"What I love to do is to teach teachers. I love to stir up their thoughts about how they learn; about how on earth anyone can help anyone else learn; and about what it means to know something. I love to help them feel that any aspect of human endeavor is accessible to them and that they can make it accessible to any person they teach. I love to try to find ways into a subject that will catch everybody's interest; to find out what people think about things and to find ways to get them talking about what they think; to shake up things they thought they once knew; to get people wrapped up in figuring something out together without needing anything from me; to help build their fascination with what everybody else thinks, and with the light that other people's thinking might shed on their own. I love to see the most productive of questions be born out of laughter, and the most frustrating of brick walls give way to an idea that has been there all along."
Showing posts with label teachers. Show all posts
Showing posts with label teachers. Show all posts
Tuesday, May 10, 2011
Eleanor Duckworth is a Poet
I read this over and over, and then over and over. It is the first Paragraph from "Teaching as Research" by Eleanor Duckworth in "The having of wonderful ideas"
Tuesday, May 3, 2011
Facilitating Discussion with Peer Instruction
Here are two trappings I've seen recently:
#1: Validating the right answer the moment you hear it, thereby short-circuiting any dialogue about the problem.
Recently, I heard a college instructor say, "I agree with you," anytime a student said something correct, and "Are there any other ideas?" anytime a student said something incorrect. My sense was that the phrases "I agree with you," and "Are there any other ideas?" were honest attempts by the instructor NOT to say "That's correct" and "That's incorrect". I caught on to this pattern of talk quickly, and I imagined students would catch on within a few days or weeks.
#2: Requesting that a nearly correct student "say more" in a manner that implies, "Could you please restate what you said using the correct terminology?" rather than, "I'm really interested in your idea, please say more about that?"
This can be subtle, as it often has to do with tone of voice, body language, and subtle phrasings. When an instructor does this, however it really gums up the dialogue. Because students pick up on the fact that it's not about their ideas, this kind talk quickly descends into a game of "the teacher is thinking of a number between 0 and 100." Students either start opting out or just trying to guess what the instructor wants them to say.
The Big Picture
Facilitating discussions is hard work. In my mind, the number one priority is getting students to invite me in to their learning through their talk. Largely, this means that they are sharing their ideas and thinking, not trying to guess what's in my mind or avoid being wrong. When I see instructors falling into these kinds of traps, I see this priority being undermined.
Some people might think the solution to trap #1 is to have a better poker face–don't have any "tells" that give away the right answer. I think that approach is flawed because it's trying to stop the symptom, but not the cause. I don't need a poker face if I am not listening to student ideas primarily through a lens of correct and incorrect.
Some people might think the solution to trap #2 is to not care about terminology. While that's possible, I don't think it's realistic. I think the solution is to distinguish the activities of "shopping for ideas" and "connecting with disciplinary formalism". The problem is in trying to do both at the same time and in the same way.
I certainly enjoy watching other people teach, because it gives me an opportunity to reflect on my own teaching. There are times when I "gum up the dialogue" and focus on correctness when I shouldn't. Sometimes by watching others, I understand better why we all fall into these traps and what impact it can have on students.
#1: Validating the right answer the moment you hear it, thereby short-circuiting any dialogue about the problem.
Recently, I heard a college instructor say, "I agree with you," anytime a student said something correct, and "Are there any other ideas?" anytime a student said something incorrect. My sense was that the phrases "I agree with you," and "Are there any other ideas?" were honest attempts by the instructor NOT to say "That's correct" and "That's incorrect". I caught on to this pattern of talk quickly, and I imagined students would catch on within a few days or weeks.
#2: Requesting that a nearly correct student "say more" in a manner that implies, "Could you please restate what you said using the correct terminology?" rather than, "I'm really interested in your idea, please say more about that?"
This can be subtle, as it often has to do with tone of voice, body language, and subtle phrasings. When an instructor does this, however it really gums up the dialogue. Because students pick up on the fact that it's not about their ideas, this kind talk quickly descends into a game of "the teacher is thinking of a number between 0 and 100." Students either start opting out or just trying to guess what the instructor wants them to say.
The Big Picture
Facilitating discussions is hard work. In my mind, the number one priority is getting students to invite me in to their learning through their talk. Largely, this means that they are sharing their ideas and thinking, not trying to guess what's in my mind or avoid being wrong. When I see instructors falling into these kinds of traps, I see this priority being undermined.
Some people might think the solution to trap #1 is to have a better poker face–don't have any "tells" that give away the right answer. I think that approach is flawed because it's trying to stop the symptom, but not the cause. I don't need a poker face if I am not listening to student ideas primarily through a lens of correct and incorrect.
Some people might think the solution to trap #2 is to not care about terminology. While that's possible, I don't think it's realistic. I think the solution is to distinguish the activities of "shopping for ideas" and "connecting with disciplinary formalism". The problem is in trying to do both at the same time and in the same way.
I certainly enjoy watching other people teach, because it gives me an opportunity to reflect on my own teaching. There are times when I "gum up the dialogue" and focus on correctness when I shouldn't. Sometimes by watching others, I understand better why we all fall into these traps and what impact it can have on students.
Saturday, April 23, 2011
The Many Roles of Content Knowledge for Teaching
Years ago, I was listening in on a group of college physics students who were working on some fairly standard torque-balancing problems. They had been given situations like the one below and they had to decide whether the situations were balanced or not.
The group had an interesting strategy that I call the “equal exchange” strategy. For example, students would take the “two blocks at the 1-notch” and replace it with “one block at the 2-notch”, because that was an equal exchange. For this situation, the strategy quickly reveals the answer, because each side now has “2 blocks and the 2-notch”, as shown below.
In working with the other graduate TAs and the professor running the prep session the week before, no one had used or even mentioned this strategy, neither as a strategy they would use or that students might use. All of us simply summed and compared the torques, by writing out 2*2 = 2*1+1*2. And we did the same for nearly every situation.
For me as a novice teacher, I was intrigued by what the students were doing. To me, it was thrilling to witness these students, all by themselves, inventing a novel way to solve the problem that I had never considered. Part of this thrill was that students were doing something different from me, but a large part of the thrill was wrapped up in me knowing that what they were doing was valid, despite being different.
Here’s something interesting to think about. For me, the physics knowledge I had to use to evaluate the validity of the students’ strategy was, in some ways, special to the task of my teaching, because it wasn’t the same physics knowledge I used to solve the problem. I (along with all the physics graduate TAs) summed the torques in order to compare the net torque numerically. The students’ strategy involved getting the situations to be visually comparable. The fact that I could see our strategies as being related and both valid is a kind of content knowledge that I needed to adequately assess what the students were doing.
Of course, some of the problems students had to work on were much harder than the situation above. So, the strategy to get all the blocks in one place can get a lot more complicated. Take for example, this situation:
In this situation, the number of moves not only goes up, but you have to do some more daunting proportional reasoning. As these students got to ever more complicated situations, the students were taking a lot longer than the other groups, and making more mistakes.
The question, for me as a teacher then, was, “At what point, if ever, should I step in to help them to discover other, perhaps more efficient, strategies?”
First, it’s helpful to reflect on some things. First, recognizing why their strategy was becoming increasingly difficult required that I have a particular mastery of the physics content and the physics reasoning. Recall that to solve the problem myself, I didn’t need to consider proportional reasoning or multi-step problem solving, because I just had to sum the torques. But now in this moment, in order to assess students’ progress moving forward, I had to be able to think about the physics concepts and problem-solving strategies in a particular way that was different than before. I had to be able to project the students’ problem-solving strategy into the future and into different problems in and make hypotheses about where it might lead them.
As a teacher, I could have chosen to engage students in developing their strategy, by helping them to be careful with proportional reasoning or with planning out more effective moves; or I could have chosen to nudge them toward my more efficient strategy. Given different goals and constraints, there is no right answer about what to do. But, for a me to make an informed decision, I had to be in the position of listening and making sense of what the students were doing. In order to be in that position, I had to have a unique mastery of the physics content and reasoning that, I’d argue, went well beyond being able to solve the problem myself.
Seeing other Connections
Looking back on this moment, other question for me as a teacher are these: “What does their strategy imply about what they are likely understanding well? What does this strategy imply about what students might not yet understand?”
To me, the students strategy shows me that they are likely making sense of Torque as Mass x Distance. They understand that idea well enough to know that there are variety of ways to get an equal torque by changing the mass and distance. In particular, most of their reasoning fell along the lines of, “if you triple the mass, you better third the distance.”
But their strategy also hints that may not be having the opportunity to develop other important ideas. For example, they might not be learning that torques are summative (e.g., Net Torque = Sum of Individual Torques). If it’s important for students to learn this, a goal could be for me to make sure that this group is provided with an opportunity to learn that idea as well. It’s not just a matter of them learning a more efficient strategy, it’s about the opportunity to make contact with important physics ideas that they might not using their strategy alone.
The Big Picture
This example highlights for me that the role of content knowledge in teaching is wide and varied. The content knowledge I mention here is often referred to as specialized content knowledge. It's the content knowledge needed to evaluate a student solution that you may have never seen or thought about before. It's the content knowledge needed to project a problem-solving strategy into the future. It's the content knowledge needed to relate problem solving strategies with important conceptual knowledge. The reasons why this is content knowledge is that it need not have anything to do with students. An expert could have proposed these strategies in a journal of physics, and it could then be my job to evaluate the validity of that approach, or to see how that strategy would play out in a variety of situations, or to see what concepts are embedded within that approach. Some of that content knowledge is, in some ways, unique to teachers and teaching; because the range and variety of alternative solutions that teachers face are unique due to the fact that they are dealing with students. Thus, some of the content knowledge that teachers need to evaluate those solutions is unique to their tasks of teaching.
A big question for researchers is, "What kinds of content knowledge do teachers need for teaching? And where do teachers develop that knowledge?"
For me, I have developed a lot of that content knowledge by paying attention to students, by listening and reflecting on what they are doing. And I have further honed this knowledge by actively seeking out and reflecting on potential connections among what students are doing and the disciplinary knowledge and skills of physics. To be sure, I will continue to develop and refine this knowledge as I continue to teach in ways that allow me to listen and reflect on what students are doing. For this reason, how I arrange my classroom teaching in ways that allow me to listen to students is extremely important.
I hope this helps other to understand my concern of misconceptions listening, in that it provides less opportunities for teachers to develop the knowledge that furthers their teaching along.
The group had an interesting strategy that I call the “equal exchange” strategy. For example, students would take the “two blocks at the 1-notch” and replace it with “one block at the 2-notch”, because that was an equal exchange. For this situation, the strategy quickly reveals the answer, because each side now has “2 blocks and the 2-notch”, as shown below.
In working with the other graduate TAs and the professor running the prep session the week before, no one had used or even mentioned this strategy, neither as a strategy they would use or that students might use. All of us simply summed and compared the torques, by writing out 2*2 = 2*1+1*2. And we did the same for nearly every situation.
For me as a novice teacher, I was intrigued by what the students were doing. To me, it was thrilling to witness these students, all by themselves, inventing a novel way to solve the problem that I had never considered. Part of this thrill was that students were doing something different from me, but a large part of the thrill was wrapped up in me knowing that what they were doing was valid, despite being different.
Here’s something interesting to think about. For me, the physics knowledge I had to use to evaluate the validity of the students’ strategy was, in some ways, special to the task of my teaching, because it wasn’t the same physics knowledge I used to solve the problem. I (along with all the physics graduate TAs) summed the torques in order to compare the net torque numerically. The students’ strategy involved getting the situations to be visually comparable. The fact that I could see our strategies as being related and both valid is a kind of content knowledge that I needed to adequately assess what the students were doing.
Of course, some of the problems students had to work on were much harder than the situation above. So, the strategy to get all the blocks in one place can get a lot more complicated. Take for example, this situation:
In this situation, the number of moves not only goes up, but you have to do some more daunting proportional reasoning. As these students got to ever more complicated situations, the students were taking a lot longer than the other groups, and making more mistakes.The question, for me as a teacher then, was, “At what point, if ever, should I step in to help them to discover other, perhaps more efficient, strategies?”
First, it’s helpful to reflect on some things. First, recognizing why their strategy was becoming increasingly difficult required that I have a particular mastery of the physics content and the physics reasoning. Recall that to solve the problem myself, I didn’t need to consider proportional reasoning or multi-step problem solving, because I just had to sum the torques. But now in this moment, in order to assess students’ progress moving forward, I had to be able to think about the physics concepts and problem-solving strategies in a particular way that was different than before. I had to be able to project the students’ problem-solving strategy into the future and into different problems in and make hypotheses about where it might lead them.
As a teacher, I could have chosen to engage students in developing their strategy, by helping them to be careful with proportional reasoning or with planning out more effective moves; or I could have chosen to nudge them toward my more efficient strategy. Given different goals and constraints, there is no right answer about what to do. But, for a me to make an informed decision, I had to be in the position of listening and making sense of what the students were doing. In order to be in that position, I had to have a unique mastery of the physics content and reasoning that, I’d argue, went well beyond being able to solve the problem myself.
Seeing other Connections
Looking back on this moment, other question for me as a teacher are these: “What does their strategy imply about what they are likely understanding well? What does this strategy imply about what students might not yet understand?”
To me, the students strategy shows me that they are likely making sense of Torque as Mass x Distance. They understand that idea well enough to know that there are variety of ways to get an equal torque by changing the mass and distance. In particular, most of their reasoning fell along the lines of, “if you triple the mass, you better third the distance.”
But their strategy also hints that may not be having the opportunity to develop other important ideas. For example, they might not be learning that torques are summative (e.g., Net Torque = Sum of Individual Torques). If it’s important for students to learn this, a goal could be for me to make sure that this group is provided with an opportunity to learn that idea as well. It’s not just a matter of them learning a more efficient strategy, it’s about the opportunity to make contact with important physics ideas that they might not using their strategy alone.
The Big Picture
This example highlights for me that the role of content knowledge in teaching is wide and varied. The content knowledge I mention here is often referred to as specialized content knowledge. It's the content knowledge needed to evaluate a student solution that you may have never seen or thought about before. It's the content knowledge needed to project a problem-solving strategy into the future. It's the content knowledge needed to relate problem solving strategies with important conceptual knowledge. The reasons why this is content knowledge is that it need not have anything to do with students. An expert could have proposed these strategies in a journal of physics, and it could then be my job to evaluate the validity of that approach, or to see how that strategy would play out in a variety of situations, or to see what concepts are embedded within that approach. Some of that content knowledge is, in some ways, unique to teachers and teaching; because the range and variety of alternative solutions that teachers face are unique due to the fact that they are dealing with students. Thus, some of the content knowledge that teachers need to evaluate those solutions is unique to their tasks of teaching.
A big question for researchers is, "What kinds of content knowledge do teachers need for teaching? And where do teachers develop that knowledge?"
For me, I have developed a lot of that content knowledge by paying attention to students, by listening and reflecting on what they are doing. And I have further honed this knowledge by actively seeking out and reflecting on potential connections among what students are doing and the disciplinary knowledge and skills of physics. To be sure, I will continue to develop and refine this knowledge as I continue to teach in ways that allow me to listen and reflect on what students are doing. For this reason, how I arrange my classroom teaching in ways that allow me to listen to students is extremely important.
I hope this helps other to understand my concern of misconceptions listening, in that it provides less opportunities for teachers to develop the knowledge that furthers their teaching along.
Tuesday, April 19, 2011
RTOP: Solid grasp of subject matter?
Here is another item from the RTOP:
The teacher had a solid grasp of the subject matter content inherent in the lesson.
At first glance this seems pretty silly for a classroom observation. But digging deeper, and reading the clarifying paragraphs gives this statement new and wonderful meaning:
This isn't about having subject knowledge. It's about knowing a subject matter well enough that a teacher can see fragments of disciplinary knowledge in all the things that students say and do in the classroom. A scientist could easily score low on this, despite having mastered the content, if that content mastery didn't allow them to listen and "see" the beginnings of knowledge in classroom discourse.
An Example from Physics
In the physics classroom, an example of this came up this semester. A lecturer was presenting on the topic of constructive and deconstructive interference, and was discussing lasers as an example of constructive inteference A student asked a question at some point about this being like polarized light. The lecturer was thrown off by this question, and went off on an explanation for why the two had nothing to do with each other. While it is true that polarizers and lasers are different phenomena, arising from different mechanisms, there is a lot of conceptual overlap between the two. In particular, with both situations there are waves, and the phenomena involves thinking about the degree to which waves are or are not aligned with each other. In both cases, those alignments can be described with an angular measure. The difference is that one involves an alignment of phase relations and the other involves an alignment of oscillating planes.
While I'm positive that the instructor understood both concepts fairly well, his understanding didn't help him to see meaningful connections between both content areas and the students' question. For that reason, I might score this RTOP item low.
Anybody have any good examples?
The teacher had a solid grasp of the subject matter content inherent in the lesson.
At first glance this seems pretty silly for a classroom observation. But digging deeper, and reading the clarifying paragraphs gives this statement new and wonderful meaning:
"This indicates that a teacher could sense the potential significance of ideas as they occurred in the lesson, even when articulated vaguely by students. A solid grasp would be indicated by an eagerness to pursue student’s thoughts even if seemingly unrelated at the moment. The grade-level at which the lesson was directed should be taken into consideration when evaluating this item."
This isn't about having subject knowledge. It's about knowing a subject matter well enough that a teacher can see fragments of disciplinary knowledge in all the things that students say and do in the classroom. A scientist could easily score low on this, despite having mastered the content, if that content mastery didn't allow them to listen and "see" the beginnings of knowledge in classroom discourse.
An Example from Physics
In the physics classroom, an example of this came up this semester. A lecturer was presenting on the topic of constructive and deconstructive interference, and was discussing lasers as an example of constructive inteference A student asked a question at some point about this being like polarized light. The lecturer was thrown off by this question, and went off on an explanation for why the two had nothing to do with each other. While it is true that polarizers and lasers are different phenomena, arising from different mechanisms, there is a lot of conceptual overlap between the two. In particular, with both situations there are waves, and the phenomena involves thinking about the degree to which waves are or are not aligned with each other. In both cases, those alignments can be described with an angular measure. The difference is that one involves an alignment of phase relations and the other involves an alignment of oscillating planes.
While I'm positive that the instructor understood both concepts fairly well, his understanding didn't help him to see meaningful connections between both content areas and the students' question. For that reason, I might score this RTOP item low.
Anybody have any good examples?
Monday, April 11, 2011
Curriculum Evaluation Task Force: Nearing the End
Since November, I have been working with a diverse group of math and science teachers to evaluate and put forth a recommendation for a new middle school physical (and earth) science curriculum.
Our group consists of the following:
We are now coming to the end of our work–last Saturday we met as a large group for the last time. On average, teachers put in about 100 hours of work each. They were paid for their time, and we always provided breakfast and lunch during our long Saturday meetings. In the coming weeks, we will be finalizing reports on our evaluation and recommendation.
For me, I'd say the most difficult part of the process has been to manage the tension between (1) pushing forward so they could accomplish the work within a timeline, and (2) providing time and space for norms, voice, and collective ownership to develop. My strategy was to almost always focus on (2), but to drive hard and with clear purpose on (1) whenever the group needed me to do so, and then to back off again to let the rewards of cultivating (2) pay off.
Although the road was rocky, I think we have accomplished much, largely in terms of planting the seeds for a strong professional learning community. The teachers feel they have learned a lot through this process, and they didn't want it to end. Throughout the day on Saturday, teachers were discussing how the were going to stay involved and not let the experience, knowledge, and excitement they've developed go to waste. A few teachers were talking about how they had already joined a curriculum selection team for math in their school. Other teachers are moving on to our 9th grade curriculum selection process. Others will be helping to plan our summer professional development academy and/or piloting in the fall. A mother-daughter pair on the team expressed to me how valuable this project has been them to spend time with each other on matters of their profession. I think this sentiment has been true for everyone. It has given just enough structure, time, and sense of purpose to allow teachers to come together on matters of their profession. I can only wish them good luck moving forward, as I won't be here to see it happen.
Our group consists of the following:
- A Grade 6 Math Teacher
- A High School Math Teacher
- A Grades 7/8 Life and Physical Science Teacher
- A College Physics Professor
- A High School Environmental Science Teacher
- A Grades 7/8 Earth and Physical Science Teacher
- A Grade 8 Math and Physical Science Teacher
- A Grades 7/8 Math and Physical Science Teacher
- A Grades 11/12 Physics and Chemistry Teacher
- A Grades 6-8 Earth, Life, and Physical Science Teacher
- A Grade 6 Math and Science Teacher
- A Grade 6 (Elementary School) Teacher for All Subjects
- A High School Earth, Physics, Physical Science Teacher
- 4 Physics Education Research Graduate Students
We are now coming to the end of our work–last Saturday we met as a large group for the last time. On average, teachers put in about 100 hours of work each. They were paid for their time, and we always provided breakfast and lunch during our long Saturday meetings. In the coming weeks, we will be finalizing reports on our evaluation and recommendation.
For me, I'd say the most difficult part of the process has been to manage the tension between (1) pushing forward so they could accomplish the work within a timeline, and (2) providing time and space for norms, voice, and collective ownership to develop. My strategy was to almost always focus on (2), but to drive hard and with clear purpose on (1) whenever the group needed me to do so, and then to back off again to let the rewards of cultivating (2) pay off.
Although the road was rocky, I think we have accomplished much, largely in terms of planting the seeds for a strong professional learning community. The teachers feel they have learned a lot through this process, and they didn't want it to end. Throughout the day on Saturday, teachers were discussing how the were going to stay involved and not let the experience, knowledge, and excitement they've developed go to waste. A few teachers were talking about how they had already joined a curriculum selection team for math in their school. Other teachers are moving on to our 9th grade curriculum selection process. Others will be helping to plan our summer professional development academy and/or piloting in the fall. A mother-daughter pair on the team expressed to me how valuable this project has been them to spend time with each other on matters of their profession. I think this sentiment has been true for everyone. It has given just enough structure, time, and sense of purpose to allow teachers to come together on matters of their profession. I can only wish them good luck moving forward, as I won't be here to see it happen.
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