Physics Class Website Template

The class website described here is one example of a successful site that seeks to maximize student access to useful resources while minimizing updates to the site itself. This website can be easily transferred to a site for use with another class, either by requesting a duplicate copy of the template site, or by applying any individual technique to a site that's already built.

This is the second year that I've made heavy use of a class website that attempts to host all the resources that students might find useful in the course. Next year I'll be moving on to a new school, and while I plan on taking the template for the site with me, I'm hoping that the current site can remain useful to folks that will be teaching the course I've taught this year. I figured I'd write a quick synopsis of everything that makes the website tick, both as a resource for teachers at my current school and anyone else who wants to use the site as a template. If the basic format of what I've described below seems useful, just contact me by on twitter or by email (josephlkremer at gmail) and I'll happily make a copy of the site for you! Thankfully, Google Sites makes duplicating sites extremely easy, so don't hesitate to ask if you'd like to use the template as a starting point.

Click here to see a template of the site I used with my Modeling-based Physics First class.

The real success of this site is in the simplicity with which I'm able to update content that's most relevant to students. As the class moves forward and students generate new ideas, I rarely have to make changes to the guts of the website itself to give them access to the information they need. The breakthrough here was to think of the website not as a repository for materials themselves, but as a central hub through which students access these materials.

(I apologize in advance that the post reads like an advertisement for Silicon Valley, but the details of specific software make specific brands quite unique. In the interest of clarity, I've advocated for some very specific solutions here, but if you have suggestions of alternatives please mention them in the comments!)

SHARING HANDOUTS & PRACTICE SHEETS

On the right side of the homepage, I've made a dedicated page for each unit/model, and filled it with a few useful links, photos, and videos. I've tried to make these pages full of useful and relevant materials, but I'm not sure how much my students use it at all... Most importantly, these unit pages make it easy for students to access any handouts from class whenever they need them, from their computer or smartphone.

To accomplish this, I create a folder in Dropbox for each unit, and save a PDF copy of every handout in these folders, unit by unit. On your main Finder (for Mac) or Home Directory (for Windows, right?), right click on this folder and click on "Share Dropbox Link". The "Public Link" for this folder will be copied to your clipboard, and you can paste it as a link to at the top of each unit/model page.

To make a new handout available to students, I just print a copy to PDF in the folder for that unit. To update a handout, I just write over the PDF file in that folder and the updates show up automatically. With this system, I rarely have to make changes to the website when I make small changes to handouts.

Thanks to Joe Morin for his Dropbox tip above - the old "Public Folder" sharing method I'd been using was outdated and much less convenient!

SHARING CLASS PHOTOS

On the iPhone, Apple's "Photo Stream" provides a convenient way to share photos of whiteboards and lab activities from class in one consistent location. (If you know of a way to do this on other platforms, please let me know in a comment and I'll update this post.) To set this up for the first time, go to the Settings app, choose Photos and Camera, and turn on My Photo Stream and Shared Photo Stream.

To share photos from your class with iOS7, go to the Camera Roll, click Select in the upper left, and choose a few photos. Click the box and arrow icon in the lower left, then choose iCloud. The first time you set it up, make a new Photo Stream for the class you've chosen, and give it a descriptive name. After this, simply choose the appropriate stream to add more photos to the collection.

To make the Photo Stream publicly available online, you'll need to turn on the "Public Website" option. Go to the "Photos" app (not the camera, the app that's actually called "Photos"), choose the "Photo Stream" tab, and click the arrow next to the name you just created. Switch "Public Website" to "On", and share the link with yourself. This link can then be used as the permanent link from each section on the class website, under the "Class Photos!!" link. Click the pencil icon in the upper right to edit the page and change the links to your own Photo Streams.


The steps are the same in iOS6. Try this support page if you get stuck.

Students can access examples of whiteboards from their own section or others, and it's easy to separate sections from each other while giving students a chance to browse work from other sections as well as their own. My AP Physics class had 224 photos by the end of the year! I've also used the Photo Stream to post solutions (one by one) to practice problems for a "Rally Coach" Kagan Structure - one student is working on a problem while their pair coaches them through the solution while looking at a suggested solution online - using a smartphone or computer.

SKILLS AND EXTRA OPPORTUNITIES

Skills Based Feedback (or Standards Based Grading as it's more commonly known) has been a crucial part of giving my students the incentive and autonomy to focus their attention where they need it most. I've used the class website heavily to make this information students need most easy to find. Skills are grouped in clusters, arranged by quiz (while I give a few tests throughout the year, new skills are almost always assessed first on a quiz). For each quiz, students have access to an "Extra Practice Sheet" for practicing those skills explicitly, as well as a suggested solution. Once a student has completed and checked their work on this practice sheet (and talked to another person about their work), they can submit a Google form that automatically sends me an email containing that student's "Extra Opportunity Request." I can prepare this reassessment for the student, and they can show their improvement on those skills.

The website serves as a hub for all aspects of this system. Students can see their current skill grades, download practice sheets and suggested solutions, and submit online forms to tell that they're ready to show their improvement, all from the "Skills and Extra Opportunities" section of the site.

Current feedback is updated similarly to handout in the unit sections, via Dropbox. (Instructions on how to create a public link can be found here.) The Skills Feedback link at the top of page itself goes to a public link for a PDF file called SkillsFeedbackSheet. By writing over this PDF, I automatically write over the file that shows when students visit this link from the page. Thanks to Paul Bianchi for sharing the Excel Spreadsheet that I use to make keep these skills grades organized. If you'd like more info on how this sheet is organized, drop me a line!

Extra Practice Sheets and suggested solutions for each quiz type, or group of skills, are also accessed via Dropbox public links, making it easy to update the files as needed without making any changes to the website itself. Unlike the files on the unit page, these have to be linked one-by-one, but if your skill groups stay consistent from year to year, this will only have to be set up once.

Extra Opportunity Forms can be submitted directly from the page. Setting this up for yourself will require first making your own Google Form (feel free to use this one as a template), then editing the page so that your own form is embedded in the page. Once you've created your form go to the Live Form page, and copy the link in the URL bar. While editing the page, scroll down to the form, which will appear as a grey box. Click on the Properties icon to the left, and paste the link to the form in the box marked "URL to content".

(NOTE: The size of the window is deliberately set so that it doesn't cut off the form when viewed on a smartphone. You may want to check that this size is working correctly when you set up your own page.)

One last Google Forms trick, for experienced users: I got sick of looking back at the form responses to see the details on each form submitted, so I modified a script to send me an email with the contents of the form whenever a student made a submission. This is pretty handy if you're getting a lot of forms! A tutorial on how to create this script can be found here, though I found that it took a little bit of troubleshooting to get it working correctly with multiple email addresses for different teachers.

CONSENSUS NOTEBOOK ONLINE

There are a few other elements of the webpage that will have to wait for future posts, but I wanted to briefly describe how the "Contribute Online" section of the class website is structured. This year I've made a lot progress toward a long term goal of making class notes a more reliable and sophisticated resource for my ninth graders. In an inquiry-based class students simply can't rely on the traditional "write down what the teacher writes down" strategy of note taking, because so little of the important information is coming from the teacher. This section of the webpage became an important part of this, in conjunction with a published notebook I called a "Consensus Notebook." (more on this here and here)

For each unit/model in the course, I create a collection of collectively editable Google Docs, where each document contains a few discrete topics within each unit (BFPM 5: Force Pairs, BFPM 6-7: Components and Analyzing on an Incline), duplicated for each section of my class. Students contribute suggestions of useful notes, ask and answer questions, and post photos of relevant examples (often pasted in from the Photo Stream described above). I'll browse contributions every few days and make my own suggestions, or point out which suggestions I think are especially helpful or problematic. Since each student has an email address that's linked via Google Drive to the document itself, I can send a comment directly to the inbox of the student who wrote a post, asking students who wrote questionable or incomplete suggestions to revise or add to their previous work, simply by adding "+name@address.com" to the comment.

As the sections grow to include suggestions of various degrees of usefulness (to put it kindly!), students need to evaluate the suggestions to determine what's most useful for them. Students keep a paper notebook with the same hierarchical organization as the online documents. Each student individually combs through the examples and suggestions in each section, and decide for themselves what's important enough to write down in their own notebook. While some notes are taken in class, most of the reflection what information is useful happens outside of class, when students have time to think about their work, and identify which suggestions from the online doc they find most helpful to write down in their spiral bound paper copy of the Consensus Notebook.

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I hope that this template can be a nice jumping off point for folks who might otherwise be reluctant to start a class website, and that the tips I've stumbled upon can help the savvier teachers improve and streamline a site that's already up and running!

Do you have any other suggestions of simple ways to make a website easy to use for both teachers and students? Do you have questions about the various aspects of the site described here? Let us know in a comment so we can get a conversation started!

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Practicing Struggle at Home and in Class

Encouraging students to practice struggling has the potential to promote perseverance that can carry over into life pursuits unrelated to physics class. But the context in which this struggle takes place will influence whether students associate it with success or repeated failure, and this can have great implications for how they approach new challenges in the future.

Since I first began teaching, I've tried to make "practicing struggle" an important element of my classes. This was partly a matter of necessity, since concepts would sometimes take weeks to develop and students would have to cope with "not knowing" answers to some very central questions as we slowly worked toward more sophisticated understanding. When I came across Modeling Instruction, it seemed to fit in nicely with this emphasis. I'd interpreted the focus of Modeling to be on building physics understanding from scratch through experiments and analysis, and I knew that this would take a lot of struggle and failure along the way. Invariably, I assumed, this would mean plenty of learning from failure, as well as learning to fail, along the way.

I tried to emphasize this to my students again and again. After completing The Marshmallow Challenge on the first day of school, I posted the diagram on the right on the projector and we talked for ten minutes about what it could mean for our class. I included the diagram on a handout explaining my policy of standards-based grading. I taped a copy to the back of my gradebook, and I'd hold it up when new understanding was emerging from our conversation about a tricky new concept that no one had grasped the first time around. When I used a homework assignment to introduce for the first time a problem that required a new concept or technique, I emphasized that students' only responsibility was to TRY. Even if they didn't necessarily SUCCEED or LEARN much the first time around, we'd struggle in small groups and struggle as a whole class until we'd figured it out. But to my great dismay, most didn't seem to become any more comfortable with approaching new ideas in this way, even after months of practice.

I've long been convinced that Physics First is as much about teaching critical thinking and problem solving skills as it is about teaching physics, and perseverance through confusion and frustration is clearly a crucial part of this. I'm certainly not alone in focusing on how we might better develop such character-related skills. Some schools have gone so far as to issue character report cards to assess how these traits are developing, encouraged by psychologists' study of the predictive power of traits like "grit" on performance in and after college. By assigning homework containing material that students hadn't worked with in class, I hoped that I was giving students an opportunity to practice their perseverance, and thereby develop "truer grit." But morale among my students was quite poor much of the time, and the pace of the class has been extremely slow. For a while, students frequently expressed frustration that they never knew what to do on homework, that they were endlessly confused, that they couldn't tell when we reached consensus in class discussion, and worst of all that they couldn't even tell when their own thinking was on the right track.

Practicing struggle? Check. But it was clear that my students hadn't been benefitting from this practice as I'd hoped they might...

I have a colleague who, like fellow blogger Kelly O'Shea, is convinced that homework as it's traditionally assigned isn't effective. My colleague teaches two sections of the "Advanced" Physics First course, and rarely assigns required homework. Citing arguments by Alfie Kohn, he feels strongly that students should be free to do whatever they need to do outside the class to succeed, and free to make these decisions on their own. Kohn's arguments are indeed convincing, and my students' comments echo some of his conclusions precisely. In a 2006 article, Kohn wrote about homework:

It isn’t of any use for those who don’t understand what they’re doing.  Such homework makes them feel stupid; gets them accustomed to doing things the wrong way (because what’s really “reinforced” are mistaken assumptions); and teaches them to conceal what they don’t know.

However, many of my students in the "Regular" physics sections lack the perspective to recognize when they need more practice, or the maturity to prioritize this practice when it's not due the next morning. Required homework, if it's not graded for correctness, can provide some much-needed guidance and scaffolding of how one might spend time effectively outside the class. I agree with homework critics that busy work promotes a false sense of security (or worse), but for a ninth grader, total freedom to choose when and how to engage with a course can be quite crippling. My students were generally embracing the guidance I was trying to provide, but despite my best intentions it was clear this guidance wasn't nearly as effective as it could be. Rather than teaching students that struggle could be rewarding, valuable, and even enjoyable, I seemed to be teaching them to dread encountering a new idea for the first time.

In my simple sequence of 1) personal struggle, 2) small group struggle, 3) whole class struggle, the most confusing and difficult stage of the process has been taking place in an environment where a student can feel alone, insecure and vulnerable. In this context, individual struggle comes to be associated with fear, anxiety, and anger (the list goes on), all of which are detrimental to real learning. If my goal is to teach students to be comfortable with their confusion, this initial stage has to come in an environment they have a fighting chance of actually building confidence. Working with others in small groups is beneficial not only because more ideas are brought to the table, but also because students see others like themselves break through from confusion to understanding. But solidarity can cut both ways: students can band together to work together to puzzle through a new idea, or they can feed off each other's anxiety and confusion. This stuff doesn't make sense to anyone... Why should I even try? is a fire I've had to put out many times this year, but it's almost always come at the beginning of a class period, when students have all wrestled with a challenging new idea on their own the previous night.

This is not to say that students shouldn't be asked to struggle with new ideas on their own - quite the opposite. If struggle is going to be developed as an individual skill, students have to practice struggling individually. To some extent, this will happen with a well-designed practice assignment, where students have to apply and expand on work that began in class when tackling a new problem at home. Moreover, after students have practiced struggling "class first" for a few months (or more, depending on the students), they may build up confidence that can be directed toward working with brand new ideas on their own as well.

We want students to embrace and enjoy the process analyzing a tricky new situation in an inquiry-based physics class. Since the first stages of this process can sometimes resemble a game of pin-the-tail-on-the-donkey, it's reasonable to think that the teacher should be there to at least point them in the general direction of the donkey and put the tail in their hand, or that other students should be there to offer suggestions and cheer them on. I'm convinced that the ability to work through confusion and emerge with better understanding is a skill to be honed through repeated practice, and I've come to see that the early stages of this practice are crucial in the development of the skill. But if students are going to embrace the cycle of "TRY - FAIL - LEARN - REVISE - SUCCEED" they need to associate their struggle with success, not repeated failure. Otherwise, there's simply no incentive to bring themselves to new physics assignments again and again. Worse yet, there's no chance of building perseverance for life pursuits that will take much longer to develop than any physics concept.

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Instructional Resources in Programming

Khan Academy's new computer science platform is a refreshing deviation from the lecture-based curriculum resources previously offered by Khan, and has the potential to further encourage the exploration of programming as a tool for teaching creative problem solving.

Khan Academy just unleashed a new computer science platform. As somewhat of a KA skeptic, I have to admit that I was doubtful when I got the news, but on first glance it seems like this thing totally rocks. Before I get into the thick of some thoughts I've been having about instructional videos and programming, let me identify a few things that they're getting right in a most beautiful way:

• The platform is elegantly constructed, and allows for instantaneous feedback on how a change in the code has changed the behavior of the program. (...and the sliders on numerical values are awesome!)

• The activities are almost completely open-ended. Users are free to mess around with the existing program in any way that that want, or to start their own program fresh. Some of the benefits of this approach are outlined in a manifesto/blog post by KA Javascript-dude John Resig.

• Instructional narration is left off most videos. When narration is included, it's entirely optional unobtrusive for those inclined toward a more playful approach. Also, the narrator of the videos is a woman - isn't it about time we razed this CS boys' club to the ground?

I've suggested before on this blog that programming can be an ideal environment for problem solving. A programming environment offers explicit connections between cause and effect, provided the programmer is able to navigate a ruthlessly picky syntactical landscape. In other words, to succeed at programming, a student needs to both become familiar with the details of the language AND apply this language conceptually in creative ways to solve problems. The role of instructional videos in the pedagogical balance of concepts and processes is hazy, but this latest resource hits closer to the mark than anything I've seen from KA.

I found myself thinking about this balance a few months ago, when I made a few instructional videos about programming in Python. In the following video, I've tried to provide instruction on some commands required to code a "guessing game" (specifically, the use of the conditional statements if and while), but withhold some details that are necessary for completing the task. In making the video, I remember struggling with the puzzle of where to draw the line between giving student the support they need to go forward and leaving some freedom to explore the programming challenge as an outlet for creative thinking:

Rather than demonstrating outright how to complete the task, my goal was to provide what a student might need to get started programming and troubleshooting. I tried to provide a concrete foundation for why the basic design of the program is valid, and to model good programming behavior in my presentation. (For example, I put the program together in small chunks, frequently testing the individual chunks to confirm that they did what I expected them to do, and I consulted the internet for the answer to a specific question about Python syntax.) It was interesting to me to compare my video to the new KA tutorial on if statements, since the KA tutorial does some things much more effectively than mine. For example, the KA tutorial targets the if command explicitly, making it a more efficient resource than my own somewhat rambling contribution.. More importantly, the KA tutorial introduces the NEED for an if statement before the introducing the command itself. This seems similar to the Modeling Instruction tenet of introducing and defining a concept before giving it a name.

Some time ago, a math teacher in New York City created this excellent video, called "What if Khan Academy was made in Japan?" to contrast KA's "Watch. Practice. Learn." approach with a more effective "Struggle. Struggle. Learn." approach. That is, in countries like Japan and Finland, where math education programs are more successful than most programs in the US, students spend most of their class time working through difficult problems, rather than being told how to solve such problems by their teacher. At the end of the video, we're given an example of what a more effective instructional video might look like.

The main takeaway from this video is that learning takes place when students struggle with questions, not when they sit through an answer. While it's clear that instructional videos are useful for absorbing procedures, they have questionable value as tools for facilitating real conceptual learning, and for this reason most of Khan Academy still stands at odds with inquiry education. Drawing a line between concepts and processes is perhaps easier in programming than in math, but the KA Computer Science platform is a refreshing change, even from previous KA programming resources.

One hugely promising feature of the new KACS platform is that there aren't really any questions and answers to begin with, so it's up to the users of the site (teachers and students alike) to decide how to direct this sandbox experience. In the spirit of guided inquiry, I can imagine a series of "mod prompts" designed to identify unique or significant elements of the code. For example, in an assignment based on this cool little KA program that draws a radar screen from ellipses and lines in a rotating reference frame, a teacher could assign various challenges,* from "Change this program so that rotating bar is shorter in length" to "Change this program so that the trail on the line takes more time to fade away." Solving either of these prompts requires the alteration of only one value in the code, but identifying which value needs to be altered can be a non-trivial conceptual challenge. (I struggled with that second question for a little bit, but figuring it out gave me a much clearer picture of how the program was constructed. I'll leave you to figure it out on your own!!)

I'm still fascinated by the potential of programming to serve as a tool for exploring creative problem solving. I'm struck by the degree to which the environment adopted by KACS, which emphasizes the modification of existing programs over building programs from scratch, eliminates the need for a lot of direct instruction on programming language process. As KACS goes forward, I hope that we'll see more programs and tasks emerge, similar to how an educational community has been built up around Python. If the inspiration behind this branch of Khan Academy someday finds its way into the other curriculum resources they offer, Khan Academy users will be better served indeed.



*A few of the introductory programs on the KACS site include prompts to Change this Program, but this is (for the time being) left off most programs. I'm not sure whether I think it'd be a good thing for these prompts to be a more dominant part of the KACS experience. Certainly it would make for a more self-contained curriculum, but it may also excessively limit creativity. I guess we'll have to wait and see whether this expands as KACS grows further.

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What We Talk About When We Talk About Physics First

Any conversation about Physics First will tend to revolve around a few distinct motives, priorities, and assumptions. In order to communicate successfully about the benefits or limitations of inverting to a Physics First sequence, it's crucial to explicitly identify what we're bringing to the table in these conversations.

I recently watched online a recording of a fantastic talk given at the recent AAPT conference by Dr. Philip Sadler, this year's recipient of the Millikan Medal for "educators who have made notable and creative contributions to the teaching of physics." A very small portion of this talk is devoted to Sadler's characterization of what he called The Physics First Hypotheses: 1) physics knowledge can inform a study of chemistry and 2) chemistry knowledge can inform a study of biology. (A slide showing Sadler's wording is shown here.) This characterization of the potential benefit of Physics First is much narrower than my own, and it got me thinking about the motives, priorities, and assumptions that have come to be associated with an inverted science sequence. Sadler is explicit in identifying his own narrow interpretation of the term, but it strikes me that we rarely do a good job of clarifying exactly what we're talking about when we talk about Physics First.

The focus of this blog has been to investigate more closely the diverse mix of ideas that get lumped together under the Physics First umbrella, so it seems useful to try to summarize some of this diversity explicitly in a single post. In the paragraphs below, I've tried to characterize a number of ideas often linked to Physics First, along with a few personal thoughts and reactions about each. I'm sure I've missed some stuff here, so please get in touch (via comments, email, or Twitter) if you can suggest anything that should be on the list!

A. Physics for All: Many schools that have implemented Physics First offer physics as a required course for all ninth graders. Rather than a physics course taught only to self-selected, highly-motivated students, physics as a required course means that physics is taught to all students. Among folks who are passionate about physics this opportunity to reach more students is one of the most popular arguments for Physics First, but it requires conceiving of the physics course as a fundamentally different classroom experience. I'm convinced that this is an extremely good thing, but it makes some traditionalists nervous. Though most Physics First schools offer physics for all, some instead offer physics as an "Honors" option for students who have passed out of a ninth grade biology course (or have otherwise demonstrated a capacity for high-achievement in science). In my limited experience such courses tend to be taught in a more traditional, lecture-based style.

B. Physics Helps Develops Mathematical Proficiency: This is a popular motivation for Physics First in districts where student struggle to achieve high scores on standardized tests in math. These schools or districts can see an early physics class as an opportunity to provide relevant context to students' study of algebra and geometry, or even simply to teach more math earlier. This motivation has positive and negative aspects, of course. In some schools, the Physics First course has led to greater communication and cooperation between the science and math departments, and students have as a result come to see the math as a powerful tool for solving real-world problems. In other schools, physics teachers are asked to take time out of their study of physics to drill algebra problems in preparation for students' upcoming state-standardized test in math, or the physics curriculum itself is centered around around drilling traditional pencil and paper problems, devoid of scientific context.¹

C. Conceptual Physics: In environments where improving performance on standardized tests is less of a priority, some ninth grade physics teachers teach a physics course that contains as little math as possible. Teachers of a Conceptual Physics course will select topics that require only rudimentary algebraic or graphical analysis. Paul Hewitt's "Conceptual Physics" text is often used as a resource in such courses.² In my opinion, any good physics course should emphasize conceptual understanding over rote memorization or blind problem solving, but teaching concepts without computational context can be quite challenging. Answering a question like, "Why does it hurt less to fall onto grass than to fall onto concrete?" requires an abstract appreciation of the relationship for impulse (F_net • ∆t = m • ∆v) that is significantly more sophisticated than that required to solve an algebra problem. In other words, removing math from a physics course doesn't always make the course easier. (The complexities raised here have been on my mind for a while, but they'll have to wait until a future post!)

D. Physics is a Foundational Science: The classic biology uses chemistry and chemistry uses physics so teach physics first line of reasoning is probably the most common argument for inverting the BCP sequence, and in my opinion the least salient. Though Sadler's data are are only questionably connected to the Physics First discussion,³ they do show that content knowledge in physics (at the novice level of an introductory student) doesn't seem to translate to greater success in biology and chemistry. Whether this is because of too little crossover of content between these respective courses or simply because of a disconnect in representation and terminology, it's clear that simply having taken a physics course will not, statistically, impact an individual's success in a chemistry or biology course.

E. Inverting the Sequence Can Spur Pedagogical Change: My most recent post identified the potential for inversion to a Physics First sequence to bring about greater change within a science department. I argued that, since inverting a sequence necessitates changes to all high school science offerings, greater cohesiveness throughout the high school science curriculum can be achieved. A similar argument can be made within the physics class itself. A transition to Physics First is an opportunity to upset the status quo at a school, and can serve as incentive for teachers accustomed to using lecture-based instruction to try something different and potentially more effective.

F. Physics Helps Develops Scientific Reasoning and Critical Thinking Skills: Some physics curricula, such as a those built on ASU's Modeling Instruction or Rutgers University's PUM (Physics Union Mathematics), are based on the notion that students can only effectively learn science by doing science. The relationships, representations, and conceptual understanding in each unit of the course are built from the ground up by the students themselves, through analysis of empirical evidence and class consensus arrived at through discussion. Aside from being an effective method of teaching physics (no small thing, of course!), this approach instills in students the unique supremacy of empirical observations. In other words, students learn that evidence matters. Physics is especially suitable for a course in "evidence-based problem solving" because the systems and relationships we study can simultaneously be both gorgeously simple and puzzlingly counter-intuitive. Not all science teaching methods emphasize this skill, but some methods do, and a transition to Physics First presents a golden opportunity to transition to using such a method (see motivation/assumption E).

In my opinion, this last motivation is the single strongest argument in favor of both inverting a curriculum to Physics First and teaching physics to all students. By designing and analyzing experiments, students learn a scientific approach to problem solving - not just a figure out how far the ball goes type of problem solving, but a broader and more relevant figure out whether this pill can do what it says it does, figure out whether this politician can do what he/she says he/she can do, or figure out how to turn this rope into a rope swing type of problem solving. Students learn to always look for relevant evidence, and to be thoughtful and critical in interpreting that evidence. They learn that failure is an essential part of any problem-solving process, and that successful problem-solvers keep an open mind as they learn from their mistakes through repeated trials and errors. They experience first-hand the immense benefits and inevitable challenges of collaborative work. In designing a syllabus for a Physics First course with this emphasis, the question is not, "What physics content is essential for my students to know?" (As much as I hate to admit it, evidence suggests that zero physics knowledge is essential for leading a fulfilling life!) Instead, the question can be, "What physics content will be effective for developing critical thinking skills in my students?" What better time to start explicitly developing such skills than in ninth grade?

Sadler points out in his talk that a crucial piece of education reform is looking for evidence that indicates whether motivations and assumptions such as I've outlined here are statistically significant. Of course, it's up to teachers and education researchers to provide this evidence, and in the case of Physics First this evidence has been particularly slow in coming. I'm convinced that this lack of evidence is partly due to the great diversity and resulting disconnect between various implementations and advocates of Physics First. Sadler's data seem to refute the notion that familiarity with physics concepts promotes success in chemistry and biology (motivation/assumption D above), but I have not yet seen evidence to confirm or refute motivation/assumption F.⁴ In advocating for Physics First, it's not enough to point to decent FCI gains in ninth graders as a reason for the switch, but with no consensus of priorities within the Physics First movement it's hard to figure out where to point. I'm hopeful that a synergy between progressive teaching methods like Modeling Instruction and the Physics First movement can provide direction toward the motivations I've advocated for here, but until we see some real numbers we'll just have to call it a hunch...


1: There is a subtle distinction to be made here. Students drilling quantitative problems involving graphs and algebra can often look similar to students using these same graphs and algebra as tools to solve a scientific problem or make a prediction. In some curricula intended for use with ninth graders, students might even develop those "drilling techniques" through small group and whole class discussions, somewhat similar to a scientific inquiry process. The difference, however, is in the students' motivation for doing this work - whether they're doing math for the sake of getting through the worksheet, or for the sake of building more sophisticated conceptual understanding. The best way to tell these apart, I'd say, is to look at what happens before and after the graphs and algebra: are students collecting data about a situation, then using the analytical techniques they've developed to make, test, and revise predictions, or are they just doing more algebra?

2: Paul Hewitt has said that he originally intended Conceptual Physics to be used with ninth graders. His publishers, he claimed, refused to promote the book as a Physics First course, since so few schools taught Physics First. Therefore, various different editions of the book have come to be used in courses for a variety of age levels, from middle school to undergraduate university students.

3: Sadler says in his talk, "We needed large numbers and there aren't large numbers of people who do Physics First. So what we looked at was how much of each of these sciences kids took in high school, and then used it to predict their college grades in these other fields." Though this approach may measure the conceptual connections between high school science courses and university level courses, it doesn't seem to me to be all that relevant to the potential benefit of Physics First.

4: I don't really know what we might use as an effective measure of gains in the rather ambiguous area I've identified as my primary focus, but I'm looking for something. A pill-purchasing or rope-swing-construction pre/post test doesn't really seem like the right way to go, so if you have suggestions, please include them in the comments below!

PS: Tim Burgess' comment below should link to the following page - a great wealth of physics first research.

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Modeling Physics First for Modeling Chemistry

A Physics First course based in Modeling Instruction provides an opportunity to rebuild a science curriculum school-wide, with stronger conceptual connections across subject lines and a more cohesive high school science experience.

As I mentioned in my latest post, I just finished a Modeling Instruction workshop last week, and my head is still buzzing with new ideas on physics teaching. Some of the other workshop participants are lucky enough to be attending the 2012 AAPT Summer Meeting in Philadelphia. Due to some extremely poor planning on my part (misinterpreting the "6" in the advance registration deadline date to mean July for one... doh!), I won't be attending the conference itself, but since I've got a few friends down in Philly that I haven't seen for a while, I decided to take a short pilgrimage to the City of Rocky (and say hello to some physics teachers while I'm down there, of course!). In any case, I wanted to make a plug for a poster presentation (tonight, Monday 7/30, at 8:30 at the Houston Hall Bistro) by one co-leader of our NYC Modeling workshop, AMTA President Mark Schober. The poster is titled, "Physics Education Through the Lens of Chemistry Education," and its focus is on examining the benefits of Modeling-based Physics First as a foundation for larger transition within a science department.

I visited Mark's school last spring, and sat in on both some physics and chemistry classes taught to Sophomores and Juniors, respectively (Mark's been advocating for a shift in sequence to full Physics First, rather than the rather unique BPC ordering currently in place, but this transition may take some time to implement.). This past year was Mark's first at the school, and although the chemistry classes have been taught by Modelers for some time, Mark is the first teacher to teach physics using exclusively a Modeling method. In the physics class I saw, Mark began with some discussion about a test on the just-completed circuits unit, in which students got into a heated discussion about a question about a classic circuits puzzler similar to arrangement shown here. Mark gave students time to discuss their various solutions, and gradually the students who had struggled with the solution came around to better understanding. After this discussion, Mark moved on to whiteboarding Worksheet 1 of the Models of Light curriculum, which develops some basic properties of electromagnetic radiation. (The basics of this curriculum were nicely summarized in a presentation given by Kofi Donnelly at EdCampNYC 2012. A screencast of this presentation can be found here.)

Earlier that day, I sat in on a Modeling-based chemistry class where students were studying solubility. In addition to playing around with an awesome PhET simulation on solubility of salts (shown here), they had just completed a lab in which they used a conductivity probe to investigate the change in solubility as different substances were mixed into a sample of distilled water. While students were preparing whiteboards on their results from this lab, I had a chance to chat with a few groups, and it was obvious to me that each student understood clearly that conductivity could be used as evidence of a presence of free ions in a solution. Interestingly, however, no student I talked to could articulate why this connection was valid. That is, when I asked them to tell me what they knew about conductivity, they told me about electrons moving in a wire, through bulbs, etc. When I asked how this might be connected to the conductivity of a solution, they were stumped.

I'm not so sure that understanding how a conductivity probe works is essential knowledge for your average high schooler (I'm pretty sure it ain't...), but I was struck with the disconnect that existed from physics to chemistry for these very bright students. This, it seems to me, is exactly the focus of Mark's poster presentation. Beginning a high school science sequence with a Modeling-centered physics course in ninth grade can create a foundation of knowledge, language, methods, thinking skills and representational tools that can be called on (and built upon further) throughout a student's high school science classes. Furthermore, a constant conversation between teachers in different subjects through this transition and beyond can help build courses that emphasize the interconnectedness of concepts in science. The students in this chemistry class had taken physics, but not through a Modeling approach. While I wouldn't necessarily suggest that a Modeling curriculum would have better prepared these students to infer that a flow of ions must be responsible for the "conductivity" they measured, I do certainly think that better consistency between courses could have helped students to connect these concepts. Similarly, representations developed in the Models of Light unit could be used with representations of energy quanta developed the in chemistry class to build a more nuanced understanding of photosynthesis in Biology class the following year. As the Modeling method expands to include more resources in chemistry and biology, a transition to Modeling within a department has increasing potential to encourage this continuity.

I may be putting words in Mark's mouth, so please go talk to him in person at the Houston Hall Bistro tonight (Monday) at 8:30!!

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Concepts vs. Processes: Still More Thoughts on Khan Academy

Until Khan Academy attempts to differentiate between concept- and process-based learning, Sal Khan's instructional videos will continue to stand at odds with inquiry-based education.

Khan Academy is in the news again! Or maybe it never left... Ok, ok, I'm sorry for contributing yet another KA post to the education blogosphere (This is my third already, and I'm far from the worst offender), but this stuff's been on my mind a lot lately!

Recently, two math teachers posted a critique of a Khan Academy video, thus stoking the flames of an endless debate over the educational value of instructional videos. This video critique, dubbed Mystery Teacher Theater 2000, or #MTT2K, has received a lot of attention, and even spawned a contest to create the best KA critique. I'm proud to say that I've made my own #MTT2K video, which is embedded below.* Though Sal Khan's response to this criticism has been encouraging, I'm concerned that much of the debate surrounding Khan Academy obscures a subtler examination of the role that instructional videos should and should not play in a "revolution in education."

A lot of the Khan-bashing that gets tossed around is focused on aspects of Khan's videos that are unclear, poorly presented, or downright incorrect. Unfortunately, plenty of the KA videos can be criticized in this regard, but it's far from the majority, and Sal Khan's positive response to the #MTT2K project made it clear that he recognizes the benefit of rooting out and correcting such mistakes. As for the the gaffs, some fans of KA have said that Khan's occasional typos and stumblings make him a less intimidating tutor, and Khan is generally showered with praise for the clarity of his explanations. The majority of comments posted below his videos reveal as much. But for my money, the most severe criticism of Khan Academy has nothing to do with the clarity, or even the accuracy of a given video. Within an inquiry approach, clear and accurate explanations are actually a threat to the learning process.

Now, I freely admit that plenty of valuable information-gathering takes place through methods that aren't based in inquiry. For communicating the ins and outs of some accepted process, the instructional video medium is a fantastic way to create and store decent explanations. When I want to know how to apply some obscure filter in a photo-processing application, I don't spend much time performing experiments to arrive at the technique by inquiry. I go find an instructional video on YouTube that was made by some 13-year-old!! But truly process-based tasks are a tiny fraction of the learning that we're asking of our students. The great fear about Khan Academy is that it encourages students to see everything they're learning - addition, multiplication, algebra, calculus, free-body diagrams, conservation of energy, or even analyzing the actions and impulses of human beings caught up in a momentous event - as process-based tasks.

Is it unreasonably picky to insist on the sanctity of the inquiry process? 30+ years of Physics Education Research suggest that it isn't... The human mind is notoriously excellent at fitting in new explanations between the cracks of the things we think we know already, just so we don't have to throw out the old stuff. In my own contribution to the #MTT2K project, I tried to portray this phenomenon at work.

Admittedly, Khan took on quite a challenge in attempting to lecture about acceleration, a topic rife with nuance and levels of partially-correct understanding. The voice-over by the "student" shows how the video reenforces many common preconceptions, including but not limited to:

   • equating a clock reading (denoted by t) with a time interval (denoted by ∆t)
   • equating the direction of velocity with the direction of acceleration
   • misinterpreting common units of acceleration (m/s², or in this case, miles/s²)

Furthermore, Khan spends most of his lesson discussing unit conversion, a process-based task as fantastically mindless (and perversely satisfying) as painting a wall. Like wall-painting, it has to be done correctly, and a target instructional video could accomplish this instruction effectively if it wasn't folded into a lesson on acceleration. Indeed, Khan has made at least two videos (1, 2) that explicitly cover the subject of unit conversions, and together they've been watched over 200,000 times. Unfortunately, both of these videos ramble through the peripherally related topic of metric prefixes, fail to sufficiently demonstrate why multiplying by a "conversion factor" doesn't change the quantity represented, and do not contain examples of more complex conversions (How many m³/s are in a cm³/hr?), but these are subtleties compared to my main criticism of Khan Academy. We might be able to effectively offload to a video the task of teaching students to convert units correctly. (I couldn't find a video I'd want to use on Khan Academy today, but I might find it on Khan Academy someday.) However, there will never be a curriculum of instructional videos that builds up conceptual understanding of acceleration.**

There are more processes than just unit conversion involved in constructing a working model of acceleration, and instructional videos may have a role to play in students gaining familiarity with them. Using computer-graphing software is certainly one example. However, try to extend this list much further, and you see that making an explicit distinction between concept- and process-based tasks is pretty tricky. Is calculating the slope of a velocity-time graph process based? How about interpreting the meaning of this slope? How about linearizing a position-time graph? In any case, how can we tell if our video-curriculum has been effective? Purely process-based approaches to solving physics problems can be quite successful according to some measures, and assessments that truly discern correct conceptual understanding are a challenge to both develop and implement.

Luckily, our goal isn't to compartmentalize pieces of our curricula into "concepts" and "processes." The bottom line is that true learning requires students to actively make this distinction for themselves, and to approach solving new problems like a thoughtful human being, not a knowledgeable robot (damn those 100% success rate robots...). If this distinction is to be made by students, it has to made by teachers first, whether they're in person or online. So far, Khan Academy hasn't shown an interest in exploring this.*** Until they do, Khan's videos will continue to stand at odds with inquiry-based education.

*Though I made my video before I knew that there was going to be big prize money involved, it's fantastic that other teachers now have some more incentive to voice their opinion. Bring on the competition! Show us what you've got!!

**Do I truly believe that no videos will ever contribute to learning something conceptually? A definitive claim like this would require a rigid distinction between concepts and processes, which is impossible and sort of pointless. Regardless, I'd suggest that any conceptual understanding that comes from watching a lecture is a result of concept "construction" by the viewer, not "instruction" by the lecturer. Just as we've seen with research into the efficacy of in-person lecture courses, we can't rely on this concept construction taking place in most students.

***As I mentioned in my last post about KA, I got a chance to ask Sal Khan a question about the role of instructional videos in an inquiry process. He was somewhat dismissive of the criticism, suggesting that evidence against the benefit of instructional videos wasn't evidence against the benefit of HIS instructional videos. Specifically, he used an analogy about sugar pills and cancer research to suggest that his pills might just be the cure for cancer.

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One Short-Lived Physics First Program: A Cautionary Tale

One short-lived implementation of Physics First at a New York City public school should serve as a cautionary tale of the challenge faced in convincing a local community that ninth graders can succeed at physics. The format of a Modeling Instruction summer workshop can establish a productive relationship between teachers to help take on this challenge.

Some time ago, I sat down to talk with the principal of a high school in New York City that opened in 2010 with a commitment to teach physics to all ninth graders. The decision to teach Physics First was one of many qualities that made this school unique in its geographical area, including an emphasis on the arts, interdisciplinary coursework, and a consistent focus on three essential questions: Who am I? Who do I want to become? How do I get there? The Physics First component, however, was a sticking point for many, from the administrators who approved the school's application to the parents who enrolled their children at the school. Many voiced skepticism that ninth graders could do physics, but the school's principal, herself a ninth grade physics teacher, assured them that Physics First could be successful. The administration selected a curriculum that was backed by promising research involving ninth graders and teachers underwent a week-long training session during the summer to prepare to use the method.

The ninth grade physics courses, however, got off to a rocky start.  As early as the initial training period, teachers felt that the chosen curriculum program lacked sufficient hands-on work to engage students. The program emphasized group problem solving with a heavy quantitative emphasis accompanied by a small component of direct instruction* involving interactive whiteboard technology. Teachers were encouraged to follow a predetermined script dictated by the developers of the program, and the training itself was lecture-oriented. When students indeed proved unreceptive to the approach, individual teachers tried to reorient the course to their own priorities, diverging independently from their common training experience in an attempt to improve their own class. 

Meanwhile, skeptics of the program looked for evidence of failure that would bolster their argument to convert to a conventional curriculum order. No other schools in the immediate area were teaching Physics First, and parents lacked a concrete measure for the success of the program. Most students wouldn't be sitting for their first state-standardized NY Regents exam until eleventh grade and parents were terrified that their children would fail this exam and be stuck without having fulfilled basic graduation requirements. Midway through the second year of implementation, this lack of direct evidence for the success of the program won out. The DOE stepped in, making the decision to abandon school-wide Physics First and removing the principal from the school completely.

How might things have gone differently at this school? Could anything have been done to set doubting minds at ease? I think that this story provides an important case study in examining what a Physics First program needs in order to be successful. In this case, the pressure to abandon Physics First was rooted in parents' mistrust that this non-traditional program would not meet students' needs, driven primarily by a concern over fulfilling testing requirements. Ironically, results from other public Physics First schools indicate that students do quite well on a standardized biology test when they take the test for the first time as Juniors (at least in part due to the fact that these tests are generally written to be taken by Freshmen). Even if this is confirmed at this school, no one will know until next June, when the test is given to the school's first ninth graders. But in an environment of high stakes testing, parents and students can't simply be asked to muster the patience to "wait and see" if such a program has been effective.

Any school planning to institute a Physics First program can expect that this decision is not going to get the benefit of the doubt from parents, students, or even faculty and administrators. Perhaps a gracious transition is more likely in an independent school, where parents might feel bound by a tuition to maintain faith in the school and its decisions. Private school students are not usually subject to external testing requirements, and if a family doesn't support a curriculum decision made by a school, they're free to take their child and their money elsewhere. But in the public school system, inertia rules. "You basically have to teach an existing class," the principal of this school told me. "New York State has defined the Regents classes, and [physics] means a very specific vision involving eleventh or twelfth graders. It's hard to do [anything different]." A larger movement toward Physics First, perhaps on a district level, might help reassure parents that their individual child won't be left out in the cold, but failed Physics First initiatives such as the program in San Diego in 2001 demonstrate that this reassurance will only go so far.

A cohort of teachers implementing a new Physics First program needs not only formal training in how to teach Physics First effectively, but time and freedom to develop unified goals and methods for a specific population of students. In interpreting this particular story, I've come to the conclusion that in order for a public school implementation of Physics First to be successful it has to meet a much higher bar than a traditional science program. Traditional physics courses that conform to parents' and administrators' expectations are simply awarded the benefit of the doubt even when the value of this status quo is deeply doubtful. The paradigm of a Modeling Instruction summer workshop suggests a means by which to lay the groundwork for implementing a program that's both informed by PER and responsive to the needs and concerns of the school community. Since Modeling Instruction is so visibly different from conventional physics teaching, individual teachers learn early in their exposure to Modeling that, regardless of their personal experience and expertise, they'll need to attend a workshop training in order to apply the method in their own classrooms. When a group of teachers in a school or district is implementing a Modeling curriculum together for the first time (as was the case at my first workshop last summer), many teachers from the same school have time during the workshop to share ideas, reactions, and come to some agreement on their collective goals for the course.

Although it's been said many times, many ways, effective classes are created by effective teachers! Likewise, effective curriculum has to foster teachers' ability to remain flexible and creative with the application of that curriculum to a specific student population. Training workshops are as much about developing a camaraderie and common language between cooperating teachers as they are about exposing teachers to new methods. As one ninth grade physics teacher at this school wrote to me, "In order to be effective, teachers need flexibility to break the rules if something isn't working. Nowadays the trust in teachers has diminished, causing classrooms to resemble more a preparation for standardized test centers than anything else." Physics First provides an opportunity to break this pattern, but only if the classes can convince local communities to give this unconventional sequence a chance. Teachers are the only people who can make that work, and to do it they need time, training, and the freedom to implement curriculum they're invested in.


* Anything that I've seen called "direct instruction" has seemed like a desperate attempt to hang onto lectures within a sea of research showing that they're simply not effective. Just like the speaker says in the video linked to here, "If you look at the trends in education today, the majority of schools are looking for scientifically based instructional programs." So... lectures work because they have to? Hmm... At least it provides for some fine comedic material!!

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101qs in Physics Class

Ugh, what a grey, rainy day we've had in New York City today...

I spent a lot of time indoors at my computer, and stumbled across Dan Meyer's 101qs site, which I hadn't seen before. The idea behind the site is for teachers to upload pictures and videos in the style of Dan's Act One prompts, where other teachers give feedback on what questions might come out of the picture. In a classroom, it would be the students suggesting questions that might be answered using the data. Meyer uses the photos and videos to introduce elements of drama and storytelling to make problem-solving relevant to students who might otherwise feel an aversion to it.

One video in particular stood out to me, maybe because it's more "physicsy" than many others I saw:

There's lots of information in this video, and it brought up all kinds of interesting possibilities for questions that could be answered: Is the acceleration of the train constant? If so, what is it? Does the train reach a constant speed before it leaves the station? If so, what is this speed? If not, how long might it take for the train to reach its top speed? What is the instantaneous speed of the train exactly 10 seconds into the video?

Of course, to solve these problems you need information that's not available in the video, but most of what you might need is freely available on the web. For example, the length of a SF Bay Area BART car is about 70 feet, and the train can reach a top speed of about 80mph. (In some similar videos, all the information needed to make estimates is included in the video itself... This video might work that way if an adult of "average" height was simply standing in the foreground.)

I've been thinking a lot lately about video-based data collection, especially as a potential solution for students missing essential lab days in a Modeling-based class. What I find exciting about Dan's approach, though, is the power of an open-ended question. Not only do students get practice applying physics and math, but they also get practice using creativity to exploit the ubiquity of useful data in the world around them. High school science has the power to change how students think - everything they need to continue to answer these questions is around them all the time, as long as they stay curious.

(btw, the answers I got were: yes: ~1.2m/s/s, no: ~30s, ~10m/s)

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Intervention in Modeling

Concept-related intervention by teachers to correct or redirect student thinking can interfere with processes of peer-instruction and inquiry, but without intervention into the complex social dynamics of a high school classroom, the trust and courage required for these processes to be effective can be slow to develop.

As I've visited various ninth grade physics classes, I'm often faced with a question that teachers who employ inquiry-based instruction face every day: When to intervene in student thought-processes that are headed down the wrong track? For an outside observer like me, a policy of little to no intervention is almost always best, as it's crucial to the observation process to tread very lightly on the environment a teacher has created. But for the teacher who has committed to an inquiry approach, this question gets wrapped up in all sorts of conflicting impulses. Just how helpful is concept-related teacher intervention during, say, the small group discussion phase of a whiteboarding activity?

Anecdotally, my observations have suggested that the short answer is, "not very." In situations when students will be presenting group work to the entire class, pointed Socratic questioning seems most efficiently used when the entire class can benefit from witnessing and participating in another group's thought process. Rerouting this group's thinking prematurely denies every other student in the room the opportunity to think about why that particular line of reasoning doesn't hold up. Teachers might limit a group-by-group Q&A to "one question per group," but in practice this gives students an excuse to sit around doodling cartoons on their whiteboards while they wait for that one question to be answered. I've talked with teachers who like to plant correct ideas throughout the room in the group phase of a whiteboarding process in the hopes that this understanding will grow throughout the class as the whiteboards are presented. However, this takes for granted that such "idea planting" is effective in the first place. Surely these conceptual seeds can be more effectively sowed through a short hands-on activity or a more targeted "auxiliary" whiteboarding problem than by teacher-driven explanations.

It's essential, however, to draw a distinction between concept-related intervention and social intervention into the dynamic between students that can make peer-instruction succeed or fail. In one class I observed, a teacher intervened to delegate responsibility when two members of a group didn't seem to be contributing to a lab activity: "Why don't you help "M" work on the algebraic representation and you help "E" with the motion map?" These students made an attempt to obey these instructions, but "M" and "E" clearly didn't want any help from them, and they eventually gave up and resumed their previous unproductive behavior. I got the impression that the students were used to having their contributions shot down, probably in quite a few more environments than this one physics class. It's unrealistic to expect ninth graders to navigate the sometimes vicious hierarchies of academic or social capability on their own, yet we often ask them to do so. An inquiry-based physics class can provide a more level playing field for these types of interactions than a locker room, but in order to generate trust and courage in students, a teacher has to act as a constantly vigilant referee.

Colleen Megowan's PhD dissertation out of ASU describes four paradigms of the roles teacher play in four modeling-based courses she observed: teacher as scout leader, teacher as stern but kindly parent, teacher as coach, and teacher as general contractor. Here is an excerpt from her description of a ninth grade physics class (illustrating the stern but kindly parent paradigm):

[Students] appeared to feel comfortable saying what they thought to each other and to the teacher, even to the extent of challenging the teacher’s assertions (about physics) if it conflicted with their own commonsense concepts. There was no evidence that they were afraid of ‘looking stupid’ to one another or to the teacher. They behaved as though knowledge resided in their peers as well as their teacher... However, there was very little effort invested by students who took the lead in whiteboard preparation in making sure that their disengaged group-mates could make sense of the whiteboarded information. The teacher often put these disengaged students on the spot by directing questions to them in the whole-group discussion, and when this happened, their more engaged groupmates often rescued them with whispered cues and gestures.       (Megowan, 82-84)*

The classroom environment described here is a direct product of the teacher's "stern but kindly" interventions that have directed class discussions, whiteboarding, and hands-on work since the first day of school. As the latter half of the citation reveals, there are certainly aspects of the peer-instruction process that might still be improved upon, and the teacher's behavior suggests a very gradual, deliberate intervention intended to do exactly this.

Most of all, it is clear that the students in this class are operating within an environment of mutual trust. Over a few months in this classroom, they have gained the courage to examine their own thinking, and to learn from mistakes they and other students have made. It's the challenge of each individual teacher to determine when their interventions enrich this process for students and when they detract from it, but resources for teachers (in the form of Modeling Instruction workshops, or support material for an activity or worksheet) can provide some assistance in meeting this challenge.


*Megowan's dissertation is a fascinating read! It's available from the ASU "Resources" site linked here, near the bottom of the "Doctoral Dissertations and Masters Degree Theses" section.

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