I think a good principle you're getting at here is to avoid broad labels (guided inquiry, explicit teaching) and to be specific about the practices we find helpful in classrooms. I think in many cases two people who use the same label often disagree on many details, and two people who use different labels agree on many details.
Agreed. The lack of precision is a problem, and also the lack of context. Different lessons can have different goals even if at first sight they look like they are about the same thing.
Does learning through struggle last longer over time? Does learning through appropriate struggle lead to deeper understanding? In that case, a little bit of struggle may make a difference in performance. I find rote learning has a half life — knowledge gained that way decays. Knowledge gained through connections seems more robust.
It seems the struggle part is what gets glorified and focused on. I think that's what a lot of teachers have a problem with when being evaluated or observed by their administrators.
If concepts are just "mental connections among mathematical facts, procedures, and ideas", then most concepts can be understood via direct instruction by the teacher and will be much faster when done so.
Thinking about biology and taxonomy, the concept of animal doesn't really need a lot of struggle for a high school student to understand. You can make connections between dozens of animal and non-animal examples and leave with a fairly solid concept of animal. There are probably a few edge case examples that are worth examining. Those examples probably blur animal as a concept a bit, which is great to push understanding further, but may or may not be entirely necessary for a high school level of understanding.
With 80 plus standards in a high school math class, the question becomes where to spend time and where to save time. Many concepts do not need elaborate discussions or struggle and students would learn more over a semester if direct instruction were used over letting them figure out it themselves. There is no bonus points for extra struggle.
We see this in sports all the time where performance matters. No one cares whether an Olympic athlete uses a coach to tell them exactly what to do in training or wastes years tinkering with training themselves to figure it all out on their own. The athlete doesn't get a "Gold Medal Plus" for being self coached, the outcome is the same and they just get a Gold Medal.
Analogously, in California, teachers are judged on test scores via CAASPP and entire schools are likewise judged by the test scores. There are no bonus points for how much students struggle or even how much they learn, just how they perform.
I really liked this post and agreed with so much of it, but the issue I have is that I have district and school administrators who read it and will then focus on the struggle part. They will expect to see students having discussions and struggling when they walk in. However, I will continue to be judged on the D and F rate of students in my classes and the CAASPP scores of our students. When that is how I am judged, I need to focus not on what they learn, but what they can perform on a test. The goal isn't learning, it's performance.
Hi Brian, I think you are right about people, particularly administrators, focusing too much on the struggle and forgetting the productive part. That's what Hiebert and Grouws' definition is meant to guard against: effort to make sense of mathematics, yes, but also problems within reach.
I'm not sure I agree with the Olympic analogy. I think it argues for Hiebert and Grouws rather than against. Coaches give athletes training exercises at the edge of their abilities. But you are right that there is no Gold Medal Plus for pointless struggle.
As for "the goal isn't learning, it's performance," I wish I had something helpful to say, but I don't. You are doing good work in an important profession and deserve better.
I think a good principle you're getting at here is to avoid broad labels (guided inquiry, explicit teaching) and to be specific about the practices we find helpful in classrooms. I think in many cases two people who use the same label often disagree on many details, and two people who use different labels agree on many details.
Agreed. The lack of precision is a problem, and also the lack of context. Different lessons can have different goals even if at first sight they look like they are about the same thing.
Does learning through struggle last longer over time? Does learning through appropriate struggle lead to deeper understanding? In that case, a little bit of struggle may make a difference in performance. I find rote learning has a half life — knowledge gained that way decays. Knowledge gained through connections seems more robust.
Yeah, that’s how I read what Hiebert and Grouws are saying.
It seems the struggle part is what gets glorified and focused on. I think that's what a lot of teachers have a problem with when being evaluated or observed by their administrators.
If concepts are just "mental connections among mathematical facts, procedures, and ideas", then most concepts can be understood via direct instruction by the teacher and will be much faster when done so.
Thinking about biology and taxonomy, the concept of animal doesn't really need a lot of struggle for a high school student to understand. You can make connections between dozens of animal and non-animal examples and leave with a fairly solid concept of animal. There are probably a few edge case examples that are worth examining. Those examples probably blur animal as a concept a bit, which is great to push understanding further, but may or may not be entirely necessary for a high school level of understanding.
With 80 plus standards in a high school math class, the question becomes where to spend time and where to save time. Many concepts do not need elaborate discussions or struggle and students would learn more over a semester if direct instruction were used over letting them figure out it themselves. There is no bonus points for extra struggle.
We see this in sports all the time where performance matters. No one cares whether an Olympic athlete uses a coach to tell them exactly what to do in training or wastes years tinkering with training themselves to figure it all out on their own. The athlete doesn't get a "Gold Medal Plus" for being self coached, the outcome is the same and they just get a Gold Medal.
Analogously, in California, teachers are judged on test scores via CAASPP and entire schools are likewise judged by the test scores. There are no bonus points for how much students struggle or even how much they learn, just how they perform.
I really liked this post and agreed with so much of it, but the issue I have is that I have district and school administrators who read it and will then focus on the struggle part. They will expect to see students having discussions and struggling when they walk in. However, I will continue to be judged on the D and F rate of students in my classes and the CAASPP scores of our students. When that is how I am judged, I need to focus not on what they learn, but what they can perform on a test. The goal isn't learning, it's performance.
Hi Brian, I think you are right about people, particularly administrators, focusing too much on the struggle and forgetting the productive part. That's what Hiebert and Grouws' definition is meant to guard against: effort to make sense of mathematics, yes, but also problems within reach.
I'm not sure I agree with the Olympic analogy. I think it argues for Hiebert and Grouws rather than against. Coaches give athletes training exercises at the edge of their abilities. But you are right that there is no Gold Medal Plus for pointless struggle.
As for "the goal isn't learning, it's performance," I wish I had something helpful to say, but I don't. You are doing good work in an important profession and deserve better.