Thoughts about physics, mostly stolen or adapted from others:
(1) The ideas of physics are relatively simple; but they are also quite subtle, especially in how they make contact with the real world, which is (undoubtedly) messy and complex. Understanding how simple ideas interface with the complex real world lies at the heart of understanding physics.
(2) Physics is not quite the study of natural phenomena nor the study of philosophy; rather physics lives in and around the boundaries of the real and the ideal. Physics, thus, flirts with the notion that our most complex experiences are quite simple and that our simplest experiences are quite complex.
(3) Physics begs us to problematize that which is not intuitively or initially problematic, and then to wonder whether and if our approaches to the unproblematic will be useful somewhere entirely different. For this reason, the world is both the source and target of our ideas, but the distances those ideas must traverse can be staggering.
Monday, June 27, 2011
Saturday, June 25, 2011
Recapturing a Sense of Science Away from School
I have recently been thinking a lot about how school distorted my own sense of doing science–one that I am only now recapturing in my post-school life. In school, a part of my own "hidden curriculum," especially in undergraduate and graduate physics, was learning that science (especially physics) was something to be done at academic institutions with academic people–in classes, in laboratories, in dedicated office spaces, at conferences, through grants, etc. School supported a view of science that science was done by people who had scientific knowledge–knowledge that was sanctioned by scientific authorities. It tacitly taught that science was done by scientists and that scientists had the right to decide what was and what was not science, as well, as who and who was not doing science.
I think the biggest impact that this had on me was when and where I felt like I was doing science
and with whom I felt like I could do science. I felt like I was doing science when I was around other physics majors (or physics-major like people), or working on physics problems alone, or tinkering in the lab, or sitting in physics classes, or reading physics articles. Of course, I talked with "other" people about physics and science, but it was not so much to do some science with them, as it was to tell them about some physics or science that I knew (that most likely they didn't). In that sense, I was modelling my interactions with them much in the way I had been interacted with. The sense was something like this: "There are people who have scientific knowledge and there are people who don't. It is the responsibility of those who have this knowledge to impart some of that knowledge to people who don't." Without doing this deliberately, I turned my interactions regarding science with other people into miniature versions of school. Perhaps I knew something cool, fun, or perplexing about quantum mechanics or relativity, and I would proceed to dole of this puzzling and fun knowledge to anyone willing to listen.
Now, I am turning back to a sense of doing science that I had two decades ago. I don't see the world through the lens of opportunities to teach science knowledge. I see the world as opportunities to do science with others, anywhere, anytime. I love walking through the woods, just noticing, and inviting others to notice and tell me about their noticing. I love wondering about how things change, and inviting others to tell stories with me about change, I enjoy trying to coordinate stories of change with evidence we might collect. I love sharing my own ideas, much more so than the ideas from books and lectures. I love listening to the ideas that people have, and how they've come to know those ideas. I love the feeling of doing science with others, and I love the learning that happens when I do this.
Whereas before I interacted with the tacit assumption that people needed scientific knowledge from some scientific authority; I now interact with the assumption that everyone is doing science all the time, and that I can uncover and make visible the science that others are doing by interacting with them a sense of mutual wonder. I find that by making all of my science and their science more visible, we can together sustain our doing of science more deeply and for longer periods of time. The spark of "Huh, I wonder how that happens?" becomes a conversation, which becomes a scurry to collect evidence, which becomes more conversation, which becomes the building of a contraption, and so on. My view of who does science is much more expansive. I'd say that now I do a lot science with friends, children, and my wife than I do with academic scientists. I do a lot more science by myself, as well, and I share that doing of science not to teach people what I have learned; but to invite them into my science in the hopes that it will become our science.
I am excited to continue to recapture this sense of science away from school, away from sanctioned authority. I hope to get better at inviting others into the science I am doing and better at encouraging others to invite me into their science. I hope to continue to expand upon boundaries of the people and places where I see opportunities for science to occur.
I think the biggest impact that this had on me was when and where I felt like I was doing science
and with whom I felt like I could do science. I felt like I was doing science when I was around other physics majors (or physics-major like people), or working on physics problems alone, or tinkering in the lab, or sitting in physics classes, or reading physics articles. Of course, I talked with "other" people about physics and science, but it was not so much to do some science with them, as it was to tell them about some physics or science that I knew (that most likely they didn't). In that sense, I was modelling my interactions with them much in the way I had been interacted with. The sense was something like this: "There are people who have scientific knowledge and there are people who don't. It is the responsibility of those who have this knowledge to impart some of that knowledge to people who don't." Without doing this deliberately, I turned my interactions regarding science with other people into miniature versions of school. Perhaps I knew something cool, fun, or perplexing about quantum mechanics or relativity, and I would proceed to dole of this puzzling and fun knowledge to anyone willing to listen.
Now, I am turning back to a sense of doing science that I had two decades ago. I don't see the world through the lens of opportunities to teach science knowledge. I see the world as opportunities to do science with others, anywhere, anytime. I love walking through the woods, just noticing, and inviting others to notice and tell me about their noticing. I love wondering about how things change, and inviting others to tell stories with me about change, I enjoy trying to coordinate stories of change with evidence we might collect. I love sharing my own ideas, much more so than the ideas from books and lectures. I love listening to the ideas that people have, and how they've come to know those ideas. I love the feeling of doing science with others, and I love the learning that happens when I do this.
Whereas before I interacted with the tacit assumption that people needed scientific knowledge from some scientific authority; I now interact with the assumption that everyone is doing science all the time, and that I can uncover and make visible the science that others are doing by interacting with them a sense of mutual wonder. I find that by making all of my science and their science more visible, we can together sustain our doing of science more deeply and for longer periods of time. The spark of "Huh, I wonder how that happens?" becomes a conversation, which becomes a scurry to collect evidence, which becomes more conversation, which becomes the building of a contraption, and so on. My view of who does science is much more expansive. I'd say that now I do a lot science with friends, children, and my wife than I do with academic scientists. I do a lot more science by myself, as well, and I share that doing of science not to teach people what I have learned; but to invite them into my science in the hopes that it will become our science.
I am excited to continue to recapture this sense of science away from school, away from sanctioned authority. I hope to get better at inviting others into the science I am doing and better at encouraging others to invite me into their science. I hope to continue to expand upon boundaries of the people and places where I see opportunities for science to occur.
Friday, June 24, 2011
Worrying about Misconceptions II
I was at a conference yesterday, where there was lots of talk and questions about misconceptions, mostly from the audience and less-so by the speakers. This isn't an exact quote but it's close:
"I'm worried that if we leave students to talk by themselves, they will develop misconceptions. I mean, where do misconceptions come from? They come from students. I'm worried that those misconceptions will crystallize and form stronger if we let them talk too long away from the guidance of an instructor."
OK. Yes, I cringed a little when I heard this. So, I want to to try to rephrase what this person said in a way that won't make me cringe, and may help me to empathize with this statement.
"I'm worried that if we leave students to talk by themselves, they won't always make adequate progress through their ideas. Where does ideas come from? They come from students. I'm worried that much of the progress they could make by working through their ideas will peter out or fall short if we let them loose too long without any guiding structures."
"I'm worried that if we leave students to talk by themselves, they will develop misconceptions. I mean, where do misconceptions come from? They come from students. I'm worried that those misconceptions will crystallize and form stronger if we let them talk too long away from the guidance of an instructor."
OK. Yes, I cringed a little when I heard this. So, I want to to try to rephrase what this person said in a way that won't make me cringe, and may help me to empathize with this statement.
"I'm worried that if we leave students to talk by themselves, they won't always make adequate progress through their ideas. Where does ideas come from? They come from students. I'm worried that much of the progress they could make by working through their ideas will peter out or fall short if we let them loose too long without any guiding structures."
Tuesday, June 21, 2011
Kinetic Energy and Temperature
A long-standing discussion among colleagues has concerned the understanding of temperature. Central to our discussions has been the heuristic, which is often taught, that temperature is a measure of kinetic energy or average kinetic energy (per something).
There are many touchstone examples we have discussed that have drawn our attention to critical features of not only the concepts and their connections, but what it means to understand them.
Included in these touchstone examples are
Ralph Baierlein in "Thermal Physics" writes the following in a section called "Temperature recapitulated" in a subsection called, "Temperature is deeper than average kinetic energy":
"The misconception that introduces this subsection is propagated with the best of intentions: to make temperature easier to understand. The root of the conceptual error lies in this: a belief that the purpose of absolute temperature is to tell us about a physical system's amount of energy. That is not the purpose of the temperature notion. Rather, temperature is intended to tell us about a system's hotness, its tendency to transfer energy (by heating). All physical systems are capable of heating or cooling others. The purpose of temperature is to rank the systems with respect to their ability to heat one another."
There are many touchstone examples we have discussed that have drawn our attention to critical features of not only the concepts and their connections, but what it means to understand them.
Included in these touchstone examples are
- An ideal gas in an external gravitational field. How do we think about the kinetic energy and temperature varying with height? Theoretically, intuitively, and empirically.
- The free expansion of a non-ideal gas. How do kinetic and inter-molecular potential energies change? How does temperature change? Why? How are these changes related?
- A gaseous systems composed of boson and fermions in near classical regime. How do kinetic energies compare?
Ralph Baierlein in "Thermal Physics" writes the following in a section called "Temperature recapitulated" in a subsection called, "Temperature is deeper than average kinetic energy":
"The misconception that introduces this subsection is propagated with the best of intentions: to make temperature easier to understand. The root of the conceptual error lies in this: a belief that the purpose of absolute temperature is to tell us about a physical system's amount of energy. That is not the purpose of the temperature notion. Rather, temperature is intended to tell us about a system's hotness, its tendency to transfer energy (by heating). All physical systems are capable of heating or cooling others. The purpose of temperature is to rank the systems with respect to their ability to heat one another."
Monday, June 20, 2011
I would never let my students within ten feet of...
At the Foundations and Frontiers of Physics Education Research, I can be quoted as saying something like the following: "I would never let my students within ten feet of those worksheet."
I didn't say this in a public talk, but I did say this in public during lunch to a handful of people. I believe the entire quote was something more like, "I love Tutorials as a resource for myself for thinking about activities, questions, and bits of sequencing in instruction, but I would never let my students within ten feet of those worksheets". As it happened, and by means of conference nearest-neighbor interactions, my comment was propagated through space and time and eventually found its way to some of individuals who created those very worksheets and whom were likely positioned to take offense at my suggestion that those worksheets should be kept in careful isolation from students.
I want to make it clear that I do stand by my statement. But that statement requires a bit of elaboration on my part to be full stood by.
First, the statement is truly meant to be about my students (with the emphasis on ME). I don't mind so much that others would use such worksheets as an orienting artifact for discourse management. In fact, I actively support instructors who choose to use tutorials and similar well-structured, research-based curriculum materials, and am committed to helping those instructors to implement chosen curricular materials in ways that maximize their productivity for students and instructors. For me, however, the set of things I want my students to experience and learn, I have personally found difficult to achieve with worksheets. I want to emphasize that it is not impossible to achieve them, but it is difficult. I must confess that have never felt extremely competent as a tutorial instructor, partially because of the feeling that, in such an environment, I am forced to co-teach with someone (i.e. a worksheet) that often undermines much of the productive patterns of listening, discourse, and engagement that I actively work to promote. Co-teaching can be an amazing experience, but it need not be, and I don't find that a worksheet is the kind of co-worker I want around, at least not very much.
Second, I learned a lot about student thinking and learning by being an instructor in tutorial environments where a highly-regimented, worksheet-driven discourse mediates much the classroom talk. By not having to mediate all of the discourse all the time, I was given the opportunity to listen without worrying about where we were going next. I didn't have to worry, because the worksheet remembered where we were going and what we would do next to get there. As a novice instructor, with all of this to worry about, I could allocate more of my resources to trying to make sense of what students were doing, what they were thinking. I believe that structured environments in which artifacts do much of the remembering can be fertile grounds for novice instructors to develop skills they might not develop without such structures. I have benefited from being a tutorial TA, and I expect that others can benefit from them as well. Do I think they are the most optimal place for novice instructors to be? Probably not, but they are certainly not the worst. On a side note, I think the Modelling Curriculum does much of this for teachers as well. It remembers what models you are supposed to help students make contact with, and some ideas for experiments and activities that will get them there.
Third, I have two concerns with highly-guided worksheet-based curriculum. First, students are intended to learn by engaging with worksheets; but they have been habituated to treat worksheets as opportunities to drill and practice what is already known. Because of this, we are always fighting the tendency to 'put down answers' and/or 'get through as quickly as possible'. There are certainly ways to mitigate this: Being explicit about your expectations for tutorial activity, providing common writing spaces like whiteboard, only giving students one page at a time, engaging with students in kinds of discourse the undermines the worksheet-driven discourse (instead of allowing it to undermine you). But that's a fight I don't want to fight, if I don't have to. Second, I find the word 'guided' curriculum problematic for me and my students. My experience is that students can quickly learn the boundaries of that curriculum–the one set forth by worksheet and the instructors who teach around it. When students sense that their ideas do not comprise a significant part of the curriculum, I believe they start to shut down. They start to think within the boundaries of the curriculum instead of the boundaries where their thinking and their inquiries lie. Sure, a good curriculum should have boundaries that overlap with students boundaries, but the reality is that they rarely do because individuals and classrooms are idiosyncratic and variable. Students don't make contact with ideas exactly when they are supposed to.
Other have said this better than I can, so I cede the remaining space here to another. The following excerpts are from David Hammer's "Discovery Learning and Discovery Teaching" published in Cognition and Instruction in 1997.
“Students do sometimes see and invent what they are intended to see and invent, and well-designed materials can improve the chances of that happening...On a traditional view of teaching and curriculum, one might expect these worksheets to succeed in guiding the flow of student learning through the predetermined sequence of ideas and observations. Thereby, one would see shortcomings in [them] for not anticipating the various aspects of students' knowledge and reasoning. The teacher's role in that view is peripheral, to help keep the students on the planned path, and the most successful materials should obviate teacher intervention."
"On the view of teaching and curriculum that I am promoting, a curriculum succeeds, not by guiding the flow of learning and instruction, but by helping to establish an arena of activity rich with opportunities for student and teacher discovery. Within that arena, the substance of the course, the curriculum, emerges. This is a view of teaching that is more flexible with respect to pace and substance, but it is also more dependent on teacher awareness and judgment. Presuming uncertainty, the teacher does not expect students to arrive at given insights at given moments; rather, it is the teacher's responsibility to recognize when and if they arrive at those insights or others, to discover their progress, and diagnose their difficulties. The teacher's role is not simply to keep students on the right path; it is to find out what paths there are, to scout
ahead to see where they may lead, and to make judgments about which ones to follow."
I didn't say this in a public talk, but I did say this in public during lunch to a handful of people. I believe the entire quote was something more like, "I love Tutorials as a resource for myself for thinking about activities, questions, and bits of sequencing in instruction, but I would never let my students within ten feet of those worksheets". As it happened, and by means of conference nearest-neighbor interactions, my comment was propagated through space and time and eventually found its way to some of individuals who created those very worksheets and whom were likely positioned to take offense at my suggestion that those worksheets should be kept in careful isolation from students.
I want to make it clear that I do stand by my statement. But that statement requires a bit of elaboration on my part to be full stood by.
First, the statement is truly meant to be about my students (with the emphasis on ME). I don't mind so much that others would use such worksheets as an orienting artifact for discourse management. In fact, I actively support instructors who choose to use tutorials and similar well-structured, research-based curriculum materials, and am committed to helping those instructors to implement chosen curricular materials in ways that maximize their productivity for students and instructors. For me, however, the set of things I want my students to experience and learn, I have personally found difficult to achieve with worksheets. I want to emphasize that it is not impossible to achieve them, but it is difficult. I must confess that have never felt extremely competent as a tutorial instructor, partially because of the feeling that, in such an environment, I am forced to co-teach with someone (i.e. a worksheet) that often undermines much of the productive patterns of listening, discourse, and engagement that I actively work to promote. Co-teaching can be an amazing experience, but it need not be, and I don't find that a worksheet is the kind of co-worker I want around, at least not very much.
Second, I learned a lot about student thinking and learning by being an instructor in tutorial environments where a highly-regimented, worksheet-driven discourse mediates much the classroom talk. By not having to mediate all of the discourse all the time, I was given the opportunity to listen without worrying about where we were going next. I didn't have to worry, because the worksheet remembered where we were going and what we would do next to get there. As a novice instructor, with all of this to worry about, I could allocate more of my resources to trying to make sense of what students were doing, what they were thinking. I believe that structured environments in which artifacts do much of the remembering can be fertile grounds for novice instructors to develop skills they might not develop without such structures. I have benefited from being a tutorial TA, and I expect that others can benefit from them as well. Do I think they are the most optimal place for novice instructors to be? Probably not, but they are certainly not the worst. On a side note, I think the Modelling Curriculum does much of this for teachers as well. It remembers what models you are supposed to help students make contact with, and some ideas for experiments and activities that will get them there.
Third, I have two concerns with highly-guided worksheet-based curriculum. First, students are intended to learn by engaging with worksheets; but they have been habituated to treat worksheets as opportunities to drill and practice what is already known. Because of this, we are always fighting the tendency to 'put down answers' and/or 'get through as quickly as possible'. There are certainly ways to mitigate this: Being explicit about your expectations for tutorial activity, providing common writing spaces like whiteboard, only giving students one page at a time, engaging with students in kinds of discourse the undermines the worksheet-driven discourse (instead of allowing it to undermine you). But that's a fight I don't want to fight, if I don't have to. Second, I find the word 'guided' curriculum problematic for me and my students. My experience is that students can quickly learn the boundaries of that curriculum–the one set forth by worksheet and the instructors who teach around it. When students sense that their ideas do not comprise a significant part of the curriculum, I believe they start to shut down. They start to think within the boundaries of the curriculum instead of the boundaries where their thinking and their inquiries lie. Sure, a good curriculum should have boundaries that overlap with students boundaries, but the reality is that they rarely do because individuals and classrooms are idiosyncratic and variable. Students don't make contact with ideas exactly when they are supposed to.
Other have said this better than I can, so I cede the remaining space here to another. The following excerpts are from David Hammer's "Discovery Learning and Discovery Teaching" published in Cognition and Instruction in 1997.
“Students do sometimes see and invent what they are intended to see and invent, and well-designed materials can improve the chances of that happening...On a traditional view of teaching and curriculum, one might expect these worksheets to succeed in guiding the flow of student learning through the predetermined sequence of ideas and observations. Thereby, one would see shortcomings in [them] for not anticipating the various aspects of students' knowledge and reasoning. The teacher's role in that view is peripheral, to help keep the students on the planned path, and the most successful materials should obviate teacher intervention."
"On the view of teaching and curriculum that I am promoting, a curriculum succeeds, not by guiding the flow of learning and instruction, but by helping to establish an arena of activity rich with opportunities for student and teacher discovery. Within that arena, the substance of the course, the curriculum, emerges. This is a view of teaching that is more flexible with respect to pace and substance, but it is also more dependent on teacher awareness and judgment. Presuming uncertainty, the teacher does not expect students to arrive at given insights at given moments; rather, it is the teacher's responsibility to recognize when and if they arrive at those insights or others, to discover their progress, and diagnose their difficulties. The teacher's role is not simply to keep students on the right path; it is to find out what paths there are, to scout
ahead to see where they may lead, and to make judgments about which ones to follow."
Tuesday, June 14, 2011
PER Summer School
At FFPER, I am in a working group that is supposed to make plans for a Physics Education Research summer school. Three overall models have been proposed and are being discussed.
The first would be somewhat like a peer-review workshop, where researchers would be invited to bring their work to be presented, examined, and critiqued.
The second would be more like a formal PER school setting, where classes would be held to learn a particular research methodology (e.g., video analysis, item response theory).
The third is a research institute, where a different institution of education research would invite a dozen or so persons to come each summer for an intensive immersion in research on the local educational context.
Curious to see where this goes. Our goals are to make some decisions and make progress of funding plan.
The first would be somewhat like a peer-review workshop, where researchers would be invited to bring their work to be presented, examined, and critiqued.
The second would be more like a formal PER school setting, where classes would be held to learn a particular research methodology (e.g., video analysis, item response theory).
The third is a research institute, where a different institution of education research would invite a dozen or so persons to come each summer for an intensive immersion in research on the local educational context.
Curious to see where this goes. Our goals are to make some decisions and make progress of funding plan.
Thursday, June 9, 2011
Feedback on Workshop Abstract
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.
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.
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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