After a rough start to Building A Thinking Classroom in Mathematics for the first time this year, things have really been rolling for several months now. The increases I've seen in student engagement, perseverance, long-term memory, cooperation, leadership, vocabulary, general comfort and happiness, and even standardized test scores have far exceeded what I expected in my first half-year of implementation. It is very hard work, but it is really worth it. For most of the good run I've had over the last few months, I catch myself almost every day thinking, I can't believe this works. This past week, however, I caught myself telling myself something slightly different. I can't believe this works with all three classes. As they always are, my three classes this year are very different. Personality, cohesiveness, energy level, motivation level... it's all different from one class period to the next. But a thinking classroom has immensely benefited all three. Here's why I think so. Class #1 - The PleasersMy first class is every teacher's dream. The first thing you'd notice about them if you visited is that they absolutely love each other. Visibly random groups help everybody get to know each other quickly, and this group is the poster child for that benefit. They adore each other. Seriously. One day recently, they spontaneously formed a welcome tunnel at the door to make everyone feel great when they got to school. All on their own. Academically, they're pleasers. Pleasers are generally very rewarding to teach. They are sweet. They are adorable. They are thoughtful. They are conscientious.
With such great classroom habits, many pleasers are highly successful students, but others use teacher-pleasing as a means to mask real struggles in math. That's the case with a good chunk of this class. So, why does Building A Thinking Classroom in Mathematics benefit the pleasers? Because disincentivizing "studenting" is what the program was designed to do in the first place. In this year's Thinking Classroom, this group of delightful kids has very few opportunities to please me through studenting. Most of the time, I'm not even around for them to please! The only way to please me is by thinking during tasks, thinking during note-making, and thinking during check-your-understanding questions. So they do. Class #2 - Big Energy, Small Attention SpanClass #2 is all enthusiasm. They have a lot of energy, and quite a few of them are "math kids" in that I like to be right and I like to be done kind of way. Quite a few of them are also math kids in that math is my best subject because it doesn't take the same extended concentration as analyzing a text kind of way. In short, they are my big energy, small attention span class. If you've had a class like this, they can be miserable to teach traditionally, even when they're strong academically (as this group is). A bunch of them can't sit still. A bunch of them zone out the second they sit down for a lesson. They just want to get to the answer. And so on. So, why does Building A Thinking Classroom benefit a big energy, small attention span class?
They could be the poster class for Building A Thinking Classroom, though. Class #3 - Anyone? Anyone?Actual footage of my trying to teach my third class traditionally. My third class is mostly made up of two kinds of kids: the unmotivated, and the motivated-but-painfully-quiet. It is as though the universe refuses to allow a single joule of energy into the room when they're with me. Everyone in the room just wants to get to the end of day either unbothered or unnoticed. Ask a question - there will be no hands. Make a joke - there will be no laughter. Read the room - there will be no feedback. Anybody? Anybody? So why does a Thinking Classroom benefit this energy vortex of a class?
But in a Thinking Classroom, there's no sitting and waiting to be done. Literally. As Liljedahl teaches us in the book, standing makes the kids feel visible, so hiding to "wait it out" isn't an option. All of their tactics are in plain sight. I'll be visiting their group every few minutes. There is nowhere to hide. What about the motivated-but-painfully-quiet bunch? The main threat to this group is that, in normal circumstances, they won't ask questions, won't ask for help, and won't give me any indication when they're struggling. In fact, they can be tough to distinguish from the unmotivated because their affect in class is so similar. But in a Thinking Classroom, they don't have to. I'll visit their group every few minutes, and I'll see if they're struggling. The impetus isn't on them to speak up or start the conversation. This way, their misunderstandings get noticed and addressed without their having to ask. And That's Everybody!And voila! It appears to me that, albeit for different reasons, a Building A Thinking Classroom in Mathematics has (greatly) benefited all three groups of kids, different as they may be. All three groups would have presented me with significant challenges last year. Instead, we've been on a roll for months. I can't believe this works for three such different groups of kids! If you enjoyed this post, please share it! Want to read more right now? You're in luck - this is my 79th post! You can browse past posts by category:
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What a moment I had in class this week. We were doing a bit of recall practice ahead of the day's thinking task, and I had posed this question: Why would the following question be considered a "spicy" ratio question - If the arcade basketball guy makes 15 shots every 6 seconds, how many shots can we expect him to make in 10 seconds? Quite a few hands went up, and I got the following response from the student who answered: "Since 10 isn't a multiple of 6, we would need to go to a lower term ratio or to the unit rate instead of just skipping straight to the answer." And the whole room nodded in agreement without hesitating. I would consider that student's response to be not only accurate, but worded using exact academic vocabulary (multiple, lower term ratio, unit rate) with extreme fluency. I would also consider a room full of students decoding that response and agreeing with it in a matter of seconds - months separated from last having worked on that concept - to be a minor miracle.
Prior to Building A Thinking Classroom, I was a big proponent of explicit front-loading of vocabulary and conventions in my lessons. In direct instruction situations, I still believe that's the way to go. "Here are the vocabulary words and conventions you're likely to see in the upcoming lesson, and here's what they mean or how they work." Sometimes those vocabulary and conventions were new ones, and sometimes they were old ones that I wanted to bring back to mind. But either way, students do best when those are presented ahead of time. Obviously, in a Thinking Classroom, these can't be front-loaded. If, as Liljedahl so eloquently explains, "thinking is what you do when you don't know what to do," then any front-loading prior to a thinking task reduces thinking, which we don't want. The kids have to make their own sense of everything - including vocabulary - in the thinking tasks for maximum effectiveness. Oh, how easy it is to teach vocabulary and conventions after thinking task, however. Here's an example. To introduce my students to the concept of percent ratios they worked on this thin-sliced thinking task using ratio problem-solving skills they had already developed prior. You'll notice that the word "percent" appears nowhere in this thinking task. The kids worked with the concept of a percentage, but not the word itself. As you might imagine, already having good mastery of ratio problems, this thinking task hardly required thinking at all. It was simply a bunch of ratio questions where, curiously, the "whole" in the ratio was always 100. When we got to consolidation, all I had to do was name what they'd already figured out.
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The holidays marked the end of my first semester of Building A Thinking Classroom in Mathematics. Looking back through my list of posts from that time, it was mostly struggle for the first six weeks, then pretty smooth sailing for the next 12 weeks, with a lot of rapid learning on my part. One of the things I've been dying to see over that time was whether or not all the obvious benefits of the Building Thinking Classroom practices would translate into the currency of our educational time - test scores. I teach in a very, very large school district, which means my students take standardized final exams in every subject at the end of each semester. These are tests that cover the standards the district prescribes for the first half of the year, and tests that I can't see ahead of time. They are pretty important for the kids and for me. The results are used, in part, to determine what math course opportunities the students get for the following year, they count as a decent chunk of their final grade, and they're analyzed heavily by my school and district leaders to evaluate how I'm doing as a teacher, too. So, did Building Thinking Classrooms deliver 'hard' results to support the 'soft' benefits visible in the classroom every day? It did. Maybe a little, maybe a lot, depending on how you look at it. Looking at the overall results and knowing very precisely how my students have typically done on these tests in the past, my best guess is that this group of students would have averaged a score in the low-80's if I had taught them the way I used to. I have a lot of data collected from a lot of years with a lot of groups of students, and I feel pretty confident this prediction. So how did they fare? They averaged a shade under 89%. Looking at it one way, that's a modest improvement of maybe 7-9 points in the average score. Looking at it another way, it's a massive improvement, nearly cutting in half the percent of the questions the students missed (from 20-ish% to only 10-ish%). Improving test scores isn't everyone's goal, I know. If you've spent any time in a Thinking Classroom, the portfolio of benefits is obvious. It transforms kids in ways that are impossible not to notice. But at least where I work, test scores talk, and I personally value them as evidence of the work I'm doing, too. Either way, the early results are in, and they're better! If you enjoyed this post, please share it! Want to read more right now? You're in luck - this is my 77th post! You can browse past posts by category
In Building Thinking Classrooms in Mathematics, author Peter Liljedahl differentiates between two types of thinking task in which to engage students - curricular tasks and non-curricular tasks. Non-curricular tasks, as the name implies, are tasks that, while qualitative and mathematical in nature, don't directly address specific learning goals for students. They are intended, rather, to capture students' attention, to broadly grow their interest in mathematics, and to serve as tasks through which we can teach them how to think and how to engage in a thinking classroom productively. Liljedahl recommends card tricks, numeracy tasks, and "good problems" for these types of tasks. I've had good luck with all of these, as well as with Ted Ed riddles. My students love all of these!
As I keep experimenting as I try to build my own Thinking Classroom in Mathematics this year, I've found that mastering thinking tasks is the highest leverage practice in the program; the gap between getting these right and getting these wrong is much bigger than it is for any other practice. While I've made breakthrough improvements with random grouping, note-making, and consolidation this year, those improvements have been more icing than cake. There were times I paused doing some of those altogether while I tried to master other practices, and we still made good progress.
In my half year of learning and experimenting, I've found myself using the two types of thinking tasks in six different ways. In the space below, I'll explain what they are, when I use them, and how I create them. 1. Culture-Setting Non-Curricular Tasks
When do I use them? I used these for the first four days of school, right in line with the advice from the book. On day one (literally the first day of middle school for my kids), I did a card trick. The kids liked it and worked decently well at it, but expected me to just give them the answer before class ended, which of course I didn't in order to establish the importance of the thinking we would be doing, so we also worked on this card trick on day 2. On day 3, I did one of the numeracy tasks on Liljedah's website. It was a blast! On day 4, another card trick, and this time, if the groups didn't figure it out, they just didn't get an answer and I told them to either keep working on it or to find another group to explain it to them. They were four great days! How do I plan them? I don't. They all come from Liljedah's website catalog. 2. Problem-Solving Curricular TasksWhat are they? Problem-solving curricular tasks involve some kind of engaging prompt or situation that can be solved using on-grade-level math. They often come from 3-act tasks, YouCubed, and other such sources that were making these types of "math worth doing" tasks before Building Thinking Classrooms came into the picture. In podcasts and webinars, I often here Liljedahl reference a task like this involving stacking books on a desk to teach linear equations, which sounds like a terrific example. The key features of these tasks are that 1) they involve some sort of graphic, video, live prompt, or other tangible, engaging "hook," and 2) they have a solution. When do I use them? I think it is important to use these at the beginning of a topic of study to "launch" the topic. For example, I used several 3-act tasks on ratios (this one, this one, and this one) to introduce the concept of a ratio before students had learned anything about ratios. Because of that timing - giving these tasks before any content-specific learning has taken place - these tasks feel like non-curricular tasks to my students.
3. Figure-It-Out Thin-Sliced Curricular TasksWhat are they? These are the bread-and-butter curricular tasks that Liljedahl gives a fabulous example of on page 161. In this type of task, you remind students of a type of problem they can already solve, then challenge them to extend that knowledge to solve a new, related type of problem. I've already written a whole post on this type of task, so I'll send you there for more details (or to page 161 in the book. Or page 27). When do I use them? ALL THE TIME. These are far and away the most common type of task I schedule. In fact, my ability to schedule these is a sign that I'm planning well - if I am, then most days within a topic of study should build off the prior day in a way students can discover on their own, meaning a well sequenced unit of study should have long stretches of days with this type of task.
4. Introduce the Minimum, Then Thin-Slice To THe Maximum Curricular TasksWhat are they? There are certain topics where I can't reasonably expect students to figure it out on their own, but I can reasonably expect students to take the briefest possible example and run with it. Take, for example, changing between fractions, decimals, and percentages. I had only a day to address this, and this is a topic that I really need them to understand in a very certain, conceptual way. My chances of having them figure this out on their own in just a day are slim, and my chances of having them figure it out the way I need them to understand it are basically zero. For tasks like these, I do a very, very short introduction to the concept or procedure with the mildest possible example, then let them run with it through thin-slicing. They get the basic idea from me, but then they have to make sense of it on their own and thin-slice their way through more advanced versions of the skill. I introduce the minimum. They thin-slice their way to the maximum. For the fractions-decimals-percentages topic I referenced above, here's a recording of our class that day. What you'll see is, with just four or five minutes of "kickstarter" questions, I introduce them to the idea that fractions, decimals, and percentages are all ways of representing the same concept, and that with some basic thinking, we can interchange between which representation we use using nothing more than our knowledge of conventions. It isn't much, but it is just enough to get them thinking about the concept the way I need them to with basic examples. If it helps, here are the slides the kids see on the screen and here is the task they move into afterward, where they take the very basic introduction I offered and extend it into more and more challenging examples.
How do I plan them? The planning for these is the same as the other thin-sliced thinking tasks (see #3). The only difference is that I plan the additional, brief introduction to the topic to help get the thinking started in the direction I need it to go. 5. Non-Curricular Task + Direct InstructionWhat are they? There are days when I simply need to teach something directly, but I don't want to have a day go by without a thinking task, so I just schedule a non-curricular task beforehand. This way, at least, I get the energy level up and get the kids' brains turned on before the direct instruction begins. When do I use them? The only days where I've used this format this year are those when I need to teach vocabulary or conventions - days when there isn't anything to "figure out." The only two days I could find where I did so were:
6. Test-Day Non-Curricular TasksWhat are they? Just like I plan non-curricular thinking tasks to energize the kids ahead of direct instruction, I do the same on test days. Non-curricular tasks get them up, awake, and engaged before sitting down to dig into a test. They also give the kids something to keep thinking about if they finish their test early.
How do I plan them? I choose a non-curriuclar task from Liljedah's website, or I use a Ted-Ed riddle (my kids love these!), then we test.
Happy Holidays!If you enjoyed this post, please share it! Want to read more right now? You're in luck - this is my 76th post! You can browse past posts by category
In my gradual journey toward a Thinking Mathematics Classroom this year, one of the most rewarding aspects has been that thinking begets more thinking.
With each successive element of class transitioning from passive receiving to active thinking, it becomes more and more painfully evident when there is an element of class that does not involve thinking. The entire energy in the room is different. I have almost no ability to hold the kids' attention anymore when we transition into something passive. They turn completely off when a portion of class is not a thinking experience. The kids no longer seem to consider me to be a source from which learning might come. "Oh, he's talking now. This clearly isn't important. If it were, WE would be talking." As I've referenced before, one of the class activities where I've yet to completely transition to the Building Thinking Classrooms practice is consolidation. It's an intimidating one, and I've heard several interviews with Peter Liljedahl where he says that it is the practice he gets the most questions about. There are definitely days where I do my best with this part of the class, but it becomes very clear that we've entered not-thinking territory and the kids are tuned out, waiting to reboot their thinking when note-making begins. One of the ways I routinely stop the thinking is when I start the consolidation process by referring to our unit success criteria after the thinking task. Keeping these front-and-center is a priority for me and for my school, so I make an effort to point out which success criteria were addressed in the recently completed task so that the kids can see where they fit into the broader unit. It's fine, but the kids are generally tuned out, mindlessly checking off whatever I tell them to.
Far and away - my best consolidation yet. If you'd care to see, I've included some (not great) video of the consolidation below.
At least for me, this is orders of magnitude more thinking than I typically get during a consolidation, so it is a big step forward! I do a lot of thin-slice thinking tasks, and I see a lot of potential for this to become a reliable consolidation formula:
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About MeI'm an award-winning teacher in the Atlanta area with experience teaching at every level from elementary school to college. Categories |