Month: March 2013

A Further Call to Arms

Entering the Discussion

Two Thursdays ago I jumped in the middle of an ongoing discussion about assessment by posting this. It was essentially a call to arms, a request to join forces in strengthening the quality of our assessments.

Then, just after midnight on Saturday morning Daniel Schneider blew my mind by posting this. If you haven’t read it yet, stop messing around on my blog and get yourself over to his. Make sure you follow all of the rabbit-holes provided in the links. (He wasn’t kidding when he said he was a master aggregator.)

(Update: While I was fiddling with this draft, Daniel threw this down as well. Go ahead and put another educator on the list of people I want to be like when I grow up.)

What’s Next

So where do we go from here? What should we do with all of the interest and enthusiasm surrounding assessment? I see one thing as a no-brainer:

Let’s create a centralized location with links out to quality posts and articles about creating excellent mathematics assessments.

I’m hopeful that a certain master aggregator will lend a hand here. (Update: He will!) Over time we can add more links to resources and even invite members of the so-called better assessments movement to write articles addressing specific topics of need.

Archive or Conversation?

Beyond that, I see two lines of attack: (1) Build an archive; (2) Foster a conversation.

Let me explain.

It would be incredibly valuable to have access to a well-populated, easily-searchable database full of rich assessment questions.

It would be even more valuable—incomparably so—if we learned, as an entire community, to write such rich questions.

In the first case (the archive-building scenario) the focus is more on writing and/or gathering good questions and assessments, and then serving them up in a helpful way. A noble task, to be sure. One I hope others will take up and carry to great heights. (By the way, if that’s you, check out OpusMath, follow them on Twitter, and start uploading like crazy.)

But more than a comprehensive archive of excellent problems with a slick user interface, I think our most essential need right now is to develop an army of amazing assessment authors.

If you agree that the ongoing, teacher-developing conversation is at least as important as the creation of a fantastic archive, then I invite you to join me in the following challenge.

Write An Assessment You’re Proud Of

In a recent email exchange with Daniel, I shared a massive vision I have for creating this group of great assessment writers. He suggested starting with something smaller (something vital, yet attainable) and building from there.

With that in mind, here is my/his/our challenge to ourselves and to you:

I want to challenge the blogotwittersphere to write an assessment they’re proud of. To pick a skill/concept/objective and write a targeted assessment that measures this objective at various depths. Or, if they already have an assessment they’re proud of, to share why they’re proud of it—what is it about this question/this series of questions that makes this assessment meaningful? That finds a way to assess both procedural and conceptual understanding. That gives students an opportunity to exceed expectations. That has an ‘explain’/’justify’ component. I don’t know if these things are possible for all skills and objectives, but this is why I want others to be thinking about it too.

The end goal is: create an assessment you’re proud of in terms of format or questions or depth or all of the above, and explain why you think this is something worthwhile.

(I tried to recast his challenge in my own words, and realized I was better off stealing the thing wholesale, with his permission, of course.)

Where Do I Sign Up?

If you’re interested in playing along at home, start with a one-minute survey. Then hop on the Twitter and spread the word! The more voices we have in the conversation, the better we’re all going to get.

What You Can Expect From Me

Once this blog post goes live, I’ll do the following:

  • Set up (the “home” for the better assessments conversation)
  • Gather already-existing resources together in an Assessment Authoring Boot Camp section of the blog (Daniel Schneider has agreed to lend a hand; additional volunteers welcome)
  • Put out an official “call for assessments” over a two week (?) period in the near future, including submission guidelines
  • Feature a small number (one to three?) of these assessments each week as guest posts on the blog (including the “explain…” bit from Daniel’s challenge), and invite the “better assessments” community to offer feedback, constructive criticism, etc.

As with any group project (and I hope this turns into a massive group project), better ideas will come as soon as brains other than my own start their wheels-a-turnin’. I’m not married to any of the details sketched out above, so long as we find a way to establish an ongoing and positive conversation about assessment.

The Dailyness is the Key

I feel I should explain the last bullet under “What You Can Expect From Me.”

Let’s dream big. Imagine that 100 math and science teachers from all sorts of different grade levels and courses submit assessments when the call goes out. The assessments range from decent to amazing, and we’re all stoked because 100 people (100 people!) played along with this little experiment and we have heaps of assessments to look at and learn from.

If we’re not careful, we’ll squander most of the opportunity for conversation presented by 100 such submissions. My intention is to highlight a few assessments at a time so that busy teachers (that’s us!) have an opportunity to dig into each assessment in depth, over the course of an extended period of time. (Whether or not my suggested approach will achieve the goal is open to discussion.)

I think we’ll experience the most growth as a community if we employ a slow-and-steady approach, rather than go after this all at once. It’s the reason many of us find blogs and Twitter more powerful tools for sustained professional growth than fantastic-but-isolated conference experiences once every year or two. The dailyness of our practice is the key to our growth.

What To Do With a Head of Steam

If this project isn’t dead in a few months, then I’ll share some details of the bigger vision I have for this assessment conversation. It has to do with recruiting and organizing people at various levels and in various subjects into assessment-writing cohorts. They’re exciting plans (at least to me), but possibly unrealistic. In the coming weeks I’ll invite some of you to tell me what has potential, what’s a waste of time, and what needs tweaking to become realistic.

Some Closing Thoughts

I think multiple-choice questions are generally inferior to free-response questions. I also think that both styles of “one-off” question are completely inferior to well-crafted performance assessments. However, I also believe that poorly-written MC and FR questions are inferior to well-written MC and FR questions. With that in mind, I think it’s entirely appropriate to allow MC and FR questions into the discussion at

With that said, I think the MC/FR/Performance Assessment classification of assessment questions isn’t as helpful as the conceptual/procedural/synthesis approach described by Daniel here and here. I certainly like this latter three-part structure better than then conceptual/procedural/application framework I’d been mulling over prior to reading all these great blog posts on assessment.

Comment Time

Heart beating with uncontrollable excitement? Bored out of your mind and wondering how you made it to the end of another lackluster post? Have a suggestion? A critique? An idea? Drop a line in the comments and keep the conversation rolling.


Expressions Challenge

The Four Fours

In my first year of teaching I came across the Four Fours challenge. I loved it. I’ve always considered puzzles, brainteasers, and trivial challenges of that sort to be rather entertaining, so I went to town on the Four Fours right away. The problem gets better as you go: easier target numbers are out of the way and the real mental effort begins as you look to fill in the gaps.

Beyond the personal puzzle perspective, as a brand new teacher (my course load then was split 50/50 between 7-8 and 9-12) I considered this challenge to be a gem for my middle school students. Here’s a few reasons why:

  • Mundane-yet-necessary practice is made more engaging in the context of a challenge (just like in this problem).
  • Shifting the task from evaluating expressions to writing expressions ramps up the critical thinking component of the task. Students have to look for and make use of structure in order to bend the expressions to their will.
  • The problem is flexible and can be presented to individuals, small groups, entire classes (class vs. class challenge, anyone?), or with a twist (find as many expressions as possible with a value of, say, 23).

And Then It Happened: The Internet Failed Me

I’m sure there are more reasons why the Four Fours is awesome. If you think of any, share them in the comments. But I know of one reason why the Four Fours is not awesome. In fact, I know of one reason why the Four Fours is worthless. That’s right, useless. Totally devoid of any value.

Wait? Just a minute ago I was singing the problem’s praises. Why the dramatic turn? One reason:

The Internet

I typically love the Internet. Defender of the integrity and usefulness of Wikipedia and all that. But not this time. Here, the Internet failed me.

See, someone decided it woud be a good idea to ruin the Four Fours by posting entire solutions all over the place. Now any time I give this problem to students, they’re one Google search away from Four Fours glory.

My Solution

So what do you do if the Internet robs you and your students of a great problem? Make another one. Keep the good stuff (see the bullets above) and tweak the parameters.

Flash back to my first year. When someone told me the full solution to the Four Fours was online, I rewrote the rules and called it Expressions Challenge. Once I got going, it was easy to make additional versions. I’ve included the directions (and handouts I mocked up this year) for the first three versions, as well as some comments on how to tweak Internet-proof the problem further.


Here are the directions for the first three versions of the Expressions Challenge. Note that there is only one difference between the three: Use the numbers in (1) any order, (2) increasing order, or (3) decreasing order. Obviously, versions 2 and 3 are more challenging.

expressions.1 expressions.2 expressions.3


Just to be clear on the order element of the directions, here are examples for each version (1, 2, and 3, respectively):



And the handouts (nothing special):

Further Defense Against the Evils of the Internet

If the Internet destroys any of the challenges above, no problem. Just tweak the problem again. Use the numbers 1, 2, 3, and 4. Or 1 through 6. Or the first four odds (or evens). You get the idea.

Also, you could change the word “numbers”  in the directions to “digits” to open up some additional possibilities. And for the record, whether your students should be allowed to use decimals, percent signs, radicals, ceiling/floor/rounding functions, etc., is totally up to you.

Let me know in the comments if you find any of this useful, or if you have a similar challenge you use with your students.

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!