Monthly Archives: September 2011

A Letter to Sal Khan

Over the summer, I spent some time following online discussions about the role that Khan Academy and similar sites can or should play in education.  Much of what I read and much of my own thinking was prompted by the tweets and posts of Frank Noschese, who has consistently been both fair-minded and critical when it comes to Khan Academy.

My thoughts began to gel as I considered how I would like to be able to use Khan Academy in my own classroom.  It became clear to me that the many great resources available on Khan Academy are not nearly as useful for my students as I would like them to be.  The main reason for this is that I have few tools to customize and curate these resources for my students.  A person who wants to be taught a potpourri of math topics on his own could find much of use to him on Khan Academy, but this is not how school courses happen.  Courses have shape and structure, and each one is unique because individual teachers bring their own ideas and approaches to the table.  School, district, and state curricula bring to bear their own powerful influences.  Khan Academy, as it stands, does not have the capacity to adapt itself to this variety of circumstances.

As my thoughts along these lines came into focus, I decided to write a letter to Sal Khan and his colleagues.  You’ll find a copy of it below.

At first I tried sending the letter through the Comments and suggestion email address provided on the Khan Academy website, as well as through the one for Feature Requests.  When several weeks passed without a response or acknowledgement, I—in a moment of audacity—blasted the letter to every Gmail and Khan Academy email address that I could think of that might belong to Mr. Khan.  After still not hearing a response, I made the more reasonable move of tweeting to a variety of people on the Khan Academy team listed on their About page.  Ben Kamens responded to my tweet and told me to email him the letter, explaining that it had probably been received already but that the Khan Academy staff doesn’t have time to respond to all of the feedback and suggestions that they receive.

When I followed up a few weeks later with Ben, he said that he couldn’t say much, but that the Khan Academy team is at the moment seriously considering ideas along the lines of those that I brought up in my letter.  Needless to say, I was really excited to hear this!  I think these kind steps could really turn Khan Academy into a powerful tool for classroom teachers.  I’m really looking forward to seeing how the development and use of Khan Academy unfolds in the future.

Not receiving a reply to my emails for a long while was a little frustrating, but I’m really glad I wrote and sent it.  It definitely helped me to clarify my own thoughts, and maybe it will have some small effect in the dialogue at Khan Academy.  I hope that by sharing my letter here it might prompt thought and discussion about the ways in which Khan Academy and similar resources can best be incorporated into the future of school.  I’d love to hear your comments.


Hi Sal,

I hope that this message reaches you and relevant members of your team.  I teach middle and high school math at Saint Ann’s School in Brooklyn, NY.  I have followed the Khan Academy with interest for some time now.  I really appreciate your efforts at creating, sharing, and popularizing resources for learning.  My own adventures in incorporating Khan Academy’s resources in my own classroom have produced promising results, and I look forward to working to find more and better ways to use it to help my students to learn.

There are three ideas I want to share with you about the future of the Khan Academy—possible to implement independently, but mutually supporting in spirit.  Perhaps you and your team have thought of them as well; in that case, consider this an enthusiastic letter of support.  These ideas have to do with the customization of learning and with putting the best learning tools into the hands of students, teachers, and independent learners.  I think it would be a quantum leap forward for Khan Academy if on the site:

  • Teachers could create and share their own instructional videos.
  • Teachers could devise and share their own exercise sets.
  • Teachers could design and share their own customized “knowledge maps”.

These three features in tandem would move Khan Academy from being a supplemental resource in my classroom to a central and crucial pillar.

For instance, one of the classes I’m teaching this coming year is a high school geometry course.  I have a list of skills that I want all of my students to master by the end of the year.  Each skill is small and focused, and each has connections to other skills.  Mastery of these skills is just one goal I have for my students, but it is an important one.  In the past I’ve created multiple practice worksheets for these skills and I allow students to quiz on individual skills at their own pace, but it is difficult to truly customize individual students’ learning experiences.  You have created videos for many of these skills and exercise sets for some of them.  Others of these skills aren’t included in Khan Academy’s offerings, and some likely never will be because they’re peculiar to my own way of approaching geometry.

Videos and exercise sets for more of these skills would be available if other teachers were building up Khan Academy’s offerings by creating their own videos and exercise sets.  I could then create and share my own content for the remainder of the skills, and other teachers and students would have access to these in turn.  Once all of the videos and exercise sets that I want for my course are available, I could organize them into a knowledge map that would be specific to my course’s goals—pruned of skills that are too basic or too advanced to be relevant.  Students could proceed at their own paces in mastering these skills and together we could chart their progress.  Being able to curate the full resources of the Khan Academy into a course-specific knowledge map would allow for focus while still retaining a connection to the whole universe of other skills that students could learn on Khan Academy outside of the structure of my course.  All told, having all of the content that I want for my class and being able to organize it in the way most suitable for my students would make Khan Academy a powerful tool for my students in taking ownership of their learning.

Now, it’s the case that an individual teacher could create their own website with their own videos, their own exercises, and their own knowledge map, entirely apart from the Khan Academy.  But there are strong arguments that creating such a learning environment within the Khan Academy would be a much better option.  First, it would allow easy access to the content that you’ve already created. Second, it would allow for the use of the coherent and powerful software environment that you’ve created.  I don’t have the knowledge needed to create my own exercise engine, but I bet it wouldn’t be too hard for me to learn how to drop a new exercise into the structure that you’ve already created. Third, the visibility and popularity of the Khan Academy provide a unique opportunity to build a wide community of teachers and learners who would mutually benefit from collaborating on and sharing learning resources.  We teachers are so often isolated in our own classrooms or schools, having access only to the limited and pre-packaged resources of textbook publishers and the small amounts of content that we can create ourselves.  We are only beginning to see teachers use the internet to share and collaborate on learning resources, and the Khan Academy could be the clearinghouse that takes these grassroots efforts to the next level.

You have created an enormous amount of learning content and a powerful portal in which to house it. Together these have already helped millions of people toward their learning goals.  I understand that the ideas I’m proposing are something of a departure from the Khan Academy’s current model, and that there would be obstacles to their implementation.  It might even be difficult for you to give up being the sole content provider on the site.  However, I believe that true customization of learning can only come with the variety and creativity that will be released upon opening up the Khan Academy to the world.  Teachers know their own students best and need to be able to adapt the structure of the Khan Academy to their own classrooms.  In particular, having a single unalterable knowledge map is not amenable to personalized learning.  Finally, projects like Wikipedia have shown that having the right portal and the right momentum will draw in remarkable and robust content.  I suggest that the brightest future of the Khan Academy lies in becoming such a portal for education.

I would be thrilled to be in conversation with you about these ideas and would volunteer all of my own energies and talents to help to implement them—from the pilot level to something full scale.  As you might suspect, I could go on and on about these topics, but I know that you must be very busy and want to remain somewhat brief.  You have a powerful position and voice in the current national conversation about schools and learning.  Please use that position and voice to help teachers create more customized learning experiences for our students.

Thank you!

Justin Lanier
Saint Ann’s School
Brooklyn, NY


SBG and Free-Choice Time: Round Two

This past week I rolled out free-choice time in a more formal way to my fifth graders.  On Thursday I handed out a list of different ways that they might spend their time after quizzing on Friday.  Telling them about this was kind of slow going, as both of my classes seemed sort of scattered and unfocused that day.  I described some of the activities that were more unfamiliar—including a brief demo of Khan Academy—pointed out some of the things on the list that I had made available to them more informally after quizzes last week, and answered a few questions.

Aside from the scatteriness, there was a lot of enthusiasm about the different activities and the prospect of trying them out.  One kid said that he wanted to do them all the next day, and I pointed out that while that probably wasn’t feasible to take on in a single day, he could definitely make that happen for himself over the course of the year.

I also gave them the “present” of a math journal.  Many of them were excited about the prospect of journaling about math.  They dove into putting the nameplates on the fronts and decorating them.  I expected to get maybe a little more skepticism or push-back about journaling in math class as too artsy-fartsy.  There was just one question from a girl who asked if they were supposed to write about their “feelings” in their journal.  She made it clear that she was anxious about talking about her weakness on paper.  She also expressed concern about privacy and whether other kids would see what she had written.

I told this student that in her journal she could write about her goals, her progress, her feelings, her excitements, and her plans.  Then I said that she should think of her journal as a safe and private place to record her thinking and that I would be asking her to share her journaling with me only—so that I could better help her to define and reach her goals.  She seemed satisfied and comforted by this answer.

The homework on Thursday night was to prepare for quizzes using the packet of practice problems that I’d previously distributed, as well as to write a journal entry.  I asked them to write about both their quizzing for the next day and the way there were planning to use their free-choice time.  The entries that they made ranged from a few words to a solid paragraph.  They all have room to grow in this regard, and I’m really excited to see how their thinking and their writing evolve over the year.

Quizzes on Friday went smoothly enough.  Overall, the amount of time spent quizzing went down, as could be expected, what with the prospect of their free-choice plans.  Only a couple of students really sped through quizzing.  I figure that with some direction, this will even out in time.  But letting them go and blow and weigh the importance of different tasks for themselves is what this whole adventure is about, after all.

The range of free-choice activities on Friday included a chunk of students trying out Light-Bot; some using the Geofix shapes again; a few doing logic puzzles; a couple playing Hex; and some metal puzzles here and there.  A couple of kids looked into the Thousand Year Game Design Challenge.

This week is a short week—we don’t have school on Thursday or Friday—so the next quiz and free-choice day is a little ways off.  I’m putting together a second practice packet to distribute—by student request.  I think the idea of having resources that help you to prepare for quizzes is starting to sink in!

SBG and Free-Choice Time: Round One

Last Friday was the first quiz-buffet of the year in each of my classes.  Some of my fifth graders really took this metaphor to heart and rhapsodized over whether they would be picking up some of the “chicken wings” or “roast beef” and deciding that they would come back later for “dessert.”  In all of my classes the quizzes went really smoothly.  I feel much more adept at putting together quizzes and practice packets and keys than I did a year ago.  It’s also nice being able to dip into the materials I made over the course of last year.

In my high school classes—Geometry and Calculus—most of my students quizzed for almost the whole period.  (Our periods are forty-five minutes.)  Those who finished before the period was over continued working on their first Investigation about defining geometrical objects (Geometry) or a new sheet about limits of sequences and series (Calculus).  I’ve only had a brief conversation with my Calculus students about what Fridays might look like in the future (free-choice time to work on problem sets and projects, with quizzing as an option) and haven’t had a chance yet to discuss this with my Geometry students.  For now I’m just happy to get my high schoolers into an assessment rhythm that feels comfortable to them.  I figure that opportunities for self-direction will open up as the material of these courses unfolds.  Also, there’s a whole lot of self-directed, choice-but-not-free-choice time in my Geometry class throughout the week already—more on that another time.  Still, for my high schoolers I’m currently in a place where I view free-choice time as purposeful but in a supporting role.  It’s an important opportunity for students to direct their own learning of course content and to personalize it, but it’s something that while good in itself is also a means to an end—getting at the content of a field of study.

With my fifth graders, it’s easier for me to see free-choice time as an essential component of the course that can stand on its own.  It’s an opportunity for kids to explore a huge variety of mathematical activities, to help them find some that they love, and to help them build identities as mathematicians and as individuals.  It’s an end in itself that has its own set of goals built in.  I wouldn’t let a high schooler investigate a mathematical game that she was into during calculus class—at least not for any significant duration—no matter how excited she was about it.  Because it’s calculus class.  But for my fifth graders, it doesn’t matter to me whether strategizing about that game is in any way related to the other content that we’re exploring in the course.  It doesn’t need to be laying groundwork for making factor trees or subtracting integers.  Having a kid build up her own relationship with math is at least as important as anything I could teach her.

Writing this makes me want to make high school more like middle school.  Think, think, think…

I decided that introducing the quiz structures and the free-choice structures in the same week would be too much to dump on fifth graders all at once.  (At the very least, it would mean way too much of me over-explaining all at once.)  So I had several activities available for kids to choose from in an informal way once they were done with their quizzes.  These are some of the activities that I’ll “announce” for this coming Friday in a more formal way, and this time around my kids will have the chance to journal about what they’d like to pursue ahead of time.  (They’ll also journal about what quizzes they’re preparing to take.)  I reasoned last week that having some prior experience with the activities in question would make that first planning/reflection this week more grounded and thoughtful.

Anyway, the activities I had for last Friday were: some books to peruse, a collection of metal puzzles, some pattern blocks, Geofix shapes, Hex boards, chess boards, and a logic puzzle—one of those grid ones.  In one class, the first few students to be done with their quizzes quickly took up the Geofix shapes.  (These are so fabulous, fun, and mathematically rich!)  As other students finished with quizzes, they one by one joined the Geofix festivities.  As they built I was able to entice, with minimal prompting—“Hey, could you get this off of here for me?”—several students to become obsessed with some of the metal puzzles.

In the other class, the choices were more varied.  The first wave of students that finished their quizzes also went for the Geofix shapes and grabbed some metal puzzles as well.  A pair of students got to a point in quizzing where they felt stuck, so I told them that they could work on this quiz together as practice.  They promptly plopped themselves down over by the door and dove into the quiz together.  I thought that this was a great use of time for them.  It arose so naturally and reinforced the low-pressure atmosphere that I’m trying to cultivate around quizzing.  They ended up doing a second quiz together as well.  Some other kids played Hex, and the last two to finish quizzing asked me if I had any origami books, which I did.  They had started in on some folding as the bell rang to end the period.

Free-choice lasted between twenty and ten minutes, depending on the fifth grader.  How long each student quizzed was entirely up to them, although I had asked ahead of time that they come prepared to take at least two of the eight that would be on offer.  Most of them took at least four; several were determined to take all eight, and did.  If you’re interested, you can look at their first list of skills here.

Last Friday was a lot of fun, and I got a lot of positive feedback from the kids about both the quizzes and the activities afterwards.  They’re already looking forward to this Friday, and so am I.

Flying Blind: Teaching Without the Answer Key

David Coffey wrote a post about teachers giving students problems that they themselves don’t know the answers to–doing this deliberately, as a pedagogical strategy.  I’d like to share an example from my own classroom, as well as some reasons why I’ve pursued this path.

Before I begin, allow me to say that what follows is a “sometimes” occurrence in my classes.  Most times when I share open-ended explorations with my students, I’ve already investigated the problem pretty thoroughly–either with a previous class, or on my own in preparation.  And of course, there are plenty of times when my classes are more closed-ended.  But on a few occasions I’ve purposefully held myself back from thinking about a problem before sharing it with students.

I think the first time I did this with serious malice and forethought–teaching in the first degree–was at the beginning of last year with my sixth and seventh graders.  In addition to beginning our diagnostic and review work with arithmetical topics, I gave out this first sheet of problems that were inspired by / stolen from James Tanton’s Math Without Words:

Not a free-form task–plenty of specificity here–but at the same time, no instructions.  I hadn’t done these problems before I handed them out.  What I mean is that I had played around with them a little, but hadn’t convinced myself that any were impossible, and certainly didn’t have any kind of general theory.  I recognized that there was some mathematical depth here and felt that there were likely many connections and extensions to be made.  I wanted to open the year by modeling problem definition, problem creation, and problem solving in a live, off-the-cuff way, and this starting problem seemed like a great way to do it.

The kids dove in–faster, slower, with frustration and accomplishment and bits of insight.  The variations they composed on the back were fabulous–different sized grids, different shaped grids, obstacles, fixed end points, three-dimensional versions, and on and on.  They shared these with each other and critiqued each other’s work, and we discussed the gradations of variation that had sprung up in these new problems.

Here’s what came next:

Here I was pushing for clear language and problem definition, as well as another go-round at creating variations to the original problem.

For the next assignment, I asked my students to explore the nearby space of the original problem–looking for insight into it by looking at variations, and especially at simpler variations.  That’s a problem-solving strategy that worth of the name.  I gave them graph paper and asked them to try out this kind of grid-path problem on some smaller and perhaps bigger boards.  I did the same.

That was actually a homework assignment.  When they came back in, I had them get into small groups to share and compile their findings:

What they uncovered was really awesome and–as best as I can remember–a surprise to me!  On the even boards, it seemed like the problem was possible no matter when the starting dot was located.  The odd boards, on the other hand, had a very suggestive checkerboard pattern.  Conjectures and excitement filled the room.

The following came next–I don’t know if the idea came from me or from a kid:

I won’t spell out the gory details, but there’s so much here–parity, induction, tiling, Hamiltonian circuits.  And I didn’t know it was all there when we started, except in my gut.  So much depends on having a stock of such problems.  Finding them is both hard and easy.  Maybe I’ll talk about that some other time.

At this point last year, some kids went on to explore their own variations during free-choice time.  (Geofix polyhedra laced with string, anyone?)  There were probably loose ends that never got resolved, but that’s not important.  What is important is that having this open-ended, let’s-figure-it-out-together exploration at the start of the year really helped to set the tone that I was hoping for.  So here’s to say that posing problems that you don’t know the answer to is entirely possible and potentially extraordinarily fruitful.  It can happen in large or small doses, but it belongs in the hands of every kid–not just the ones who are “good at math” in conventional ways.  Everyone needs the experience of a math classroom where there are no “haves” and “have-nots”–the teacher included.

Right now I’m in the midst of doing something similar with my fifth grade classes.  We’re working to figure out how many different combinations of pattern blocks can fit together to make a full turn at a point.  I have no idea of what the answer is, or what patterns will crop up.  I’ll let you know when we figure it out!

I hope you find something worth chewing on in the above.  Wow–it feels so great to finally share some math!

PS  With respect to all of this business about problem creation and variations, extensions, and generalizations, let me say that I owe so much Avery Pickford.  I had the great fortune of cutting my teeth on this crazy profession while sitting next to Avery in our math department office at Saint Ann’s.  Louder voices than mine have sung his praises, but I know firsthand how thoughtful and awesome he is.  Just a for-instance: check out this sweet description of the problem cycle and variations, extensions, and generalizations that he wrote and I tweaked.  For this and so much–thank you, Avery!

That Itchy Feeling, or, Asynchronous Quizzing

Never am I more passionate about giving students choices and helping them to find their own learning groove than when I find myself sitting in a PD session.  There I am, waiting to find out what the presenter has in store, suddenly thrust back into student-mode.  From deep inside, up arises this wily and irreverent and pushy punk who is so used to being in charge of his own learning and time.

I’ve been to plenty of great PD and am so thankful for the amazing learning opportunities that my colleagues-from-afar often put together for me to experience.  But boy am I uber-ready to be a critic when walking into a PD session.  I mean, they had months to plan this one lesson and they’re seriously going to show me a video I could have seen on my couch in my pj’s?  Or read me a Powerpoint that I could have skimmed or dug into at my leisure?

These kinds of experiences have sowed in me the conviction that the time and effort spent to bring people together to learn—be it hundreds of miles or just a subway ride—makes that gathering at least a little sacred.  It should be social and interactive, and it had damn sure be aiming to meet the needs of the individuals who have hauled themselves there.

That’s the introductory bluster.  Maybe I’ve got your dander up a little.  What I want to analyze in this post is a thought related to this emotion, and it has to do with trying to avoid misusing my students’ time.

Thesis: Students taking solo-and-silent assessments is a poor use of classtime.

Looking at that statement now, it strikes me as more radical than it seemed in my head.  It runs contrary to a lot of classroom practice, including my own.  Still, I think I have convincing arguments to support it.  What it would imply on a practical level is encouraging students to quiz outside of class, as they often do for requizzes.

Before I start, I should say that this thesis is contingent on a couple conditions being present in a school.  All are present in my own case.  First, there have to be at least some open periods in students’ schedules for them to quiz during non-class time.  At my school, middle school students have study halls and high schoolers usually have free periods in their weekly schedules; both often have discretionary time during lunch.  Second, I’m taking for granted an SBG-like assessment system that admits of modularity—where there are several versions of quizzes for a given standard.  I can certainly see serious obstacles to allowing student to asynchronously take a unique quiz.

What is required for a student to take a quiz?  The student, the quiz, and probably some amount of monitoring to keep things on the up-and-up.  Possibly access to a teacher to ask clarifying questions, but one could argue that—especially SBG-style—quiz questions should be clear, low-stakes, and non-surprises anyway.

For a student to take a quiz, the following are not needed—interaction with peers; a teacher giving instruction or even much attention; nuanced human intervention to change the course of proceedings.  A student certainly has no need of having other students around them who are also taking quizzes.

Most of the time I aim to have an interactive, social, and personal classroom that is an occasion for sharing, collaboration, and spontaneity.  Somehow, though, I drop these values completely every time I give a solo-and-silent assessment in class.

Why do I do it, then?  I’m really curious to hear your own reflections on the question; here is what I’ve come up with:

  • Classtime is the time that my students have for my class; to ask them for some of their “outside of class” time break a tacit agreement.  (This concern somehow completely evaporates when it comes to assigning homework.)
  • Duh, class is when things happen?  (i.e. inertia)
  • I don’t know.

Not particularly compelling.  So I’m going to try to this out.  I’ll work out a master schedule with my students for when and where they can take quizzes outside of class.  We’ll see what they do with it.

In the past, I’ve had a day in class each week where quizzes were taken for the first part of the period and free-choice time happened for the second part.  What I’m planning on doing this year is making that whole day free-choice.  If some students choose to use that time for taking solo-and-silent assessments, that’s fine by me—I’ll have the quizzes ready and on offer.  If they calculate that quizzing is a good use their in-class time on a particular day, then it’s the right move for them.  Super.  But I have to imagine that many students will find it more choice-worthy to use classtime in other ways to further their learning and cultivate their experiences—and to find time outside of class to quiz, at least on occasion.

These thoughts have arisen for me as I’ve slipped deeper and deeper into a combination of the SBG Borg and SteveMiranda/PaulSalomon-esque personalization.  There may be other influences, and I don’t claim that these ideas are original.  They were perhaps first instigated in my head last year when I had seventh graders showing up in my room for the last fifteen minutes of lunch on Fridays.  They wanted to start working on their quizzes early so that they could have more free-choice time with their friends.  They were giving up the freedom of recess in exchange for more free-choice time in class.  I think that’s a huge testimony to how much value and fun can be created by the combination of choice and a rich classroom environment.

I’ve read about others’ efforts at arranging times outside of class for requizzing, and I appreciate how difficult and time-consuming it can be.  I have no illusions that it will be easy to encourage outside-of-class quizzing and recognize both logistical and hearts-and-minds obstacles.  But I really want to push this in my classes, plant the seed in my students’ heads, and see what happens.  Maybe you’ve tried something similar; if so, I’d love to hear.  I’ll certainly be posting about what comes of my attempts.  Maybe—just maybe—this will help my students to become more wily, irreverent, and pushy, and used to being in charge of their own learning and time.

PS  Speaking of that itchy feeling, classes started today!  Ahhhhhhhhh…

A (Partial) Solution to the Feedback Swamp

October is when the quicksand hits.  I’m up to my knees in student work and am starting to feel serious pangs of conscience for not being able to give every scrap of paper the care and attention that children and young adults deserve.  So I hold onto the work, thinking that I’ll be able to properly process it soon enough.

There’s no way that’s going to happen.  There are how many of them and one of me?  They can produce far faster than I can respond.  I can try to expand the audience for their work–with peer review and even more daring ideas like student blogging that I haven’t tried out yet–but I still feel this intense obligation to give them personal, thoughtful feedback myself.  So their classwork and write-ups and reading logs pile up, and soon enough I’m in over my head.

Every year I struggle with this.  Every August I prepare a new plan to combat it.  I’ve racked my brain trying to find the solution.

Sometimes when you’re so deep into struggling with something, you have to hear a fresh perspective more than once for it to stick.

I read this post by Steve Miranda the other day about his experiences trying to give thoughtful feedback to his English students.  Amazing stuff.  I recognized myself in his frustration with students who do not seem to appreciate the labor of commenting, and I loved both his experiment and his ability to understand the logic of his students’ motivations.  But no lightbulb went off in my head just then.

The next day I was in the park re-reading The Open Classroom by Herbert R. Kohl.  I first read it after my first year of teaching, and it had been calling out to me from my shelf at the beginning of the summer.  I came across this passage toward the end, in a section entitled On Correcting:

“It is not a matter of whether one corrects a student’s paper so much as a question of when and how.  Students produce some papers that they care about and others that they would just as soon forget.  In school, teachers have a tendency to consider all the work of a student on the same level.  Everything a student does is supposed to be a finished product.  There is little allowance for hesitant beginnings, false starts, bad ideas, impossible dreams–all the explorations writers attempt before finding their own voices and the forms appropriate to expressing them.  They are expected to be perfect every time.  In my experience when students produce a work they care about they want it to be correct in every way–that is, to communicate as fully as possible.  They ask for corrections and want to get things right” (p. 111).

Whoa.  Students can decide what matters to them, and they can tell me about it.

Steve’s post warmed me up for this thought, and Herbert Kohl’s paragraph drove it home.  I’ve held the conscious belief for a few years now that it’s more important that my students do good work than it is for me to know about it.  I don’t think it has affected my behavior nearly enough.  What I need to know about my students’ work is whatever allows me to assemble good future tasks for them that will meet them where they are.  That, whatever information I need to be able to write fair and descriptive end-of-term reports.  If my attention to my students’ work isn’t serving those two purposes, and if my feedback isn’t particularly desired by a student on a particular piece of work, then I am wasting my attention and time.   If my efforts to interpret and respond aren’t shaping my lesson plans, giving me something to say about the kid come report time, or helping me to build up a relationship with the student around a piece of work, then it’s just ornamental–a mental game that I’m playing alone and with no real-world consequences.  I’m just writing comments for myself.

I don’t want to do that.

So I’m going to start asking my students what kind of feedback they want from me, and when.

I’m going to stop treating every slightly-mashed worksheet as though it’s an exotic flower with mysteries in the offing.  These products of student thinking and work are entirely secondary to the thinking process they engaged in.  Most of what was going to happen for them has happened already.  There’s no point to autopsies for worksheets.  The kid is still alive and kicking.  The question is less, “what happened here?” and more, “what can I do to shape what happens next?”

Finally, I’m going to trust my students more–trust that if I show my willingness to give them attention and advice, celebration and critique, that they’ll seek it out.

I’ll let you know what that looks like in practice.  Check back in October.

Free-Choice Time: Gearing Up

Finding the balance of freedom and structure that is good for kids—who are of course all different from each other—is hard.  Still, I know that giving my students a fair shake at some real autonomy is a principle that I’m willing to work for and stand by.  My dear friend and colleague Paul Salomon and I collaborated last year on making free-choice time happen for our middle schoolers.  For me, this meant that every Friday, my sixth and seventh graders would take their SBG skills quizzes; after finishing these, they were free to pursue whatever they pleased.

Inspired by my mom, I distributed a bingo grid of different activities at the beginning of the year to encourage my kids to dig into a variety of tasks.  It looked like this:

last year's bingo board

(BTdubs, Bloxorz was a huge hit.  You should definitely give it a whirl.)

I thought I would roll out other boards as the year progressed.  I didn’t.  The school year, as school years are wont to do, took on a crazy, unkempt life of its own.  While I introduced a few new activities to my classes over the course of the year, the activities that I put on offer at the beginning were basically the ones that students worked on.  In addition, I never got around to providing the resources for students to actually do some of the activities, so this cut down on their options even more.

To better serve our soon-to-arrive new batch of students, Paul and I are aiming to improve upon our last year’s attempts to provide students with structure and rich resources during their free-choice time.  This year I’m giving out a board that has categories of activities, rather than individual things to do.  Like so:

free-choice bingo board

Really broad stuff, plus a center square that rivals in making the sky the limit.  To accompany the board will be a list of some possible activities for them to pursue:

Those are the ones that I’ve penciled in for the start of the year.  The full brainstormed list currently stands as follows:

…although that will probably be out of date as soon as I publish this post.  Over the course of the year, the list of pursuits that my students will have in hand will expand to include more items from this larger list.  I’m planning to limit the options at the start for a few reasons.  First, I didn’t want all of the possibilities to overwhelm kids.  Second, for some of the activities on the full list, I want to have the chance to introduce the activity in a whole-class setting—for instance, to have a day or two where we talk about cellular automata, run some by hand, and take a look at the Game of Life.  Finally, I figure for the sake of diversity, it won’t hurt to put off the unveiling of Bloxorz for a little while.

An important part of my plan to make free-choice time an opportunity for my students to grow is to have them record and reflect upon the progress they make on their free-choice projects, as well as to help them to set goals for themselves.  Students will be able to write their goals into their bingo grid, and they’ll also have opportunities to goal-set and reflect in their journals.  By design, the items in the list above aren’t very specific.  Yes, here is a Rubik’s Cube.  But what’s your goal?  Try to figure out how to solve it on your own?  Watch some videos online and try to internalize some algorithms?  Solve a cube in under five minutes?  Take one apart?  Only you can decide.   My thought is that putting this decision down in writing–even if it will change a few days from now–can give kids more empowered visions of themselves and of mathematics.  That’s what I’m betting on, anyway.

I’ll have a poster-sized copy of the bingo board on the wall of my classroom.  When a kid completes a goal in one of the categories, she’ll get to write her name into that square on the poster.  She’ll also get to share her accomplishment with her classmates, either by announcing it, making a presentation, or displaying it in the room.

It may feel to you—I know it does to me—that in my description of this supposedly free-choice time, I’m emphasizing structure over freedom.  My excuse is that I don’t have live, kicking, and wooly fifth graders to share this stuff with yet, to run rampant in my classroom and test and break and remold my structures—until they aren’t really even structures any more, but rather the culture of our classroom.  Right now, the build-up of thoughts and hopes just lies in potentia, waiting to go live and spring forth.  I can’t wait to share with you the awesome things my students do!

There’s a lot of good stuff on that list of activities, and I’m excited to uncover, stumble across, and get suggestions for even more.  And I feel that the list is not only good, but that it includes things that often have no place in our mathematics classrooms.  And so if I may…

<ascends soapbox>

We as teachers, by the tasks and opportunities we provide in our classrooms, define what mathematics is to our students.  If we don’t model activities like reading books about math, creating mathematical games, or communicating with “outside” people who are interested in math, then our students may never encounter these activities.  And to me, that’s a lot scarier than a kid missing out on any particular fact, theorem, or skill.

<descends soapbox>

To conclude, let me say that I’m working to find ways of incorporating more free-choice time into my high school courses, but this is a challenge.  While I’ve made room for choice in my high school courses, free-choice feels more difficult.  In the usual mold, middle school is more student-centered, while high school is more content-centered.  Still, just typing this out has got me thinking about how I might construct a similar board for my high schoolers to encourage them to try out different kinds of tasks over the course of the year in a non-deadline way.  Stay tuned for that, and for lots of sharing of how free-choice goes down with my fifthies!

At the moment, though, I would love to hear your suggestions for pursuits for my middle schoolers to take on.  Help that list grow!