I have to run a workshop for secondary math and science teachers at a conference in two weeks, and have to turn in the abstract/title tomorrow. I'm looking to do something new I haven't done before, and this is something that has been stuck in my brain these past 6 months.
The session will be one of five parallel sessions, with around 20 teachers each. This is what I drafted this morning. I'm looking for feedback. What do you think? Would you got to this session?
You are your own guide post: Fostering our own sense of inquiry
There are many calls for engaging students in scientific inquiry, and there are equally as many definitions of what constitutes inquiry. This workshop is based on the premise that we can better position ourselves to know and to teach inquiry when we cultivate our own inclinations to inquire as part of our everyday lives. We'll explore the following four strategies aimed at re-invigorating and sustaining everyday engagement in inquiry: capturing spontaneous wonder in multimedia, drawing others in to wonder with you, tinkering and exploring in the everyday world, and exercising one's authority to know and learn. In this workshop, we'll do a bit inquiring together, explore each strategy with concrete examples, and discuss connections to classroom inquiry.
Thursday, June 9, 2011
Monday, June 6, 2011
Exploring and then Naming in Upper-Level Physics
Corrinne Manogue at OSU is the source of this one:
You teach upper-level physics. Say, you want to teach your students about eigenvectors. You could
(A) Introduce the word "eigenvector" before or at the beginning of lecture, explaining what the term means and where it comes from. And then lecture on how to solve for eigenvectors, and then have students practice.
OR
(B) Put students in groups: give each group a different (carefully chosen, of course) matrix and ask them to see if they can find any vectors that don't change direction when you multiply it by the matrix. Let them explore, remember how to perform matrix multiplication, encourage them to draw (not just do algebra), watch them develop an intuition for what each matrix is doing, and try guess and check, encourage them to use geometrical insight to rule out or hone in on solutions, let them struggle with whether there can be more than one solution. Then let them share their solutions with their peers. Point out important similarities and differences across problems and solutions strategies. Point out important things you'll need to bring up later. Then, then introduce the word "eigenvectors". Draw on the insights they have (and haven't) made and present the formal method for finding eigenvalues.
The argument for doing A could be this: "Students don't have any intuitions about eigenvectors and linear algebra. It's a weird word that's distracting. If I introduce the word before lecture, it will help them focus on the mathematical structure and methods I want to teach, rather than on the weird vocabulary."
The argument for doing B is this: "By drawing on what students do know and can do, you can quickly build up a set of intuitions that orient students to the concept of eigenvectors. Since, they are not likely to formally develop all the methods on their own, I can capitalize on what they end up doing to anchor the formal instruction to their own ideas and methods."
Anyway, what do you guys think?
You teach upper-level physics. Say, you want to teach your students about eigenvectors. You could
(A) Introduce the word "eigenvector" before or at the beginning of lecture, explaining what the term means and where it comes from. And then lecture on how to solve for eigenvectors, and then have students practice.
OR
(B) Put students in groups: give each group a different (carefully chosen, of course) matrix and ask them to see if they can find any vectors that don't change direction when you multiply it by the matrix. Let them explore, remember how to perform matrix multiplication, encourage them to draw (not just do algebra), watch them develop an intuition for what each matrix is doing, and try guess and check, encourage them to use geometrical insight to rule out or hone in on solutions, let them struggle with whether there can be more than one solution. Then let them share their solutions with their peers. Point out important similarities and differences across problems and solutions strategies. Point out important things you'll need to bring up later. Then, then introduce the word "eigenvectors". Draw on the insights they have (and haven't) made and present the formal method for finding eigenvalues.
The argument for doing A could be this: "Students don't have any intuitions about eigenvectors and linear algebra. It's a weird word that's distracting. If I introduce the word before lecture, it will help them focus on the mathematical structure and methods I want to teach, rather than on the weird vocabulary."
The argument for doing B is this: "By drawing on what students do know and can do, you can quickly build up a set of intuitions that orient students to the concept of eigenvectors. Since, they are not likely to formally develop all the methods on their own, I can capitalize on what they end up doing to anchor the formal instruction to their own ideas and methods."
Anyway, what do you guys think?
Vocabulary and Jargon
If you taught physics before, you've likely heard something like this from a student: "The ball's energy force went into powering all the momentum of the collision vector."
Many of us cringe when we hear sentences like this, but maybe not for the same reasons. Some of us may cringe because students are mis-using a lot of vocabulary. Others may cringe because it seems such an unproductive way to approach talking and making sense of the world with other human beings.
Perhaps, all this jargon from students really signifies nonsense--the student is just grasping at whatever vocabulary they can, hoping that with a shotgun of terms, something will sound right. Or, perhaps, the student was thinking something more like, "The ball was moving fast, and so it had a really big influence in the collision," and they were trying to communicate this idea using terms they thought they were supposed to. I tend to think it can be one, either, both, or something in between. My inclination is to gently encourage students to stop doing this, and I try to help them express their ideas using familiar words, pictures, etc. In the PER community, there have been and continue to be lively debates about whether this kind of jargon-infused talk can be productive for learning.
Jargon-infused talk is not limited to physics. As an education researcher, I've heard new PER graduate students say things like this: "The framing was made of and led to symbolic forms and p-prims resource schema activation, but not a coordination class." I sort of cringe when I hear students say these sorts of things, too. If I listen really hard, I can imagine maybe they are trying to say, "The students seem to be engaged in the activity with a mish-mash of ideas that are both mathematical and physical". Like the physics students, I encourage them to articulate, elaborate, clarify, and refine their ideas in their own words, and not worry (yet) about technical vocabulary.
The role of vocabulary in learning is a tricky thing, because it's not all the same. Learning that the french word "pomme" means "apple" is easy, because we already have the concept of apple. We have likely felt apples, tasted apples, smelled apples, seen apples. You've probably had apple juice, apple sauce, apple pie. You've head phrases like, "the apple of my eye". You've distinguished apples from other fruits like pears or plums. You probably know that apples come from trees, and not from the ground (like the pomme de terre). You know of different kinds of apples. With this rich network of ideas, distinctions, and experiences, it's easy to just add on "pomme".
With scientific terminology however, it's not always as simple, because we aren't likely to have all the (right) conceptual anchors in place to hook those words to. The question of when and how to introduce vocabulary is an interesting one. Recently, I was discussing two different approaches to managing vocabulary in the physics classroom:
(1) Frontload the introduction of vocabulary, so that students can better make sense of ideas discussed during class. This will help reduce students' cognitive load, and students can spend mental effort on understanding ideas and not just getting lost in a sea of vocabulary.
(2) Backload the introduction of vocabulary, after you've had a chance to introduce ideas in class. This will provide students with some conceptual "hooks" to anchor the vocabulary to.
I want to talk about this more, but I want to pause with the following questions:
What are some situations in which you think #1 would be better than #2? Why?
What are some situations in which you think #2 would be better than #1? Why?
Many of us cringe when we hear sentences like this, but maybe not for the same reasons. Some of us may cringe because students are mis-using a lot of vocabulary. Others may cringe because it seems such an unproductive way to approach talking and making sense of the world with other human beings.
Perhaps, all this jargon from students really signifies nonsense--the student is just grasping at whatever vocabulary they can, hoping that with a shotgun of terms, something will sound right. Or, perhaps, the student was thinking something more like, "The ball was moving fast, and so it had a really big influence in the collision," and they were trying to communicate this idea using terms they thought they were supposed to. I tend to think it can be one, either, both, or something in between. My inclination is to gently encourage students to stop doing this, and I try to help them express their ideas using familiar words, pictures, etc. In the PER community, there have been and continue to be lively debates about whether this kind of jargon-infused talk can be productive for learning.
Jargon-infused talk is not limited to physics. As an education researcher, I've heard new PER graduate students say things like this: "The framing was made of and led to symbolic forms and p-prims resource schema activation, but not a coordination class." I sort of cringe when I hear students say these sorts of things, too. If I listen really hard, I can imagine maybe they are trying to say, "The students seem to be engaged in the activity with a mish-mash of ideas that are both mathematical and physical". Like the physics students, I encourage them to articulate, elaborate, clarify, and refine their ideas in their own words, and not worry (yet) about technical vocabulary.
The role of vocabulary in learning is a tricky thing, because it's not all the same. Learning that the french word "pomme" means "apple" is easy, because we already have the concept of apple. We have likely felt apples, tasted apples, smelled apples, seen apples. You've probably had apple juice, apple sauce, apple pie. You've head phrases like, "the apple of my eye". You've distinguished apples from other fruits like pears or plums. You probably know that apples come from trees, and not from the ground (like the pomme de terre). You know of different kinds of apples. With this rich network of ideas, distinctions, and experiences, it's easy to just add on "pomme".
With scientific terminology however, it's not always as simple, because we aren't likely to have all the (right) conceptual anchors in place to hook those words to. The question of when and how to introduce vocabulary is an interesting one. Recently, I was discussing two different approaches to managing vocabulary in the physics classroom:
(1) Frontload the introduction of vocabulary, so that students can better make sense of ideas discussed during class. This will help reduce students' cognitive load, and students can spend mental effort on understanding ideas and not just getting lost in a sea of vocabulary.
(2) Backload the introduction of vocabulary, after you've had a chance to introduce ideas in class. This will provide students with some conceptual "hooks" to anchor the vocabulary to.
I want to talk about this more, but I want to pause with the following questions:
What are some situations in which you think #1 would be better than #2? Why?
What are some situations in which you think #2 would be better than #1? Why?
Sunday, June 5, 2011
Engineers vs Construction Workers
In the car with the 3.5 year old that my wife watches. He says, "Engineers are smart, and construction workers are not very smart."
Sigh. We get to hear a lot of the dumb things parents say through their children.
Sigh. We get to hear a lot of the dumb things parents say through their children.
Friday, June 3, 2011
Flow into the Rainbow
I've been having conversations with a graduate student here about student engagement. In particular, we've been discussing the concept of flow. Flow is a psychological construct that is meant to capture the feeling of being fully immersed, focused, and engaged in what one is doing.
There are many aspects to flow, but some that stand out for me are the following:
This past semester, students enrolled in my seminar on "science teaching and learning" seemed to have had one collective flow experience that has really stuck with (many of) them, and consequently, it has stuck with me. It was a discussion around the question, "Is every color in the rainbow?" If you are curious, this activity has a facilitators guide written by Leslie Atkins and Irene Salter over at SGSI.
Certainly, from my perspective the lesson seemed very fun and engaging. But it was also engaging enough that, apparently, several random groups of people walking by the classroom stopped to watch for some period of time. Of course, we were so engaged in our own discussion that we didn't notice, but in the following days, several faculty in the department commented about it or asked what that class was about. The students in my class also spontaneously wrote about it in their weekly reflections; brought it up in the course feedback; and talked about it in exit interviews at the end of the semester (with a 3rd person).
That same day, after the Rainbow discussion, we had a discussion about what makes for a good science conversation. And this is what they came up with:
I'm interested to know what everyone thinks their students would say to the question, "What makes for a good science conversation?"
There are many aspects to flow, but some that stand out for me are the following:
- loss of self-consciousness
- high levels of concentration
- intrinsically rewarding
- absorption into the activity
- distorted sense of time
This past semester, students enrolled in my seminar on "science teaching and learning" seemed to have had one collective flow experience that has really stuck with (many of) them, and consequently, it has stuck with me. It was a discussion around the question, "Is every color in the rainbow?" If you are curious, this activity has a facilitators guide written by Leslie Atkins and Irene Salter over at SGSI.
Certainly, from my perspective the lesson seemed very fun and engaging. But it was also engaging enough that, apparently, several random groups of people walking by the classroom stopped to watch for some period of time. Of course, we were so engaged in our own discussion that we didn't notice, but in the following days, several faculty in the department commented about it or asked what that class was about. The students in my class also spontaneously wrote about it in their weekly reflections; brought it up in the course feedback; and talked about it in exit interviews at the end of the semester (with a 3rd person).
That same day, after the Rainbow discussion, we had a discussion about what makes for a good science conversation. And this is what they came up with:
- having relevant everyday experiences to draw on
- having a diversity of opinions and people
- having a culture of trust (already established)
- having fun and laughing
- being challenged
- making progress, getting somewhere
- feeling like part of a group but also an individual
- listening and sharing, not just waiting to talk
I'm interested to know what everyone thinks their students would say to the question, "What makes for a good science conversation?"
Thursday, June 2, 2011
Images of Teaching
I was reading a recent book chapter by Russ, Sherin, and Sherin. In the chapter they discuss, among other things, four images of expertise in (mathematics) teaching:
Teacher as diagnostician
"Examining the mathematical thinking of students, looking for symptoms, and diagnosing their underlying causes"
Teacher as conductor
"Directing and shaping the classroom discourse... to orchestrate whole-class discussions in ways that advance the mathematical learning of the whole class"
Teacher as architect
"Selecting and implementing curriculum materials...choosing tasks to use with student as well as deciding how those tasks should be carried out"
Teacher as river guide
"To be flexible in the moment...responding quickly and effectively...responsive to the context, to students, and to what occurs in the moment."
----
I like this breakdown, both for thinking about research on teaching and how we conceptualize teaching, but also for thinking about my own teaching. How do I imagine myself as a teacher? In which of these images do I feel competent? In which do I feel more novice?
I will say that my weakest area is as architect- especially thinking about the design of a whole course. I haven't had a lot of experience designing courses, but I think I am also weakest here because I am a decent enough in the other three areas that I get away with not being a good architect. In this sense, the willingness and ability to improvise is both an asset and a liability. I have become more aware this year of my needs to mature as an architect, and have taken some steps to reflect on and enact some novice architect moves. One professor here at UMaine has been helpful in nudging me in this direction.
I'd say conducting is where I am strongest. Of course, I still need a lot of improvement, but I feel pretty comfortable and confident navigating whole-class discussion. This is a lot based on my experience in teaching as a summer kindergarten "teacher" in an Americorps program, as a tutorial TA and instructor at UMD, and even more recently as an instructor and PD facilitator at UMaine. But I also had the opportunity to watch a lot of good conductors. In particular, during my second year at Maryland, I watched David Hammer lecture everyday. A few times I even got to substitute teach for him, and try it out. Having role models helped a lot, but it helped even more that these role models were often the same persons coming in to observe me and give me feedback. Now that I think about it, I also got a lot of good feedback from my mentor teacher in the Americorps program. Mrs. Patterson was always nudging us to make sure that children had opportunities to learn from mistakes, and to not let them feel bad OR to let those mistakes just pass by.
As a diagnostician, it shouldn't be surprising that I feel adequate in some ways and less adequate in others. This is because I feel more confident as a conductor than as architect. I am good at diagnosing when I am conducting, but I need to improve my skills at designing more and better opportunities for diagnosing.
I think the river guide image is the hardest for me to assess. I feel like I am almost always playing river guide, largely because I fail to play architect well enough, but that doesn't mean I am good at being the river guide. I suspect my expertise is patchy. There are certain rivers I feel very competent reacting to rapids and obstacles; but there are other rivers where I would be lost and tumble over ungraciously. Being the river guide means you both know the terrain have all the skills down, but that you can perceive and react quickly and appropriately. It'll be interesting after my first year at MTSU to revisit this list.
Anyway, where do you all feel more or less competent as a teacher?
Teacher as diagnostician
"Examining the mathematical thinking of students, looking for symptoms, and diagnosing their underlying causes"
Teacher as conductor
"Directing and shaping the classroom discourse... to orchestrate whole-class discussions in ways that advance the mathematical learning of the whole class"
Teacher as architect
"Selecting and implementing curriculum materials...choosing tasks to use with student as well as deciding how those tasks should be carried out"
Teacher as river guide
"To be flexible in the moment...responding quickly and effectively...responsive to the context, to students, and to what occurs in the moment."
----
I like this breakdown, both for thinking about research on teaching and how we conceptualize teaching, but also for thinking about my own teaching. How do I imagine myself as a teacher? In which of these images do I feel competent? In which do I feel more novice?
I will say that my weakest area is as architect- especially thinking about the design of a whole course. I haven't had a lot of experience designing courses, but I think I am also weakest here because I am a decent enough in the other three areas that I get away with not being a good architect. In this sense, the willingness and ability to improvise is both an asset and a liability. I have become more aware this year of my needs to mature as an architect, and have taken some steps to reflect on and enact some novice architect moves. One professor here at UMaine has been helpful in nudging me in this direction.
I'd say conducting is where I am strongest. Of course, I still need a lot of improvement, but I feel pretty comfortable and confident navigating whole-class discussion. This is a lot based on my experience in teaching as a summer kindergarten "teacher" in an Americorps program, as a tutorial TA and instructor at UMD, and even more recently as an instructor and PD facilitator at UMaine. But I also had the opportunity to watch a lot of good conductors. In particular, during my second year at Maryland, I watched David Hammer lecture everyday. A few times I even got to substitute teach for him, and try it out. Having role models helped a lot, but it helped even more that these role models were often the same persons coming in to observe me and give me feedback. Now that I think about it, I also got a lot of good feedback from my mentor teacher in the Americorps program. Mrs. Patterson was always nudging us to make sure that children had opportunities to learn from mistakes, and to not let them feel bad OR to let those mistakes just pass by.
As a diagnostician, it shouldn't be surprising that I feel adequate in some ways and less adequate in others. This is because I feel more confident as a conductor than as architect. I am good at diagnosing when I am conducting, but I need to improve my skills at designing more and better opportunities for diagnosing.
I think the river guide image is the hardest for me to assess. I feel like I am almost always playing river guide, largely because I fail to play architect well enough, but that doesn't mean I am good at being the river guide. I suspect my expertise is patchy. There are certain rivers I feel very competent reacting to rapids and obstacles; but there are other rivers where I would be lost and tumble over ungraciously. Being the river guide means you both know the terrain have all the skills down, but that you can perceive and react quickly and appropriately. It'll be interesting after my first year at MTSU to revisit this list.
Anyway, where do you all feel more or less competent as a teacher?
Wednesday, June 1, 2011
College Instruction: Dollars and Sense
Yesterday I realized that the the University of Maine, in-state students pay about $20 an hour for instruction. In a lecture, where there are 150 students, this means that students collectively throw out $3000 every time they sit down and listen to a lecture.
I was wondering how students would feel if every time they walked into lecture they had to fill a bucket with $3000 dollars before the lecturer began. How would students feel differently about their investment? Would they perceive the value of instruction differently? What might they demand in return? What do they deserve in return for that money?
A colleague of mine helped to put this in a different perspective: an adjunct faculty at UMaine only gets about $3000 dollars to teach an introductory physics course. This, of course, means that an instructor who teaches all semester long only gets to keep one of those buckets, the rest goes to paying TAs, administration, maintaining libraries, computer labs, paying electricity and heating bills, providing labs, paying support staff, and so on and so on and so on.
But it makes me wonder again: How would an instructor feel if they had to teach all semester long watching those buckets fill with money, knowing that they only got to keep the last one? How would they feel differently about students' investment and their own compensation? Would they perceive the value of the university infrastructure differently?
I was wondering how students would feel if every time they walked into lecture they had to fill a bucket with $3000 dollars before the lecturer began. How would students feel differently about their investment? Would they perceive the value of instruction differently? What might they demand in return? What do they deserve in return for that money?
A colleague of mine helped to put this in a different perspective: an adjunct faculty at UMaine only gets about $3000 dollars to teach an introductory physics course. This, of course, means that an instructor who teaches all semester long only gets to keep one of those buckets, the rest goes to paying TAs, administration, maintaining libraries, computer labs, paying electricity and heating bills, providing labs, paying support staff, and so on and so on and so on.
But it makes me wonder again: How would an instructor feel if they had to teach all semester long watching those buckets fill with money, knowing that they only got to keep the last one? How would they feel differently about students' investment and their own compensation? Would they perceive the value of the university infrastructure differently?
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