfenton Via Twitter I can connect w/ other like-minded teachers, teachers who teach the same subject, find resources, & collab to improve.

— Lisa Henry (@lmhenry9) July 13, 2015

@mjfenton Inspiration, Resources, Support, Collaboration.

— Jami D Packer (@JamiDanielle) July 13, 2015

@mjfenton It’s personalized professional development. Helps me grow almost daily, into a better instructor.

— Jackie Stone (@MathEdJax) July 13, 2015

@mjfenton Twitter connects me w/ passionate educators that want to share, collaborate & celebrate. It keeps me updated & gives me new ideas.

— Annie Forest (@mrsforest) July 13, 2015

@mjfenton best PLC, amazing resources, partners in crime, people who love learning and teaching, … <3 #MTBoS

— John Golden (@mathhombre) July 13, 2015

@mjfenton Like a hallway with many doors to reflective blogs by great maths educators who will engage with, encourage, extend your thinking.

— Simon Gregg (@Simon_Gregg) July 13, 2015

@mjfenton as a new T it allows me to access brilliant minds and vet Ts for advice and ideas

— Kristen Dodson (@mathwithmrsd) July 13, 2015

@mjfenton It’s the place for connections, rich discussion & exchange of ideas. People here support, question, and challenge me to be better.

— Anna Blinstein (@Borschtwithanna) July 13, 2015

@mjfenton it gives me a supportive environment of like minded educators – think I’d be lost w/o it at this point

— Kathy Henderson (@kathyhenderson) July 13, 2015

@mjfenton So many professional colleagues! They are my math ed personal trainers: sharing expertise, making me work harder & stretching me!

— peg cagle (@pegcagle) July 13, 2015

@mjfenton My weekly #elemmathchat is the best PLC ever! Connections, ideas, inspiration & validation are priceless! Math nerds rock!

— Melynee Naegele (@buffalogal03) July 13, 2015

@mjfenton The MTBoS challenges me to continuously strive to be a better teacher, offers resources, and reassures me when I am feeling low.

— Sheri Walker (@SheriWalker72) July 13, 2015

@mjfenton twitter connects educators around my state and the US; it is a primary source for news, trends, and practices in enacting CCSSM

— Abe Wallin (@id_rms1) July 13, 2015

@mjfenton I don’t need to specialize in everything, just know who to connect to. Awesome group to keep learning from. #MTBoS

— Jedidiah (@MathButler) July 13, 2015

@mjfenton Not only as a teacher but as a math coach! I need information, I only need to ask & someone tweets back Or I start reading blogs

— Chris Harris (@CHarrisMath) July 14, 2015

@mjfenton @jreulbach Almost immediate help/advice/wisdom at my fingertips. Amazing sense of giving at all times

— Jim Doherty (@mrdardy) July 15, 2015

@mjfenton @jreulbach I use twitter/MTBoS as a “idea well” to draw refreshing ideas from.

— Eric Fleming (@dailyvalueomath) July 15, 2015

@mjfenton Late to this, but I’ll put in my 140 anyway. Twitter lets me know I’m not alone — in my success and in my struggle.

— Fawn Nguyen (@fawnpnguyen) July 15, 2015

@mjfenton A PLC like no other. Imm access to resources and so impt discussion of how they are used in so many diff ways in real classrooms

— Nicole Paris (@solvingforx) July 15, 2015

@mjfenton @jreulbach constant learning. Joy in the struggle to keep getting better and in the process.

— Matt Leiss (@MrLeiss) July 15, 2015

@mjfenton it’s an inspiration for a new a better way of teaching. It has completely altered my educational philosophy more than any PD.

— Jennifer Thien (@mathchick75) July 15, 2015

Assuming you already have an account (if not, go here), here are five things every teacher should know about Twitter.

1. Don’t skimp on your profile setup

There’s a lot to do when you first join Twitter. It’s easy to stop halfway and think, “I’ll go back and add that later.” Before you dive any deeper into the world of Twitter, make sure you’ve at least taken care of the following:

• Add a profile photo. I recommend adding a photo of yourself (ideally, of your face). You don’t need a professional headshot, just something that adds a human element to your online interactions.
• Add a profile description. A few words about your passions and the various hats you wear (professionally and/or personally) will help the Twitter world know who you are and what you’re about. If you’re looking to expand your online learning community, a description-less profile will hold you back.

2. Learn the different message types

Not all messages on Twitter behave in the same way. Here’s what you need to know:

• Regular tweets. These will be seen by everyone who follows you.
• Mentions. You can “mention” someone by including their name somewhere in the middle of your tweet. All of your followers will see these messages, and a special “ping” will go out to the person you mention (even if they don’t follow you).
• Replies. When someone mentions you in a tweet, you have the ability to reply. Only those who follow both you and the person you’re replying to will see your message, unless…
• Dot replies. If you add a character before the @ symbol in your reply (the most common approach is .@, or the “dot reply”), then all of your followers will see your message. (Warning! Use dot replies sparingly, as many of your followers will only see half the conversation—and that can be awkward, confusing, and annoying. The best use of a dot reply is to share a comment—or better yet, a resource—that would be valuable to many of your followers.)
• Direct messages. If you follow someone on Twitter, and they follow you, you can send private tweets (called direct messages, or DMs). While some things are best shared privately (maybe an email address, or a link to a private document), unless there’s a specific reason for talking on the “down low,” I prefer mentions and replies rather than direct messages.

3. Hashtags are a simple way to achieve Twitter Ninja status

Ah, the hashtag. A source of much eye-rolling for those older than 17 and not named Jimmy Fallon. Believe it or not, hashtags have the potential to change your life as a teacher. Here are two reasons why:

• Communities gather around hashtags. Have you ever seen #MTBoS at the end of a tweet? It stands for mathtwitterblogosphere, and it’s a way that a rather large and decidedly amazing group of math educators share ideas, questions, lessons, activities, and feedback with one another. Have a question about standards based grading? Include #sbgchat in your tweet. Need some advice or feedback from (fill in the blank), chances are there’s a hashtag that will allow you to speak into an ongoing conversation within a particular community.
• Hashtags are used for weekly chats. Did you know that every Sunday night at 8 pm (PST), hundreds of passionate educators gather for an hour to discuss the latest developments in the California education landscape? It’s one of hundreds of education-themed chats taking place during each week, and all you need to get in is the “hashtag key” (in this case, #caedchat).
• Bonus. For math teachers who can’t commit to a chat at a particular time of the day/week, check out #slowmathchat (details here)

UPDATE: Shortly after sharing this post online, I participated in a discussion of Twitter etiquette. We briefly discussed dot mentions, hashtags, and retweets. Kate Nowak captured the gist of our conversation with this comment about intentionality:

@crstn85 @dandersod @mjfenton @TypeAMathLand It boils down to tweeting intentionally, no? Use a # because it’s part of a conversation.

— Kate Nowak (@k8nowak) January 30, 2015

4. Follow to your heart’s content

I used to watch my “following” count, thinking that if it got too high I wouldn’t be able to keep track of everything. Recently, I let go of that fear and started following whoever I wanted to, whenever I wanted to. Here are two thoughts that may encourage you to do the same.

• Skipping tweets is not a sin. I’ve tried two approaches: (1) Limit who I follow and read every tweet, and (2) Follow whoever I want and read as much—or as little—as I want. I’ve found this second approach to be particularly helpful, especially since you can…
• Add your favorite Twitter folks to a list. Let’s say you’re following several amazing people (just for illustration, we’ll say @jstevens009, @mrvaudrey, @mr_stadel, @fawnpnguyen, @robertkaplinsky, @ddmeyer) and you don’t want to miss a single thing they say. Add them to a list, and add that list as a column in Tweetdeck. (Again, more on that in a moment.) Voilà! Now you have a slow-and-steady stream of goodness from your favorite folks on Twitter, without restricting the overall number of people you follow.

Here’s how to add people to lists in Tweetdeck:

5. Get better software

Twitter works in a standard web browser. It has its own free app for smartphones. It even works on flip phones (via text messaging)! But you’re shortchanging yourself (in my opinion, anyway) if you don’t download and use these tools:

• Tweetdeck. An application for Macs and PCs, this is essential if you want to track multiple hashtags/chats/lists with absolute ease. Oh, and it’s free. You can learn more and download it here.
• Tweetbot 3 for iOS. Are you using an iPhone? The official Twitter app has its pluses and minuses. But in my opinion, nothing on the iPhone comes close to Tweetbot. While it’s not free, when you’re talking bang-for-your-buck, this $4.99 is well worth it. You can learn more about the app right here.
• Android users… I don’t have an Android phone (at least not after that incident with the washing machine), but word on the street is that Talon and Tweetcaster are worth a look.

Parting Shots

If there’s only one thing you pick up from the list above, make it Tweetdeck. You’ll probably be able to get up and running on your own. If not, come back to the blog in a week or so (or subscribe via email—there’s a form on the top right of the blog) for a walkthrough of how to set up Tweetdeck from scratch.

Update: One Two More Things…

• If you’re looking for a list of Twitter educators by subject area, check out Alice Keeler’s crowdsourced list.
• If you’re looking for a list of Twitter education chats, try this list. (ht: educatorstechnology.com)

I love Twitter chats. This is probably less well known. And the less-well-known-ness is likely a result of my general lack of participation in Twitter chats.

Here’s a run through of the scheduled chats I’ve (in)frequented over the past year or so:

• #alg1chat (Sunday, 6 pm PST)
• #caedchat (Sunday, 8 pm PST)
• #msmathchat (Monday, 6 pm PST)
• #connectEDtl (Tuesday, 7 pm PST)
• #calcchat (Thursday, 6 pm PST)
• #paedchat (Thursday, 6 pm PST)

Now consider the fact that I love eating dinner and that I have four small children and you might begin to see where I’m headed with this.

As much as I enjoy these conversations with digital colleagues, it’s a huge sacrifice to drop what I’m doing to engage online during these key family hours. Between dinner time and bath time and story time and bed time there are enough “times” in each evening without adding a “chat time” to the list as well.

So here’s my solution:

Launch a new chat, one that borrows the structure and intentionality of a scheduled chat (e.g., #caedchat), but marries that with the freedom and flexibility of an ongoing conversation (e.g., #MTBoS).

Intrigued? Click the #slowmathchat tab in the menu for more details. Read up, get psyched, and add a new column to your Tweetdeck. I hope you’ll consider joining in the fun this Monday.

Post Script

Before you go… Consider this a reverse-tl;dr: