Writing curriculum, but having too much fun digging around in this archive…  http://edgerton-digital-collections.org/

Today I was thinking about how categorize force:

Pushes vs Pulls

Vertical vs Horizontal

Centripetal vs Tangential

Contact vs Noncontact

• Within contact we have for classes for solid objects (normal, tension, friction, etc.), and classes for fluids such as lift, drag, buoyant, etc.
• Within non-contact we have forces associated with fields such as gravitational, magnetic, electric, etc.

When talking about energy, we identify forces as “working for”, “working against”, and “neither working for nor against”

We also have categories like constraint forces, conservative forces, applied forces, dissipative forces, which sort of overlap with the categories above.

And I suppose there are fundamental forces, macroscopic vs microscopic, etc.

Forces that belong to an interaction pair.

Forces that all belong together on a single free-body diagram.

Apparent Forces!

I’m sure there are others I’m missing…
And I guess I’m not sharing anything new, except that I’m choosing right now to think of these as all the same kind of thing. Given some forces, in what sense do they belong or not belong? Learning these skills gives you different lenses to see forces.

The other thing I’m thinking about is how there is a certain fixed order in which we often teach these; and I’m also thinking about how there are some that we explicitly see as skills to be practiced, and others that are sort of invisible. Like many times students learn about Newtons 3rd law before they are practiced at identifying pairs, which is a recipe for trouble. Or, this was first year that I explicitly spent time talking about the practice of just identifying forces that are working for, against, etc.

The last thing I’m thinking about is how some difficulties in understanding force can only be resolved by doing cognitive work across these ways of categorizing.

If a student says something like, “the small box is pushing down on the big box with its weight.” There is no one fix that is needed. Instead, you need all of the ways: Forces that belong to pairs, force of different types (normal/weight), and forces that are either contact/non-contact, and forces that all belong to a free body diagram. You’ve got a set of forces you have to continually repackage in different ways.

One of things I’ve been thinking about recently is the metaphor of problem-solving as “traversing a path”, and the ways in which the metaphor influences instruction. I don’t want to spend too much effort defending this claim, but I think it’s somewhat defensible for me to say that it’s one of a few primary metaphors we use to conceptualize problem-solving.

• For example, there are problem-solving “steps” (and even missteps) and “paths” / “pathways”.
• We might say to students, “You’re almost there!” or perhaps remark how “you got there a different way than me,” or “I think we’ve gotten off track somewhere,” or “You took the long way,” or “That’s an interesting short cut.”
• It implies there’s some starting point, ending point, and the goal is to construct a path that gets you from the one starting to place to the one end place.
• This metaphor allows us to bring in language such as dead ends, obstacles, and impasses.
• We make use of this metaphor I think when we want to emphasize to students that it’s not the answer that’s important, but the solutions. We are saying, “It’s not the end point that matter as much as the path that gets you there.” In some sense, this makes problem-solving metaphor includes “route-finding” not just “path traversing”, and like even “orienteering” since you don’t even always no where you are and where you are headed.

Problem-Solving as “Map Making”

I guess I’ll start this blogpost by putting up front a slightly different alternative metaphor–one that is very Skempian, I suppose. I want to suggest here that something more akin to “map making” needs to be a part of the collection of metaphors that accompany  “route-finding” and/or “path traversing”. I’ll try to motivate it this way. If the mindset we want students to avoid is being to focused on “answer-seeking” (getting to the destination) and instead focus on “route finding” (constructing and traversing path), I might suggest that we as instructors might be making a similar mistake at a different level. We are focusing on problem-solving as “route finding” when we might be better served as seeing the activity as “map making”.

So here are some of my thoughts:

I think one of the concerns I have with “path traversing” is that there is often no landscape to even traverse, at least not initially in problem-solving. One has to explore the territory and then actually construct the landscape. The landscape is not simply there to be traversed. Now, I think we do kind of have language for this, like the whole metaphor of a “problem-solving space”, but the path-traversing metaphor draws attention to the path as the end-product. And the path is sequential in its nature. Certainly, in order construct that path you may wander around and explore, but the wandering and exploring is not the point. And so we admit, as experts, that it may take a non-sequential process in order to produce an end-product that is sequential (a traversed path).

I guess I should state that I don’t think I’m really adding anything new about what we know about problem-solving. We know that problem-solving is typically taught poorly, etc. Perhaps, what I am trying to add is is the idea that problem-solving is taught poorly (in part), because it’s wrapped up in this implicit metaphor. What I suspect might be true is that changing the way we teach problem-solving requires a new metaphor. And I don’t mean abandoning the old metaphors, because I’m sort of just using the same metaphor and taking a broader perspective. Students are focused on destinations, we want them to be thinking about paths. We are focused on paths, when we might be better served by thinking about maps?

So how might the map-making metaphor help? I think that map-making may help draw attention to a different end-product. There’s still, in the metaphor, a landscape to explore and routes and such, but the point of map-making is not to construct paths. It’s to know the terrain well enough to make a map–maps (I think) are useful in that they show relationships among parts of the landscape and they also foreground/background certain parts. Maps are not sequential, they are relational Any given path on the map is sequential. Hence, my reference to Skemp’s instrumental and relational.

I should probably get more concrete with this idea. So here is a student solution that I think is more “map like” then “path like”.

It shows a lot of relationships. And certainly, in this map, you could probably route a path (or paths) of how they got from some beginning point to the final point.

So here what’s I’m interested in continuing to think about:

1. Is this the useful twist on the metaphor? Or if not new metaphor, metaphorical extension? How so? Why not? What other metaphors may be useful?
2. How might awareness of this metaphor help instructors to work from a different vantage point on “problem-solving” that can support students? Perhaps it can shape the way we model, ask questions, or set the stage for problem-solving?
3. How might the adoption of the metaphor influence the way we as instructors think about assessing student work? Perhaps the path metaphor draw our attention to (show all the step), and with map-making it might draw attention to (shows relationships).
4. If students think they are constructing maps rather than traversing paths, what different attitudes about problem-solving might develop? Will they talk about their work differently? What upsides / downsides might there be?

I want to say again that I don’t think that this “map-making” metaphor that I’m proposing is necessarily novel, nor do I think  that it will necessarily generate any new /novel instructional practices on problem-solving. But, it may be a useful way to think about (and package) practice that are already “map-like”.  My practices with problem-solving were changing before I had the metaphor, and I’m curious if the metaphor will allow me to further hone my practices and or better communicate the practices.

I’d be happy to know any of the following, plus anything else:

1. How I am getting this metaphor all wrong?
2. Examples of your students’ work that you think is more “map-like” or “path-like”?
3. Pointing me to places that help me see where I’m just reinventing the wheel?

I can’t believe we are week into July.

I plan to get Ss more involved with this from the start next time, and cycling back to it more often.

Its teaching evaluation season… so here’s my idea for a new survey.

An online version of this course would be equally effective.

This class helped me to understand how to learn the material.

This course was a waste of time.

In this class, I formed meaningful relationships with other students and/or instructors.

I feel like my instructor cares about me.

This course was one of the best courses I’ve ever taken.

No one would notice if I were absent from class.

This course challenged me to reconsider how I think about certain topics.

Participating in this course makes me feel like being part of something.

I feel isolated and secluded in this class.

I feel a sense of responsibility to the students and instructors in this class.

I am valued as an individual.

If I had to miss class, I would feel like I missed out.

I feel excited about the things I am learning.

Most days I have a good sense of what we are learning and why.

I know what’s expected of me and what I need to do to be successful.

My instructor cares that we learn.

I am given opportunities to learn from my mistakes and failures.

Thoughtful reasoning is valued in this class.

You need to be one of the instructors favorites to do well in this class.

Students are treated with very little respect.

The instructor of this course regularly shows contempt and disdain for students.

This is the type off course students take to get an easy A.

My instructor seems to put a lot of work and care into the organizing the course.
I wish I could take other classes with this instructor.
Students wanting to really learn should avoid this instructor.

This is the type of class that if you put in a lot of hard work, you will learn a lot.

This course was much better than I expected.

This class was disappointing.

The grade I expect to get in this class will reflect my level of mastery of the material.

The instructor promoted a competitive atmosphere among the students that was damaging to morale.
Everything we learned in this class was disconnected and random.

I received meaningful feedback on the work I produced.

I am proud of what I’ve accomplished in this class.

I need to write up a more complete debrief from this week on momentum and impulse stuff, but here are a few things I don’t want to forget:

1. Spending a lot of time inquiring into (and being puzzled by) force vs. time graphs before mentioning impulse or momentum helped create a “need and interest to know”. We did invention tasks, observations, discussions, and predictions that all together made us really ready to hear about how physicists had invented an idea to simultaneously think about the effect of how much force and how much time. We did a lot of thinking and investigating with jumping off of and landing on to the force plate. I would definitely do landing first, and then jumping. Landing is more intuitive and orients us to what’s going on, and then jumping is what creates the real need to know. How can you jump higher with less force? We then looked at cart collisions with stiff and soft bumpers, to practice measuring impulse two ways in logger pro: Area under curve and Average Force x duration.
2. With impulse, I also modeled how to make sense of it the number. I wish I had had more time for this, but I helped interpret impulse as how much force I would need to exert for 1 second to get the same effect (or how many seconds I would need to exert a 1N force). think kicking hover pucks vs. pushing them is a good way to show this. It’s important mostly for students to hone in the fact that there are many ways to get the same outcome.
3. For impulse, having a class feel continuous (temporally expansive, such that everyday seems connected to now) really helped students make sense of impulse and momentum by drawing on what they know. Without prompting, students were bringing up a lot of good knowledge, including force pairs upon talking about collisions and explosions. It was really easy this year for students to conclude that impulses delivered are equal and opposite, because they really knew how to identify forces pairs and that force pairs must be equal and opposite.
4. To get toward momentum conservation, we examined explosions carefully,  with 1:1, 2:2, 3:3, 1:2, 2:1, 3:1, 1:3, and 3:2 mass ratios. Two carts were placed on a track with 120 cm of space to move (so 146 cm of actual space, since carts together take up 26). Through this sequence, we observed some, discussed, developed some rules, and then did predictions on how to divide up that 120 cm of space so that after the carts exploded they reach the end of their respective side at the same time. 3:2 was really hard. This discussion gradually folded in conversations about how the velocities compare, how the momenta compare, and how the impulses delivered compare. They did a few more practice scenarios, and then I did some direct instruction on why physicists think of momentum as “commodity” that is transferred, why that implies conservation, and what that means. A little neutrino history was folded in as well.
5. We then took a look at a few collisions to further talk about momentum transfer and conservation. I did one demo of elastic collision with equal masses just to make the transfer visually compelling, and where story is simple to tell. But then went straight to looking at completely inelastic collisions. Instead of predicting what would happen, we starting observing, and I modeled the story telling process… I told the story two ways: one way was a conservation story (two carts come into collision each brining a certain amount of momentum, they “pool” their momentum, which then must be shared”. The transfer story is more about how much one cart had to lose, and the other to gain in order for that to happen. I did the stories quantitatively, but the emphasis was still on the narrative.
6. Getting students to tell impulse-momentum stories / momentum transfer stories is a good goal. I had students use the physics classroom collision simulator to first observe (without predictions)… using momentum analysis to tell the two types of momentum stories.  “Combining momenta, and pooling together”” as a conservation story and then also “Individual loss and gain of momentum” as a transfer story. After telling the story (quantitively and narratively), then I’d ask students, “Do you think you could have determined that this would have been the speed before hand? Like predicted it? How would you do that?” Students progressed from telling stories, to anticipating how stories would end. I had students do whatever inelastic collisions they wanted from the start, but next time I would direct them to do a few key ones first, and then let them explore more.
7. A few groups ended up trying elastic collisions, and found that they couldn’t predict what would happen, even though after watching it, they could tell the momentum story. I hadn’t intended that to happen, but it will be nice to return to this after learning about energy.
8. In the week, we also did a more momentum-impulse type problem, how much impulse is delivered to a baseball. Can you draw a force vs. time graph that is consistent with this? We played the game of asking students to tell me what information they need, and then we researched on the internet values for baseball mass, pitching and hitting speeds. Students thought they would need mass and speed of bat, so we looked that up to. I would definitely watch this video with students before hand next time…

A student shared this … hope to see yours in the comments.

“I would give anything for students who are…”

However you would complete that sentence—whatever characteristics you most desire to see in the students who walk through your door…

Make it your main goal, day after day, to develop those qualities in your own students.