Really interesting post! I think your AI baseball example really sells the difference between adding context and adding experience to a problem. It's not enough to just put words and a story to an example, it also has to share some space in the experience of students, which is often what's missing from these recontexualized examples we give. I am curious, what would you suggest should be the work we do to find these shared experiences? Obviously, taking your entire math class to a baseball game to have that experience is costly, time consuming, and risks missing the point (even if it might be a fun time), but just stating "It's like how a baseball flies through the air" doesn't really cut it either. How can you create these experiences in a practical way? Is it just gauging your classroom and seeing what the culture of your students is like, or do you have to create an in classroom experience, such as with the example where you have to guess if the circle does cover an x intercept, doesn't cover an x intercept, or might cover an x intercept?
"do you have to create an in classroom experience"
Bingo IMO. If you ask ten people what the best thing digital media has done for classroom learning, you'll get lots of different answers. Mine would be that digital media lets you create more of those shared classroom experiences.
I love this post, and I believe we as teachers sometimes only get halfway to fixing the problem:
The problem: By relying on our own experience, we suffer from "The Curse of Knowledge." (https://en.wikipedia.org/wiki/Curse_of_knowledge#cite_note-10) This causes blind spots that make it hard to truly know what our students (mis)conceptions are from their perspective.
The halfway fix: Trying to correct these "curse of knowledge" gaps, we seek to infuse lesson plans with examples or analogies that "are relevant" to our students. Hey, my students like ______, so let me connect this to ______. While this is a step in the right direction, I think this is still an artificial attempt at the "shared experience" that you cite from Schwartz and Bransford.
The "best" fix: This is why I always loved using 3-Act tasks--they allow me to participate in a story with my students thereby creating a shared experience that leads towards mathematical discovery.
The idea of creating shared experiences seems like a great way to build a rapport with your students while also getting them engaged in mathematics in ways that they can relate to with you. I would love to hear more about how you have utilized 3-act tasks in your classroom. I have only looked into them a little bit and would love to hear how your students responded when you first started using them versus how they respond to them now.
Click on the tab "Dan Meyer's Three-ACt Math Tasks." They have labels by standard and grade (i.e. "6.RP" = 6th grade ratios and proportions)
A couple of things I learned over the years that helped implementation:
1. I started using a "See, Think, Wonder" or "Notice and Wonder" talk routine whenever I'd start with a picture or video. Students would jot down their thoughts and share out. This helped focus discussion and the "Wonder" part led us towards the question(s) we wanted to explore/answer.
2. When I learned about the work of Peter Liljedahl and Vertical Non-Permanent Surfaces (VNPS), I started using these almost every time students worked on a 3-Act Task.
The best advice I can give: Just try one. Experimentation and risk taking is as much a teacher's job as it is a student's job. If it doesn't go perfectly, just reflect and adjust. You will love teaching this way, and your students will love it even more.
So much to contemplate in the Bball video. Enjoyable! Going to have to have another dozen listens to get past the mesmerizing bball lingo. đŸ˜‚
Also, as an aside, I literally just worked through that fabulous IVT activity 15 min before this post dropped in my inbox. I’ll be using it (adjusted with edits) on Fri and my fav slide is the ‘surprise’ where the continuity requirement is made real to students. So good!
I may even cite your kid example to my class before we get started. đŸ˜‚
I had an interesting chat with chatgpt discussing the role of description vs explanation. The context was why heavier objecf fall at the same rate as light ones in vacuum. It became clear to me that unless the user asks the right prompting questions it does not provide explanation.
Given that students being students may not know enough to ask the right question I don't see how it can be effective at helping students learn
Really interesting post! I think your AI baseball example really sells the difference between adding context and adding experience to a problem. It's not enough to just put words and a story to an example, it also has to share some space in the experience of students, which is often what's missing from these recontexualized examples we give. I am curious, what would you suggest should be the work we do to find these shared experiences? Obviously, taking your entire math class to a baseball game to have that experience is costly, time consuming, and risks missing the point (even if it might be a fun time), but just stating "It's like how a baseball flies through the air" doesn't really cut it either. How can you create these experiences in a practical way? Is it just gauging your classroom and seeing what the culture of your students is like, or do you have to create an in classroom experience, such as with the example where you have to guess if the circle does cover an x intercept, doesn't cover an x intercept, or might cover an x intercept?
"do you have to create an in classroom experience"
Bingo IMO. If you ask ten people what the best thing digital media has done for classroom learning, you'll get lots of different answers. Mine would be that digital media lets you create more of those shared classroom experiences.
I love this post, and I believe we as teachers sometimes only get halfway to fixing the problem:
The problem: By relying on our own experience, we suffer from "The Curse of Knowledge." (https://en.wikipedia.org/wiki/Curse_of_knowledge#cite_note-10) This causes blind spots that make it hard to truly know what our students (mis)conceptions are from their perspective.
The halfway fix: Trying to correct these "curse of knowledge" gaps, we seek to infuse lesson plans with examples or analogies that "are relevant" to our students. Hey, my students like ______, so let me connect this to ______. While this is a step in the right direction, I think this is still an artificial attempt at the "shared experience" that you cite from Schwartz and Bransford.
The "best" fix: This is why I always loved using 3-Act tasks--they allow me to participate in a story with my students thereby creating a shared experience that leads towards mathematical discovery.
The idea of creating shared experiences seems like a great way to build a rapport with your students while also getting them engaged in mathematics in ways that they can relate to with you. I would love to hear more about how you have utilized 3-act tasks in your classroom. I have only looked into them a little bit and would love to hear how your students responded when you first started using them versus how they respond to them now.
I used them about once every week or two. The best way to prepare is to do the task yourself and ask the following:
How might my students solve it?
Where might they get stuck?
How can I ask questions to keep their thinking going without doing the heavy lifting for them?
The first tasks I used came from this shared "Live Binder": https://www.livebinders.com/play/play_or_edit?id=330579
Click on the tab "Dan Meyer's Three-ACt Math Tasks." They have labels by standard and grade (i.e. "6.RP" = 6th grade ratios and proportions)
A couple of things I learned over the years that helped implementation:
1. I started using a "See, Think, Wonder" or "Notice and Wonder" talk routine whenever I'd start with a picture or video. Students would jot down their thoughts and share out. This helped focus discussion and the "Wonder" part led us towards the question(s) we wanted to explore/answer.
2. When I learned about the work of Peter Liljedahl and Vertical Non-Permanent Surfaces (VNPS), I started using these almost every time students worked on a 3-Act Task.
The best advice I can give: Just try one. Experimentation and risk taking is as much a teacher's job as it is a student's job. If it doesn't go perfectly, just reflect and adjust. You will love teaching this way, and your students will love it even more.
So much to contemplate in the Bball video. Enjoyable! Going to have to have another dozen listens to get past the mesmerizing bball lingo. đŸ˜‚
Also, as an aside, I literally just worked through that fabulous IVT activity 15 min before this post dropped in my inbox. I’ll be using it (adjusted with edits) on Fri and my fav slide is the ‘surprise’ where the continuity requirement is made real to students. So good!
I may even cite your kid example to my class before we get started. đŸ˜‚
I had an interesting chat with chatgpt discussing the role of description vs explanation. The context was why heavier objecf fall at the same rate as light ones in vacuum. It became clear to me that unless the user asks the right prompting questions it does not provide explanation.
Given that students being students may not know enough to ask the right question I don't see how it can be effective at helping students learn
Just a thought
Best
Joe