Monthly Archives: August 2011

Free-Choice Time: Origins

As I mentioned in a previous post, having regular free-choice time for my students has become an important part of my middle school classes.  (Plans are still simmering for bringing free-choice into my high school classes more explicitly.)  Last year was my first go at this.  My original inspiration for sharing free-choice time with students probably sprung from a number of influences, including The Open Classroom by Herbert R. Kohl and Mindstorms by Seymour Papert.  As I remember it, however, the notion really crystallized for me when my mom, who is an elementary school librarian, told me about a way that she helps her students expand their reading horizons.

Mom and me

Mom and me, bundling up for the harsh Louisiana winter.

Now you’d think that picking library books would have a lot of choice built into it, and you’d be right.  However, the circumstances surrounding selection can affect what choice (and reading) feel like to kids.  You may be familiar with the Accelerated Reader program.  I did it when I was in elementary school, and for me it felt like an add-on.  Whenever I happened to read a book that was a part of the Accelerated Reader program, I took a short computerized test on it and accrued “points”.  There were incentives involved, but it didn’t wholly shape my reading experience.  In the two decades since, the AR program has evolved from being an add-on to a core concept, at least in some schools.  My mom found that her students had been trained to seek out books that were in their AR reading level range—which could be something as specific as 3.2 to 3.6.  I know—it sounds almost like a horror story.

My mom worried that the narrow focus that these kids had on their reading levels was getting in the way of their relationship with reading.  In an effort to help kids to stretch themselves as readers, she designed a “bingo card” with a different genre of book in each square—science fiction, poetry, biography, and so on.  This allowed kids to keep track of the genres they had read.  Over time, she more often heard kids asking for help to find a mystery novel rather than a 3.2 to 3.6 book.  She was fostering personal, eclectic choice just by giving kids a different window into the selections they were making.  (I think there was also a reward for bingo “black-outs,” which certainly didn’t hurt.)

There was already room for choice in my mom’s library.  Unlike the status quo in most math classrooms, she didn’t have to make a conscious effort to install choice.  What was needed was curation of the available resources—a reframing of the decision-making of her students.  By imposing a small amount of structure, she actually gave them more power to find things that they liked and to pursue them.

I think that before my mom shared this organizing principle with me, free-choice sounded very amorphous and abstract.  Even with my experiences at free-wheeling Saint Ann’s, it was unclear to me what–if anything–students would do without direction from me.  Somehow, what my mom said made it click for me that free-choice isn’t the same thing as structurelessness–that choice at its best happens in a context.  In my next post I’ll go into some details of how I’ve used and am planning to use this bingo card idea in my middle school math classes to help create context for free-choice time.


SBG: Affective Quizzing

When has a student mastered a skill?  Part of the purpose of Standards-Based Grading is to help us answer this question.  (I’d even say it helps us to articulate the question in the first place.)  Different teachers establish skills mastery in their versions of SBG in different ways–for instance, getting everything right on a skill quiz, or getting everything right on two skill quizzes in a row.  In these versions, once a student achieves a certain outcome, she is exempt from further quizzes on that skill.  For other teachers, a kid is never “done” with a skill until the year is over; skills continue to come up on new assessments, and the student’s grade for that skill is his most recent one.  On top of these, I’m sure there are many other awesome variations and hybrids that people have devised that work well for their classrooms.  I’d love to hear about your own twist.

This past year I was in the “one-and-done” camp, and I’m planning on staying there.  That said, I think I will be keeping a better eye out for occasions when a student is struggling with the mechanics of a skill that he has previously quizzed well on.  That may be a good time for a conversation and perhaps reviewing and requizzing.  (Without grades in the picture, there won’t be anything punitive about this–just an opportunity to learn.)  But I’m looking forward to including a new facet to my skills quizzes themselves this year.  Like so:

"How did that go for you?"

It’s that last bit.  I’m curious to see how asking students about their quizzing experiences affects the whole assessment process.  I can’t say exactly where the idea to do this came from, but I think it was at least partially inspired by a student of mine from last year.  She would often write notes to me on her quizzes explaining what she still felt fuzzy on.  This was on quizzes she was choosing to take, buffet-style.   I found that her notes both gave me a better sense for her understanding and provided a really natural way for us to start conversations about remediation.  While there were times that she struggled with our course material, her ability to self-evaluate helped to make her year a successful one.

I’m sure you’ve taught both over-confident and under-confident students.  I feel that by asking “How did that go for you?” on quizzes I may sometimes hear anxiety and doubts from under-confident students even when they get everything right.  In the past, I’ve just checked off their correct responses, said “good job” and moved on.  They were “done” with that skill, despite not feeling at home with it.  No doubt they were in the short-term relieved, but perhaps they were left feeling uneasy about this skill in the long run.  That isn’t what mastery should look like.  By putting that quick gut check at the bottom of each quiz, I’m trying to give my students a safe and immediate place to tell me about their relationship with the skill, right after they’ve shown me their attempts to apply it.  And if they’re telling me they don’t feel like they’ve mastered it yet–even with a perfect paper–then they haven’t.  More steps need to be taken.

I’m sure you can fill in the corresponding things that could transpire with an over-confident student.

Of course, it’s entirely possible that a kid will pose as more confident than he really is, or decide not to respond to the question at all.  To me, it’s not important that all of my students share their feelings toward their skills with me in this way.  If providing the occasion helps even a few of them to do so, the fruits of that will make me feel like it’s well worth asking.

To sum up, I’ve come to think that any answer to the question “When has a student mastered a skill?” needs to include, “when she feels like a master of it.”
I hope that finding room in my classroom for the affective aspect of learning skills will make for more effective assessment and feedback.

(Ah, there’s the punchline.  It turns out I’m not a spelling dummy after all.)

SBG: Skills Mastery as the Beginning, Not the End

Ah, the interminable design cycles that we as teachers put ourselves through! Something that I often find challenging is how lengthy these cycles can be–I mean, if the day after you’ve shared a lesson with kids you have a great idea about how it could have been way better, it could be up to a year or more before you get a chance to try it out.  And that’s if you remember your idea.

The cycle that has thrown me for the biggest loop is the one I’ve been in about SBG (or Standards-Based Grading).  When I first got into this mathedtweetblogiverse two years ago, I was excited by the work Dan Meyer and others had done to make their expectations about skills clear to their students.  Until that point, my own assessment arc had not been going well.  From the start, it had been really hard to match up my previous experiences with assessment with Saint Ann’s culture and ideals.  Giving quizzes and tests in arbitrary and knee-jerky fashion after we had covered “enough” material fizzled in the face of not giving grades.  Also, neither the tests themselves nor the feedback and corrections I labored over seemed to improve anyone’s understanding.

When I pulled back from those traditional assessment methods, however, I found myself in something of a vacuum.  The fact that I’m in charge of my own curricula and evaluations with little to no constraint–coupled with the fact that I tend to spontaneity and disorganization–often meant that I did few formal assessments whatsoever.  I knew that my students were learning things from the work they were doing for my class.  I could make records about my observations of their activities to include in my anecdotal reports.  Still, I couldn’t help but to think something was missing–my students just weren’t being best served by the lack of clear expectations, a systematic way of pursuing them, and a feedback cycle.

Enter SBG.

Trying to bring Standards-Based Grading into a no-grades school was an interesting adventure.  Suffice it to say that after trying out several different formulations over the past two years, I’m really excited to try out my new approach very soon.  I’ve decided to go binary with respect to my skills quizzes, since trying to measure progress toward understanding numerically never felt fruitful to me in practice, and there’s no need for me to establish a final “average” for each kid.  (Shawn Cornally’s thoughts here also helped to get me there.)  I’ll continue to have skills lists for my kids and weekly quizzes for them to choose from in order to demonstrate their mastery.  I’ll be giving them copious feedback and letting them know if they nailed it or still have work to do, and we’ll both keep track of the skills they’ve mastered.

Still, I really wanted to find a way to encourage students to see that skills mastery is the beginning of the story, rather than the end.  Skills are tools that let you do new things, that empower you, that even give you a new bit of social capital.  With these thoughts in mind, I designed the following sheet to help kids to track their progress toward skills mastery and to inspire them to use their knowledge in fruitful ways.  I’ll be using the same document to track their progress.

That first column gets checked off once a kid aces a weekly skills quiz–that’s the binary got-it-or-don’t.  The space below is for me and students to keep track of feedback that I give them and reminders they might make for themselves.  The other three columns are by no means sequential and don’t represent “stages” past mastery.  Rather, they are suggested asperations and goals for the newly-minted master geometric-series-summer.  Would you like to try a non-routine problem that involves geometric series?  Just ask me for one.  Does someone you know–in our class or out of it–need help with this topic, or just curious about learning some new math?  Share your new knowledge and document it by journaling, snapping a photo, or making a video.  Did you recognize three months later that knowing how to sum geometric series opened up a route to solving a problem as you worked on a project?  Sweet!  Include it in your project write-up.

The point is that those other columns are an ever-present alert: You know things!  You can seek out ways to use your knowledge!  All three of the “choice prongs” are here–the suggested tasks are big and open-ended, the timeframe is as long as needed, and students can choose these for themselves as goals and record and reflect on their successes as they happen.

A final thought: it seems to me that something like this could be easily adapted to a grades environment.  I’m not well-practiced at designing grading schemes, but I’m thinking:

  • non-mastery of a skill in isolation is a high F
  • mastery of a skill in isolation is a high B or low A
  • mastery of a skill in isolation plus a further use of the skill is a high A

And then average them up.

Thoughts on the practicality of such a grading scheme?  Comments on the set-up I’m going to try out?  Ideas for other ways of building and sharing skills mastery beyond use in isolation?

Choice in Class: Three-Pronged Attack

So at the EdCamp session about choice, I shared three ways that I’ve tried (and am trying) to encourage student choice in my classroom:

  • “free choice” time
  • wide-open projects
  • goal setting

When I wrote those up on the board at EdCamp, I had them associated with three of the classes that I’m teaching this coming year–fifth grade math, high school geometry, and calculus, in that order.  Upon further reflection, I’ve begun to see how I want to have all three features embedded into all of my classes, as well as how they all rely upon each other.  I’ll say more about these three prongs individually at a later date–and writing about how they actually happen in my classroom on a day-to-day basis is what I’m here for.  For now, I just want to say a few words about each to give some context.

Briefly, free choice time is time set aside in class when students are working on their own thing without my giving them direction.  I make available a variety of resources and suggest a range of possibilities.  I did this for the first time this past year with my 6th and 7th grade classes.  Each week on Friday after their SBG-style quiz buffet, students would pick up some new activity or continue on their ongoing project.  As a point of reference, think of Google’s “20% time”.

By wide-open projects, I mean some piece of extended work where the steps haven’t all been laid out for the student.  Further, the end products that individual students produce may look very different–either because they’ve investigated different problems, or approached the same problem in different ways, or because they’ve chosen to share their efforts through different media.  It’s easy for me to point to examples from my geometry course, like this project about geometric properties.  But now that I think of it, the free choice time activities could fall into the same category.

For goal setting, I mean asking kids to figure out what they want to accomplish and helping them to do so.  I’ve done this some with my middle schoolers with their skills quizzes–which ones they want to prepare for and take the following week–and now that I think of it, in helping them navigate their free choice time activities.  This year I plan to ask my 5th graders to reflect on both their quizzes and free choice time activities as weekly journal assignments.  However, my mind for whatever reason has recently been thinking about this in the context of my upcoming calculus class–having my students do the same kind of journal reflecting, for one, but also helping them to establish larger goals about what “success” in the class will mean for them.  A student could decide that basic proficiency on the items on my skills list is what he’s after.  Or maybe he wants to get almost all of them, but to try tackling some additional challenge topics.  Or who knows what.  Allowing him to make that decision and then helping him with following through on it seems huge to me in terms of motivation and learning that’s bound up with integrity.

To summarize: give students the time to dig into a rich variety of possible activities and the freedom and guidance to choose among them.

Finally, I should say that at Saint Ann’s we don’t give grades to our students and that curriculum is by-and-large decided upon by each teacher for his or her classes.  The way I give an account for how my students use their free choice time is the same as how I report on anything else they accomplish–through a semi-annual page-long report, individualized for each kid.  Having no grades definitely frees me up to take chances with what I do in my classes, and not having to worry about attaching points to tasks makes something like free choice time easier to legitimize in my classroom.  But even with no grades, fostering student choices is countercultural, it runs against my own inherited habits and thought patterns, and it’s really hard.  Still, I deeply believe and hope that real student agency and empowerment is important and that it can happen in any school.

I’m excited to find out whether these ideas resonate with your own experiences and your own hopes.


Two years ago, Sam Shah planted a seed in my head.  We met at a summer teaching conference at Phillips Exeter Academy in New Hampshire, despite the fact that we teach nearby each other.  Through Sam, I was introduced to the delights of the edumathoblogisphere and soon I was on Twitter and reading blogs with relish.  (Thank you!)  Despite his encouragement, I was reluctant to blog myself.  I didn’t feel like I had much to say, and certainly not in an extended format.  Writing has always been a ponderous process for me.  It takes me forever just to write a short email because I edit and proofread to an admittedly absurd degree.  I like talking and conversing a lot more—how provisional and reshapable and easily qualified everything can remain when you’re just talking.  Print seems awfully definitive.

But that seed has slowly germinated over the years, like a pot simmering on the back burner, and from time to time I’ve almost started in on the project.  To entirely mix metaphors, going to EdCampCT on Thursday was the straw that broke the camel’s back.  I helped to create a session on giving students choices and autonomy in the classroom—a topic that has been much on my mind as the new school year approaches.  Two things happened.  First, I heard myself say some things that didn’t so much surprise me as struck me.  That’s another great thing about talking.  Sometimes in explaining myself to new people I find myself saying things that I had never really articulated before, even to myself.  Over the course of that session, I realized how much I’ve at least begun to make choice a core value and governing principle in my classroom.  I hope that by blogging about helping my students to choose mathematics for themselves, I’ll continue to learn about and develop my thoughts on the matter.

The second thing that happened was that Frank Noschese—who has blown me away in the few months I’ve been following him—asked me afterwards about some details of how I’m implementing SBG in my classes.  Later on, he tweeted me about whether I had a blog post or something explaining some of this.  I told him I would have have one up as soon as I started up a blog.

So here I am.  :)