I got myself into some trouble yesterday while out to breakfast with a few friends. Our conversation was perfectly civil until I brought up an idea for an informal research project I'd been curious about taking on to reveal common misconceptions about Newton's 2nd law. I'd been imagining walking the streets of New York City with a microphone and performing an informal survey of how people answer a question such as, "Why does an egg break against the floor when you drop it?"
My friends and I first discussed the logistics of such an operation: whether a person on the street is more or less likely to walk hastily away if the interviewer is wearing a lab coat and bow tie... or maybe even just holding a clipboard. We agreed that it would be important to record the audio, so I could go back and listen carefully to the wording of the answers.
I then gave my friends an opportunity to respond to the question in their own words, and this is where the trouble/fun began. I got a variety of answers, such as "the force of gravity collides with the force of the floor and the egg gets caught in the middle." I expanded the question to include an egg breaking when thrown against a horizontal wall, and these answers included "the egg is too brittle withstand the force of your throw when that force encounters the resistance of wall." I, unfortunately, did not record the audio, so I can't give you the precise responses, but the most relevant point here is that I felt that their answers reflected some common misconceptions about Newton's 2nd law.
However, when I revealed to my friends that they'd answered the question incorrectly, they all got very defensive. They felt that a) I had tried to trap them into giving incorrect answers by asking an unclear question, b) I had tempted them with incorrect reasoning by paraphrasing answers I knew were incorrect ("It sounds like you're saying..."), and c) I was nitpicking about the precise definitions of words like "force" and "inertia," rather than focusing on the conceptual validity of a response.
Their first two criticisms were certainly valid. My friends said afterward that they had been focusing on what aspects of the structure of the egg shell cause it to break, in contrast to "a steel egg." They felt that my clarifying questions interfered with their reasoning process unfairly, and that my facial expressions and tone of voice helped to convince them that these incorrect explanations were in fact correct. When they finally learned that this explanation was incorrect, they felt betrayed and angry. One friend remarked that treating a person on the street in this way might get me punched in the face.
The third criticism, however, is much more complicated. When I ask this question, I am most interested in whether the conceptual framework of the answer is correct: whether the individual is invoking the spirit of Newton's laws in their answer. However, I believe strongly that some mistakes in terminology do reflect actual flaws in understanding. If someone doesn't use the word "force" at all (the word push is equally valid in this context), I would certainly be satisfied with answer that was conceptually correct: The table had to push against the egg really hard to stop it quickly, and eggs break when they get pushed that hard. But is it possible for a conceptually valid answer to misuse the word "force" to mean inertia? I would say no, that if someone is using that same word "force" to describe the interaction between the floor and the egg, then this reflects true misunderstanding of the force concept.
If I'm actually going to go out on the street and ask people this question, I might need to change a few things:
• The question needs revision. For starters, an egg doesn't break when you drop it, it breaks with it hits the floor! Perhaps this prompt would be better: Imagine you drop a fragile object on the floor and it breaks. Describe the interactions between any objects involved that result in the breaking of the object.
• I'd need to shut my mouth and let people explain to their own satisfaction with no interference on my part. I imagine this is common practice for researchers collecting data in this way.
• I could ask for an explanation that did not use some words (force, acceleration, mass), so as to prevent confusions arising from confusions with these terms.
• I could ask a series of smaller, simpler questions to hone in more closely on where the misconceptions lay. This is the approach of a multiple choice diagnostic like the FCI, but this approach runs a risk of categorizing people's misconceptions too early in the process.
If I was able to collect adequate data, I could examine the relevance of each of these factors. Since I often use this question as an example of the validity of a conceptual approach to physics education, this would be worth pursuing. I'll keep you posted on my progress!
Dec 22, 2010
Dec 13, 2010
Differentiated Instruction in Physics
Physics First provides opportunities for an interesting type of differentiated instruction, where students might arrive at a complex understanding of fundamental concepts through their exposure to a variety of experiences.
I just got back from a trip to Baltimore to observe Physics First classes. I had a chance to visit two of the fifteen Baltimore public schools now teaching CPO Physics First, but the details of this visit will have to wait until I have a chance to wrap my head around it somewhat!
In the meantime, though, I wanted to describe my experience at a monthly workshop for Baltimore physics teachers, called "Physics Works." Physics Works is a monthly gathering of physics teachers in the Baltimore public school system, and my trip happened to coincide with this month's meeting. The day's 2-hour workshop was based on planning differentiated instruction geared toward students' varied intelligences. (This idea was first suggested by Howard Gardner in 1983: humans exhibit multiple different types of intelligences: bodily-kinesthetic, interpersonal, musical, etc. An effective teacher can give students opportunities to participate in activities geared toward their personal strengths.) After discussing the varied strengths of the people in the room, we worked in small groups to complete the following task: develop a plan to teach Newton's laws that considers the multiple intelligences of students in a class.
Most groups in the room interpreted this task to mean providing students with a variety of assessments to choose from. These assessments could range from writing a physics rap to drafting a letter to Isaac Newton to analyzing of video footage from a football game. This is what the teacher running the workshop intended for us all to do, and she provided us with a handout on suggestions for creating a "menu" of options for students to choose from.
It took our group a while to notice this "menu" handout, and as a result our group interpreted the task to mean something very different. Instead of giving students a choice between assessment styles that might suit their strengths, we asked ourselves how we could exploit these intelligences to engage the students through different perspectives. We designed an activity on Newton's third law that began with students pushing each other outward in rolling chairs, to engage them through their bodies. We then imagined students breaking into smaller lab groups to discuss fictional students' interpretations of the results*, to engage them through words and conversation. Student might then work to design an experiment to collect quantitative data on mass and change in velocity with spring-loaded carts, to engage them through manipulating objects in space. This brought up a discussion of the link between logical-mathematical intelligence and spatial intelligence in data analysis using graphs and pictures, and so on.
What was exciting to me about this activity was that the concept of Newton's third law exists somewhere at the intersection of all these related activities. Students aren't just given the freedom to choose which types of activities they identify with more than others. Instead, they are expected to engage with the physics through each of the various activities, through areas of intelligence that they both excel at and struggle with. This seems similar to the multiple representations which lie at the heart of Modeling Instruction, discussed in the 11/17 post below.
When taken one-by-one, the "multiple intelligences" seem like a simplistic interpretation of human strengths and weaknesses, and indeed there is much to criticize in Gardner's theory. But perhaps the interaction between these intelligences is something to devote more attention to?
*These fictionalized discussions are used in Lillian McDermott and Peter Shaffer's Physics by Inquiry and Tutorials in Introductory Physics. These programs were developed by the Physics Education Group at the University of Washington, and they are both excellent. The format might look something like this for the activity discussed above:
Consider the following statements:
Student 1: A smaller student is always going to move faster because the larger student pushes them harder. Larger people are usually stronger than smaller people, so they have more pushing power.
Student 2: The recoil effect makes the person who did the pushing move backward, but this recoil never makes that person move faster than the person they pushed because their push is directed forward, not backward.
Student 3: Whenever two people interact, they push against each other exactly the same amount. A smaller person moves away from the interaction faster because they have less inertia, it’s easier for that same push to make them move.
Do you agree with any of these students? Explain.
I just got back from a trip to Baltimore to observe Physics First classes. I had a chance to visit two of the fifteen Baltimore public schools now teaching CPO Physics First, but the details of this visit will have to wait until I have a chance to wrap my head around it somewhat!
In the meantime, though, I wanted to describe my experience at a monthly workshop for Baltimore physics teachers, called "Physics Works." Physics Works is a monthly gathering of physics teachers in the Baltimore public school system, and my trip happened to coincide with this month's meeting. The day's 2-hour workshop was based on planning differentiated instruction geared toward students' varied intelligences. (This idea was first suggested by Howard Gardner in 1983: humans exhibit multiple different types of intelligences: bodily-kinesthetic, interpersonal, musical, etc. An effective teacher can give students opportunities to participate in activities geared toward their personal strengths.) After discussing the varied strengths of the people in the room, we worked in small groups to complete the following task: develop a plan to teach Newton's laws that considers the multiple intelligences of students in a class.
Most groups in the room interpreted this task to mean providing students with a variety of assessments to choose from. These assessments could range from writing a physics rap to drafting a letter to Isaac Newton to analyzing of video footage from a football game. This is what the teacher running the workshop intended for us all to do, and she provided us with a handout on suggestions for creating a "menu" of options for students to choose from.
It took our group a while to notice this "menu" handout, and as a result our group interpreted the task to mean something very different. Instead of giving students a choice between assessment styles that might suit their strengths, we asked ourselves how we could exploit these intelligences to engage the students through different perspectives. We designed an activity on Newton's third law that began with students pushing each other outward in rolling chairs, to engage them through their bodies. We then imagined students breaking into smaller lab groups to discuss fictional students' interpretations of the results*, to engage them through words and conversation. Student might then work to design an experiment to collect quantitative data on mass and change in velocity with spring-loaded carts, to engage them through manipulating objects in space. This brought up a discussion of the link between logical-mathematical intelligence and spatial intelligence in data analysis using graphs and pictures, and so on.
What was exciting to me about this activity was that the concept of Newton's third law exists somewhere at the intersection of all these related activities. Students aren't just given the freedom to choose which types of activities they identify with more than others. Instead, they are expected to engage with the physics through each of the various activities, through areas of intelligence that they both excel at and struggle with. This seems similar to the multiple representations which lie at the heart of Modeling Instruction, discussed in the 11/17 post below.
When taken one-by-one, the "multiple intelligences" seem like a simplistic interpretation of human strengths and weaknesses, and indeed there is much to criticize in Gardner's theory. But perhaps the interaction between these intelligences is something to devote more attention to?
*These fictionalized discussions are used in Lillian McDermott and Peter Shaffer's Physics by Inquiry and Tutorials in Introductory Physics. These programs were developed by the Physics Education Group at the University of Washington, and they are both excellent. The format might look something like this for the activity discussed above:
Consider the following statements:
Student 1: A smaller student is always going to move faster because the larger student pushes them harder. Larger people are usually stronger than smaller people, so they have more pushing power.
Student 2: The recoil effect makes the person who did the pushing move backward, but this recoil never makes that person move faster than the person they pushed because their push is directed forward, not backward.
Student 3: Whenever two people interact, they push against each other exactly the same amount. A smaller person moves away from the interaction faster because they have less inertia, it’s easier for that same push to make them move.
Do you agree with any of these students? Explain.
Dec 7, 2010
Teacher-Driven, Student-Centered
The
ninth grade physics class at this Quaker school is an example of how a
creative and dedicated teacher can make extensive use of resources from a
variety of places to design a unique and popular course.
I'm quite partial to the emphasis that Quaker schools place on holistic education, and I think that philosophies of Quaker education match nicely with some the ideas behind Physics First. This particular Quaker school I visited is fairly small. The 70 or so students in a typical ninth grade class are split into four sections, at 15-20 students each section. The physics class is required for graduation, so students who enter the school as a Sophmore or Junior take the physics class along with the ninth graders. The school also offers AP Physics B, which approximately 15 students a year elect to take in their senior.
The school has been teaching physics in ninth grade for many years (15+), and most sections of ninth grade physics have been taught exclusively by one teacher for the past four years. This teacher was a middle school math teacher before teaching physics, at MS104 in NY for six years and at her current school for five, after which she was recruited by the science department to take over the ninth grade class. She has a background in chemical engineering, and worked for 10 years as an engineer before deciding to get into teaching.
I'd been in touch with this teacher for a while before arranging a visit, and she was very generous about sharing the teaching materials that she uses in her course. This is especially notable because she uses a lot of different materials! Though students have access to Hewitt's Conceptual Physics text, the class seemed to be mostly built around activities and handouts that she has found in various places and sometimes altered slightly to better fit her course. (She models for her students a responsible respect for intellectual property by using material that has been distributed online for exactly this purpose, and by citing the author of a resource if she alters it from the original.) In the classes I saw, she made use of or referred to having used: a PhET simulation-based lab activity on graphs of accelerated motion, a handout on skydiving written by JL Stanbrough at Batesville High School, a clip from an episode of the Discovery Channel's Mythbusters (about Keanu Reeves and Patrick Swayze's timeless classic Point Break!), a short lab activity on dropping coffee filters taken from Hewitt's supplementary lab activities book, as well as some handouts of her own design. This type of diversity is exciting to see, and it's evidence of a class that's engaging for students.
To facilitate a discussion on the air resistance on a falling object as it approaches terminal velocity, she employed teaching method that was similar to Ron Thornton and David Sokoloff's Interactive Lecture Demonstrations, or ILDs. ILDs were initially developed for use in large classrooms where the availability of materials and time prevented students from performing their own inquiry-based labs on a topic. Students are given two copies of a handout filled with prompts for predictions and explanations relevant to a demonstration that is performed with equipment large enough to be seen by every student in the room. Before the teacher performs each step of the demonstration, students record predictions and explanations on one copy of the handout, to be collected at the end of class and checked for completion. After the demonstration is performed, students record the correct result and explanation on a copy of the handout that they keep in their notebook. She applied this method to a discussion about the shape of position, velocity, and acceleration graphs of a skydiver approaching terminal velocity. Since the size of her class was rather small, she was able to check student's guesses simply by walking around the room. I was especially impressed at one moment after students recorded their own individual guesses: She gave them permission to discuss their answers with other students in the class, and the room erupted into substantive, engaged conversation. After this, the teacher facilitated a discussion that included references to free body diagrams and a slope analysis of the graphs, and all students seemed quite invested in the explanation of what was wrong about their own graphs (almost every student drew acceleration increasing gradually from the moment of the drop, when the acceleration is the greatest at t=0s). The determined look on the faces of students who had passionately and convincingly argued a graph that turned out to be incorrect is an excellent example of cognitive dissonance in physics education. (A note about this link: This paper from 1982 examines an approach to teaching the particle model of gases that first exposes students preconceptions, but the first half of the paper gives a nice summary of some relevant cognitive psychology. A student's interpretation of the motion graph of a falling object is certainly more removed from their understanding of the natural world than their picture of the matter they interact with every day. But in comparing their own graph to the correct graph, many students in this class were directly confronted with their own incorrect assumption that acceleration increases as speed increases. The role of identifying "alternative frameworks of understanding" in physics education is a huge topic, one that is certain to come up again in future posts!)
The summer before teaching the ninth grade physics course for the first time, this teacher attended a physics teaching workshop through the Institute for Inquiry at the Exploratorium in San Francisco, CA, during which she was exposed to a wide variety of demonstrations, labs, and online resources. She attributed a lot of her exposure to good physics teaching practices to this workshop, and maintains frequent contact with individuals she met at the program.
The course has evolved significantly since this time, but the central focus of the course has remained constant. After attending the Institute for Inquiry workshop, this teacher made the decision to cover less significantly less content than her predecessor, choosing instead to cover material in greater depth. The content of the course changes from year to year, but her decisions have been informed somewhat by conversations with other teachers in the science department. For example, she does not include thermodynamics because the chemistry class covers these concepts. The decision to remove thermodynamics from the physics class was made after the chemistry teacher taught a section of physics a few years ago. It strikes me that this sort of crossing-over of teachers between the sciences facilitates greater communication between these teachers, and can in turn allow for a more consistent presentation of science throughout a student's high school education. That is, if science teachers at a school are familiar with each other's classes, the language in which concepts are presented in different classes can be more consistent, and the logic of the PCB sequence (physics informs chemistry, chemistry informs biology) can be exploited more effectively. Furthermore, one aspect of the science program at this school that's worth noting is that the format and priority of lab reports is consistent from year to year, through the different subjects. The teacher explained that this consistency was a recent development in the science department, but it's one that was surely facilitated by good communication between teachers in the different disciplines.
The physics classes are split into three sections of Quantitative Physics and one section of Regular Physics (for students that particular difficulties with math). For students that attended Friends for middle school, recommendations on which students belong in which section are made by the middle school math and science teachers. Placement of new ninth graders is based mostly on their performance on a math diagnostic test. Tracking students with difficulty in math allows the difficulty level of the "quantitative" sections to be higher than it would be otherwise, though none of the sections of Quantitative Physics I saw had much of a quantitative emphasis at all. The primary emphasis of the physics class at the school was on conceptual problem solving and exposure to new physics concepts through experience. The tests and quizzes I saw reflected this priority, and the teacher made a point of emphasizing that the algebra-based questions students were asked to solve in her course were never the questions they had trouble with.
The classes I saw on this visit were diverse in their presentation of material, and emphasized student discussion and involvement in activities. The teacher has not attempted to use diagnostics to gauge the effectiveness of the class, but the class fits well with the progression of the classes at the school.
I'm quite partial to the emphasis that Quaker schools place on holistic education, and I think that philosophies of Quaker education match nicely with some the ideas behind Physics First. This particular Quaker school I visited is fairly small. The 70 or so students in a typical ninth grade class are split into four sections, at 15-20 students each section. The physics class is required for graduation, so students who enter the school as a Sophmore or Junior take the physics class along with the ninth graders. The school also offers AP Physics B, which approximately 15 students a year elect to take in their senior.
The school has been teaching physics in ninth grade for many years (15+), and most sections of ninth grade physics have been taught exclusively by one teacher for the past four years. This teacher was a middle school math teacher before teaching physics, at MS104 in NY for six years and at her current school for five, after which she was recruited by the science department to take over the ninth grade class. She has a background in chemical engineering, and worked for 10 years as an engineer before deciding to get into teaching.
I'd been in touch with this teacher for a while before arranging a visit, and she was very generous about sharing the teaching materials that she uses in her course. This is especially notable because she uses a lot of different materials! Though students have access to Hewitt's Conceptual Physics text, the class seemed to be mostly built around activities and handouts that she has found in various places and sometimes altered slightly to better fit her course. (She models for her students a responsible respect for intellectual property by using material that has been distributed online for exactly this purpose, and by citing the author of a resource if she alters it from the original.) In the classes I saw, she made use of or referred to having used: a PhET simulation-based lab activity on graphs of accelerated motion, a handout on skydiving written by JL Stanbrough at Batesville High School, a clip from an episode of the Discovery Channel's Mythbusters (about Keanu Reeves and Patrick Swayze's timeless classic Point Break!), a short lab activity on dropping coffee filters taken from Hewitt's supplementary lab activities book, as well as some handouts of her own design. This type of diversity is exciting to see, and it's evidence of a class that's engaging for students.
To facilitate a discussion on the air resistance on a falling object as it approaches terminal velocity, she employed teaching method that was similar to Ron Thornton and David Sokoloff's Interactive Lecture Demonstrations, or ILDs. ILDs were initially developed for use in large classrooms where the availability of materials and time prevented students from performing their own inquiry-based labs on a topic. Students are given two copies of a handout filled with prompts for predictions and explanations relevant to a demonstration that is performed with equipment large enough to be seen by every student in the room. Before the teacher performs each step of the demonstration, students record predictions and explanations on one copy of the handout, to be collected at the end of class and checked for completion. After the demonstration is performed, students record the correct result and explanation on a copy of the handout that they keep in their notebook. She applied this method to a discussion about the shape of position, velocity, and acceleration graphs of a skydiver approaching terminal velocity. Since the size of her class was rather small, she was able to check student's guesses simply by walking around the room. I was especially impressed at one moment after students recorded their own individual guesses: She gave them permission to discuss their answers with other students in the class, and the room erupted into substantive, engaged conversation. After this, the teacher facilitated a discussion that included references to free body diagrams and a slope analysis of the graphs, and all students seemed quite invested in the explanation of what was wrong about their own graphs (almost every student drew acceleration increasing gradually from the moment of the drop, when the acceleration is the greatest at t=0s). The determined look on the faces of students who had passionately and convincingly argued a graph that turned out to be incorrect is an excellent example of cognitive dissonance in physics education. (A note about this link: This paper from 1982 examines an approach to teaching the particle model of gases that first exposes students preconceptions, but the first half of the paper gives a nice summary of some relevant cognitive psychology. A student's interpretation of the motion graph of a falling object is certainly more removed from their understanding of the natural world than their picture of the matter they interact with every day. But in comparing their own graph to the correct graph, many students in this class were directly confronted with their own incorrect assumption that acceleration increases as speed increases. The role of identifying "alternative frameworks of understanding" in physics education is a huge topic, one that is certain to come up again in future posts!)
The summer before teaching the ninth grade physics course for the first time, this teacher attended a physics teaching workshop through the Institute for Inquiry at the Exploratorium in San Francisco, CA, during which she was exposed to a wide variety of demonstrations, labs, and online resources. She attributed a lot of her exposure to good physics teaching practices to this workshop, and maintains frequent contact with individuals she met at the program.
The course has evolved significantly since this time, but the central focus of the course has remained constant. After attending the Institute for Inquiry workshop, this teacher made the decision to cover less significantly less content than her predecessor, choosing instead to cover material in greater depth. The content of the course changes from year to year, but her decisions have been informed somewhat by conversations with other teachers in the science department. For example, she does not include thermodynamics because the chemistry class covers these concepts. The decision to remove thermodynamics from the physics class was made after the chemistry teacher taught a section of physics a few years ago. It strikes me that this sort of crossing-over of teachers between the sciences facilitates greater communication between these teachers, and can in turn allow for a more consistent presentation of science throughout a student's high school education. That is, if science teachers at a school are familiar with each other's classes, the language in which concepts are presented in different classes can be more consistent, and the logic of the PCB sequence (physics informs chemistry, chemistry informs biology) can be exploited more effectively. Furthermore, one aspect of the science program at this school that's worth noting is that the format and priority of lab reports is consistent from year to year, through the different subjects. The teacher explained that this consistency was a recent development in the science department, but it's one that was surely facilitated by good communication between teachers in the different disciplines.
The physics classes are split into three sections of Quantitative Physics and one section of Regular Physics (for students that particular difficulties with math). For students that attended Friends for middle school, recommendations on which students belong in which section are made by the middle school math and science teachers. Placement of new ninth graders is based mostly on their performance on a math diagnostic test. Tracking students with difficulty in math allows the difficulty level of the "quantitative" sections to be higher than it would be otherwise, though none of the sections of Quantitative Physics I saw had much of a quantitative emphasis at all. The primary emphasis of the physics class at the school was on conceptual problem solving and exposure to new physics concepts through experience. The tests and quizzes I saw reflected this priority, and the teacher made a point of emphasizing that the algebra-based questions students were asked to solve in her course were never the questions they had trouble with.
The classes I saw on this visit were diverse in their presentation of material, and emphasized student discussion and involvement in activities. The teacher has not attempted to use diagnostics to gauge the effectiveness of the class, but the class fits well with the progression of the classes at the school.