Graphical solutions put sense-making at the center of problem solving. They work for all levels of students. They make more challenging problems accessible to students with less math confidence/experience and they scale to calculus, allowing more advanced students to make deeper connections and write more elegant responses to questions.

I won’t spend time rehashing what I’ve written about before. The post that I wrote advertising the unofficial workshop that Casey and I led last year has a lot of info, summary, and links.

First up, a weeklong workshop for STEMteachersNYC that I am co-leading with Mike Pustie. This workshop is also being billed as an “introduction to Modeling Instruction” workshop. With the luxury of time for the workshop, we’ll get to do activities that support the skills students need to be successful with graphical solutions (for example: activities that get them internalizing and thinking in velocity-time graphs). We’ll also get to explore graphical solutions in momentum and energy, and we’ll get a lot of practice with each skill—so participants can leave feeling really confident about using and implementing the ideas (I hope!).

Here is the official description for the workshop:

Graphical methods for solving problems are elegant, connect to calculus, and support students who typically struggle with strict formulaic problem solving. In this workshop, we will see how to use diagrams (including vector addition, bar charts, and slopes and areas on various graphs) as problem solving tools in kinematics (1-D and 2-D), dynamics, momentum conservation (1-D and 2-D), and energy conservation. These approaches emphasize conceptual understanding and allow students to use diagrams as sensemaking tools while solving challenging quantitative problems. Students often enjoy thinking geometrically—and you’ve never seen as true a joy as when a student realizes she can use the Law of Sines outside of math class. Participants will see how these ideas can be introduced to students, will practice using the tools to solve problems, and will also practice student-centered discussion techniques through several modes of “whiteboarding” (https://kellyoshea.wordpress.com/whiteboarding/).

To register for this workshop (and to learn more about the other NYC summer workshops offered by this group), visit the STEMteachersNYC page.

I am also excited to be leading an official, day-long workshop at the AAPT meeting in MD this summer. This workshop will focus on forces and kinematics (just not enough time for momentum, energy, etc all in one day) and on whiteboarding skills and modes.

Here is the official description for the workshop:

**W11: Teaching Graphical Solutions for Forces and Kinematics**

Graphical methods for solving problems are elegant, connect to calculus, and support students who typically struggle with strict formulaic problem solving. In this workshop, we will practice methods for solving kinematics and dynamics problems graphically using velocity-vs-time graphs and force vector addition diagrams. These approaches emphasize conceptual understanding and allow students to use diagrams as sense-making tools while solving challenging quantitative problems. Students often enjoy thinking geometrically—and you’ve never seen as true a joy as when a student realizes she can use the Law of Sines outside of math class. We will also learn and practice student-centered discussion techniques through several modes of “whiteboarding” (https://kellyoshea.wordpress.com/whiteboarding/). Using table-sized whiteboards to facilitate small group work and large group discussions supports students as they voice and debate their ideas with their peers. We will try a variety of techniques that focus on normalizing mistakes in the classroom, thinking through other students’ work, and giving multiple opportunities for quieter students to engage their peers during class.

To register for the meeting, this workshop, etc, use the AAPT Summer Meeting 2015 website.

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If you know anyone who might be interested in either of these workshops, please pass along this information. Thanks! :)

I hope to see you this summer!

(P.S. Come to Physics Teacher Camp!)

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On the first day, they built and explained the electrophorus.

They made whiteboards at each table to work through the step-by-step charge situation.

On the second day, one group talked us through their whiteboard. (They were ready to present it at the end of the first day, but as soon as they got everyone paying attention to them, the fire alarm went off for a drill.)

After that, they went to work on some extensions. They tested the pan and the plate against Upper Tape and Lower Tape. They made an aluminum foil person with hair (as described in the document) and explained their observations when they tested it out. One group took their entire apparatus to the bathroom (which doesn’t have windows) because they wanted to know if you could see the sparks when you got shocked. Some groups tested pieces of their setups against other groups. Some got more involved in the foil person. Some only barely got started with the foil person. Some followed the prompts given by questions that I had put in their packets. Some ran off to test their own ideas.

**When it was time to clean up the classroom, one group stopped me and asked, “Kelly, what if we didn’t finish all of the questions?”** It was one of those great moments when a student helps you clarify something you’ve been doing, even doing intentionally, but hadn’t verbalized or made explicit before (even for yourself).

So here’s what we talked about. If you didn’t finish the questions, that’s okay. That’s generally always okay. No question is really that important. *None of the questions are important?* Well, none of them are important on their own. No packet falls apart from not doing one of them. **The knowledge we are building isn’t so fragile as all of that.** We’re building in redundancies in our explorations. We’re constructing ideas and then testing them multiple times and in multiple ways. We’re reconstructing these ideas. We’re modifying them. We’re strengthening them.

Maybe you noticed something peculiar about how this class is structured. Probably for the first few days, you left thinking, “Well… okay. I was able to do what we were doing, and it was fun, but I don’t think I really *get* it.” *Um,* y*ep! *It was probably like that for a few days, and then all of the sudden, it really started clicking. And now you feel strongly that you really understand what you’re doing. *True, true.* It kind of layers itself like that. It takes a little while, but then you really, really get it.

I brought up the same idea that afternoon in my 9th grade math class. (They are doing “mixed martial problem solving” all year with problems from a few different awesome sources.) It’s okay if you don’t do every problem in the problem set. It’s not okay if you opt out of the ones you think are hardest. It’s not okay if you do none of the problems. But it’s okay if you don’t get to do every problem. We’re building something that is strong enough anyway.

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How great would it be to have a day at AAPT that was designed to be totally collaborative and interactive? Where you could decide on that day what you were excited to share with other high school physics teachers? Where you had time and space to work together on a new idea?

Pretty great, right? Yes, amazingly great. **And how about if it only cost $20 to attend?** And if that included food for breakfast and lunch?

AAPT announces the first AAPT High School Physics Teacher Camp. The Teacher Camp will be held Sunday July 26, 2015 at the American Center for Physics in College Park, Maryland. This coincides with the national AAPT meeting held nearby at the University of Maryland from July 25-29, 2015.

The Physics Teacher Camp is designed to be a low-cost, organic, teacher-directed event where teachers gather to discuss topics of interest and to network, connect, and collaborate with like-minded peers. The format is inspired by the Edcamp unconference model combined with other active-learning elements. Unlike an Edcamp, however, the AAPT camp is limited to high school physics teachers. Throughout the day, breakout sessions will be held in several rooms, and participants can join any group they choose. Final discussion topics for those sessions will be decided on the day of the camp, and participants will also have a time to share something of their own with the group. Some pre-reading may be recommended based on the topics that are suggested by registrants, and time will be set aside for small-group discussions of the readings.

One session will be dedicated to “A Conversation with Eugenia Etkina.” Dr. Etkina is a leading figure in the Physics Education Research (PER) community and has developed the ISLE and PUM curricula for teaching physics. She will give a very brief presentation about her latest work and then participate in a “town hall” style discussion with the group.

More information about the schedule and the camp can be found at https://sites.google.com/site/physicsteachercamp/

Registration is $20 and covers lunch and a light breakfast. Participation is limited to 50 teachers who will be chosen based on a very brief online application. This application can be found here. Priority will be given to high school teachers who are teaching at least one physics class in the 2015-2016 school year.

Participants are invited to register for and attend the the AAPT meeting as well, but this is not required for participation in the Teacher Camp. This experience can be extended into a 2-day professional development experience by registering for the High School Teacher Day at the AAPT meeting held the next day (Monday July 27th) and available at a smaller cost than the full meeting. Please feel free to contact the organizers of the camp with any questions.

If you are even a tenth as excited as I am about this camp, then you already know how amazing it will be. **Of course, what will really make it amazing is the group of people who sign up and attend.** If you are a high school physics teacher and you are planning to attend AAPT this summer, please consider signing up.

If have never attended a national AAPT meeting, *definitely* think about signing up. You can attend the camp by itself (a low cost, high gain scenario!), and you could also extend your PD by a day by signing up for the High School Physics Teachers’ Day (a one-day registration for Monday, the day after the camp, that costs $85, still keeping it at a relatively low cost).

**If you live within an easy road trip, train ride, bike ride, etc from College Park, MD, think about signing up!**

Spread the word. Tell the other physics teachers you know. If you read this blog and teach another subject, please tell the physics teacher(s) at your school or in your district. If you write your own physics teaching blog, tweet with physics teachers, participate in a physics teaching list-serv, have a physics teaching PLC, etc—please think about passing on this message. Let’s make this happen.

There’s a lot of text in this post, so now enjoy some photos of teachers participating in that #unsanctioned workshop last summer. This could be you!

We (the camp planning committee) are all eager to answer questions here, on Twitter, or by email (find the contact info for everyone in the planning committee on the camp info website).

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Finally, I should give a quick shout out and thank you to the people who have helped get this started—Martha, Diane, and Steve (the planning committee); my virtual PLC past and present who answered the bat signal when we needed brainstorming help; Tina and the Twitter Math Camp folks for help with ideas about innovative, teacher-led PD; the AAPT executive board for supporting this effort and making it #sanctioned; and everyone who has been tweeting, retweeting, and otherwise helping to amplify this news. Thank you! Come to camp!

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The next section of the class starts on Monday, and I’ve been spending some time cleaning up materials to prepare for it. I made a new course handout and incorporated some updated advice from former students (which I’ve written about before) on the back of the page. A lot of this set of advice comes from this past trimester’s group of sophomores who gave me a lot of great feedback a couple of weeks before their final assessment. They were particularly fond of the grading system and the way that they saw themselves as being able to learn something challenging that they didn’t necessarily expect they could do.

Here is my draft of the full document. As always, feel free to borrow, steal, modify, etc anything you’d like (except, I mean, your students would probably rather have advice from your own former students than *my* former students). And ideas, reactions, feedback, etc are of course always welcome.

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For one thing, the one-trimester class means that students don’t go through multiple cycles of grading periods—they pressure is high for them to understand the system and make good use of it immediately. (For that reason, I’ve been experimenting with different variations on standards-based grading schemes in each of my classes during this middle trimester, and I hope to write more about those experiments here in a future post.)

In any case, the urgent piece remains—how to get students to understand how they can control and improve their grade quickly enough for them to really appreciate take advantage of the feedback and reassessments on offer. I consulted with our awesome learning specialist, Allison, and we devised a mini-conference approach (similar to what students might do in a writing class when working on papers).

On a day when students were working problems in groups, I got them set up and then moved over to the other end of the room (the physics classroom has lab tables on one end, so the space is divided enough for some privacy in these short meetings). One at a time, students came over and had a super short meeting with me. We looked at which objectives they had mastered, what was available to improve, and talked through a plan for when they might meet with me or take extra quizzes. They left the meeting with a sheet containing all of that information (including their plan). I was able to talk to all 16 students in about 20 to 25 minutes, and the students seemed much calmer about the grading process and more ready to use the remaining time in the term when they left. Allison was even kind enough to visit my classes when I first tried this activity to help make sure the students working in groups kept going and used the time well. (What an amazing support! I’m so lucky to have such wonderful people working with me here.)

After the success of the meeting in my 10th grade classes during trimester 1, I’ve put it into wider use in this new term. I already had one meeting with my new section of 10th graders (before interim reports for students-of-concern came out so that they had time to position themselves where they wanted to be at the halfway mark). There are now three weeks left before our second set of final assessments, and I’m planning to roll out this mini-conference system to each of my classes.

For each conference, I create a check-in form and fill it out for each student in advance. That helps make the conversation quick and to-the-point, and it lets each student leave holding an organized way of thinking about how they are doing and where they can improve. I’ve just worked through my 10th grade physics sheets and my 9th grade geometry sheets, so I will share a sample of each one here.

My 9th grade math class is actually a year-long class, and my approach to grading is really similar to what I’ve done in the past for physics (not conjunctive, but pseudo-binary, most recent score counts, weekly-ish quizzes, and with the portfolio component that my seniors in Advanced Physics last year really liked).

My 10th grade physics class is one trimester on E&M topics (without having had mechanics). I’m grading this one in a more experimental-for-me way (bigger assessments (tests instead of quizzes); scores for each objective can be 5, 6, 8, or 10; best score counts; each objective has lots of detail to guide them about what I’m looking to see (not included on this form, but will be included on a future post); retakes of objectives happen in subsequent tests (at least 2 tests per unit) and outside of class by request). This post isn’t the place to say lots more about this system, but I wanted to at least give some context for the image.

While I was writing this post, one of my math colleagues just asked me if I think this system will take away from kids using ActiveGrade—e.g. “I’ll just wait for Kelly to give me the sheet.” I suspect it won’t—the kids who use it will still use it, and the kids who don’t still won’t. I’ve seen 10th graders keeping their sheet up to date (updating it after subsequent assessments), but I suspect in general it is just a way to have a more personalized conversation and to make sure each student knows where they stand and how to get to a better standing place (if they want or need to do so).

I’d like to do these meetings more frequently in each class (maybe two or three times per trimester—the insanity of four preps, all of which are new-to-me (and some new to the school) has kept me from being more on top of this idea earlier in the term, but hopefully I can do a better job of it in the spring).

As per always, please feel free to borrow, modify, steal, improve, question, etc.

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Overall, both workshops seemed to be successful, even if one had to be #unsanctioned, and at least one participant has already been reporting success with implementing the strategies in class:

https://twitter.com/TRegPhysics/status/504352708925870082

Hooray!

I had a great time sharing with everyone and learned some new things myself, too! Thank you to everyone who helped make the workshops happen (including the participants!).

1) There is a “Part 2″ to this workshop scheduled for Sunday October 19th (2014) via STEMteachersNYC. It will be on Graphical Physics Solutions for Momentum and Energy (including going beyond just bar charts for problem solving in those models). If you’re in the NYC area, I hope to see you there! I’ll also post some recap information here, too, once that is complete.

2) I should be presenting a full day workshop in a more “sanctioned” manner at next summer’s AAPT meeting in Maryland. The plan for the workshop is to spend half of the time on this graphical solutions material and half of the time on what I’m calling “advanced whiteboarding techniques”—strategies for whiteboarding beyond the basic student presentations (practicing using mistake whiteboarding, speed dating, etc). I’m really excited about getting to do that, and I hope it will be appealing and helpful to others.

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On the Sunday of the AAPT summer meeting (July 27th), Casey Rutherford and I are offering a free, unofficial^{1} workshop on using velocity graphs and force vector addition diagrams to solve kinematics and force problems. I was really lucky to get to also work with Mike Pustie earlier this month to give a similar workshop for the STEM Teachers NYC (née PhysicsTeachersNYC) group.

Our hope is to show how our students use these diagrams as sense-making tools to solve problems, to give you time to try using them yourself, and to show how and why we’ve found them useful for physics students. These strategies can be more accessible for students who have less experience or confidence with math while also allowing for more subtlety, depth, and original thinking for students who have more math confidence and/or experience, so we think that teachers in a wide range of schools/classes/etc might find something useful in this workshop.

You can find more details about the July workshop including our description, the location, and the sign-up form on our workshop website.

And now, to make this a legit blog post, here’s a preview of the content:

In my observations, the kinematics equations can be a big stumbling block for intro physics students for a couple of reasons. (1) Solving problems with these equations means keeping careful track of algebra and dealing with a lot of symbols at once. (2) The procedure that many students adopt in using equations for kinematics often separates that work from making sense of physical situations. In that case, students may just be hunting for equations with the symbols they want and not doing a lot of (what I would call) real physics thinking.

Enter the velocity graph. (My favorite graph, as my students might tell you. It’s just so useful! The slope and the area both mean things, and (in intro physics) it’s usually a straight line, so the area is made up of rectangles, triangles, or trapezoids—all areas I can find easily.) With this approach, students always start problems in the same sort of way (making for a comfortable-to-students procedural-type feel)—they draw and annotate graphs that represent the situation. They immediately make decisions on what model is useful, direction of motion, how the speed is changing, etc. Their work is all about sense-making.

Here’s a taste of what it looks like when real life students solve problems this way. *(Note, the “Yay!” is the student’s—she wrote it while looking over the solutions when she turned in the quiz.)*

On the one hand, solving problems this way gives students who struggle with algebra, keeping track of signs, and remembering equations better access to solving quantitative motion problems at any difficulty level. On the other hand, it makes the connection to calculus really clear for students (they come back in subsequent years to exclaim that they are basically generalizing in math what they’ve done in physics—they leave the class with a real appreciation for the meaning of slopes and areas on graphs)—I see their work as being more mathematically sophisticated than it seemed to me when I was teaching students kinematic equations.

Here are a couple of old, related posts: On Annotating Graphs | On Students Noticing Patterns (Equations)

When it comes to procedural solutions that can allow students to move through problems without necessarily making physical sense of the solution, Newton’s 2nd Law in component form was a major offender in my classroom. Students were often bogged down in trigonometry (which they might not have even understood because they hadn’t gotten that far in their math classes yet) or sign problems or lining up the correct parts of the equation in just the way I had told them to write it. Every “good solution” to a problem basically looked identical, so there was (sometimes) little of a student’s own creativity or sense-making needed.

I found vector addition diagrams really compelling when I first encountered them, and I started showing them to students as an additional representation. Eventually, I started teaching balanced forces this way (and delaying components until unbalanced forces when students might be more comfortable with trig). And finally, students convinced me that this method was better and told me to stop teaching components. (Never fear—the idea of components comes up naturally for students as they analyze their diagrams, so they don’t really miss out on that concept, and they are ready to break velocity into parts when they study projectile motion.)

I only teach my students to draw vector diagrams to scale (if they are using them quantitatively—they always start with a qualitative sketch anyway). As they learn more math, they start seeing how they can apply trig ideas to their physics work and transition as they are ready. I can always tell when they’ve just learned law of sines (they are always so in love with that idea that they try to use it for everything, even right triangles, as soon as they’ve learned it). There is a lot of ownership and joy from students when they are deciding how to solve each geometric problem.

And again, here’s some delicious student work on force problems.

I think you can see from even just these three examples that this method allows for a diversity of approaches, that students are thinking about relative sizes of forces, and that students do end up inventing their own ideas about components in the context of the problem. Love it!

Here’s an old, relevant post: No More Components

If you will be in Minnesota for AAPT this summer and would like to join us for the workshop, please fill out the form on our website to let us know and to reserve a spot. Casey and I are excited to share this work with you! (Click the sign up button to go to the workshop website.)

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^{1} Casey and I started planning this workshop many months ago (January at least, but maybe earlier). Unfortunately, we didn’t understand how to get an official workshop and later found out we would have had to request that at least a year(!) in advance and not the several months in advance when the contributed talks are due as we’d thought—we asked if we could be added to the schedule once we realized that, but we were told it was too late for this year. We didn’t want to wait over a year to share what we’d been doing with students (and a 10 minute contributed talk wouldn’t have accomplished the same sort of sharing), so we decided to go the unofficial route for this year. So worry not—we didn’t set out to be especially subversive, and we plan to participate in many other, more official, AAPT events at the conference.

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One activity that I’ve done to help students build higher-level organization into their thinking is concept maps (which I got from Matt Greenwolfe, and which I hope to soon write a post outlining—so hopefully there will be a link here eventually). Concept maps have students put a structure to how the models they’ve built interact (or don’t interact) with each other. They are sort of a system schema for models. But in addition to that work (which we tend to do about twice per year), we also frequently talk about the biggest ideas we have as we go through physics (our fundamental principles).

At the end of my mechanics materials, I’ve long had a unit that returned to momentum and energy to pick up the idea of elastic and inelastic collisions and to try out harder problems that combined the big ideas in mechanics. It’s gone through a lot of names (like *Conservation of Momentum, Part 2* and *Momentum Transfer Energy Transfer* (aka MTET)) and is now drifting toward the name *3 Fundamental Principles: Problem Solving*. Here’s this year’s packet cover:

This year, we started the unit right when we returned from spring break. As a gentle review/re-entry and a start to the new unit, we begin with an activity that had each class break into three teams.

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We’ve had three really big ideas this year. Three basic ways that we’ve viewed everything. We’ve been referring to them as **fundamental principles**. Can you tell me one of them? (Newton’s Laws.) Great. [*I write it on the board.*] How about another one? [*It might take a little talking back and forth, but eventually we get*] (Conservation of Energy, Conservation of Momentum.)

Cool. Okay, in a moment, not yet, let’s break into three teams. Let’s say… Newton’s Laws in that back corner, Energy in the other back corner, and Momentum somewhere around the front here. Make sure there are people on each team. Grab a whiteboard for the team and put together a board of the different representations for the principle. Work right on the whiteboard first, because your ideas might change as you go along.

Okay, ready set go. [*They organize themselves pretty quickly, and I start cycling around from group to group asking questions and nudging them a bit here and there.*]

If you had to pick one of Newton’s Laws to be the banner one, or the one most useful for solving problems, which would it be? (The 2nd Law.)

[*The toughest part for every board is getting them to write the principle, not write about the principle or write a title for the principle in the verbal representation. This part takes the most nudging as I cycle through, and the conservation laws come together more easily than N2L. The class whose board I put below actually had the easiest time of putting a verbal statement together, opting to state it as Newton’s 1st Law, which worked really well.*]

[*The big idea graphically is the connection between the slope on a velocity-time graph and the unbalancedness of an FBD or force vector addition diagram. (I wish my students had put more labels on their diagrams here, but I think the intent was to leave them looking generic.)*]

[*The students usually identify this principle as Newton’s Laws collectively, but when it comes up, we talk about how it’s really the 2nd Law (which includes the 1st). And how the 3rd Law is really part of the momentum principle.*]

Models of N2L:

- Kinematics (Constant Velocity (CVPM), Constant Acceleration (CAPM))
- Balanced and Unbalanced Forces (BFPM, UBFPM)
- Special cases of Unbalanced Forces: Projectile Motion (PMPM), Uniform Circular Motion (CFPM), Universal Gravitation (CFPM), Simple Harmonic Motion (OPM)

So what’s the big idea? (The total momentum stays the same.) Always? (Unless there’s an unbalanced force.) Any force? (Unbalanced outside force.) That sounds good.

One thing I notice—your equation doesn’t seem to say the same thing as your verbal description.

[*The verbal description for each class came together most easily for momentum transfer. The toughest part was instead the equation. In each class, the group started with *p = mv* for their mathematical representation. After pointing out the inconsistency, they easily moved toward a statement of total initial plus change = total final. Their graphical description (IFF charts, or momentum bar charts with a Force-time graph in the middle to show the ∆p) followed along easily. I liked how this group put the F-t graph in parentheses to show that you only need to draw it if there is a change in total momentum.*]

Models of Momentum:

- Momentum Transfer Model (MTM)

What do you have for your verbal description so far? (Energy can neither be created nor destroyed.) So are you saying the total energy of a system never changes? (Right. No, wait. Unless there’s work.) Okay, so that probably needs to be part of the statement, too. You need to find a way to include that “unless”.

[*I found it really interesting that the statement “energy can neither be created nor destroyed” showed up in each class, even though it wasn’t something that we ever said in class nor something that I ever heard them say often when they talked about energy before. It was a good reminder of how what they’ve learned before still exists alongside what they are learning now and that they really want to find ways to connect those ideas (and especially to honor their oldest ideas).*]

[*This group also chose to include very generic diagrams, and I loved that they included the F-∆x graph for finding the work done on the system.*]

[*I had a good conversation with many groups about choosing just one mathematical representation (the one that communicated the big idea, even though there might be other mathematical components involved, like the formulas for each flavor of energy or each type of force). The group from this class even noted that conversation on their board when they identified the most inclusive statement they could make about energy.*]

Models of Energy:

- Energy Transfer Model (ETM)
- Universal Gravitation (escape velocity, etc) (CFPM)
- Simple Harmonic Motion (OPM)

Once the groups had their boards together, we regrouped and put the three boards up front. Students basically stayed in their seats and one person from each group spoke a little about the choices they made. Students wrote down what they wanted from the boards on that front page of the packet. Nothing was new here except the way we were writing it all together or organizing it on paper, so the questions and anxiety of starting something new were pretty minimal.

If students didn’t bring it up themselves, I pointed out that all three of our fundamental principles are pretty similar—each is about how **some quantity** stays them same unless there are **unbalanced outside forces**. So what we really have is three sets of glasses for viewing, describing, explaining, and predicting change.

Now, when we start solving tougher problems and/or problems that require more than one big idea, we are ready to add a new mantra to our list of problem solving advice: if you’re getting stuck, switch fundamental principles.

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Sometimes it is easier to choose from a menu than to create the shape on the spot. So, if you’re having trouble deciding the shape of your x-t graph, draw a circle and divide it into four pieces.

These sections of the circle are the four possible x-t parabola shapes. Now you can identify the matching graph instead of generating it.

I discourage them from trying to use this as a memorization tool. Instead, I tell them to use it as something they can quickly sketch and then use as a thinking tool while trying to draw a graph. They can identify which of the four shapes is the one that matches their verbal description of their velocity-time graph and draw that shape on their position-time graph.

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In my usual approach to grading, the quarter grades are just snapshots. Since they weren’t (at my old school) and aren’t (at my current school) put on transcripts, I have felt free to use them as moments for students to check in with themselves, get themselves up to date (especially on core objectives), and keep themselves on track for the real (grade) goal (the exam at the end of the semester). For seniors, though, quarter grades will be sent to colleges, and the end-of-year grade isn’t of as much consequence. In fact, my new school only has exams at the end of the year, so there’s actually no exam in my senior course. My usual grading system will work for my three sections of sophomores, but I was going to need a new plan for Advanced Physics.

Luckily, I have been planning my fantasy Advanced Physics course for a few years now. The only wrinkle is that the plans I had been scheming for SBG with seniors were plans for students who had already taken a physics course using SBG (that is, for my own students, take 2). The good news is that I think the seniors I have this year, even though they’ve never had anything like SBG before, are going to be fine with this SBG 2.0 plan that I’ve made. I just think it’s going to take them a little longer to wrap their brains around it than it otherwise would have.

First up, here’s the description I gave to my students on our course website. (For this class, I didn’t make them binders. So I didn’t print out a course handout (aka syllabus), instead just putting that sort of information all online. I think it’s working well.)

Each major skill that we seek to develop this year will be associated with a major objective (see the list per topic (link to a future post with the list will eventually appear here)). On our weekly assessments, rather than giving you a numerical grade or a percentage, I will instead give you feedback on those skills and a temporary score of 0 (no mastery has been shown), 1 (developing mastery), or 2 (demonstrated mastery—use of the skill must be perfect).

Objectives will be tested more than once throughout the term, and scores can go up or down—only the most recent score counts. You will also have some opportunities to request that you be tested on a particular objective during a weekly assessment.

At the **end** of the term:

0 = 50 points

1 = 65 points

2 = 85 points

Through non-mandatory out-of-class work (one homework slot per 6-day cycle will be considered a protected time for this sort of work—nothing else will be assigned for that time), each objective can be enhanced by adding a piece of excellent, polished, relevant work to your physics portfolio. Some examples of portfolio work include screencasts of interesting problems; compelling video analyses; identification, explication, and correction of misconceptions and errors in found work; and other extensions that show depth, creativity, and mastery. I am eager to talk with you about your ideas for portfolio work and to advise and support what you do.

Adding an excellent piece of work to your portfolio will add a “+” designation to each relevant objective. Submitting a piece of work for your portfolio does not guarantee that it will achieve that “excellent” status. In that case, I will give you feedback and advice about how to bring that work to the next level, and you will of course be able to continue that work. There are no deadlines for portfolio work, but because I will need time to review it, work must be submitted at least one week before the end of a grading period to be considered for that term.

A “+” on any objective is worth 15 points at the end of the term, and you keep the “+” designation, even if your score goes down on a particular objective through in-class testing. That is, as you go through the normal process of making and correcting mistakes, you will not have to repeatedly add work for the same objectives to your portfolio. Each objective can only garner one “+”, even if you show many examples of excellent work for that skill.

Your numerical grade for the term = your total current (cumulative) score / (total # of objectives so far)

It will be possible, but not recommended, to calculate an interim grade during the term. As you learn new material, your scores will fluctuate as you gain mastery and consistency. Only where you are at the end of the term really matters, so try to allow yourself to make mistakes and to learn while you are “in the middle of things”. If you approach the task of learning physics with commitment and in earnest, your first attempts will not resemble your final, masterful work.

Notable differences between this plan for seniors and my approach with the sophomores: (1) There are no leveled objectives (that is, no A or B objectives); (2) 0s and 1s do count for something; (3) Mastering all of the objectives is an 85 rather than a 90; (4) Portfolio work (see below).

The one thing I don’t really like here is that there sort of are points and averages in this plan, though neither the points nor the averages are used in the traditional sense.

I’m really excited about the portfolio work that my students are going to build this year. I’m also a little nervous, since I don’t fully know what to expect, but I’m mostly excited. It will be great for them to walk away from the class at the end of the year with some solid, cool pieces of work that they’ve produced.

Portfolio work shouldn’t necessarily mean huge projects every time (again, a link to a post that hasn’t been finished yet should really be here—eventually I will update this with a link to that future post about Exhibitions). It should be more of a journal, really. Maybe it should be slightly more polished than a journal, but just slightly. I also wouldn’t necessarily expect students to do portfolio work for every objective (especially since this school uses letter grades, so cementing 100% for the class isn’t as significant as at my last school).

The students also seem both nervous and excited. Here’s a sample of what’s been suggested so far (for kinematics) by students:

- A vpython program that lets the user choose initial conditions for motion and produces graphs of the motion at the end (I think this one is even finished already, but it hasn’t been sent to me yet.)
- A study (probably including video analysis) of real airplane take-off motion compared to idealized motion based on data published about the planes
- Investigating the motion of a runner on the road as perceived by someone in an accelerating car
- I’ve also had a student take home a motion detector (I forgot to ask what he plans to do with it).

We’ve also talked about how what I’ve termed “excellent work” (that is, work that would earn a + for one or more objectives) should really be “brag-worthy work” (**©** Andy Rundquist). So, for a piece of work to earn a +, it has to be something I could brag about to other physics teachers. If I tell other physics teachers about it and they say, “meh”, then we (the student and I) need to talk about how to take what they’ve done to the next level.

Of course, nothing has been turned in yet (we’ve only had two weeks of school so far, and we’ve only practiced two objectives so far). I’m sure some of the brag-worthy work will make its way to this blog over the course of (or maybe at the end of) this year. I mean, I’m going to want to brag about it, you know?

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