“It’s a fun unit, but it’s not really necessary.”

A colleague of mine made this statement to me a few weeks ago, and it’s been rolling around in my head ever since. In many ways, this summarizes so much of the system right now, both that is good and that is bad, depending on how you read this statement. And that’s just it, there are different ways to understand what she was saying when she made this statement. In the course of this discussion, my colleague was describing a unit that she was going to do that was about shopping and decimals, and that while the unit was ‘fun’, the work that was related to decimals (the content standard that she was going to teach), was not really that necessary. After all, no one gets out paper and adds up decimals at the grocery store as they are shopping. Her comment, then, was that while she thought the context of the unit was fun, the actual point of it was not really that necessary. And isn’t this true of so much of what we do? We plan units and activities around learning that is not really that necessary or relevant any longer, because it’s what’s we’ve always done, or we need to have them take a test on something, or the textbook says they should learn this skill. How much of the planning that we do is actually for things that are not necessary? And do we even have the right to deem something not necessary? I mean, we are employed by, ultimately, our districts, and/or our ministries of education. They are paying us to teach the curriculum. Do I have the right to determine what parts of the curriculum I teach and what parts that I don’t?

Of course, there is another side to this statement. One can argue for cases where we are engaging our students in learning that is just that, engaging and empowering, and yet, potentially unnecessary. One might look at a period spent learning how to do do KenKen or Yoharu or Wordle as being fun, but unnecessary. But, perhaps it is those things that ARE necessary….more so that some of the other content standards our textbooks or curriculum documents seem to dictate. This is the challenge that we face often times — what’s necessary isn’t fun, what’s fun isn’t necessary…..and I mean, is fun really the point? I don’t actually think it is. Fun isn’t our goal. Empowering is our goal; fun might be a side effect of that.

I see both sides of this statement. When she first uttered it, I said to her: You’ve just summarized the state of the whole education system right there. While I now see the second side, I’m stuck ruminating about the first side of this statement. I believe much of what we are doing in school is irrelevant. There. I said it. Most of the content that I spend my time teaching? Do I really need to? I think that the honest answer to “When am I going to use this?” is never. Most of the time the answer is that, this content? you’re not. School has to move away from being about the content. Students can access content at any time now. It’s not about that content anymore; it’s got to be about what to do WITH that content, with that information, with that problem, that challenge, that unknown. That is what we need to be spending our time focused on. I’m not sure if that is the fun side or the necessary side, or maybe it’s neither. I think we need to be on the empowering side, and that means letting go of so many things. Even those lovely binders of page-protected lesson plans so carefully curated. Even those.

Radically reimagining my classroom

I have this dream. In this dream, my learners enter the room, gather materials they need and make a plan for the learning time. They set about the learning tasks that are assigned, as well as learning of their own choosing. Students work at the pace that they feel is most efficient for them. And what do I do? I coach. I help reflect. I provide feedback and assessment as needed and at just the right time. The lines between subjects becomes blurred as students work on different tasks based on what they have decided their day will look like. At various points in time, there might be a whole class discussion, or lesson, or a small group or a one on one lesson, based on the needs of the learners. In other words, the learners lead the way and set the tone for the day. There is structure for those who need it, and flexibility for those who need it. I am a learner within the community, as well as coach and mentor. This is my dream.

It’s winter break right now, and it’s always a time for deep reflection for me. January, although technically midway through a term for my learners, is always a time for a fresh start for the classroom. It’s a time to think about what is working and what is not working. It’s a time for trying new things and this year, I have a big dream that I want to tackle. I want to reimagine my whole classroom. It’s physical set up, and it’s theoretical and pedagogical set up. In short, I want to put my dream into motion. I’m not quite sure how to do it, but I know the features that I want it to have:

  1. De-fronted. Seats are facing all the different directions of the compass point.
  2. Thinking, thinking, thinking — mostly by the students, and sometimes by myself, as a model for students.
  3. Opportunities for creativity within all learning areas.
  4. Opportunities for curiosity. — lots of questions being asked, and some of them being answered.
  5. A combination of learner-directed and whole class learning, as needed.
  6. Small groups that form organically based on student need and interest.
  7. Appearance of messiness. But only because learning materials are out, being used and engaged with.
  8. Kind chaos — discussion and debate, questioning, proving, justifying happening all around.

How do I do this? It’s a totally different set up from what is currently happening. There are lots of things happening in my room that I like, but as I reflect on it, it’s still very teacher directed, and I want it to be much more student directed. I have this word ‘module’ floating around in my head, as if I could maybe set up modules of learning that students progress through, but that they can also adapt to their own interests and learning styles. There is a lot that would go into this, I realize. But change never happens unless something changes. I want change to happen. I think we’re ready for it. This could all be moot, of course. I could be reimagining my classroom in an entirely different way in three weeks. But the truth of the matter is this: We should all be ready and thinking about reimagining our classrooms all the time. We teach humans. And humans change. They grow. They develop. They become different people. And our classrooms should reflect that difference. My students are not the same people they were in September. They are different people now, and they need different things. I can’t just teach them as if they were the same people. I don’t know exactly how this will go. But that is the nature of teaching. We never really know how any day will go. But we do need to be open to it, to change, to disruption, to growth.

Reflecting on Rubrics

I’ve been known to enjoy a good rubric. I have, at times, enjoyed writing them. I have, at times, felt that they were helpful tools to provide feedback to my students. And I have, at times, shared examples of them with my colleagues in the hopes that they might provide some encouragement to reflect on their assessment practices. Lately though, I’ve been reflecting on rubrics in other ways. Is is possible that rubrics cause harm to students? One of the things I’ve liked about rubrics in the past is that they help the students to know what my look-fors are in an assignment or learning task. Without them, it seems that students are being asked to read my mind. I think the majority of assessments are built on this notion — that students need to have memorized what’s in the teacher’s head with respect to what the particular answer is.

In the end, I don’t think rubrics are really the problem, although they can be, certainly, problematic. I think the real issue when we really boil it down is that rubrics, and all the other tools we use are still a part of an assessment practice that is outdated, and harmful for students and student learning. In other words, it’s not the rubric that is really the issue, it’s the grading in general. It’s the grading that takes the humanity out of learning. Ultimately, we are still required to give grades, even though many of us believe that grading is not in our students’ best interest, and we feel we must be objective in some fashion while assigning these grades. Hence, rubrics. We use rubrics as the stop-gap to help us work within the system we find ourselves in. But what does this accomplish? Is using a rubric similar to being a bystander to a bully? Are we continuing to support the system if we use grading tools that we know support the ideals of a system we don’t really believe in? The question we’re left with is: how do we work within the system we find ourselves in in a way that starts to dissolve the very system we must be in? This, ultimately, is our desire; to so fully work against this system that it starts to break down and change is forced to arrive. Because arrive it must. We can no longer be silent about it. Yes, it’s the way it’s always been, and it’s the way it will stay unless we speak up. And we can speak up by radically changing our assessment practices. Not sure where to start: well, one place is the pick up the book Ungrading, edited by Susan D. Blum. It’s a collection of essays all about the process of ungrading. (In a few weeks, my book, Unschooled, which is about the very same thing, will be out as well. ). It’s time to start the breaking down of the system. Nothing will change if nothing changes.

Woes and Worksheets


Direct Teaching.

Practice Questions.

Do Nows.

I’m reflecting on my teaching over the past few days, and it’s been characterized by a lot of things I don’t really like. Not that it’s been bad — my classes have been quiet and focused and participated in the tasks that I have asked them to do. We’re working on fractions, and decimals, and I’ve found myself standing at the front of the room talking, writing notes and passing out worksheets. My students have completed the worksheets, and then handed them in. I looked at them, and passed them back out to them. Today, as I sat looking through the stack of papers from today’s class, I realized that although my students had all completed the work, I wasn’t convinced that any learning had happened. (Now, I know that there are effective ways to use worksheets; my usage today isn’t one of them, I don’t think). They completed the worksheets, but didn’t build their understanding, what they built was their compliance and memorization of what I told them to do. I can tell this because looking through their answers I know they were just going through the motions.

There are effective ways to use direct teaching; and I know that there is a time and place for this in the mathematics classroom. My issue with what has happened in my classroom is that I didn’t choose to intentionally use direct instruction and a worksheet; it was just…..easy. It was what is expected by my students, even now, three months into the school year. It was familiar to them, and they just slid into that without even blinking. No one questioned that I was giving them a worksheet. I think maybe that is what hurt my heart the most. After trying to establish this entirely different mathematics community, I slid into what was comfortable and no one was surprised. No one complained even, they just did it.

It feels like a rut. It feels like I’m getting away from myself and what I believe in. And I’m not quite sure how to get back there. What do I do with all these completed worksheets that really have no purpose? They don’t tell my students anything particularly useful, nor do they tell me anything I need. Really, they should probably just get recycled; but how do I tell that to my students? I’m not sure where I’m going with this post, just putting my discontent out into the writing void. I’m discouraged, but that doesn’t mean I’m done or that I’m giving in and giving up. I will continue to work towards a culture that is based on curious and creative conjecturers. I just need to find my way back there. My students deserve it, and so do fractions.

The Textbook Paradox

I don’t believe that math textbooks are inherently bad on their own. I do think that the way they have been used has significantly contributed to the trauma that many students feel with respect to their math education. I know my current group of students mostly loathe the math textbook, and therefore feel that they also loathe math. So something happens when I pull out the textbook — they almost have a visible reaction to it, even just seeing it sitting on their desk.

97% of the time (yes, I just made that statistic up, but it’s pretty close), all of the math work that my students are engaged in is not directly connected to the textbook, to a notebook or to a traditional I do, we do, you do lesson. We engage in problems, practice different steps, work collaboratively, and keep track of a lot of rough draft thinking and conversation. Recently, though, I’ve started wondering if there is a way I can also have my students engage in the literacy of the math textbook in a fruitful manner. The two times we have used the textbook this year have been two of the most frustrating classes of the year. There are two things that I see happening during these times. 1. It’s almost like their thinking brain shuts off and they have all these questions about the content I’m asking them about that they hadn’t had when we were not using the textbook. 2. They have no idea how to use the textbook, so it’s not a tool that is helpful to them. So here is where my struggle begins. Is there a way to use the textbook that still engages their thinking brains, and in a way that they can develop their textbook literacy skills? Do they even need textbook literacy skills? I know that they have used textbooks in prior grades. Most of the work that gets turned into me that is a textbook exercise does nothing to really show me what they know — is there a way to develop that that doesn’t involve my classroom just becoming a room full of compliant automatons? I remember using the textbook, and taking notes in a notebook and it was all about following the format of the teacher. Even if they did that, it wouldn’t really show me that much learning. I often wonder, am I doing my students a disservice by not developing that skill for them? Do they need it?

There are so many questions here that I”m wrestling with, and maybe it’s simply that I’m wrestling with wondering about my approach, which I believe in, compared to that of those around me. So yes, my students will probably never be literate math textbook users….will they be upset with me in the years to come because of this? I don’t know. I want to hope that I will have shown them a different way; maybe a better way. It’s certainly a different way. I don’t want to become a classroom that is known for compliance. I want it to be known as a place of creativity, curiosity and conjecturing. (Shameless plug for my next book…..). Does the textbook have a role in that classroom?

Unpopular opinion: Let’s stop with the Long Division already.

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When I saw Long Division being discussed on my Twitter feed, I decided it was time for another instalment in my unpopular opinion blog series. Of all the topics I was taught in school, long division might have been the most mind boggling one to me. All the, “okay how many times does this go into this? Okay, now subtract, and now we bring down the 4…..” What? Bring down the 4? Where are we bringing it down from? Why? Oh, and don’t forget the bringing down the 0, and then just adding it and subtracting it and don’t even get me started on remainders. I spent a lot of time doing worksheets of myriad long division problems and can’t for the life of me figure out why. It literally did nothing for my understanding of mathematics. All it really did was make me hate math more. Long division is one of those things that teachers used to tell me that I needed to learn because “I wasn’t going to carry a calculator around in my pocket”. Granted, I didn’t start carrying a calculator around in my pocket until I was a teacher, but still. I didn’t do any long division in high school, or university, and I studied science. In fact, the only time I have done long division since I did it in school was to help my daughter do long division on her homework.

To this day, I’m not sure why we devote so much time to long division. I have encountered students who have told me that they aren’t good at math because they can’t do long division. It seems to hold the same amount of ‘awe and wonder’ as the memorization of times tables. By the time kids get to me in Grade 7, they seem to have internalized that to be good at math you need to : have your times tables memorized, be able to do long division, and solve word problems. That’s the holy grail of being good at math in elementary school. Good grief. No wonder kids have lost of the joy and wonder of mathematics by the time they get to upper elementary. They usually have had it sucked out of them by repeated practice of these things. Now, okay. I’m not saying that I don’t want kids to be able to understand division. And I’m not saying that word problems aren’t important (well, maybe I am….I think we use word problems in the wrong way most of the time…but that’s another instalment in the unpopular opinions series). And I”m not saying I don’t want kids to know their math facts. Automaticity is important. Understanding division is important. Problem Solving is important. But we spend so much time on teaching kids to be compliant by following a set of steps that have been pre-determined that we actually are missing out on helping our students learn about what division actually is. The forest for the trees analogy, if you will.

What would happen if we didn’t start with the standard algorithm for division? What if we let kids kind of puzzle their way through figuring out what 654 divided by 12 is? What might we discover about our mathematics learners? What might they learn about strategies, perseverance and efficiency? What if we introduced the standard algorithm for long division LAST and present it as option, as a tool for efficiency, rather than a set in stone, you must do this, requirement? And what if we spent less time on this over and over again, letting it be part of a bigger picture of the landscape of mathematics? How might our students’ perspectives change? How might ours? What might we have time for if we let this go? What are you willing to give up in order to find or restore joy to your classroom?

1/4 and other fractional mysteries

One of my favourite activities to do with my students when we first start fraction work is Quarter The Cross. It’s a great activity to really get at fractional understanding of the whole, and causes a lot of stretching and growth as students realize that the cross is made up of 5 identical boxes, and that they can’t simply colour in one of the five boxes. This happens inevitably for at least one or two students each year and then they have the light bulb moment when I ask them what the ‘whole’ is constructed from. For the past two years though, this activity has lead to a similarly frustrating conversation: “What’s 1/4 mean?”, I’ll ask a student who seems to be stuck on colouring in 1/5 boxes. And then I get back: ” I don’t know. I don’t know what 1/4 means”. Today, the student who stated this had successfully participated in some fraction talks at the beginning of the class, identifying parts and wholes in other pictures. And yet, still struggled when asked to explain or describe what 1/4 meant. Last year, when I had the same conversation with a different student, I learned that that particular student thought that 1/4 simply referred to any small piece of something. In both cases, I had students coming to me with a very large misunderstanding or misconception or missing information about what a fraction is. The thing is, in grade 7, rarely do we ask questions of that nature. Unless you’re doing Quarter the Cross, you’re probably not asking Grade 7 students to define 1/4; we assume that at this time in their journey, students know what 1/4 means. And so we carry on with our lessons about adding and subtracting fractions with like denominators and unlike denominators, and wonder why they aren’t getting it.

Fractions is one of the concepts that seems to frustrate students the most, and it’s no wonder. We press on with fractional operations, teaching algorithms and procedures without knowing that our students are coming to us without an understanding of what a fraction is. Every year I wonder, where is it that things go off the rails with fractions? Is it that we go too fast through the introduction? That we don’t spend enough time with concrete materials? That we spend too much time with concrete materials and not enough time looking at symbolic representations? My gut says we spend too much time on the symbolic representation and not enough time working with concrete representations and making solid connections. Somewhere on the landscape of fractions, we are losing kids and they never really get their feet back under them, and they press on and try to memorize what steps to go through to end the torture.

Fractions don’t need to be torture; but they do need time. They need crockpot learning — slow and steady and incremental learning to ensure a solid conceptual understanding before we introduce symbolic procedures.Otherwise we have kids just ‘doing math’ without actually learning math.

I don’t understand, but I think I’ll get there.

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This was a statement one of my students made while working with another student on a factoring puzzle. They were working together on a strategy, and after one student explained his thinking, the other said, “I don’t understand, but I think I’ll get there” and continued on exploring the strategy to solve the puzzle.

I love everything about this.

I think we need to normalize this kind of statement in classrooms all over the world, in every subject, but particularly mathematics. Growth mindset is baked into this, perseverance is present, and collaboration at it’s finest is on display. I wish all of us were able to be this honest with our peers — to admit that you don’t understand something, but that you think you’ll get it soon if you keep working — this is what learning really is all about. We need to encourage this honesty, this openness, in our staffrooms, in our classrooms, in our hallways, in our professional learning, in our team meetings. This is how we grow. This is how we develop our humans into the kind of humans we all hope for and that the world desperately needs.

I actually wrote down this statement in my day planner after I heard it. I plan to write it on a sticky note to post on my desk, both to remember that it happened, but also as a reminder to continue to work towards honest and open reflection and learning in the classroom.

I told my kids they could learn about whatever they wanted today; here’s what happened.

So, I’ve played around with Genius Hour and Passion Projects before in my program, and I confess, I didn’t love them. They felt….disconnected. Like a thing I was doing on the side and not something that was truly a part of my classroom culture. Some kids bought it, but some of them didn’t, especially when they found out how many strings were attached. aka what assignments they had to do as part of it. But I have become more and more convinced of the need to empower my students to have agency over what they are learning, even in my middle school classroom of grade 7s. (I think even in younger classes too….). I have long had a vision of students simply entering the room, picking up their learning, and going about it, collaborating where needed, conferencing where needed, sharing when ready. As if they are all individual learners with individual needs and ideas and wants and strengths and challenges…..oh wait. They are. But even though we know this, we continue to use a one-size-fits-all to education, and wonder why it doesn’t work for all of them. So, today, I told them that we were launching The Learning Project. Time, long chunks of it, where they could decide what they wanted to learn about, and go about learning it. There wasn’t a handout. There wasn’t an assignment to look at; there was me saying, “I want you to learn about things that you are interested in, that you care about, that you are good at, that you want to learn more about. I’m going to give you time and space to do that. And then, later on, we’ll talk about it. If you want to present it, you can. If you don’t want to, then you’ll just share with me. ” And then, they went about it. They each opened a notebook full of blank pages, and after a few prompts, decided what they wanted to learn about. Every kid had something they wanted to learn about without my helping or giving them ideas. Some of them knew almost instantaneously and couldn’t wait to tell me what they were going to learn about. They spent 2 hours in total, just…..learning. And sharing things with me that they’d found. And sharing with a friend when they wanted to. And then going back to learning. Some kids drew sketches. Some made notes. Some watched instructional videos. Every kid was engaged and, I dare say, each felt empowered.

As a tag on to this, I asked my students to respond to a Jamboard prompt, “In Math…. In Science…. In Social Studies…..and In ELA….” where they shared their ideas about what we should learn and how it should look. I told them whatever they wrote there, I’d take seriously, so to make serious contributions. Turns out, for example, my class is very divided about tests; some want them, some want never to see a test again. So I told them that tests would be options, that there would be a test option as an assessment that students could choose from to show me their learning. I wish I had a camera to capture the looks on their faces. The amount I learned from my students as part of this — about what they want, what they are interested in, what their ideas are….it’s invaluable. I wish I had started doing this earlier in my career. I wish I could bottle the feeling of peace and productivity in the room today. The reluctance of my students to stop was palpable — and now my challenge will be to weave this into everything we do, this empowered learning, because I’m not sure I could go back to any other way.

What’s really at the heart of the times tables debate.

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I memorized my times tables. Well, mostly. I memorized the columns and rows by chanting them over and over, with my class, and on my own. It was a rote practice. And I was assessed on how well I knew them using a timed test. Generally that timed test was a filling in of the same patterns I’d memorized, so this was okay. I could just fill in the numbers some what mindlessly, that is, if my brain wasn’t paralyzed by the thought of a timed test. Because often what happened was my brain got all confused and stressed out in these situations and I did poorly, forgetting the patterns, or going too slowly for the amount of time I was given.

Understanding multiplication and the relationships between numbers is important.

Automaticity is important. Fluency is important.

None of those things are the same as rote memorization of facts. Often rote memorization is a crutch we lean on — we say, just memorize these so you can get to the next thing. And kids do. Or they try to. And then they ‘get by’, like I did. I got by. I went to university and did math as part of my biology degree. But I didn’t truly understanding multiplicative relationships until about 10 years ago when I learned my primes, and finally understood that standard algorithm I’d memorized about a million years ago.

But the real core of this conversation is assessment. The how and they why. We assess kids understanding of multiplication with times tables — what kind of feedback does this assessment provide? Are we assessing in a manner that leads to growth? Or is our assessment static? Are we assessing in a manner that promotes fluency and an understanding of patterns and relationships? Or are we listing 50 facts and asking students to fill them in? What message are we sending our students about assessment when we test them on times tables? And why the emphasis here? We are so focused on math facts as the holy grail here — there is so much more to mathematics than times tables and multiplication. YES, knowing facts is helpful as it opens up space in our brains for later learning. But KNOWING a CONCEPT, really knowing it, takes up way less space in our brains than a memorized table. Understanding a concept allows us to use our brain like a zip drive — it zips away and then when we need it, we can expand it out and build from there. Memorization leads to a big filing cabinet of information we need to rifle through to find stuff.

So, it’s not really about memorization or not. It’s about pedagogy and we can’t truly change our pedagogy until we have addressed the most foundational part of our pedagogy: WHAT WE BELIEVE ABOUT ASSESSMENT. We have to start talking about assessment more openly and honestly. The conversation is beginning to start, but I fear that it will miss the mathematics world for far too long. In general, we hold our assessment cards close to our chest, wanting to trust in it’s numbers and percentages. But what we believe about those numbers influences everything we do, and way too often those numbers are for us, and not our students.

It’s time to start changing this narrative. It’s time to change the narrative around times tables, and tests, and memorization and understanding. It’s time to change to a narrative of growth and learning and falling and getting back up again and really allowing all our learners into the rich world of mathematics.