I appreciate this post! Teaching calculus to Harvard students is definitely a niche experience at one end of the education-privilege spectrum. Did you have similar teaching experiences in other contexts? I'm wondering how big of a role the context plays in determining what works.
I've taught at the university level all my career, Harvard, UC Berkeley, and the University of Arizona, from college algebra to graduate courses, including some teacher preparation courses. Harvard was not as niche as you might think; students in calculus have the same problems everywhere.
I do worry that there's a false dichotomy here. If you're comparing to lectures, then absolutely problem-based learning will win by a large margin. I'd be curious for your take on something like Rosenshine's principles: https://www.aft.org/sites/default/files/Rosenshine.pdf
(By the way, I'm not making the argument that "research shows Rosenshine's principles are great. There are plenty of flaws in the research base here. I'm trying to articulate what a serious pedagogy looks like between lecture and problem-based learning.)
If you look at the principles you will see: not very much emphasis on explanation and a large emphasis on active student participation and checking for understanding. Both of those lean more toward problem-based learning than lecture. You will also see an emphasis on providing models, guiding practice, small steps -- things that may or may not be present in problem-based learning depending on the instantiation. I think the emphasis on a high success rate is maybe the thing most different from problem-based learning?
Hi Dylan, I absolutely agree there is a false dichotomy here. I've lived on and appreciated both sides of it. I wanted to tell the story of how I ended up where I did. I've been planning to get to Rosenshine's principles at some point, so thanks for bringing them up. They represent a coherent approach to teaching and as you point out there is a lot of overlap in the elements, although the details of how they are laid out and executed are probably different. Having a coherent approach is better than not having one, and there is more than one coherent approach out there. I would never tell a teacher who has found one that works to change it because of a philosophical stance. My main goal in the last few posts (and one more coming on Friday) has been to get people to stop saying "the research says" when it either doesn't, or says something much narrower than claimed. You could equally well do that on the discovery learning side . . . there's plenty of thin research there too.
I am wondering about the high success rate. Are we aiming for it right away? And could that cut short important paths to learning? You are right that that could be an important point of difference. Something to think about in a future post.
Thanks, Bill! If you haven't heard it yet, this podcast features Steven Strogatz discussing his math teaching philosophy, I found him to be up there with best Maths teachers I've had, definitely worth a listen- https://freakonomics.com/podcast/steven-strogatz-thinks-you-dont-know-what-math-is/
I appreciate this post! Teaching calculus to Harvard students is definitely a niche experience at one end of the education-privilege spectrum. Did you have similar teaching experiences in other contexts? I'm wondering how big of a role the context plays in determining what works.
I've taught at the university level all my career, Harvard, UC Berkeley, and the University of Arizona, from college algebra to graduate courses, including some teacher preparation courses. Harvard was not as niche as you might think; students in calculus have the same problems everywhere.
You’re right - being a brilliant lecturer is isn’t enough. Students don’t care how much you know until they know how much you care.
I do worry that there's a false dichotomy here. If you're comparing to lectures, then absolutely problem-based learning will win by a large margin. I'd be curious for your take on something like Rosenshine's principles: https://www.aft.org/sites/default/files/Rosenshine.pdf
(By the way, I'm not making the argument that "research shows Rosenshine's principles are great. There are plenty of flaws in the research base here. I'm trying to articulate what a serious pedagogy looks like between lecture and problem-based learning.)
If you look at the principles you will see: not very much emphasis on explanation and a large emphasis on active student participation and checking for understanding. Both of those lean more toward problem-based learning than lecture. You will also see an emphasis on providing models, guiding practice, small steps -- things that may or may not be present in problem-based learning depending on the instantiation. I think the emphasis on a high success rate is maybe the thing most different from problem-based learning?
Hi Dylan, I absolutely agree there is a false dichotomy here. I've lived on and appreciated both sides of it. I wanted to tell the story of how I ended up where I did. I've been planning to get to Rosenshine's principles at some point, so thanks for bringing them up. They represent a coherent approach to teaching and as you point out there is a lot of overlap in the elements, although the details of how they are laid out and executed are probably different. Having a coherent approach is better than not having one, and there is more than one coherent approach out there. I would never tell a teacher who has found one that works to change it because of a philosophical stance. My main goal in the last few posts (and one more coming on Friday) has been to get people to stop saying "the research says" when it either doesn't, or says something much narrower than claimed. You could equally well do that on the discovery learning side . . . there's plenty of thin research there too.
I am wondering about the high success rate. Are we aiming for it right away? And could that cut short important paths to learning? You are right that that could be an important point of difference. Something to think about in a future post.