Sep 29, 2012

VideoLabs as Instructional Videos

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Today I made a submission to an instructional video contest/program called EDU Guru, sponsored by YouTube, Google, and KhanAcademy (sorry... not gonna link those). Being somewhat of an instructional video skeptic, I tried to use this as an opportunity to illustrate the value of a genre of instructional video that would be less at odds with inquiry instruction. The video I submitted is here:


There's also a companion video which shows the force meter readings for 65 mph, so a student who makes the prediction could then check it against actual measurements. I included a link down below1, but I recommend collecting the data and making the prediction yourself before ruining the surprise!

I've called it a VideoLab in conversations with friends. My hope is to create quite a few more of them this year. The relationship depicted here, of course, is less central to most introductory physics courses. We generally ignore air resistance precisely because it's messy, as the uncertainty in these measurements shows2. But I think it's actually pretty remarkable how even a system as gnarly and variable as this one can fit a simple model (as long as you give yourself some healthy error bars). In any case, the model of an "instructional video" that contains everything you need for collecting and analyzing quantitative data on a relationship could be quite powerful. It's no substitute for hands-on work, of course, but students who wouldn't otherwise have access to a proper physics lab (or simply missed class on lab day) could benefit greatly. Imagine if a whole slew of VideoLabs were accessible online... How 'bout it, folks? #videolab?

There's at least one precedent for using video this way, in the wealth of videos created and hosted by Rutgers Graduate School of Education (where I am currently a student!). Each of the videos on this site is designed to serve as part of a cycle in which students observe a phenomenon, form a hypothesis that explains what they've seen, consider the implications that their hypothesis might have for further observable data, then make a "testing observation" to see whether what's depicted in the video agrees with the prediction they made. The video I've made here is similar, but my goal is more to present students with data that can be analyzed quantitatively, in a style similar to the analysis of data collected during a paradigm lab of a Modeling Instruction unit.


I still plan on making a few more companion videos, including a qualitative "observation-oriented" video that could be used for asking, "What could we change? What could we measure?" before any instruments are shown. I have a lot of footage of stuff sticking out of my car window, and I want to make good use of it!! Maybe the next step is just to upload a bunch of raw footage set to a soundtrack of Empire State of Mind. Concrete jungle where dreams are made of... videos about air resistance! So that's how the line is supposed to end!



1 65 mph check video here!

2 I also did the same experiment with a flat disk instead of a plastic bag (a cd, as you can see from the picture above), but it's a lot less fun to watch and the numbers are no less messy. I'm planning on editing that together too though, for comparison's sake, when I get a moment.



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Aug 15, 2012

Instructional Resources in Programming

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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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Aug 7, 2012

What We Talk About When We Talk About Physics First

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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 (Fnet • ∆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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Jul 30, 2012

Modeling Physics First for Modeling Chemistry

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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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Jul 26, 2012

Notes on Consensus

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Tomorrow is the last day of our Modeling Workshop here in NYC. Everyone involved, from the workshop leaders to the participants (Big digital shout out to @elbee818, @jsb16, @d2thelhurst, and @fernwig!) have been amazing, and to say that I'm going to miss hanging out with these folks all day long is a gross understatement. On the bright side, though, looking back through my notebook on the train ride home today got me chomping at the bit to spend some much-needed alone time working out how I'll be putting this stuff to work with my ninth graders in the fall. As anyone who's completed a workshop has seen, Modeling Instruction is a method, not a curriculum - the worksheets and activities used in any workshop are meant to serve only as a starting point for applying the method to your student population. As I've mentioned before in this blog, it's a fascinating experience to leaf through other Modelers' revisions of activities, and take inspiration for what to include in revisions of my own.

One thing that came up a couple times in our workshop discussions was the role of note taking in a Modeling course. In a classroom that's using a Modeling method, students build all knowledge through consensus. This consensus emerges slowly as students struggle  collectively to interpret empirical observations of a unit paradigm lab, present solutions on a whiteboard, and ask questions about these solutions of their peers. Flashes of insight will come at unexpected moments, often when the class is at its most exciting and engaging, but a more nuanced understanding of the complexities of a model must be built gradually over many days. It seems to me that only the most sophisticated note takers will emerge from a lab or whiteboarding session with detailed records of the knowledge developed during that class period. Students new to Modeling are suddenly asked to think about science in a radically new way, and (by necessity to the inquiry process) often denied access to the resources that they've come to rely on during their previous years as a science student. Sure, some teachers pass out a textbook, but these books turn out to be more useful for building inclined planes than for working through most worksheet problems or lab practica... For ninth graders in particular, this whole new ballgame begins on their very first day of high school, simultaneous to a transition that already induces utter panic. It's my hunch that some minor restructuring of worksheets and other Modeling curriculum resources can go a long way in helping younger students get the most out of this complex process of knowledge-building.

When I was teaching Physics First in a "lab, lecture, & discussion" format, I developed a system of handouts to try to provide students some hierarchical structure for their class notes. (A description of these Notes Outline handouts was published in the "For the New Teacher" column in The Physics Teacher in September of 2011, and you can find an old blog post about my approach here.) Through these handouts, I felt I succeeded in providing a consistent and reliable resource for students in a class where very little emphasis was placed on textbook readings. As I've delved deeper into Modeling Instruction, I've become more convinced that providing some similar structure is crucial to helping ninth graders succeed in a class with such a strong emphasis on higher-order thinking.

I recently revised a few worksheets on force diagrams (click to view, then click on the "Print" icon in the view to download: 1a, 1b, 1c, 2), designed to be used at the beginning of a Balanced Force Particle Model unit with ninth graders. At the end of each of these documents, I've included a blank box labeled Notes on Consensus. In this box I've placed one or two very general questions that are directly relevant to the content of the specific worksheet (I've included one example to the right, mostly just to fancy up my post with a picture... Check out the worksheets themselves to see the scope of the prompts I'm suggesting!). In using these handouts, I plan to call attention to these Notes on Consensus prompts at the beginning of the whiteboarding session for a given worksheet. At the end of the session, I'll direct students to them again with language like, "Remember, it's your responsibility to write down anything that you might need in order to answer this question on your own later on. Can anyone offer suggestions about what would be helpful to include in these notes?" (From my experience with ninth graders, it's necessary to devote verbal cues and class time explicitly to this process.) As the course progresses, I plan to remove the prompts from the Notes on Consensus boxes, and ask students to give their own suggestions about what questions they think should be the focus of their notes. By isolating the most sophisticated and personalized form of note taking in these Notes on Consensus sections, I hope to provide a forum for students to both practice note taking explicitly and construct useful resources for developing content understanding over time.

The idea of prompting students to record notes on class consensus is far from new. Debbie Rice, a co-developer of a collection of Modeling materials designed for use with ninth graders, told me in a phone conversation that if teachers aren't explicitly drawing out class consensus from work done, then they aren't doing true Modeling. On the Modeling Instruction revisions of handouts to accompany Melvin Steinberg's excellent CASTLE curriculum (downloadable from the "Legacy ASU Modeling site"), most worksheets include a blank space marked "Consensus." However, such direct prompts are by no means the norm in most Modeling resources I've seen. Most Modelers encourage students to record corrected solutions to worksheet problems somewhere in the space provided, but I'm not sure that this alone sends the right message about the role of worksheets in the consensus-building process. As a Physics First teacher pointed out after looking over my revisions, placing Notes prompts on the worksheets themselves illustrates explicitly to a student that "the worksheets are a learning process on par with the lab activities... Ninth graders need a clear understanding of when they're expected to be building knowledge and when they're demonstrating knowledge." Furthermore, having specific conceptual targets for a whiteboarding session can help novice Modelers, since "a teacher can pace discussions better when they know they need to uncover certain consensus points by the end of the period."

In thinking about the value of inquiry, I've always wrestled with the degree to which "less is more." That is, when students are building knowledge for themselves, how much top-down scaffolding is too much? For example, it's become strikingly clear to me through this workshop that worksheet problems must be sufficiently ambiguous or open ended to allow for a variety of relevant interpretations. I'm very aware that providing Notes on Consensus prompts will put limitations on how a given worksheet or lab can be interpreted by students, and that this may seem in opposition to others' visions of true modeling. Indeed, one teacher's response to the Notes on Consensus format on these worksheet revisions was more along the lines of a general template for "whiteboarding notes" that includes separate spaces for recording points of confusion and similarities and differences with other groups' whiteboards, but no content-specific prompts. At this point in time I'm convinced that the content-specific prompts will be useful, but only time will tell.

In any case, it's clear to me that there is value to including consistent reflection activities throughout every step of the Modeling cycle. If students learn better note taking skills in the process, that's all the better! I'd love to hear any comments that YOU have on either the Notes on Consensus format, or the specific worksheet revisions I've posted here. If you end up introducing similar modifications to the curriculum resources you use, please, please send 'em my way!!


PS - A huge THANK YOU to Leah Kanner Segal and Lucas Walker for their feedback on the collection of materials I've posted here!

PPS - If you want the MSWord files of the PDFs I've posted, just ask! They're revised versions of the 2010 Modeling materials (revised by Mark Schober, one of the co-leaders of our workshop!), which are available on the main AMTA site, but I've included some fancy new pictures that you might feel like using.

PPPS!! - Speaking of which, those amazing cartoon hands in the worksheet revisions are drawn by cartoonist Jamie Sale. If you feel like trying to draw some hands yourself, Jamie will show you how to do it!!


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Jun 27, 2012

Concepts vs. Processes: Still More Thoughts on Khan Academy

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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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Jun 21, 2012

Advice for a New Teacher: Watch Others Teach

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A couple days ago, a certain math teacher/blogger put out a "Call for Advice for New Teachers." The response has been amazing so far, and I'd wondered at first what I could possibly contribute... But I decided to mention something that's been on my mind a lot for the past couple years.

I'll keep it quick, because lots of folks have already given remarkable advice, and and my suggestion is pretty simple: Every now and then, or even just once or twice during the year, sit in on another teacher's class and watch them teach.

A couple posts have alluded to this idea with advice like "engineer friendships," and "observe, observe, observe" in the case of advice to a student teacher, but I think the call to observe is equally relevant for anyone in the classroom. This seems to be one of those things that everyone agrees would be helpful but somehow doesn't actually happen all that often. Some schools have organized peer observation programs, but most don't, so it's usually up to the individual to give up a prep period to do something that will never, ever seem pressing. But it's worth it...

It doesn't have to be a teacher in your subject area, or someone who works with students who are the same age as yours. Simply getting out of your own class and into a fresh environment can be amazingly eye-opening. Lots of unexpected things can happen when you venture beyond the walls of your own classroom. If you witness students you teach working in another environment, for example, this can help you see their strengths in a different light and appreciate all the other classes they're taking simultaneously to yours. If you see students in a class that comes before or after yours in the school's year-to-year sequence, you'll get some perspective on where they're headed or where they've been. Heck, it doesn't even have to be a teacher who's all that fantastic. Some of the most valuable observations I've made have involved watching someone and cringing to myself, "Why, oh why, are they doing it this way??" and then realizing immediately afterward that I do exactly the same thing. The goal isn't necessarily to see models of how to teach effectively, although this will certainly happen. In my experience, it simply about shaking things up and giving yourself some fresh perspective.

If this kind of thing isn't common at your school, you'll have to muster some courage to make it happen. Make friends with folks at your new school, then brooch the subject casually at lunch ("Hey, does anyone ever do peer observations here?") Then, if your new friends seems receptive, try suggesting that you might stop by their class some day, at their convenience, with plenty of advance notice!! I've found that usually people are amazingly receptive, and even excited to have a visitor. You might even inspire them to sit in on a few others' classes, who'll sit in on a few others' classes, who'll sit in on a few others' classes...


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Jun 18, 2012

One Short-Lived Physics First Program: A Cautionary Tale

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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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May 24, 2012

101qs in Physics Class

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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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May 19, 2012

Sharing Modeling Resources

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A web-based hub for uploading and distributing Modeling curriculum materials is on the horizon. The potential significance of such a resource is huge, and a healthy conversation at this early stage can help ensure that it becomes both dynamic and user-friendly. 

In preparing materials for my own Modeling-based Physics First course, I've been looking through materials posted on a password protected portion of ASU's Modeling site. In particular, I've been spending a lot of time with two remarkable collections of materials developed and prepared by small groups of teachers in St. Louis (Debbie and Rex Rice, and Gabe de la Paz) and Pittsburgh (Shady Side Academy faculty, including Kathy Malone - recent recipient of the Albert Einstein Distinguished Educator Fellowship). Both collections have firm roots in the Modeling materials originally developed at ASU. However, in addition to revising these canonical materials, both collections also offer entirely original activities and even some major restructuring of the order of the conventional Modeling curriculum. In spending more time with these collections, I've been getting more experience with what I need in order to make efficient use of work done by another teacher, and it's been quite illuminating.

There are quite a few similarities between these two sets of materials. Both collections provide a large text file containing "Teacher Notes" for each unit in the curriculum. (The materials for one such unit are shown in the picture to the right.) These notes generally begin with suggestions on the Scope and Sequence and Instructional Goals of the unit as a whole, then go on to provide details about implementing the activities or worksheets contained within the unit package. Both collections include handouts or worksheets composed in Microsoft Word, and usually include one document file for each physical handout. (For example, a handout made to accompany a lab activity and a homework assignment directly related to that activity are usually included as separate files, sometimes in separate folders/directories.) The documents in both collections are formatted quite precisely, and I experienced frustrating formatting errors when opening some of these documents on my own computer. Most importantly, both collections reflect the great passion and expertise of the teachers who created them, as well as an enormous investment of time.

One key factor in the success of Modeling Instruction, I believe, is that it has been almost entirely teacher-driven. Workshops are run by teachers and interest in the method has spread largely through word-of-mouth. Curriculum resources are developed and shared by teachers as well, though this practice is somewhat cumbersome at the moment. However, like the ASU Modeling site, the online home of the American Modeling Teachers Association (AMTA) is already hosting sets of materials developed by high school teachers, such as the extensive work of Dr. Matt Greenwolfe. This site is going to be updated any day now to include a Modeling Curriculum Repository, in what will hopefully be a big step toward an online hub for Modeling-related resource sharing for teachers by teachers. Like any big crowd-sourcing project, there are some logistical hurdles, but I'll share here some of my thoughts and reactions to how this might be accomplished. 

• Efficient subdivisions of documents can help clarify which materials are relevant to a given topic or activity. Both of the collections I've mentioned were made to be downloaded as a package. As a result, the "Teacher Notes" pertinent to each package are rather lengthy documents. The notes that are specifically related to one worksheet or activity can occasionally be difficult to locate, and isolating one activity from the unit as a whole can be slightly tricky. This makes sense given the overarching goal of Modeling Instruction - Modeling is a unified approach, not a collection of activities to be blended piecemeal into a traditional curriculum. But as more and more teachers convert to Modeling, I believe the need to isolate individual activities will become greater. I think there's a lot to be gained in breaking down these large unit-based collections of files into smaller chunks. Individual files in the unit can contain a few closely related handouts (a couple of related worksheets with teacher notes, for example, or perhaps a lab handout and with both pre-lab and post-lab supplements). I've posted an example of collection of resources I've prepared for an investigation into friction here. 

• Maintaining a hierarchy of organization on the web (rather than within a single .zip file for a unit) can provide both flexibility and manageability to the resource collection. AMTA President Mark Schober has told me that, in his opinion, the ideal resource-sharing mechanism would include access to both individual materials and recommended collections of materials comprising an entire unit. These collections would be curated by an individual or group for use with specific student populations, like playlists of songs curated by notable taste-makers or music communities. The choice of what to include in these playlists evolves over time, and the files contained within the playlists evolve in parallel. The inertia of large collections of curriculum materials can make them slow to change according to teachers' evolving needs and wisdom, and a system based on individual files is bound to be more nimble. 

• If teachers have access to multiple versions of similar materials, user ratings and recommendations can identify versions that are unique, valuable, and appropriate for use with different student populations. This is a model already in place in many communities, including our own community of science educators. For example, exemplary resources designed for use with PhET applets can be nominated for a Gold Star, which identifies "high quality inquiry-based activities that follow the PhET design guidelines and that teachers find useful." The challenge of such a system is to find a balance between maintaining democracy in contributions from individual teachers and keeping the collection of recommended materials concise and manageable for teachers using the site. 

• SBCD - Standards-Based Curriculum Development. Fellow physics blogger Kelly O'Shea just published a fantastic post about bundling established stablished standards for her course to facilitate communication with students about what will be covered on tests. This got me thinking that curriculum materials hosted on the AMTA site might be organized according to standards as well. That is, a worksheet on motion maps could be tagged (in a database and on the document itself) as relevant to one or more standards, such as O'Shea's CVPM1 - I can draw and interpret diagrams to represent the motion of an object moving with a constant velocity. Perhaps the entire Modeling curriculum could be broken down into agreed-upon standards, varying from "I can design an investigation into the relationship between acceleration and mass for a constant force" to "I can solve problems involving the separation of two slits and the distance between bright fringes in an interference pattern from a laser." Specific standards could likely be consistent between courses of widely varying ages and student populations - a more sophisticated course would simply include a wider variety of standards and different supporting materials. For example, the CVPM1 standard above would be a part of a Physics First course and a university course, but the materials used to support this standard might look quite different for such different courses. 

• To avoid formatting errors, documents can be distributed in robust, universally readable file formats. In producing my own curriculum materials, I've taken to saving a version of everything in PDF format, to ensure that I'll always be able to open a specific version to print it out for use in class. Both Greenwolfe and O'Shea have chosen to distribute their materials as PDFs as well. A disadvantage of this method, of course, is that the PDF format cannot be edited, but a text file or word processing document can be included as well to make updates more flexible. Alternatively, a universally available word processing application like GoogleDocs could be used to avoid such formatting inconsistencies. Andrew Stillman, an administrator of the online professional development site YouPD, has advocated such an approach.

Creative Commons is key. Most Modeling documents I've come across have included at the bottom of the page a copyright tag like "© Modeling Workshop Project 2006," indicating that the work in the document stems directly from the original work done at ASU. Sometimes individual authors are identified and sometimes they aren't but this tag ensures that the owner of the intellectual property contained within the document is crystal clear. AMTA Executive Officer Dr. Colleen Megowen has told me that it is a priority for the AMTA to prevent the materials from being used for commercial purposes at any time in the future, but according to this page the copyright isn't explicitly protected against commercial use. It seems to me that without a watertight license, the entity that officially owns a given piece of work (whether it's the AMTA or an individual teacher who has designed their own materials) could at some point choose to restrict access to it, or aim to make a profit off its distribution. There's nothing wrong with teachers making money off of work they've done, but the alternative of an open source Modeling Curriculum Repository seems even more attractive. By attending a workshop, a teacher would be introduced to a wealth of free resources and a community of like-minded peers, both of which would aid them in their transition to Modeling Instruction. In order to protect this dream, a Creative Commons license can be used by any original author of material to prevent the work from being used commercially. Looking through descriptions of the various CC licenses paints some striking pictures of what the Modeling curriculum at large might look like!


Now that I've stepped off my soapbox, let me clarify that this is not intended to be a set of recommendations for how to structure the AMTA site or the files contained within it. Rather, this is just an early collection of personal thoughts on a topic that I find quite exciting. As the work of assembling both the site and the materials goes forward, I hope that this conversation evolves. What are YOUR thoughts?
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