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dy/dan Toggle navigation Search About Starter Pack Archives Three-Act Math Subscribe Join 30K+ other people in receiving Dan's monthly updates on innovations, ideas, and news in math education. FYI By Dan Meyer • June 13, 2021 • 6 Comments All my action is over at Substack for now. uncategorized Area Man Who Talks a Lot About Teaching Teaches His First Full Day in 10 Years By Dan Meyer • October 7, 2021 • 12 Comments I have taught demo and observational classes regularly since I left full-time teaching but yesterday was the first time I taught every class for the day. Leaving myself some quick notesimpressions. The setup. I taught four classes of students in three different rooms. Plug. Unplug. Plug. Unplug. Plug. Unplug. This works for me. I am the Mirrorworld Sarah Carter with how little attention I generally pay to the physical environment of the classroom. Another growth area for me, but great for modular subbing. Teaching is tiring. The pace doesn’t quit. I brought a thermos of coffee with me and brought every drop of it home. I also forgot that you absolutely abuse your vocal cords for the first few days of teaching. Then they realize you’re seriously going to talk this much throughout the day. They relent, and you’re set. Wearing masks all day. The best of a bunch of bad options, I guess, but I didn’t like it! Beyond the discomfort, they really shrink down the non-verbal communication channels. Hard to get a vibe check on anybody! It was also hard to hear and understand quieter students. Prep time. I have taught three courses before and never loved the prep time that schedule required. Up until the day I left the classroom, I spent multiple hours outside of class every day creating materials and planning lessons for the next day. Not to plug our curriculum too hard here, but it was unreal how it let me spend so little time planning for subbing overall and how I was able to spend the majority of that time thinking about facilitating the lesson and all the ways students would develop their ideas about math throughout— teaching in a word! Whether or not it’s our curriculum, I don’t know, but every teacher deserves that kind of experience IMO. Interacting with the youth. From my notes: How is everything I’m saying an innuendo somehow?” Is there some kind of almanac I can use to keep myself up to date here or something? What our plan for AirPods, please? Or even corded headphones? Music in class? Are we just going with this? One ear only? Only during classwork? Is this one of those battles we just aren’t picking these days? I love the energy of a school. Love it. Where else can you find so many different people all growing so dramatically in every conceivable way? Where else do you get to work with such a huge cross-section of society as your peers in a hierarchy that’s nearly flat, everyone relying on one another in crucial ways, but also accountable and trusted individually with their own pieces of the overall mission. Next time. My interest in subbing divided into roughly 25% field-testing our program, 25% giving some local teacher friends a break, and 50% because teaching is unique among all other jobs I have ever had. It’s only in teaching that someone with my particular interests and aptitudes has the chance to help people understand their immense value and power in a moment (being a teenager) where they are very actively sorting out the question What is my value?” in a context (math class) where they often feel like the answer is not much.” In just one day, so many students communicated to me that they aren’t any good at math and they were absolutely incorrect every time. You don’t know how to calculate the angles in that diagram? Fine—but which ones look the same? See—your eyes are mathematically smart. That’s smart.” Or You don’t know the scale factor. Fine—but what’s it between? Between 2 and 3? How’d you know that? Okay let’s call it two-ish for now. That’s good math.” There’s so much I don’t know how to do in this world, but I know how to do that . I have only ever created human connections of that sort in math classrooms. Nowhere else. For now, I’m happy I get to create tools and experiences that help other teachers create those connections. But I think I know what I was made to do and it isn’t obvious to me how long I’ll be able to go on not doing that. classroomaction Computer Feedback That Helps Kids Learn About Math and About Themselves By Dan Meyer • December 15, 2020 • 16 Comments Students are receiving more feedback from computers this year than ever before. What does that feedback look like, and what does it teach students about mathematics and about themselves as mathematicians? Here is a question we might ask math students: what is this coordinate? Let’s say a student types in (5, 4), a very thoughtful wrong answer. ( Wrong and brilliant ,” one might say.) Here are several ways a computer might react to that wrong answer. 1. You’re wrong.” This is the most common way computers respond to a student’s idea. But (5, 4) receives the same feedback as answers like (1000, 1000) or idk,” even though (5, 4) arguably involves a lot more thought from the student and a lot more of their sense of themselves as a mathematician. This feedback says all of those ideas are the same kind of wrong. 2. You’re wrong, but it’s okay.” The shortcoming of evaluative feedback (these binary judgments of right” and wrong”) isn’t just that it isn’t nice enough or that it neglects a student’s emotional state. It’s that it doesn’t attach enough meaning to the student’s thinking . The prime directive of feedback is, per Dylan Wiliam, to cause more thinking.” Evaluative feedback fails that directive because it doesn’t attach sufficient meaning to a student’s thought to cause more thinking. 3. You’re wrong, and here’s why.” It’s tempting to write down a list of all possible reasons a student might have given different wrong answers, and then respond to each one conditionally. For example here, we might program the computer to say, Did you switch your coordinates?” Certainly, this makes an attempt at attaching meaning to a student’s thinking that the other examples so far have not. But the meaning is often an expert’s meaning and attaches only loosely to the novice’s. The student may have to work as hard to understand the feedback (the word coordinate” may be new, for example) as to use it. 4. Let me see if I understand you here.” Alternately, we can ask computers to clear their throats a bit and say, Let me see if I understand you here. Is this what you meant?” We make no assumption that the student understands what the problem is asking, or that we understand why the student gave their answer. We just attach as much meaning as we can to the student’s thinking in a world that’s familiar to them. How can I attach more meaning to a student’s thought?” This animation, for example, attaches the fact that the relationship to the origin has horizontal and vertical components. We trust students to make sense of what they’re seeing. Then we give them an an opportunity to use that new sense to try again. This interpretive” feedback is the kind we use most frequently in our Desmos curriculum , and it’s often easier to build than the evaluative feedback, which requires images, conditionality, and more programming. Honestly, programming” isn’t even the right word to describe what we’re doing here. We’re building worlds . I’m not overstating the matter. Educators build worlds in the same way that game developers and storytellers build worlds. That world here is called the coordinate plane,” a world we built in a computer. But even more often, the world we build is a physical or a video classroom, and the question, How can I attach more meaning to a student’s thought?” is a great question in each of those worlds. Whenever you receive a student’s thought and tell them what interests you about it, or what it makes you wonder, or you ask...