The learning to learn series continues this week as I taught my students about metacognition. Below are the notes from lesson plan.
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When we give students the space to create their own meanings and understandings, marvelous things happen. Her is a problem on a recent problem set: Find an example of an equilateral hexagon whose sides are sqrt(13) units long. Give the coordinates for all for all six points. In class we looked at three different solutions strategies...
1. Start at point (a,b) and count "over 2, up 3" to find the next point. At some point we needed to a horizontal translation of sqrt(13) to get to the next point. As a result, the points were in radical form. 2. Start at point (a,b) and assume the hexagon is regular and the side relationship of a 30-60-90 triangle to find the sides. Again the points are in radical form. 3. One student wanted integer coordinates. We had previously talked about lattice points. After some experimentation with "horizontal 2, vertical 3" and/or "vertical 2 horizontal 3" on GeoGebra they found a solution that was not convex! Recently, a student visiting our school was sitting in my class. After the usual introductions, I turned to the class and said, "Can somebody explain how this class operates?" Quickly, a student spoke up and said, "We do math and then talk about it" This is the first time I've heard them say this so succinctly and I like it because, from their perspective, it's exactly what we do. I used to be really good at lecturing. I worked on the craft, orchestrated illuminating examples, dialed my questioning, wait time, and board work. I worked hard to help my students understand. "If you can't explain it simply, you don't understand it enough." -Albert Einstein But, the better I got at delivering a clear and logical lecture, my students didn't seem to be making the same gains in understanding. My teaching schedule usually had me teaching two sections of the same class so I could deliver the same lecture twice a day. Often, there was enough overlap in our curriculum that I would teach a different class in the next semester that covered the same topic. So, it was entirely possible that I could teach the same lesson four times a year. But the students didn't seem to be learning the material any better as I further nailed the lesson. Something was missing.
While I was perfecting my lessons, teaching strategies, and board work, I realized that I was constructing and refining my own understanding of the material and then forcing my students to understand it my way. No wonder they didn't learn learn better. They weren't constructing their own understanding of the material, they were trying to figure out mine. For some, it must have been like fitting a square peg in a round hole. Fast forward several years and now I'm using problem based instruction to promote classroom discussion. Instead of showing students how I organize and make sense of the material, they are encouraged to make their own mental representations and connections. The primary vehicle to do this is through carefully designed problem sets that first tap into their previous knowledge, then introduce new material, and finally extend or challenge their understanding. The key is to offer a just enough of a challenge so students have a chance to explore and investigate a problem before hearing explicit instructions on a possible solution. Ideally, there are multiple ways to solve the problems and this is what enriches the discussion. Students present their solutions and strategies to the class and a discussion ensues. During class discussion, as a teacher, I'm on alert to dispel misconceptions but mostly I'm trying to understand their point of view and how to develop it further. Student to student conversation is encouraged and is usually where the magic happens. Often I find that many of the conversations around problems start outside of class and then continue when the problem is presented. As a result, students are usually well versed in the details of the problem and often simply want a nudge in the right direction. When I lectured, it got to the point where I felt like I was the main character in a sit-com and the students were watching me on TV. My lessons and presentations got to be so polished that there were times I could look out over my class and see the same passive faces they make when watching TV. Something wasn't working...well actually I was working and they were not. Problem based instruction and discussion changed all that for me. This is a follow up to a previous blog post entitled, "Competency Based Learning Core Elements", which focused on what it should look like in the classroom. This post focuses on what it should look like at the school level. The list below is liberally taking from this article.
We have been discussing the ideas behind growth mindset and deliberate practice in class all semester. One of my students pointed out that nearly all the examples discussed have been learning a physical activity or skill. The connection between learning a physical skill, like shooting free throws, and learning calculus concepts is vague at best. So the next series of film festivals will be to address what deliberate practice looks like in an academic setting. In particular, we will be looking at 1) metacognition, 2) interleaving, 3) spaced practice, and 4) retrieval practices.
All the film festivals I've showed by class has focused on learning a physical skill. My students are starting to wonder, "what does this have to do with learning math?" So they are now primed to see how class is structured for learning.
Our learning model is built off the learning model proposed by Anders Ericsson in his book Peak: Secrets from the New Science of Expertise. In particular, we focus in using deliberate practice to create mental representations. Here is how we do it. This is my follow up to our first film festival, Growth Mindset. The theme in the following four short clips is intended to raise a students awareness to what happens in the brain when you learn a skill. Students have all heard of muscle memory so this adds a little more background knowledge. We had a really good discussion when I asked students why the feel rusty when they put skis on for the first time each winter. Collecting student feedback on classroom culture and their learning experience has been difficult. For a long time the format was lots of questions that students answer by checking a box rating from 1-5. Lately I've been using just three short answer questions:
We have been using the following as the core elements to build a competency based learning model.
At the beginning of the year, in an attempt to set the classroom culture, I try to get students talking about three questions...
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Author"Your only as good as your record collection." -DJ Spooky Archives
September 2020
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