In doing Newton’s 3rd Law, here was the process that seemed to work pretty well, but will need a little tweeking:

1st : Introduce idea of multiple objects of interest, and multiple free-body diagrams. Worked through drawing FBDS for case of pushing two unequal mass blocks on a frictionless surface.

2nd: Introduced the idea of a force pair, show the example in the Free-body diagram, and talk about the property of forces pairs:  They are “two” perspectives on the same “interaction”; they are forces that act between two different objects; for contact force pairs, they occur at a single location (the boundary between where two object meets), and they always occur on different free-body diagrams

3rd: We did one example clicker question about identifying force pairs (I would do a few more next time) or even have them work whiteboards. It helped having a list of properties of force pairs, because we used them to argue about it.

4th: I told them that we already know the rules about how single forces acting on one object behave (they superpose to generate a net force, which causes acceleration). Now we needed to determine the rules for how force pairs behave.

5th: I introduced, diagrammed, and demonstrated three cases where the force pairs are equal:  “Tug-o-War” Scenario where no one wins (linked to carts with hooks, and pulled on equal mass carts equally hard on both sides with identical rubberbands ).  Collision scenario where two equal mass carts head on collide with equal speed with equal stiffness bumpers. And a “pushed together” scenario where equal mass carts are pushed together at constant speed. For each situation, the force pair was identified and then measured using force probes. We saw that in each case, the force pairs were identical in magnitude.

6th: We brainstormed changes that we could make that would make the force pairs unequal. Students suggested a tug-o-war where one side wins, collisions with unequal speeds, or unequal masses, or unequally stiff bumpers, and “push together” scenario with unequal mass as well as speeding up.

7th: Every group had to try out at least one variation from each of the three categories (tug, collision, push together)… Some groups already kinda guessed what they would see, but many groups were honestly (and pleasantly) surprised. I let a lot of groups really show me what they had found and shared in their cool findings. Given the different place of each group, my conversations were very different. I talked with some groups about what they were observing, and what that implied. With other groups we talked explicitly about Newton’s 3rd Law, and when it did (and didn’t apply, haha!). With other groups, we talked about how could it be that the forces were the same (tug-o-war). At the end, I did a lot of the work of synthesizing (at the whole-class level) our findings due to time constraints.

8th: We ended, by watching Frank’s Newton’s 3rd law Video, and talked about the squishing as evidence for force pair equality. We could have spent more time here, but also given them more explicit tasks. Need to rework how to engage this task for sure.

From there we took a dive into problem-solving. If I did it again, I probably wouldn’t do it right now. I would do more scenario representing and reasoning. The problem we did was pretty hard, too–two blocks in an accelerating elevator. Students worked well through it, it was definitely productive struggle. But there was a lot of struggle, still, around normal force and weight. That doesn’t surprise me. Vertical stuff is just hard, and to pile on vertical toughness with the newness of Newton’s 3rd Law and multiple objects is just a bit much. They still did pretty good.

Part of what I learned they needed a little more scaffolding on managing just thinking about 2 (or 3) net force vectors simultaneously–that each net force gets separately attached to the free body diagram for that object. Some of it was just labeling issues, but it was also more than that. I’ll have to think more about what other scaffolding they need. But all and all, the Newton’s 3rd Law day was a good day.

My approach here was very much “elicit confront resolve”… And I know there can be some criticisms of such an approach, but what matters is how we as a class frame what we are doing. Students aren’t  perceive in my class the activity as “tricked you” (you were wrong!), because they have learned to have a response that’s more “so cool” — being pleasantly surprised by circumstances when nature is different than you expect. The activity is also just fun because we are brainstorming and testing our ideas… I’m not presenting a specific situation for them to be wrong about. They are proposing scenarios, that they themselves are tricked by. That feels more playful, I think. It’s harder to feel like you got suckered, when you are the one who proposed the trick in the first place! Anyway, I’ve just been thinking about this more… about how a lot of “elicit confront resolve” criticisms are criticisms not of the instructional technique, but of an instructional framing that is commonly developed around them. It can unproductive for students to frame it as “guessing”, or “being tricked”, “or always being proved wrong”, or “intuition is never right”, but that’s definitely not the only framing that can happen. Anyway, this last rant was a little unrelated, but it’s been on my mind. I also did very elicit confront resolve tasks for static friction, and that went really well too. With students really engaging their ideas, having a combination of being right and wrong, that led to being intrigued curiously by being wrong (rather than feeling stupid about being wrong). blah blah blah blah…. It’s Friday and Just wanted to keep typing my thoughts…

I’ve learned a lot last year and this year about how my students solve problems that involve Newton’s 2nd Law. I’ve paid attention to two different aspects of their work:

• their difficulties in understanding and carrying out standard algorithms
• nonstandard algorithms that students employ (spontaneously)

A lot of what I’ve learned centers around the fact that typical instruction on solving Newton’s 2nd Law problems ignores students’ intuitive problem-solving approaches to these types of problems.

Conceptual Understanding Research: Identifying Difficulties and Productive Seeds

We know from research on student difficulties with conceptual understanding in physics that effective instruction needs to be designed with students’ initial conceptions in mind. We have also progressed as a community that not only focuses on the need to address “misconceptions” but how to build on and even from students’ productive ideas (e.g., anchoring intuitions).

Problem-solving Research: We know the difficulties but what about the productive seeds?

I’m not super familiar with all the research on problem-solving in physics. Some of the work I do know focuses on how novices are different than experts, and likely promotes a deficit model of students as problem-solvers. I also know there are some other frameworks for being more descriptive about students’ problem-solving, but this often happens at “general level“, rather than focusing on problem-solving in a particular topic area. And despite being descriptive, such studies still often focused primarily on using the description framework to draw attention to specific difficulties. Which is fine, we need to know difficulties. And, I know there are exceptions to this, where problem-solving in specific areas is the focus, but even then the focus can, at times, be more about the development of general theory.

One exception, that I have really enjoyed for some time is Andrew Heckler’s research on the consequences of prompting students’ to draw free body diagrams. This research now makes even more sense to me in that it does two things well–it shows the unintended consequences that occur when students interact with aspects of the standard algorithm but it show cases non-standard approaches to solving problems (often correctly). The question that has been on mind for a long time, but is becoming more into focus now, is something like:

Problem-solving Research and Instruction: Call for Supplementary Approach?

How can problem-solving instruction be more attentive to students’ “intuitive” problem-solving approaches? What does it look like to do this in ways that are not solely focused on deficits students bring? What does it look like to this in ways that are (at least partially) attentive at the level of specific content areas / topics? In other words, what would it look like to build on and from students’ initial approaches, rather than supplant them with our own algorithms. I’m not naively saying, ‘students are already great problem-solvers, they don’t need any help’. But I am saying that students do bring a lot of good stuff to task of solving (force problems specifically), and that more research on what that good stuff is and how it can be used in instruction is needed.

Where this kinds of approach may have some footholds?

And I’m not naive enough to think that lots of teachers in the trenches don’t already do this (attend closely to students’ problem-solving and build on it), or that some problem-solving approaches haven’t been developed with the learner more in mind. I think a lot of the work in the Modeling Instruction around interaction diagrams, LOL charts, actually were designed exactly with students in mind. I’ve even written about how these approaches actually turn students misconceptions into correct insights. Kelly O’Shea has been running great workshops on using graphical representations to solve kinematics and forces problems,  which can really empower students and move them away from the “plug and chug”. My approaching to teaching problem-solving has been tremendously influenced by all of this, and the research has for a long time promoted the multiple representation approach.

I do love these alternative pedagogical approaches that make use of multiple-representations. My sense is these approaches were developed from #1 rich insight and practitioner knowledge on student difficulties in specific content areas, #2 a commitment to crafting alternative algorithms that emphasized big ideas and relationships (rather than equations), and #3 iterative cycles of use and revision across many different teacher’s classrooms to hone-in effective models. I have personally witnessed the demoralizing aspects of teaching standard algorithms, and the empowering aspects of effective teachers using these pedagogically-focused algorithms.

So what am I saying is missing? I’m still not exactly sure. And I still think that what I ever I think is “missing” is not likely missing from the practice of the teachers I admire so much. It certainly must be the case that teachers who begin using pedagogically-focused algorithms in their classes begin to notice new things about students’ problem-solving, and to notice that students have ways of making sense of problem-solving that are really insightful (and different that one might one expect)… and they begin to adapt their instruction to build on those student-generated approaches.

Forces Problem-Solving as an Example

So what’s an example of a student approach that is “common” enough and “productive” enough to serve as an anchor for instruction. I’ve basically written about this specific thing before, and in the cases I had seen then students are still using the standard algorithm (sort of). Now I know these approaches (or even deviations from standard) are pretty common, and that you can see the effect that supporting students in using them has.

Here are a few examples of conversations with students this semester:

1. I was working with a student through a standard algorithm.  What was really confusing them was how they get the “total tension” (i.e., magnitude) from an the y-component equation of Newton’s 2nd Law. In their mind, the y-component should have given them the y-component of the tension. See in the standard algorithm, you often substitute Ty = T sin(theta), so that you do solve for the magnitude of T. In talking with these students, we ended up back-tracking in the algorithm to solve for Ty first, to actually get a numerical value for Ty. Then, go about using trig to figure out what the total magnitude needed to be to guarantee that Ty would have that value. That process made a lot more sense, but it also gave the students insight into the problem. It was a static equilibrium problem, where Ty was holding all the weight. That the student could “see” a value for Ty and that Ty was holding the weight made a lot of sense. They carried this sense-making with them to many other problems involving equilibrium…  I see this as similar to the “two-step” process talked about in the prompting force diagrams paper. The experts algorithm tries to take advantage of every relationships simultaneously, along the way bypassing important insights that students can glean in the process.
2. Another group was working problems, back and forth between more standard algorithms and less standard ones, mostly depending on who in their group was taking the lead. In one case, when they worked a standard algorithm, they got the right answer, but were confused about some things. In talking with them, it was clear that they could not see the chunk “T sin(theta)” as a component of a force. To them it was just a bunch of symbols. Like they knew that’s how they calculated it, but their brain couldn’t just look at the equation T sin(theta) – W = 0, and see this as saying the y-component of tension is equal to the weight. This is a bit of why the standard algorithm doesn’t work for students. I see this as related to “disciplined perception“, but also the idea of chunking in long term memory. But it also made me think about how I can scaffold their seeing better. If they are to become experts in the standard algorithm, it’s not enough to use sine and cosine, one needs to see particularly arrangements of algebra as “chunks”.
3. Where I saw my helping students build on these approaches pay off was when we were working problems involving dragging a block across a rough surface at at angle. We had a clicker question like this: A block is on a horizontal rough surface, such that it takes a horizontal force F to break static friction. The question was if you now pull with same force at angle will be “more effective”, “less effective”, “similarly effective” in getting the block to budge. We talked about this for a while, and got a lot of the ideas on the table– by pulling up you are lessening the normal force, and thus lessening the grip that surface has… by pulling at an angle, less of your force is horizontal and available for doing the job of breaking it free … others saying that maybe this means it will be equal out… others were talking about how with vectors, we’ve seen the two sides don’t up to the magnitude… so that a 10 N force horizontal is just a 10 N force, but a 10N force at angle, could be like more than 10 N of force… like you could get maybe 9.5 N of horizontal force and 3 N of upward force. It was such a weird statement to say, ” A 10 N force can be more than 10 N”… but it made total sense within the context. We decided to work the problem the following way: 2 groups work 30 degrees, 2 groups work 45 degrees, and 2 groups work 60 degrees. Students worked the problem, mostly not with the standard algorithms, and there were some pretty amazing conversations going on, both within and across groups. Those great conversations, I’m pretty sure, were made possible because of their “solve for the components numerically” approach, rather than “solve for the magnitude directly” approach… It constantly guided their sense-making.

From this I think what I think is missing from the research base is stuff about this–like here are ways that students spontaneously solve physics problems successfully, and here’s how you can leverage those ways to really get students doing sense-making. Here’s the good stuff that they tend to do (and are more likely to understand) that you can build.

So, an activity I want to do is have students make “cards” for each of the types of forces. 

The card will require some picture but also have information like this is example for weight.

Personality: reliable and down to earth

Special Powers: Can pull from long range
Stats: varies force depending on the mass of victim, using an invisible web (aka gravitational field) to pull with a strength of 9.8 N for every 1.0 kg.

Fun Facts:  

favorite song is Tom Petty’s “free falling”. 
… 

Feel free to play along in the comments! 

Today in Physics was an assortment of challenges related to mass, weight, and friction, ranging from easy to hard. None of the situations was inherently hard, but what makes them hard is seeing the situation for the problem you need to see it as. Students productively struggled, and along the way really strengthened our understanding of static friction, normal force, net force, and Newton’s 2nd Law.

1.  An object hangs from a scale. From a spring scale reading, determine unknown mass.
2.  A mass is suspended from above by a rubberband and below on a surface. The bottom surfaces has a force sensor reading that is shown to students. Students have to predict the force reading for the rubberband above and then check.
3. A mass is pulled by rubber bands both from above and below. Again, students can see the force reading from below, and must predict scale reading above.
4. An object with known mass rests on a rough surface. Students have a force probe and are asked to determine an estimate for coefficient of static friction. Then they are asked to put an unknown mass on top of the first one, and determine the mass of the unknown.
5. Building on task 4, they are also asked to connect the original known mass to a rubber band that pulls up slightly on it (vertically, but not enough to lift it off the rough surface). They can read how much force the rubberband is exerting with a spring scale, and they have to predict how much force it will take to budge the object.
6. A Half-Atwoods setup is shown. Students have a 1.0 kg block, moving along horizontal surface, with hanging mass being equal to 500 g. Students are asked to use a force sensor  and a motion detector to determine a value for the kinetic friction force, and the coefficient of kinetic friction.

Students were encouraged to work all the stations, but had to turn in three carefully worked out problems: Station 2 or 3, and station 4 or 5, and station 6.

For each problem students had to draw a pictorial representation, which identified the object of interest, its boundaries, and the contact forces. They had to draw a free-body diagram that included a separate Fnet vector. They had to include the readings of any data they used. And then show the work they did to arrive at their predictions, and for the ones you could check, how they compared.

Before we did this, we had a short conversation about mass and weight, and reviewed big ideas from forces so far. Over the course of discussing, reviewing, and circling around during the challenges, I made good use of our “forces” and “teams” analogy.

A Fnet Analogy: This is going to drive the force ontology people crazy: 

I’m finding it in class very useful to think of forces drawn on a FBD as showing what individual “players”, and the net force as what the “team accomplishes together”.  We’ve been using this analogy to organize our problem-solving without algorithms.

During the review, I talked about we can extend this analogy since we have learned more about the individual players–their behavior and personalities.  Weight, for example, is a player who always does the same thing, no matter what anyone else is doing. His job is to pull downward with a force of 9.8 Newtons for every kg. He doesn’t change what he is doing in response to what other team members are doing, or in response to what the motion is. Normal is quite different… the normal force is always adjusting what he is doing, depending on what other forces are doing. It’s useful to think of him as being lazy, he will pick up whatever slack is left over, but he will only do what he has to. Tension and normal are pretty similar in this way, except that one only pushes, the other only pulls, and when multiple tensions  and normals are at play, they have to work out a compromise as to who does how much. Finally there is friction, and friction is not so much lazy as “reactive”… Static friction sits around waiting to react to any other player’s efforts to get things moving. But he is only so strong, and can be overpowered. Once static friction is overpowered, he can only rely on a weaker form of himself, kinetic friction, and he works do brings thing to a stop if he can.

I haven’t even started thinking about this beyond just asking, so join in!

Say you have a half-atwoods setup with friction on the horizontal object. You start with a light enough hanging vertical mass such that the tension is not large enough to break  static friction. Everything stays put, and so the tension is equal to the weight of the hanging mass.

Let’s say you then keep adding mass until it breaks static friction. The moment you break static friction, two things change:

1. The tension in the string lessens, and
2. and we switch from static to kinetic.

What are the different possibilities of things that can happen? Under what circumstances do they happen?

Play. Brian. Play 

https://playbrianplay.wordpress.com/

First post: 

Examining My Own Discomfort: Learning to Respond rather than React

“This is a new blog I’ve started for the purpose of reflecting about my experiences playing and learning in the family childcare that my wife runs in …”

https://playbrianplay.wordpress.com/2017/03/10/examining-my-own-discomfort-learning-to-respond-rather-than-react/

We got a lot of leverage in the Teaching of Physics out of watching this new Veritasium clip, “The science of thinking…”

First, “Gun” and “Drew” are great shorthands, and the examples in the video make it easy to relate to. (It actually reminded me of Liza and Ellen from this lesson and this revision as shorthands, although in a different way). The humor embedded in the video, together with these shorthands, allowed us in class to be more jokey about our thinking and who was behind it. Knowing that we all have a Gun and a Drew made it fun to share what Gun and Drew were thinking, rather than embarrassing to be wrong. It almost, depersonalized our thoughts… as if we were sharing the thoughts of the different characters in our mind, rather than sharing our “real thinking” (whatever that means).

Second, it helped us to value each other’s pauses and to honor wait time (it was evidence that the person was letting Drew do the hard work he was meant to do). I have one student is often apologizing for being a “slow thinker”, and this video helped her (and us) to see this slow thinking as exactly what you are supposed to be doing.

I’m thinking of showing it in my regular physics class…

I forgot to mention another thing I have learned through our struggles with L’s pestering. L’s pestering used to be more physically aggressive, often pushing. At the time, I think I saw it as bullying? I’m not sure at this moment how the pestering and bullying are or aren’t related. But anyway, L definitely had the power to make the other children upset by pushing them or stealing toys, and it was something he was definitely exploring and trying out. Like, “Oh you are going to scream when I push you? I wonder if you’ll always do that… What if I only pretend to push you but don’t actually push you? Oh, cool, this is kind of fun… oh if I steal this toy, you are going to scream, and then an adult is gonna come swooping in. I’m game for that… ”

So, one thing I have realized recently about acts of “pestering” or “bullying” is that it actually takes two (or more) to make that dance happen. One person starts with a bid–an action offered as a pester or bully, and the second person has to respond by acknowledging it as so. Only in retrospect, can the initial act be declared a pester or bully. It is like a contract–an offer and an acceptance. One way to address the pestering and bullying is to work on preventing the offer (or bid) from happening–that is to work to stop L’s behavior. But it is just as important to work on the other side–that is help the children to refuse the offer. This lines up with the notion that such problems are community problems (not just individual problems), and everyone must share responsibility for helping to repair trouble.

One way we worked on the kids being better at refusing acts of pestering, was through the development of physical and emotional resilience to physicality. We didn’t necessarily know we were doing it at first, but we quickly noticed its effects. Several months ago, we started teaching the kids to rough-house. It started with mostly the expert rough-housers (i.e, Bethany and Brian), mostly manipulating the kids’ bodies around, keeping it feeling exciting and even a bit scary, but still safe. We would push them over playfully, bear hug them and roll them across the carpet, pretend to smash them, throw them into something, let them jump on us. Over time, as the children became more expert at rough housing, multiple novices playing might roughhouse with expert at the same time and then gradually it became more and more the novices rough housing with each other. Rough housing offers lots of opportunity to encounter episodes of getting into trouble during play and working on its repair. The children also learn how to brace their body for a fall, to tense their muscles before a dog pile, to communicate when it’s too much, to stop when someone has communicated it’s too much, to recognize when to take a break, and whether to relax for a while or recover quickly to get back in the action.

The children also just got used to rough physical contact, which took away the power that L had to get them upset. Before, L would push and get screaming, whining, yelling in response. Now, L would push, and they could just brush it off, or ignore it, or walk away, or even push back. The skills they developed during rough housing gave them the physical and emotional skills to refuse to accept his pestering / bullying bids. And so gradually, L stopped making so many offers…

The second way that the children learned to refuse L’s bids is something we actually learned from one of the children, Ar. One day, L came over to Ar and just kept saying, “No!” right in his face, which would have more normally been responded to with even more and louder, “No”s and whining high pitched voices, and screaming. This time Ar decided to respond playfully, by saying No in a singsongy and goofy way, basically dancing and singing happily as real good “no no” song. L decided to join in on the silliness together. Another time, we saw A responding to pestering bids with smiles and tickles. L decided to playfully accept the tickles. Once we realized what A was doing, we all started doing it more. Maybe L would use his body in some weird way to invade someone else’s space, and that would become a dance move we would all try out. I want to be  clear, that this is different than taunting L back or mocking L. Instead, Ar modeled for us how to respond playfully, not vindictively or mockingly. Ar had turned L’s bids to pester into bids to be silly. In doing so, we all learned how to counter offer or redirect the bid into something else.

Finally, I realized that even seeing L’s pestering as pestering was problematic, because it wasn’t pestering until someone (an adult, a child) oriented to it as such. We got better at seeing the bid as full of more possibilities than just pestering, and seeing that we all had at least some role to play in pestering. It wasn’t just “L’s” pestering… it really was trouble occurring at the community level, not the individual. Trying to solve the problem at the individual level was probably not going to be as successful. This isn’t to say that we have worked it all out, or that we don’t fall into the pester trap. But it’s changed my view, from “L is pestering again” to “How did we fall for that again?”, or “What lead me to respond that way this time?”

Anyway, maybe there are people who read here that don’t want to read about daycare, and if so, I’m sorry. But it’s the most interesting learning/teaching work I’m immersed in these days.