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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VideoLabs as Instructional Videos

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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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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Notes on Consensus

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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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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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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Khan Academy II: Discussions and "Khanversations"

"Khan Academy" style instructional YouTube videos could be more effective for introductory physics if they used a discussion model rather than a lecture model.

I had a fine time last week at the WNET Channel 13 Celebration of Teaching and Learning (which consisted of about 30% substance, 20% patting teaching on the back for doing "such an amazing job," and 50% advertising), and I wanted to follow up on the post I wrote about Khan Academy.

Over the course of the day, I saw Sal Khan (the Silicon Valley superstar shown in the camera-phone screens to the left) give his standard talk, and then follow it up with an hour-long question and answer session. In general, I came away convinced that Khan's heart is in the right place, and that Khan Academy strives to be far more than a YouTube channel. The goal of Khan Academy, he said numerous times, is to off-load a number of tasks traditionally done by teachers in order to free up the teacher's time to do more valuable things. During the Q&A, I got a chance to ask Khan essentially the questions that I posed in the last post: What is the role of an explanatory video when we know that clear and concise explanations can be counterproductive to student learning? His answer was basically that students should have access to whatever resources that might be helpful to them, and they're taking seriously their responsibility to measure the effectiveness of the videos to identify which ones aren't working. Here's a quote from his response:

When I think about my own learning, there are some times when I learned something through the experiential, where finally when I had to write a program when I was doing some computer graphics, trigonometry finally kicked in... But for some things, you know, especially when I was doing higher level math, it really sometimes was a friend in a coffee shop giving me a clear and concise explanation. And I was just like, "Wow, that really hit the spot. That was really much better than what was in the book, and that got me through my stumbling block."

I agree with what Khan is saying here, but this response reveals a slightly simplistic view of how learning works. I can't deny that clear and concise explanations from friends or teachers have gotten me through some tricky spots as well. However, I'd also suggest that hearing those explanations in clear and concise terms sometimes didn't actually help me as much as other approaches might have. Precisely because I was hand-fed exactly what I needed to fill in the gaps in my understanding at that moment, a few days or weeks later, those gaps sometimes returned.

When I think about what Khan Academy videos might look like if they were truly out to correct student misconceptions about, say Newton's Third Law, I imagine something more like the "dispute between students" prompts you find in Lillian McDermott's Physics By Inquiry books (see my previous post on this topic). In the Khan Academy model, picture a "Khanversation" between two voices, in which both individuals make arguments supported by diagrams to support a claim their view is consistent with observations in the natural world. This approach would provide opportunities to bring common misconceptions out into the open and model effective argumentation for students as they practice these concepts and skills in their classroom.

In a 2010 review paper in Science, Stanford School of Ed Professor Jonathan Osborne calls attention to a great irony in many science classes - traditional science teaching fails to develop the skills of argumentation and debate that are at the heart of the way science actually operates. Not only do student-centered teaching methods help to develop these essential skills, they also facilitate learning of science concepts far more effectively. Osborne writes: "Learning is often the product of the difference between the intuitive or old models we hold and new ideas we encounter. Through a cognitive process of comparison and contrast, supported by dialogue, the individual then develops new understanding. Consequently, learning requires opportunities for students to advance claims, to justify the ideas they hold, and to be challenged." We should be teaching our students first and foremost how to navigate their way through this process, as this is a skill that will be far more relevant to them than any science concept. (excepting, of course, Newton's Third Law...)

One of the most productive aspects of whiteboarding is that students are expected to formulate a verbal argument to support their answer, and present this argument to the teacher and their peers. Not only does this give a teacher instant access to their students' reasoning, but the students themselves are constantly exposed to effective and ineffective arguments. What role might other methods play in this process? I have tried to use handouts to structure and spur dialogue between students, but I've never gone so far as to upload such a dialogue to YouTube. At first glance, however, this possibility seems intriguing.

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What's to Learn from Khan Academy?

The video lectures on Khan Academy don't address the complexities of how people actually learn. What might these videos look like if they did?

I was lucky enough to secure a free ticket to the Channel 13 Celebration of Teaching and Learning this Friday in Manhattan. Sal Khan is giving a talk about Khan Academy, the series of YouTube tutorials that have been touted as a revolution in education. Here's an example of Sal Khan layin' down some knowledge about Newton's Third Law:

There's a healthy discussion in the physics teaching blogosphere about why these videos aren't the revolution to education that 60 Minutes might lead you to believe. Physics teacher Frank Noschese makes a very strong argument on his blog in this post and others (there is also a nice set of links to other blogs at the bottom of this page).

Khan Academy lectures seem to me to be a new type of textbook for a sort of curriculum that has been around for ages. The problem is, we've seen that this curriculum just isn't effective. The idea that YouTube lectures can be useful to students isn't flawed in itself, but video resources for more effective pedagogical approaches just aren't posted on Khan Academy. Rather than bashing Khan, let's think about what types of videos might be used as part of more effective curriculum, like Modeling Instruction.

Modeling isn't about lecturing, of course. It doesn't matter whether the lectures take place in a classroom or on YouTube, lecturing just doesn't work. So, what video resources would be effective in a Modeling course? Much of the most valuable student experiences in a Modeling course can't be replaced by videos - hands on lab work, interpreting unique data, discussions with other students, presenting a whiteboarded solution to the class. Somewhere in the midst of all this I imagine there's room for, say, example problems worked out using language and representations specific to a Modeling course, but how would you prevent such concise explanations from interfering with a student's natural struggle to build their own understanding? Perhaps, as Derek Muller suggests in this video, students might benefit from watching a conversation between students as they gradually work toward a correct understanding of a concept or problem.

For me, the takeaway from Khan Academy is simply how easy it is for individuals to make simple instructional videos that are available to a very wide audience. There's still a ways to go in thinking about how such videos might supplement progressive pedagogy, but the method is there for the taking.

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Active Physics and Inquiry

An independent school in New York City provides an excellent example of a successful application of the Active Physics curriculum, but aspects of Modeling Instruction could have potential to make the course even more dynamic.

Active Physics is a project-based curriculum with a conceptual focus, designed to be used with ninth graders. Active Physics groups concepts by themes, such as "Communication," "Sports," or "Home," in an attempt to make the physics more relevant to students' daily life. The work done in each unit culminates in a "Chapter Challenge," where students must apply their knowledge to solve a real-life problem. One independent school in New York City has been using the Active Physics curriculum since 1994 as the foundation of a physics course for all ninth graders. When I visited this school, students were studying the efficiency of various methods of heating water, and were just about to begin the "Chapter Challenge" of selecting appliances to meet the basic needs of an average family, capable of being powered by wind-generator with an output of only 2400W.

When class began, students were seated in lab groups, discussing a question from their textbook: "Are high-efficiency appliance worth the added cost?" Students' responses reflected a common misconception - conflating the efficiency of an appliance with an assessment of its overall quality: "Well, yeah they're worth it... they're better." "They're more durable, work faster, and just work better in general." When students were asked to present the results of their discussion, only one group in three appreciated the more subtle implications of the concept of efficiency, stating, "A higher efficiency appliance will make up for its cost with less power used over time," but even this group was confused by the difference between the terms "power" and "energy." The stage was set for an inquiry-based activity to root out the would root out these misconceptions and lead students to a more sophisticated understanding of the concepts of energy, power, and efficiency.

The lab activity for the day consisted of heating up a beaker of water on a hotplate. The procedure steps outlined in their textbook were summarized on a projector: "Measure: 150mL of water, initial and final temp of water, measure time appliance is on (increase temperature by 20˚C)." After a brief discussion of how to use the equipment, students got to work carrying out these steps. They made a few potentially problematic procedural choices along the way (measuring water volume with a beaker rather than a graduated cylinder, plugging in the hotplate before starting their stopwatch, resting the thermometer against the bottom of the beaker, for example), but the teacher caught most of these and gave suggestions for improvements when he felt it was necessary to do so. In class discussion, students struggled with how to use the values they'd measured to make the required calculation of efficiency, but the teacher coached them through the process (partly by referring them to a similar activity done a few days earlier with immersion heaters):

Teacher: "Who remembers how we calculate the thermal energy gained by the water?"

Student: "Was that the thing that was 4.18...?"

Teacher: "Yes, we need the specific heat of water. Anything else?"

Over the course of the discussion, each group eventually arrived at calculations that basically agreed with one another, confirming an efficiency of about 10%.

While watching students carry out this activity and discuss the correct method for calculating efficiency, I tried to imagine what the same basic procedure would look like using a whiteboarding approach. Students might start the lab by brainstorming steps they'd take to to collect whatever data they felt were relevant to a calculation of efficiency, then writing these steps on a whiteboard and presenting them to the class for discussion. Once students had carried out these steps with their lab group, they could attempt a calculation of efficiency (again, on a whiteboard), and discuss as a class whether the calculations they'd made were relevant to the central question of the efficiency of appliances. Different groups could even use different methods of heating the water: an immersion heater, a hotplate, a microwave...

I emailed a prominent advocate of Modeling Instruction to ask about crossover between Active Physics and Modeling Instruction, and she told me that "Active Physics and Modeling Instruction don't go well together." Modeling Instruction is about developing basic models for the most fundamental interactions in physics, whereas the projects in Active Physics tend to highlight more complex applications of these concepts: efficiency of electric appliances, acoustic properties of instruments (watch your ears...), how to build a DC motor or generator, etc. Both of these approaches have merit, and it seems to me that there's a lot to be gained in exposing students to aspects of both. That is, a whiteboarding approach might have avoided the more "cookie-cutter" aspects of this particular lab activity on heating water (and probably brought misconceptions to the forefront more effectively), and a project-based "Chapter Challenge" in a Modeling course might give students a better appreciation for how even the simplest models they develop can be applied to their daily life.

In my observations, I've noticed a trend among teachers of Physics First: in the absence of a single universally-accepted ninth grade physics curriculum, teachers tend to pick and choose aspects of various programs that appeal to them. This dynamism is healthy and exciting, but there is something particularly thrilling about the momentum that has been building around Modeling Instruction. A lot of aspects of Modeling just feel like the right way to teach physics: whiteboarding, student-designed experiments, modeling phenomena with multiple representations, and it's tremendous to see the Physics First movement marching forward hand-in-hand with Modeling Instruction. Still, we'd be wise to keep in mind the potential benefits of a diversity of approaches and try to maintain some of the freedom and flexibility that characterizes so many ninth grade physics classrooms.

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