Reason and Wonder

5 Things Every Teacher Should Know About Twitter

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Over the past few weeks, several people have asked me how to take the next step with Twitter, whether that meant joining for the first time, or taking their tweeting to the next level.

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)

Embracing Mistakes with a New Weekly Routine

Over the last 11 years in the classroom, I’ve had the same teaching schedule exactly zero times. Every time August rolls around, it’s a different ballgame. Some years the shifts are subtle. In other years they’re quite dramatic.

Within each year, I’ve never taught more than two sections of the same course. In fact, one year I taught seven different courses. (Assuming, of course, that you’ll allow me to count Algebra 2 Honors as distinct from Algebra 2.)

With all of this variety from year to year (and class period to class period), I’ve come to rely on classroom routines not only to preserve my sanity, but also to challenge myself to pursue growth.

The latest initiative I’m considering? It’s right in line with my recent bent on extracting every ounce of growth-mindset goodness from the abundance of mistakes we (teachers and students) all make in the classroom.

With that background in mind, here’s what I intend to put in front of my students (and myself) during the last few minutes of class each Friday for the rest of the semester.

There’s no guarantee I’ll stick with this routine, or that we’ll benefit from it. But I am holding out hope—on both counts, in fact.

As for my actual goals with this prompt, I’m looking to further develop my students’ growth mindset. In particular, I want to foster a sense—across the entire classroom—that mistakes are actually opportunities, and that they can help launch us into the next level of awesome-ness.

As for sharing my thoughts here… There’s a sense of commitment that comes with writing about something.

I’m counting on you to hold me to it in the comments.

Twitter Chats vs Family Dinners: Do We Really Have to Choose?

I love Twitter. I think I’m on record in several places with this. (Actually, it’s probably more along the lines of “I love the Twitter,” just because it’s more fun to say it that way. Go ahead, give it a try.)

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:

Four Points, One Line

As my students have worked through a series of linear graphing challenges this month, I’ve been looking for a way to challenge them to synthesize (and hopefully even extend) what they’ve noticed over the past few weeks.

I think I’ve found my culminating challenge.

My Goal

My goal is to elicit a variety of equation styles (point-slope, slope-intercept, etc), and my hope is that the restriction (which numbers they may use in the equations) is not only clear enough, but also provides the right dose of structure to encourage students to think more deeply about the relationships between the rate of change, intercepts, non-intercept points, and the parameters in each equation.

To give it a test run before sharing it in my own class, I hereby offer you this:

Your Challenge

How many different equations can you write using only the numbers included in the ordered pairs? Can you get to three? How about five? Maybe even 10? Or more?!

Do the work in Desmos, and drop a line in the comments!

As always, feedback—on the challenge in general, or the restriction in particular—is 100% welcome.

Update

I struggled with the wording in the original challenge. As I shared above, my goal is to draw out from students a variety of equation forms, each one utilizing information revealed by a particular point or pair of points. After some back and forth on Twitter, I settled on this reframing of the task:

I’d love to know whether you think that drives more quickly and clearly to the heart of what I want students to focus on (while leaving it open enough that students will feel freedom to tinker and explore).

“I would give anything for students who are…”

However you would complete that sentence—whatever characteristics you most desire to see in the students who walk through your door…

Make it your main goal, day after day, to develop those qualities in your own students.

For the record:

Two Wrongs and a Right

Thoughtful analysis of mistakes is a great way to develop and deepen mathematical understanding. Ever since I stumbled across Michael’s Pershan’s Math Mistakes website, I’ve been looking for ways to incorporate more error analysis into my classroom and department.

One practice I’ve been using for years is Assessment Corrections, where students identify, correct, and reflect on recent assessment mistakes. (Here’s the form I use to guide the process.)

One practice I’ve wanted to use but never followed through on is starting math department meetings with a five-minute discussion of a mistake from one of our students.

Whatever the format, I’m convinced that my own teaching practice would benefit from an increase in thoughtful error analysis. I suspect the same is true for many other teachers. And since developing new habits is difficult, I’ve been considering how to incorporate math-mistakes-style reflection into my classroom through simple, repeatable routines.

Two Truths and a Lie, Math Style

Here’s what I’ve come up with:

Display three solutions to a problem. Ideally, include photos of original student work. If that’s not possible for some reason, photos of teacher-written solutions on post-it notes or index cards will do the trick. So will typed-out solutions.
Facilitate student reflection and discussion. There is much to be gained from each of the following: individual student reflection, discussion in pairs or small groups, and whole-group discussion. Whatever format (or combination) you choose, lead students to think about the assumptions behind each mistake, whether there are fragments of correctness in a given mistake, and how they might help a classmate who was prone to such a mistake.

Looking Ahead

I’m excited to use this approach more often in my classes throughout the rest of the semester. Will it be perfect? Probably not. I can imagine some errors that simply won’t fit in this side-by-side-by-side format. And I’m uncertain whether a projected slide is as useful as a paper handout, or if I should lean toward the latter. Even with these lingering questions, I do know this: This routine has the potential to add considerable value to my classroom, as it provides students with repeated opportunities to develop their sense-making and argument constructing/critiquing abilities. And if I had to rank the CCSS Standards for Mathematical Practice in order of importance, it’s likely I would place those two (SMP 1 and SMP 3) at the top.

Questions

How do you incorporate thoughtful discussion of math mistakes into your classroom or department? Do you have ideas for how to make my “two wrongs and a right” approach better? Drop a line in the comments below.

Amazing Alfred

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Have I mentioned that I love my job?

After a great first week back in the classroom, my Saturday night just ended on an even higher note. First, I got this notification just before heading out for an elegant dinner with my wife:

I ignored it for the time being. When I returned home and fired up my email, I found this lovely spreadsheet:

Not only is it amazingly cool that a student is working some Desmos/Google Drive combo magic on the weekend, but his challenges are pretty slick.

Alfred’s Match My Graph #3

At this point, all Alfred has seen in class is Match My Graph #1-2 in the Linear Functions set. I think it’s pretty cool that he’s considering how to increase the difficulty for the next linear challenge, without ramping things up too quickly. (There’s a slope pun in there somewhere.) Some linear-functions-in-slope-intercept action seems perfect! Here’s what he created:

As if that wasn’t cool enough, there’s even an answer key—made with a list!—that can be toggled on and off. (Alfred mentioned that he would present these to other students without the answer key. But when collaborating, having the answer key in there is a nice touch. A scholar and a gentleman!)

Alfred’s Match My Graph #4

In my linear series, I included several more linear functions (for a total of eight), but Alfred appears ready to tackle quadratics. First up in his mind: Vertical dilations, with vertices fixed at the origin. To be honest, that’s probably the exact move I would have made. I especially like how he avoided pure symmetry across the y-axis by plotting points where x equals –1 and 2 (rather than –1 and 1, or –2 and 2).

Alfred’s Match My Graph #5

It wasn’t until #5 that I paid attention to Alfred’s directions. (I suppose students aren’t the only ones who skip those from time to time.) I like his language here: “…through the color-coded ‘objective’ points…” And mathematically, he seemed to think that translations would be a good next step.

I think I know what he has in mind for challenge #6. (Maybe dilations and translations together?) I’ll have to wait to find out as the link in the spreadsheet for #6 has a typo.

Future Math Teacher?

I can’t wait to get started on the Match My Graph: Quadratic Functions sequence, especially since I’ve been given this great head start! I also wonder if this student has a future in math education. (He’s mentioned it as a potential interest before…) There’s a great deal of thoughtfulness that went into each challenge. And his excitement can’t be denied.

Math on the weekend for the win!

Postscript

Alfred is the name of several fictional butlers, not my student. In the interest of privacy and awesomeness, I’ve selected a name from this most excellent list.

I Need Your Help: Building Statistical Reasoning

I need your help. And it shouldn’t take long.

A Few of My Favorite Things

I have a handful of go-to routines that work well in a variety of courses for a wide range of students:

I’ve used some of these for years, and others for just a few months or days. But they all have a few things in common:

Students find them engaging and enjoyable
They spark meaningful classroom discussion
While they have the potential to become full-fledged lessons, they also work very well as mini-tasks
Their relatively small “size” (5 or 10 minutes, as opposed to 45-90) makes them repeatable, even on a regular basis

How You Can Help

Alright, that’s the context. Here’s my problem:

I need more bite-sized tasks for statistics and probability.

True, there are a handful of #wyrmath prompts that address stats and probability topics. And you can certainly do some nifty statistical analysis with the data streaming in during Estimation 180. However, while I love those resources, I’m greedy for more.

So if you know of anything that is engaging, sparks lively discussion, and is brief enough to repeat on a daily or weekly basis… I would love to hear about it, either in the comments below, or on the Twitter (@mjfenton).

Whether it’s a one-off mini-task you’ve created, a treasure trove ready-to-serve statistical/probability goodness that you’ve discovered, or even just something you’ve half-imagined, I’d be thrilled to expand my resource pool, especially in a stats and probability direction.

And If You Think You Can’t Help…

If you don’t have any resources to share—or even if you do—maybe you’ll consider punching one of those “Share this” buttons below to get some other people in this crowdsourcing mix.

Thanks in advance for your help!

Postscript

The title is an intentional reference to Andrew Stadel’s gold-mine of estimation challenges.

Age-Appropriate? Not Exactly. Valuable? Absolutely.

I started something new this week. I’m not entirely sure where it will end up, but I like how things are shaping up after just one challenge.

Here’s what I presented to my students:

https://www.desmos.com/calculator/kposfnfytr

Age-appropriate for Precalculus and Calculus? Not exactly. With a slight nudge, this is something a group of Desmos-equipped 6th graders could tackle.

But… Oh. My. The blank stares. The confused looks. The surprisingly non-isolated bewilderment.

I could write a post about how students “get rusty” with things they don’t practice, et cetera, but I think something else is going on here. Many students struggled in such a way that I suspect—rather, I’m convinced—they never learned much of anything about linear functions at any depth. (I shudder to think about how deep their understanding of exponential and logarithmic functions goes, even as we’ve been working with these functions all throughout the year.) Presented with a problem in a format just slightly askew from what they’re used to, they struggled and stalled.

I could write a blog post lamenting the quality of the students passed along to me by various colleagues. But there’s more to the story, especially since I’ve taught most of these students in two, three, four, or even five other classes. An indictment on their former teachers is an indictment on myself.

So what’s my next move? How do I address the current state of graphing affairs in my own classroom and in our department as a whole? With a few resolutions:

Resolved, never to treat a particular mathematical topic in isolation when valuable connections are readily available.
Resolved, to present students with tasks which demand that they make connections between numerical, graphical, and algebraic representations.
Resolved, to allow key topics to spill over across the confines of individual lessons, chapters, and units.
In particular… Resolved, to develop a series of “match my graph” challenges to develop students’ “function sense” (or “graphing sense”?) over the course of the entire year.
Better yet… Resolved, to collaborate with my colleagues (in real life as well as online) to develop a series of thoughtfully sequenced/coordinated “match my graph” challenges for every course in the 7-12 sequence.

For now, I’ll create two or three challenges per week to share with my Precalculus and Calculus classes. They’ll gradually grow in difficulty, and we’ll soon shift from linear to quadratic, to power and exponential and logarithmic, to conic, to parametric, to trigonometric, and even to polar. Eventually, I hope to tag the challenges by grade level (with some challenges receiving multiple tags) so we can more easily integrate them into the rest of our courses in the department.

I’ll report back on our progress later this semester. In the meantime, if you want to create a few challenges of your own, I’d love to see them!

Postscript

In fairness to my students, some solved the challenge rather easily (as they should have). I’ll soon provide them with a more demanding challenge, but for now, I’m interested in seeing how I can address the blank stares and confused looks that popped up on more than a few faces earlier this week.

Update

I’ve added a lesson called Match My Graph: Linear Functions to the Lessons page. The lesson (actually, a series of mini-lessons) contains eight linear function challenges, including this one:

https://www.desmos.com/calculator/phmxercufm

Another Update

One of my students brought a huge smile to my face with an email this weekend. Read about it here.

6 Goals for 2015

2014 was a blessing-filled blast. I think 2015 will be too.

I’ve set a few goals for the year; some personal, some professional. While several of them are too private (or boring) to share here, I’ll share the rest in the hope that someone else will be encouraged, possibly because they’ve set similar goals, or because they haven’t (but might now be inspired to).

Personal

Here are three personal goals I set for 2015:

Run a total of 365 miles. My physical health hinges on running. If I run consistently, I have more energy, eat more nutritious food, and get sick less often. I failed miserably at last year’s goal of 500 miles for the year. For 2015, I’m aiming for an average of a mile per day.
Read 25 books. Whether fiction or nonfiction, I feel like I’m a better person when reading books regularly. Possibly because I am becoming a better person. My goal is two per month, with another thrown in for good measure.
Write 52 journal entries. In the same way that blogging reflectively has helped me grow as an educator, writing reflectively on a regular basis helps me grow as a husband, father, and friend. The only problem? I rarely keep up with this habit. My proposed solution for this year? To carve out 30 to 45 minutes at the same time each week to write.

Professional

Here are three reasonandwonder-related goals I set for 2015:

Write 52 blog posts. In general, I want to write more consistently. But “write more consistently” is a terrible goal for the year. So I attached some numbers to it: A post a week (on average) for the entire year. 52 posts sounds like a lot of writing, but once per week sounds within reach. Here goes!
Write 36 lessons (12 of each type). I had a blast adding the lessons page to my blog at the end of last year. I want to keep the content flowing, and also to challenge myself to write a variety of lessons. My goal is to write one lesson in each style (problem based lessons, open middle problems, and Desmos lessons) per month. If I’ve added 36 new lessons to the blog by the end of the year, I’ll be a happy camper.
Present 20 workshops/presentations. I have a desire to grow my consulting business over the next few years. At this point, I already have 10 events on my speaking calendar for 2015. Not a bad start! I look forward to adding a few more workshops and professional development sessions to build toward 20 for the entire year.

Resources

A quick word about the resources I’ll use to create and track my goals this year:

Evernote. There are about 1000 reasons why I love this app. Make that 1001, as this year’s goal-setting got an inspiration boost from this Evernote blog post.
OmniFocus. It’s a bit pricey, but I already use it for all of my to-do list and project tracking, so it made sense to roll my 2015 goals into this tool as well.
Google Sheets. When it comes to tracking miles run, books read, and the like, I’m a sucker for a simple spreadsheet.
Day One Journal. While I love Evernote for note taking in general, when it comes to journaling in a non-distracting app, I absolutely love Day One.
WordPress. I guess it goes without saying that none of my blog-posting or lesson-writing goals would be possible without this. By the way, if you’re reading this and you haven’t started a blog of your own yet… What are you waiting for?

Your Turn

Willing to share your personal and/or professional goals for 2015, or the tools/resources/practices that help you stay on track? Drop a line in the comments!

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