The Great Blog Exchange

All Your Blogs Are Belong To Us

Strange as it may seem, the impending death of Google Reader has me on the hunt for more great blogs. I know I could go to a few of my favorite blogs, check out their blogrolls, and go from there. But personal recommendations feel so much more… personal.

With that in mind, I hereby announce the inaugural edition of The Great Blog Exchange.

From Me To You

My favorite three blogs Three Four of my favorite blogs are:

    Not exactly a hidden gem, but prior to finding Dan’s site I didn’t know there was such a thing as a math blog. Great place to start, continues to inspire and challenge.
    I’ve been thinking about assessment lately, and so has Daniel Schneider. Only, his thoughts (and performance assessments) are miles ahead of mine. Good reading!
    If there was nothing else on Christopher’s blog besides the conversations with his kids, it would still be one of my favorite blogs. (P.S. There is much, much more.)
    Had a tough month teaching? Me too. Reading One Good Thing is like group blogging therapy. Three posts and you’ll feel better already. I promise. (And if you start looking at each day through the lens of what you might post as a guest-blogger, you’ll feel even better.)

From You To Everyone

Ready to play along? Leave a comment with your favorite one, two, or three math/science/tech education blogs. Add a (brief) note about why you like each one, or just do a drive-by link drop.

P.S. Feel free to share old blogs, new blogs, famous blogs, or hidden gems. If no one shares this or this because they’re not obscure enough to mention, then we’ve collectively missed the point. Let’s share it all, and help newbies like me get to 100 amazing feeds in our soon-to-be-dead Reader lists. (Don’t worry, I’ll have an exit strategy soon too.)

Tasks and Assessments

More Awesome, Please

Either I’m a glutton for punishment, or there’s just too much awesome on the Internet and I can’t help myself. Whichever is true, I want to build something, and I need your help to do it. Here’s what I propose:

Let’s do for assessment what Dan Meyer, Andrew Stadel, Fawn Nguyen, and countless others are doing for rich, engaging tasks.

Here’s what I mean. As a math teacher, there are two things I need more than anything else: awesome tasks and awesome assessments. And maybe it’s because I just joined the party, but it seems like people are absolutely killing the task-creation side of the equation right now. The number of people creating tasks, as well as the number and quality of the tasks they’re creating, is exploding. And with some recent changes, Dan’s appears to be morphing into a place where entire tasks can go to live. I hope I’m right. If I am, the proliferation of creators and their creations will only accelerate.

But that’s only half of the equation. I need more than great tasks. I also need great assessments. I firmly believe that the quality of my courses will rise or fall with the quality of my assessments.

Why is my AP Calculus course stronger than my Precalculus course? The assessments my Calculus students take (throughout the year, as well as in May) are better than the ones I give my students in Precalculus.

Why am I stoked about the Common Core? It’s not because the standards are better than my state’s old standards (which they are). It’s because the assessments promise to be worlds better than the CST (fellow Californians know what I mean).

Weak assessments allow me to teach a weak course and get away with it.

But awesome assessments force the issue. If students aren’t doing some serious learning, we’re going to know. And it’s going to be uncomfortable. And we’re going to have to get better.

So Let’s Get Better (By Sharing Like Crazy)

So what if we all started sharing more of our assessments? What if they had a place to live, with room for rubrics and commentary and comments and suggestions for improvements and whatever else will make it easier to share and steal and tweak.

Let’s share the ones we think are fantastic (like this one from Daniel Schneider) so others can learn from our best moments. Let’s share the ones we’re embarrassed by so others can tell us why they’re terrible and how to make them better. Let’s share the ones we’re not sure about, so others can tell us what works and what doesn’t, what to keep and what to throw away.

Let’s start sharing. And giving feedback. And revising. And making our classrooms better by making our assessments better.


Are you in? If so, head down to the comments, hit me up on twitter (@mjfenton), or drop me an email (mjfentonatgmaildotcom). And by all means, let’s all use our megaphones to get others involved.

I’m next to nothing without you guys. But together… This could be exciting.

More than Skillful?

I’m new to the standards based grading world. I’ll share more in another post about what I’m loving, what I’m struggling with, what I’m dreaming about, how I want to use the power of the Internet to make all of my assessments fantastically awesome, etc.

But a question just popped into my head after a rather successful (though entirely skill-focused) class period in Honors Algebra 1:

How do you use standards based grading to help your students become more than just skillful?

My current implementation is heavy on skills, and I’m having trouble moving beyond that (more a shortage of time than vision, but my vision is lacking as well). I have some ideas of my own on how to use SBG to create a classroom where skills are the launching point, not the end goal (again, future post forthcoming), but I’m curious to hear what others think as well.

To the comments, if you please!

Quadratics Matching Activity, Take 2

Visitors and Commenters? Woohoo!

I’m amazed anyone reads this blog, and even more blown away that people have posted so many thoughtful comments. Shortly after my long-winded sky-is-falling post, I added a quick note about launching an activity with as few words as possible. There were a few great comments on this shorter post about how to improve one particular activity (matching equations, intercepts, and graphs of quadratics).

The comments that caught my eye include:

Could you build on the task with an addition to the end where they create their own quadratic and then write up a key for the graph, intercepts and factors? They could switch it with another group and verify their answers? – Dan Anderson

One thing I’ve done occasionally with matching activities is deliberately leave one out. So they end up with an equation that has no graph, or vice versa, and have to generate the missing one. For added chaos, leave out one of each – just let them know that this was done… – Gregory Taylor

Love this activity! I think the concise written directions are a good idea, too. On my first day of Algebra 2 class, I had a similar but less pretty handout where each quadratic has a graph, an equation (in some form or other), a table of values, and a word problem. Each kid as they walk in the door gets one, and they need to find the others who have the same quadratic in order to form their groups of 4. – Joshua Zucker

Activity Revamp

So tonight, while standing guard next to the boys’ bedroom door (they have a tendency to leave their beds when they should be drifting off to dreamland; my wife calls it whack-a-mole, probably because of this)… Where was I? Oh yeah, standing guard…

So while I was standing sitting guard next to the boys’ door I revamped my rather unassuming matching quadratics activity to include some of the suggestions above. (Disclaimer: My activity doesn’t include Joshua’s table of values or word problems, but I think those are awesome ideas, and will probably find a way to include them in another activity, either for linear or quadratic functions.)

For reference, the old activity handout is here. And for what it’s worth, the new one is here. My game plan is to start with an entire-class matching activity and follow it up (either on the same day, or on another day for review/additional practice/to beat a dead horse) with a small group activity (groups of two or three students, matching at their tables). For my students who don’t hate school and who think meaningless competitions of an academic nature are enjoyable (read: third period, not fifth period) we might play three quick rounds of “fast as you can” matching. Fist bumps to the fastest group in each round, and fame and glory for the fastest time of the day.

I think the new wrinkles make it a much better activity. We’ll see what my students think/how they respond. If you use it with yours, let me know how it goes.

P.S. The handout no longer includes directions, as I’ve included those on a slide that can be displayed for the entire activity. (Once we start cutting up the old handouts, the directions made their way to the blue bin by the door pretty quickly.)

Pockets of Time

I’m a little worn out after my last couple of posts, so I’ll aim for something more cheerful today.

Several years ago (okay, maybe closer to 20 than several) my mom went on a trip with a friend to Monterey. She stopped at a game shop, picked up this little gem, and brought it home for me and my sisters to play.

set_box_ over25

The game consists of 81 cards. Each card has four attributes (color, number, shape, shading) and each attribute has three flavors (red, green, purple; 1, 2, 3; squiggles, ovals, diamonds; and open, striped, solid). The goal:

Find a set of three cards where each attribute is either all the same or all different on the three cards.

If that explanation isn’t sufficiently helpful (it usually isn’t enough for my students), then check out the online (semi-creepy; I usually mute the audio) tutorial here.

At any rate, I have since played untold thousands of games of set, first with the physical deck of cards, then using the (free) online daily puzzle, and more recently on the iPad app. Partway through my first year of teaching I began playing the daily puzzle with nearly all of my classes nearly every day of the week. This year I’ve begun using the iPad app (since it offers a few additional ways to play, including a basic mode where the shading component is simplified by using only the solid cards). Regardless of how I’ve accessed the game, here are a few of the benefits to my students, at least as I see it.

  • When we start with Set at the beginning of class, nearly every student is engaged.
  • It’s a great way to develop spatial reasoning (probably a weak part of my courses, aside from this game/puzzle).
  • With a little bit of thinking it can be turned into a competition between classes.
  • After teaching the kids how to play, it lasts only 60 seconds (for basic) or 90 seconds (for advanced).

This last point is really what inspired me to write this post, as I’ve been searching for short, engaging activities to weave into my classroom this year to fill out the pockets of time at the beginning or end of class. While I’ve been using the Set Game to start class for years, the online puzzle only offered one game per day, so repeats in a given class period were off limits. With the iPad app, I can pull up as many puzzles as I want, so when students are finished with an assignment and there are two minutes left I can fire up the app and challenge them to another game.

Two other great ways to fill those extra minutes (whether they fall at the beginning, middle, or end of a period) are Andrew Stadel’s Estimation 180 and Fawn Nguyen’s Visual Patterns. They’re not quite as short as a game of Set, but in just a few minutes I can have the students doing something far more interesting (and mentally profitable) than sitting quietly while they wait for the bell to ring.

So here’s my list o’ questions to you:

  • Have you ever played Set? If so… Cards, online, or app?
  • Do you use Estimation 180 with your students? If so… How long do you spend on a typical estimation challenge (start to finish)?
  • Do you use Visual Patterns with your students? If so… How often do you use them and how much class time do they take (once your students have become familiar with the concepts/format)?

And if you just answer one question, make it this one:

  • What do you do with your students when your students finish an activity or assignment and you look up at the clock to realize you have two minutes left?

P.S. If you’re interested in hearing the three ways I play the game with students in class, just holler in the comments. I’m happy to share, but this post needs to be done and I need to be in bed.

Launching an activity: Cut to the chase!

Howdy. If you’re reading this and you haven’t read my super long post from last night (technically, it went live early this morning), this post might not have enough context. At any rate, I’m aiming for a better day today in fifth period (Algebra 1) and my game plan is this: When giving directions for a group activity, cut to the chase.

The original activity is here. In the past, I’ve introduced this activity with a minute or so of verbal directions and then cut the kids loose. I fell on my face yesterday using that approach (verbal directions as the means of launching an activity), possibly because I haven’t spent the necessary time clarifying in my own mind both the goal of the activity and the directions for students.

My attempt at more concise directions (in non-verbal form) comes in the form of these slides:

activitylaunching.003 activitylaunching.004

I’ll probably let you know how today goes in another post. I’m hopeful that this new wave of constant reflection will provide my students (at least in the long run) with a better teacher. In the meantime, feel free to comment on what you like/dislike about the activity and the “launching” (key question and directions) of the activity.


Blogging as Therapy

My Inflated Sense of Awesomeness

I used to suffer from an inflated sense of awesomeness. I blame my honors students. Now, stay with me for a moment. I don’t dole out blame like this too often, but I think I have a case here.

Picture this daily routine from my not-so-distant past: I bring mediocre to a classroom full of awesome kids on a regular basis. The experience is, well, awesome. Such regularly fantastic interactions lead me to believe my teaching is, well, fantastic. Little do I know, the awesomeness is often in spite of my efforts, rather than a result of them. Things only go swimmingly because my kids are so swell.

Reality Settles In

I mentioned that I used to suffer. No longer. In fact, my sense of awesomeness has been plummeting for a couple of years. I’m so mixed up right now that it’s about to crash into the floor. Here’s a graph of my current crisis in confidence:


Good News, Bad News

So the bad news is this: I’m not half as good at this teaching thing as I thought I was, and that’s more than a little discouraging.

Here’s the good news: I’m not a quarter as good as I think I could be, and that’s more than a little exciting.

More good news: I’ve realized that my primary teaching style (I’d call it “conversational direct instruction” with a lot of “What do you see? Why does that happen? How can we generalize?” in an all-eyes-on-the-front-of-the-room style) is seriously limiting my students’ potential.

I think the “What do you see? Why does that happen? How can we generalize?” elements of my teaching are incredibly valuable. I don’t plan on throwing those out, and I only hope to get better at creating opportunities for students to ask and answer questions like these.

But the all-eyes-on-the-front-of-the-room style is starting to kill me. What’s worse, I expect it’s been killing some of my students for a while. The delay in seeking a remedy is because my mostly-honors students have been so amicable and cooperative that they haven’t pushed back through bad behavior, inattentiveness, or poor learning results.

Enter this year’s course load. The pushback is alive and well. I have a few classes this year that are helping me see through the mirage and have given me a clear view of my strengths and weaknesses.

Class Portraits

Take today’s classes in fifth period (Algebra 1) and eighth period (Honors Algebra 2) as portraits of what sometimes goes wrong in my room.

In Algebra 1 we’re making connections between the x– and y-intercepts of the graphs of quadratics and their equations (in factored and expanded form). At least, that’s what we’re trying to do. Today was an absolute train wreck of a lesson. Their attentiveness during yesterday’s lesson (where we reviewed some factoring techniques to prepare for today) was so poor that I decided to transform today’s direct instruction lesson (remember, they’re almost all written that way right now) into a small group activity. I figured if they spent less time listening to me walk through problems and more time thinking their own way through problems that they would have a better chance of making the relevant connections (which are not terribly profound). We eventually got there, but I felt like a slave driver while giving what should have been 30 second “getting started” directions that lasted far, far longer because I couldn’t hold their attention for the life of me. I left class thinking “There must be a better way.” So what is it? Type the directions on a Keynote slide and keep my mouth shut? Type more detailed activity directions out at the top of the handout so they don’t have to wait for me to get started on the activity started? Would they even jump into the lesson right off the bat without any teacher explanation? Is it even possible to train a class to become self starters when they’ve always relied on me as their teacher taking the lead? I expect that it is, but how?

Just to be clear, as I tried to move away from direct instruction today, we couldn’t even get past the directions for their small group task. At the risk of sounding conceited, I feel it’s appropriate to note that outside of this group of students my classroom management is typically stellar and discipline is a non-issue. With that being said, it’s still on me to make things work with this group of kids. It’s just going to take better lessons, better ideas, better systems, etc.

In Honors Algebra 2 I fight another battle. These students are noticeably more interested in the mathematics, and their behavior is mostly excellent. However, they struggle to remain focused, partially because it’s the last period of the day but also (I think) because the pace of our discussion is just right for about one third of the students, too fast for another third, and too slow for another third. I want to break out of direct instruction mode so that students can proceed at their own pace. I expect all of the students would learn at least as much as they do now, and a full half of the class might have an opportunity to learn a great deal more because they aren’t tied to my pacing for the entire lesson. But I don’t know how to make this happen.

More Bad News and a Plea for Help

As you can sense, there’s some more bad news: Even though I’ve identified what I want to change (my teaching style) I don’t know how to get from here (“conversational direct instruction”) to there (something better than what I’m doing now), or really even where “there” is.

So here’s what I need from you. I need some help vision casting (what could my classroom look like). And maybe more importantly, I need some advice on how to get there.

A few things to keep in mind while you’re dishing out the good stuff:

  • I typically teach 4 to 7 different courses, so lesson planning, activity creation, and so forth, is a challenge.
  • I desperately want to design a curriculum where the most challenging thing for students is to think about the interesting, non-trivial tasks they have been given. I do not want to remain mired in a curriculum where the most challenging thing for students is to pay attention when every part of their being is shouting “Boring! Don’t pay attention, it’s boring!”
  • A part of me wants to go all Sam Shah on my students with guided discovery packets like this, but I’m terrified of the monumental task of transforming my direct instruction lessons.
  • I want to include more open-ended problems in all of my courses.
  • I think well designed three act tasks are the bee’s knees, but I’m currently more of a stumbling bumbler than a Dan Meyer when it comes to creating my own.
  • About four years ago I shelved my Algebra 1 and Algebra 2 books and wrote my curriculum from scratch (lessons, homework, and assessments, the whole shebang). The curriculum is heavy on concept and procedure, but light on application (i.e., problems in genuine, engaging contexts).
  • I still use a textbook for Precalculus (Foerster), Calculus (Foerster again), and AP Statistics (Starnes), though I may “escape” from the Precalculus book when we transition to Common Core in 2014-2015.
  • I’m trying to build a Pre Algebra course from scratch, aligned to Common Core standards, but it’s been an uphill battle (and until recently, almost entirely based on direct instruction for new content).

So there you have it. I’m in trouble. And you can help. Get thee to the comments!

(By the way, if you made it this far, you deserve a gold star. Two gold stars for anyone who leaves a comment.)


Pre Algebra is on my teaching list this year. The last time I taught it was five or six years ago, and I’ve changed quite a bit as a teacher since then, so I’m building everything again from scratch. (It feels appropriate to note that my philosophy of teaching/learning has shifted more significantly than my actual practice, at least in my other classes.)

For the past week or so we’ve been constructing, measuring, labeling, identifying, and discussing triangles (where the constructing has been mostly with non-digital tools). Given three sides, given three angles, given some combination, similarity, congruence, impossible triangles, etc. Our progress has been frustratingly slow, in large part because my routine of late has consisted of me going into class with an activity and some excitement only to discover that some key element of the activity is seriously flawed. I spend the next evening revising the activity (thereby rekindling my excitement) in order to try it again the next day. I imagine (hope?) our progress won’t be quite as slow next year, but I’m not sure if that’ll be the case.

This is the activity I wrote for today. Since it’s late, I’ll cut to the chase: The conclusions students drew at the end of the activity were on the disappointing side, both in terms of the depth of insight of their observations, as well as their ability to express what they noticed.

This (here and here and here) is what I have planned for tomorrow. I’m hoping that by giving them space to record their measurements (in an organized manner) our debriefing conversation will include more insightful comments from students. We’ll see.

If you’re game, have a look at the handouts and let me know in the comments what you like, what you don’t, and how you’d make it better.

Estimation 180 Rocks

I learned about Andrew Stadel’s Estimation 180 a few weeks ago. I decided this morning it was time to stop watching and time to start playing along. We’re a bit behind the rest of the estimating world, but in first period (Pre Algebra) we worked through Days 1 and 2 and in third period (Honors Algebra 1) we worked through Day 1.

It. Was. Awesome.

I won’t spend a lot of time in this post talking about Estimation 180 in general or how I used it in class today. If you already use it, you’ve probably formed your own opinion and approach by now. If you don’t use it (or have never heard of it), get yourself over there as fast as you can.

What I will say is this: My students were more engaged today, even in those ten short minutes, than they have been in quite a while.

I imagine it had something to do with the accessibility (everyone can make a guess, even if it’s horribly, horribly wrong), the anticipation (“Am I right? Am I right? Am I right?”), and the way these estimation tasks present a natural, un-intimidating opportunity for students to defend their responses by explaining their reasoning. The reasoning—to students, at least—often doesn’t appear very technical or mathematical, but it’s great exercise anyway. And it’s a healthy start to making sure this is a regular part of my students’ experience.

So where to from here? Well, for one thing I’ll continue to use Estimation 180 with these students. But beyond that, I’ll try to incorporate those three elements (accessibility, anticipation, and ready-made opportunities for answer-defending) into other tasks and courses.

I just have one question: When this year’s Pre Algebra students have me again next year in Algebra 1, will there be an Estimation 181-360?

Reason and Wonder

In my third year of teaching I taught AP Calculus AB for the first time. I had 10 students (I teach at a small school; more on that later). All of them passed. In fact, six of them earned 5’s. I felt like the king of the world. In reality, I had no idea what I was doing. (In many ways, I still have no idea what I’m doing; more on that later as well.)

A couple years later, four of my students (out of 18) failed to pass the exam. I had a minor crisis for at least a couple of reasons. One, as I continued investing exorbitant amounts of time and energy into my calculus course, as I thought I was getting better, my students’ results (by one measure) were declining. This was more than a little discouraging. Two, if my goal was to equip students to pass the AP exam in order to earn college credit, then I had failed.

I had to stop and think: Was the year of teaching and learning and struggling a complete waste for these four students (and for me in relation to these four students)? My gut told me no, it was not a waste, not even close. So if it wasn’t a waste, then I must have been deceived when I thought (in no uncertain terms) that the primary (only?) goal of the course was to pass an exam and earn some college credit. So what was the goal?

I sat down on September 17, 2009 and tried to sort out the thoughts in my head by writing in a private journal. After a few passionate, yet meandering paragraphs, I settled on this as the reason I taught calculus:

I teach calculus in order that students may reason more soundly and see the beauty of the created world more clearly.

The reason I share this story now, as the first post in what I hope will be more than a few over the days ahead, is that with some minor revisions it expresses why I teach not just calculus, but anything at all. It also explains why I chose the name for my blog. (Thanks to Justin Lanier and Michael Pershan for encouraging me to finally start blogging, and to consider naming the blog in a way that expresses what I’m most passionate about in teaching.)

So here goes:

I teach mathematics in order that my students may reason more soundly and that they may have the capacity to wonder more deeply and profoundly about the world.

That’s it. That’s why I teach. And while I still wait anxiously for AP results to show up online each July, I no longer count my year as a waste or a success based solely on the numbers that appear in those reports. If I’m helping my students to reason with skill and precision, and if they’re growing in their capacity to wonder about and be amazed by the world, then I think I’m doing alright.