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Impulse: Lesson Planning

April 11, 2017

[Once again, there’s way too much I want to do here, and will need to think about how to scale back]

Constant Force Warm-Up?

Students have  warm-up with a “square” force vs. time pulse (constant over a time interval). Given initial velocity, they have to calculate final velocity using Newton’s Laws and Kinematics.

Edit: I may split groups into two warms up… different width / height pulses with same impulse. Why did these two force scenarios result in same change in velocity?  

Introduce Jump off the Force Sensor:

Orient students to how shape of graph (being constant) force allowed us to assume the acceleration was constant. Tell them I want to show them a force vs. time graph for a real world situation– me jumping off the force sensor. I want to ask them about what they notice about the graph, but before hand I want them to think about what they might expect to see.

I will show them the jump first without the force sensor data (it will be a shallow knee bend and then jump), and ask them to draw a motion diagram and free-body diagram for three stages.

Edit: well Ss work on this, I will encourage  them to do jumps and talk about it. 

  • At Rest on the sensor (before attempting to jump)
  • Jumping but still in Contact with the
  • In the air, before hitting the floor.

Then I will show them the Force vs. Time Graph. Question will be, “What do you notice about the shape of the graph?” Lot’s to notice and talk about here. 

Edit: why did value start where it did? Why did the value go up? Why did the value drop to zero? 

Brief Direct Instruction: Impulsive Forces

Introduce concept of impulsive forces with a few examples, and some features of impulsive forces:

  • Often involve relatively large contact forces between two objects
  • Magnitude of the forces rises and then falls
  • Often occur over short periods of time
  • Maximum force often occurs at maximum compression
  • Shape of the graph is non-constant and can be complicated.

I have a few clicker questions about to apply these ideas to the jump if I feel it’s needed:

  • Where on the graph did I lose contact with the scale?
  • Where on the graph did maximum compression of scale occur?
  • Where on the graph might I have been at my highest point?

Deep Knee Jump Discussion:

Students are going to be asked how the force vs. time graph might be different for a deep knee jump. Once again, show them without the reading. I could ask them to free-hand sketch, which I think, but I will use a clicker question to say, “Which of these does your graph best resemble?).

We will discuss and then observe. Key idea for discussion after is, “How did I jump higher with the deep knee bend even though the maximum force was less?” Key in on the idea of time.

Brief direct instruction to show how force vs. time graph allows us to see two things at once, how much force and for how much time.

Apply Idea of Force vs. Time to Landing on the Scale:

This time I’m going to jump down onto the scale from same height. Once by doing a heal landing with no knee bending, and another by doing a toe landing with knees bending. Students will be asked to whiteboard important features of how the graphs will be similar and different. Students discuss and then we observe.

Direct Instruction:  Representing and Interpreting Impulse

I will either lecture or students will do a close reading of a section on impulse as the area under a curve, followed by some direct instruction to clarify. A big goal I have here is how the impulse takes into account both the of variables that matter (how much force and for how long), but then also scaffold how to interpret the impulse number.

I want to show them that the area under both jumps was the same. That makes sense since the same job had to be accomplished — either way, I fell from same height with same speed, so the job that had to be done was stopping my fall. I will have to guide here strongly, but the idea is that number is how much force would be needed over 1.0 s to get the same result. That another way of stopping me would be to exert a constant force throughout 1.0s = to impulse number in N.

Short Practice Exercise (Hand Calculation):

Students will then have a triangle pulse to calculate the impulse for, to interpret the number, and then draw a different shape graph that was same impulse delivered over half the time.

Short Practice (Logger Pro Calculation):

Students will crash a cart into wall with a stiff bumper and squishy bumper, and calculate impulse delivered to cart. Guiding question will ask them to predict how shape of the force vs. time graphs will be similar / different? [Photogates are not for careful measurement now, but for making sure incoming velocity is same across trials).

What effect to impulse have? Jumping Animals and Marshmallow Blow Guns

From the reading, they talk about how animals that are good jumpers have long legs. Help them relate this to “extending the amount of time”. Just the idea that if you want to deliver a lot of impulse, sometimes it’s easier to extend the time rather than increase the force. But increasing the force is always an option as well.

Show the Marshmallow blow gun. Remind them how with projectile motion we often just assumed that projectiles “started” with some initial velocity. We ignored how they got that initial velocity. Watch I use this blow gun to deliver an impulse to the Marshmallow so it projectiles off with some initial velocity.

Ask students: What could I change about the blow dart gun so that the marshmallow shoots at a higher velocity? Ask why, but also how is consistent with what we’ve learned today about impulse? (Blow harder to increase force, or make a longer tube to increase the time). Let students play for a bit.

Is it possible to use a weak force and a hard force and get the same velocity? How?

Now ask students: What do you think will be different if I deliver the same impulse to a marshmallow that is twice as heavy (two in the gun)…  Let them go observe.

We need to draw out two big ideas here:

There are many different ways to deliver the same impulse, and have same end result (if object is same).

The same impulse delivered to a more massive object, however, results in less change to velocity:

Direct Instruction:

 

I will either have them do a careful reading or brief lecture on Impulse-Momentum Theorem. Key here is to connect lecture and /or reading to our activities.

Clicker Questions to Practice Applying Idea:

One problem that shows force vs. time graph… ask about change in momentum. Then ask, how much velocity that would translate into for 1.0 kg object, 2.0 kg, 0.5 kg?

One problem that shows a cart rebound off a wall, ask how much impulse was delivered? This will be very similar to quick lab exploration they did, so may do as a demo as well.

Problem-Solving (New Skill in Isolation):

Impulse delivered to a baseball hit off end of the bat?  Draw possible force vs. time graph

Impulse delivered to a passenger colliding into a wall:  Draw force vs. time graph for hitting dash vs. hitting the air bags. How similar / different?

Challenge Problem for Next Time (New Skill Integrated into Broader Skill Set):

Launch marshmallow gun horizontally and mark the landing location. Work backwards to find the impulse delivered!

 

What Student Say that they Want in Group Members

April 10, 2017

I’ve been experimenting with having surveys where students can tell me one student they would prefer to work with (and why), and anyone they would prefer not to work with (and why, no character attacks), but then also ask them about what makes for ideal people to work with.

This last question has opened a few themes:

A very common one is just wanting to work with people who “care” to learn

  • “Care to learn/understand the material”
  • “I’d like a group that cares about physics, if that makes any sense”
  • “I would prefer to be with the students who really care, because I want really learn the material”
  • “people who aim to understand”

Another is people willing to put in time, effort, and who contribute

  • “I would like to work with people who do not mind staying over, doing the extra problems.”
  • “People who give input or ideas for solving problems and not just waiting for the others to tell them the answers.”
  • “I’d like to be with people who are there to try to do their best. If I was with someone who didn’t want to put in the work and just tried to slide by it would be a bit frustrating for me.”

Pacing  (goes both ways)

  • “I want to work the faster paced group”
  • “I don’t want to work with people who are trying to finish as quickly as possible.”
  • “Similar pace to me — It’s just hard to be patience and not go ahead and finish something on a problem when you know what to do but another person doesn’t.”

Talkative / Outgoing:

  • “People more outgoing than me – I tend to be more reserved at first and it helps me become more involved in discussion if someone else is more open to starting it.  “
  • “I want to work with more outgoing people, who talk and make the work more fun”

Attention to Detail:

  • ” With people who work their problems very neatly on the boards, so that we learn how work through problems clearly.”
  • “People who care about details, instead of rushing to get done”

 

I think a lot more themes could come out if I asked the right questions… but these are still interesting.

Quantitative Circular Motion Recap

April 7, 2017

We had a pretty awesome day in physics. 1 hour long warm-up. 1 hour long “preparation for future learning” (making predication, analyzing data) and direct instruction. 1 hour of problem-solving.

Long Warm Ups: Applying the Concept of Centripetal Force to Tricky Cases

We spent WAY more time on the warm-ups, then I was anticipating. But it was really needed, and engagement was high so I it took up basically an hour to do 4 clicker questions.

The two we spent the most time on was Car Cresting the Hill, and Roller Coaster Cresting the Top of the loop. Partially it took long because I framed our goal as two fold:

1. To answer the questions on the basis of what we have learned about circular motion the previous class.

2. To decide whether the answer made sense. Students had to vote on the FBD that they thought was correct (A,B,C,D), but also had to vote on a 1-5 scale of how much that answer made sense.

I’m having a hard time remembering what the details of our conversations were, but they touched upon lots of stuff… apparent weight, normal force, object of interest, weight force, velocity vs. force, knowing that the rules say the normal force lessens, vs. figuring out how (what would make) the normal force lessen, trying to connect that to the sensation of… which free body diagram would be correct if you were hitting the bottom of a hill instead of cresting the top.

For the roller coaster, we were pretty split again among many choices, but about 75% of the students picked one that had a central force (with weight down and a second upward force). After brief small group chat and whole class discussion, I re-voiced ideas to navigated us to use what we had learned about circular motion to rule out all but 2 FBDS. Normal and Weight down, or Weight down and an upward force (less than weight). After going to back to small groups to decide which of those were correct, everyone but one person voted weight and normal down. So many people changed their mind to correct answer. Weeks ago, that would have signaled to me we were ready to hear an explanation or two, and then move on. But today was different. I asked the one student, if they felt comfortable telling us why they were sticking with their original choice, and then since so many people had changed their mind, they could tell us what had convinced them to change their mind. The hold out student voiced some good ideas, but the main idea he had was that if the only forces acting on the ball were down forces then the ball would get to the top and fall straight down. I helped make that idea clear, and then truthfully left the classroom while students discussed. I told them I had to go to the bathroom (which was true and urgent, because I had like 4 cups of coffee), and that they should continue the conversation with out me. I came back a few minutes later and they were still passionately discussing the question. (After class the physics major who is undergraduate teaching assistant in my class told me that right when I left, a student who is usually pretty quiet immediately spoke up). Anyway, some of the arguments I heard and others I didn’t, and we gave the holdout student the final say.

Transition to Quantitative:  Preparation for Future Learning and Direction Instruction

The transition to quantitative went smoother than I thought, even though I stream lined it  because of the longer than expected warm up. I reintroduced the pendulum that we had studied before, and asked the question, about what we could change. Students suggested increasing mass, increasing the speed, and strong agreement that would make the force stronger. There was not agreement on what effect changing the length of the string would have… between taking more net force, taking less net force, and taking more net force. I modeled using the pendulum how I actually did these experiments, made groups pin down predictions with reasoning, and then looked at the data– graphs. Students were asked to describe which graph went with which experiment, and patterns in the data, and whether it agreed or disagreed with their conclusions. I thought it might be too abstract to look at the data without actually exploring, but students had enough contexts from our extended discussion to understand the data without actually playing the equipment.

With short time, this led to met doing about 5 minutes at most of direct instruction showing how the patterns from the graphs can be integrated as mv^2/r, and how comparing with Newton’s 2nd Law, this means a = v^2/r.

Ranking Tasking:

Students did a quick job of the ranking tasks. A few students needed guiding questions on some on the ones that were tied.

Problem-Solving: Building the Problem

We did have time to work both problems and to “build” the problems together. I had students tell me what they wanted to me measure and how to predict the tension. I told students the list of must haves. They did a good job of “reasoning” through the problem using representations, and not mindlessly using equations. Honestly, even with thoughtful discussion, good diagramming, they answered the question in about 15 minutes or less. We checked our answer against the demo, and then we were on to the second problem.

We watched the you tube video of car sliding out the exit ramp. I motivated the question of, “So how fast can you go without sliding off?” I asked students to tell me what information they would want to know:

Students said mass of the car, radius of the circle… we had a short debate about whether we needed to know kinetic or static friction. I guided here strongly, by demo-ing. We haven’t studied rolling without slipping specifically, and so I didn’t want to linger here too long, just show the difference between sliding vs. rolling (without any sliding). We talked about needing to know conditions and we talked about ice, wet, and dry. We also talked about assumptions we might need to make:  they suggested we should assume constant speed, and I suggested we should assume a flat surface (even though most are banked).

I gave some canned data rather than have them estimate or research. Everyone did the exit ramp nearest to our highway, where I estimated from google maps it was about 100m radius.

Two groups did icy road conditions: One a 1000 kg car, the other 2000 kg car.

Two groups did wet conditions: One a 1000 kg car, the other a 2000 kg car.

Two groups did dry conditions: 1000 kg / 2000 kg.

Students were asked to predict which in their pair would be able to go at higher speed. Students struggled through this a little more, having to recall things they knew about friction. Some groups struggled with which direction the static friction force points. I used good questioning to help here: “How can you decide which way the forces must point based on what we’ve learned about circular motion during the past 2 days?” “How can you make sense of that answer?” (e.g,. “we need net force toward center of the circle.” and “that makes sense because that force is preventing you from sliding out, not causing you to slide out.”)

Students also needed help with what perspectives to draw things. I could have modeled this, but I ended up just asking each group to make a top view, side view, and a head on view of the car. And to decide which of those three would be useful for representing what kind of information. Now would be a good time to introduce the x and . notations.

Students were pretty surprised to see that the speed didn’t depend on the mass! As we wrapped things up, I had a chance to chat with groups on a one-on-one basis about this. Some groups could explain why pretty well, others needed a bit more direction. It was key to say that heavier one still needed more force, but that is got this greater force by gripping the ground better (normal –> friction).

Reflection:

I’m really happy to NOT be making these problems super difficult in terms of angles and such. Students were really doing problem-solving as a sense-making thing, applying new knowledge to practiced ways of representing and reasoning. I literally have not done an example problem since early February, and it’s never felt like we’ve fallen into the pit of “blindly trying to work the example problem”. Still, students work is sophisticated and not haphazard. High standards are maintained through “must haves” and culture, and most of the high expectations are around representing the work carefully and meaningfully, not in carefully structuring algebra.

UCM: Day 2 (Getting Quantitative)

April 6, 2017

Warm-Up to Activate Prior Learning:

Start the day with some warm-ups to review what we learned about UCM in terms of a central net force and tangential velocity. A clicker question about the FBD for a car rounding a hill and one for the FBD of a cart rounding top of a roller coaster loop. Then there will be two clickers questions about the path taken once central force is removed. The first one will for horizontal UCM, but the last clicker question will for a vertical swing, released at bottom.

Reorient to our Story Line:

Then I want to return to the pendulum swing that we had talked about the previous time, where Tension Force must be greater than the Weight Force at the bottom. I’m going to take some quick force sensor data and model reasoning through how Fnet = T – W. I’m going to note that this value of Fnet must be just right amount of net force to keep the object rounding the circle. What determines how much force is necessary to keep an object going in a circle? We know from our discussion last time that too much force would cause the circle to “tighten up”, and that too little force would cause the circle to widen out. How much force was “just right”?

Elicit Ideas about How to Increase:

To answer that question I’m going to suggest we think about what could we change about the pendulum swing so that the Net Force would need to be larger in order for an object to round its circle. If needed I might suggest the following framing–think of changes we could make to the scenario that make it more likely that the string would break! The force required to make the loop would more than the string could withstand. I think this framing I’m likely to get heavier mass and faster swing. I’m less sure that students will think about size of the circle (at least in this context)… if needed, I might ask, “Is there anything else about this situation that we could change that we think won’t effect the force?” I’ll suggest we could change the length of the string.

From our list of things students are going to be asked to design and carryout an informal investigation to either answer questions like:

  • Does swinging a heavier mass result in a higher net force?
  • Does swinging faster through circle require a higher net force?
  • Does changing the size of the string have any impact? (This one is harder to think about control of variables for speed, since we have not learned about energy yet).

Short Lab Exploration, followed up with a Data Set to Examine

I don’t want us to get bogged down in the long process carrying out each of these experiments carefully, so I’m just asking students to run two trials to see if our predictions hold up. I may even break up the groups to run tests. I do want them to think through the experiments, however, because I’m going to ask them to examine the data I took earlier in the week.

I will then show students data for Fnet vs mass, Fnet vs. Speed, Fnet vs. Radius. Students will be asked to describe which experiment we did linked to each graph, to describe the patterns they see in the graph, and to state whether the data was consistent or inconsistent with our predictions and initial findings.

Direction Instruction Lecture or Scaffolded Reading

One option will be to do some direct instruction on how these graphs relate to the textbook passages and equations, but I’m also inclined to ask students to read those passages and equations and do the work of relating the text to the experiments. They will need some scaffolding to do this well. I’ll probably then to some direct instruction to tie up loose ends, emphasize some of the points that need to be clarified etc.

Ranking Task as First Application of New Ideas (in isolation).

Then we will practice applying the quantitative ideas to a ranking tasks. If this is easy for students, we will move on. If it’s challenging, I’ll have groups present and we will discuss.

Problem-solving as Integration of New Ideas into Broader Skill Set

I didn’t want students to get too bogged down in actual lab work, because we need to turn a corner into problem solving. Even though it’s not uniform circular motion, I’m going to have students work problem about bottom of pendulum swing. My setup at the front of the room will have a photogate and a force sensor. I’m going to asks students, if I put an object on the pendulum and let it go, what information would you need to know to predict the force sensor reading? Hopefully, students will come up with mass, speed, and radius. Whether or not, I’ll be ready with questions asking them how their answer(s) relate to our learning earlier in the day (either experiments, lab data, or reading).

I’ll measure the information they say they need: mass from scale, radius from meter stick, and speed from the photogate sensor. Students will be asked to work toward a prediction.

I will either give students a list of must-haves or ask them to help me generate one:

  • A pictorial representation of situation, with object of interest and boundary identified.
  • A free-body diagram that shows both the individual forces (in red), the velocity (in green). Separately, they should include a vector that shows the direction of net force.
  • A list of know information from our measurements.
  • Mathematical work and reasoning for a solution.

Once students have a prediction, they’ll have to check out with either me or another group, and then they can check their prediction if they feel they are ready. I expect some students will calculate the net force only, and forget to reason about what value of tension is required to achieve that net force.

Additional Reinforcement (or Reflection)

I’m hoping we have time for a second round of problem-solving. This one I will use the vague question technique. I’m going to show a you tube video of a car sliding off an exit ramp, and pose the question, “If you wanted to predict how fast you could go around a curve without sliding off, what information would you need to know?”

Students I think are likely to say the mass of the car, type of car, how wide or tight the turn is, the road conditions, type of tires, and maybe even whether the road is flat. I’ll do the work of catching students contributions and connecting them to either things we could estimate or research, or connecting to assumptions we might need to make (flat road, constant speed around the turn, let’s assume the car doesn’t tip over!). If we are short on time, I’ll be ready with a list of reasonable values, but if we have time I’ll make students estimate and research values based on conditions they want to work out.

Before I let students go off, I’ll want students to do work of guessing “a number they think is probably about right”, “a number they are pretty sure is too low,” and “a number they are pretty sure to to high”… we’ll also review our list of must haves. Then students will be off to solving problem.

Too much? Maybe

Some ways to possible save time are:

  • Skip warm-up questions
  • Skip mini-exploration before examining lab data
  • Skip examining the lab data, and just include that in my direction instruction
  • Skip the part where students read the textbook passages and discuss
  • Skip the “what do you need to know” discussion before solving 1st problem
  • Just give them a word problem for the 2nd one.
  • Or don’t do a second problem.

The draw backs of skipping each are:

  • It’s really helpful to cycle back and activate prior knowledge from last class
  • Doing the mini exploration is critical to students actually being able to make sense of what the lab data is even about.
  • Skipping the lab data means it’s even more abstract… like, “Hey guys, someone could do careful experiments, and this is what the graphs would look like, and this is the equation you could infer” –> pretty horrible.
  • Doing the explore and lab analysis, I could just do direct instruction, and not have students do the text reading stuff. This is a lot of what I normally do, but I need to work on this part of my courses.
  • I don’t like skipping the part of the process where we turn a scenario into a problem. It makes the problem seem uninteresting and more likely for students to not know what they are doing or why.
  • Giving them a word problem for the second problem could probably be ok… it’s more meaningful to do the work of turning the question into a problem.
  • It could also just be by the end of the day we are either exhausted or out of time, and we just won’t do a second problem. I shouldn’t do a second problem, if we are rushed for time. Instead, I should have a reflection activity task ready.

Yah!

 

Constant Force is as abstract as you can get 

April 5, 2017

We often think that naive conceptions of force arise, in part, to living in a frictionful world. And while I think that’s true, I also think it’s just at important to recognize that we basically never ever push or pull things with anything approximating a constant force. Our world is full of impulsive forces, forces that rise and fall in intensity. That would be true with or without friction.
There are lots of cases that are super impulsive like hitting a baseball, kicking a ball, or slamming a door, but even seemingly more constant pushes are not. Pushing a shopping cart, you push and the cart gets away from you, lessening the force you exert on it. It may get away from you enough that you lose contact, but more likely you’ve learned to lessen the force in just such a way as to push only hard enough to get the cart up to a speed, the speed you are comfortable, and then you just exert enough force to maintain a speed (against friction). 
It makes me think about how foreign the concept of “constant” force really is. We often like to say that a force is simply a push or a pull, but I’d argue that a constant force is not anything like the pushes and pulls we experience in our lives. It makes me curious to spend more time helping students explore the notion of constant force by learning about just how impossible it is to accomplish. And to realize that the situations textbooks commit ask about are so weird as to almost be absurd. 

UCM: Summary of Day 1

April 5, 2017

Step 1:  Get students thinking and talking about their experiences 

Uniform Circular Motion was first introduced by thinking how it “feels” to be a rider on a swing carousel.

Students described what it feels like differently:

  • You feel weightless, like you are not that heavy, almost floating
  • You feel heavier than normal, feeling pressed into the seat.
  • You feel like you are being thrown outward.
  • You are leaning in, or tilting into, to not be thrown out.

Next we had a clicker question about where a rider would go if at a specific point the cables suddenly broke.

Top View of Circle

Choices were varied, about 1/3 saying it would go off tangential (B), 1/3 radial (E), and 1/3 something between tangential and radial (C/D). There were very few who felt it would continue curving along A (e.g., circular impetus). We had some discussion about each of the answers, and why. Some felt the velocity (or force) would throw you out, others felt like velocity (or force) would be tangential, and yet others felt like the two would compromise to curve slightly outward while going around.

Step 2: Help re-establish and practice applying what we already know

We next did a review of what we already know about forces and motion. Students were asked to use meterstick to exert forces on the hover puck in order to

  • to get the hover puck speeding up
  • to get the hover puck moving with constant speed
  • to get hover puck to slow down.

Summary

I summarized these ideas at the board with motion diagrams and force vectors. We then did a clicker question about what the hover puck would do with a constant force that starts 90 degrees from the velocity. This one was hard, for students. Besides solving projectile motion problems (before forces), we hadn’t really talked about this. After discussion, we watched a simulation and tried it out with the hover pucks to see that it curves while speeding up. I helped them link this observation to motion diagrams and force diagrams for free-fall in 2D.

Step 3: Students explore what we don’t yet know

I told students this was a good review of what we currently know about forces– we know how forces can maintain velocity, speed up, slow down, and turn while changing speed. BUT we didn’t know how to turn without changing speed, and that’s what we needed to investgiate

Next students were tasked with exploring out how to get the hover puck to move pretty much in a circle at pretty much constant speed using the meter sticks. Students were asked to discuss a few questions: how getting the puck initially started moving in a circle was different than keeping it moving in a circle, and questions to direct them to think about how they would describe the direction of the force. Then we gathered consensus around the following video of me doing it:

I then ended up introducing the demonstration where the hover puck moves also moves in a circle in using a string. I had originally wanted them to do this (which may have been better), but I/we were feeling the need to pick of some momentum with class. We watched the demo in class, and then I showed them these pictures, which helped identify what is meant by “uniform” circular motion.

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Step 4: Clarify the idea that a central force seems to be required

I then drew a “top view” motion diagram that showed both the velocity vectors and the forces we were exerting. I put forth the idea that we had now seen 2 situations where an inward force was needed to keep an object moving in a circle – the inward pull of the tension from the string and the inward pushes of the meter stick.

[Note: Old me would have definitely been inclined to think that we are pretty good at this point. But I know better, and know better how else to keep us moving along]

Step 5: Press at students’ understanding of the new idea

Then was a clicker question about, “Why is a inward force needed?” I had four statements

A. An inward force is needed to balance the force that the puck experiences outward.

B. An inward force is all that is needed to turn the puck around the circle.

C. In addition to an inward force, a force around the circle is needed to keep it moving as it goes around.

D. There are actually three forces:  One force that keeps the puck going around the circle, and two forces that are balanced to keep the hover puck from being thrown out of the circle.

I gave students time to think and talk with their small group. We were widely and almost evenly split between all choices. We spent a little time talking in whole class, to clarify what was meant by each idea. Instead of having them talk in small groups, I had them get together with people with similar answers. They had some time to chat, and then elected a spokesperson to make the initial presentation. I allowed questions aimed at clarifying, and added clarifying comments myself, but didn’t allow back-and-forth until each group had a chance to present. Then, we started talking more freely with ideas bouncing around.

  1. The inward only group focused on explaining that all you are doing is tapping inward, so that’s the only force, and that while they agree there’s a velocity around the circle, that doesn’t count as a force. They agreed that you initially needed some velocity around the circle to get it started, but the question was about “keeping it in the circle”, and they didn’t think it needed any force around the circle to do that.
  2. The inward + force around the circle went next and said that a force was needed to get it started and to keep it going. They came back to the spinny ride, saying that the ropes have two jobs, to pull you in and pull you around the circle. There were a few who said after hearing group 1, they weren’t sure whether it was just velocity of force around the circle.
  3. The next group talked about the in and out forces needing to balance. During discussion it became clear that some in the group thought the “balance” force was the velocity, that made it want to go out, and others thought there really was some outward force. Through this conversation, it became clearer to us all that issues around whether something was a force (or velocity), and whether or not these were pointing around the circle or outward from the circle was an crucial difference among the ideas (both within and across groups).
  4. The last group, made a compelling argument for why an inward force was needed. Without an outward force to balance the inward force, the inward force would “win” and make the circle spiral inward. We referred to this as the “death spiral”. To maintain a circle, the argument goes, a balance of forces would be needed. This was pretty convincing to lots of folks.

During the more open conversations time here are some of the ideas that came up:

A.  A big question came to identifying what the outward force was. We’ve been pretty picky all semester about identifying forces. Someone eventually suggested that it might be the force pair. I helped flesh out what the student meant by this, by identifying the forces specifically. But I initially didn’t press for the implications of that idea. I wanted that idea alone to be important. Yeah, what is that force? Maybe it could be this force, the force pair. I probably could have asked, “Do people have others ideas about what the outward force could be?” to further value that line of reasoning.

B. Another idea was that a force can’t be needed around the path of the circle, because a force around the circle would mean that force and velocity were parallel. Our rules state that when force and velocity are in the same direction, speeding up occurs. Through discussion and re-voicing, I helped them to articulate a possible new rule that they were seeming to suggest: “If force stays 90 degrees from velocity, all you do is change direction, without changing speed.”

C. Someone argued that they don’t think that an inward force necessarily means a spiral inward. They were trying to think of what would make something spiral in or out, and they came up with situations where spiraling in or out would be associated with a change in speed. People gave examples of twirling keys with a lanyard, and letting it swing around your finger vs. wrap around your finger. Since we were talking about uniform speed, not spiraling should happen unless you speed or slow the object.

D. There were also more conversation about getting it started vs. keeping, that were helpful, but I can’t quite remember, and ‘m sure there were other ideas that I’m forgetting.

Step 6: Help clarify the different possibilities 

Anyway, we took a break, and I chatted with some more students. During break, I talked with several students about the “force pair” idea, and helped connect that to our previous learning about how force pairs shouldn’t be on the same FBD. So that if the outward force was the force pair, it shouldn’t be included in the diagram that shows forces that act on the puck (or rider). I also talked with the two students who brought up the spiral in idea and the counter proposal.

After break, I tried summarizing some of the big ideas, and helped the whole class in on two ideas:

  1. That if the outward force is the force pair, then it’s a force on another object, and thus shouldn’t be included, and
  2. that there are two different ideas that I see as similar. I told them that the “inward” only group thinks that what the puck will do without a force is “go straight” and that an inward force is needed to “bend” the puck so that it moves around with a constant spiral (not spiraling in or out).  The “balanced force” idea seems to focus on the fact that the puck is already moving in a circle, so that any extra force would “bend” the puck into a tighter circle. I emphasized that both groups agreed that inwards forces cause “bending in”, but they disagreed about the detail.

There was a bit more conversation after I introduced those ideas, and students had some time to be back at their groups to rethink.

Step 7: Introduce a Testing Experiment

I then introduced a new experiment that might help us decide. I showed them a metal ball going around inside of a metal ring. I told them that I could suddenly pull the ring upward, and that it would be like “breaking” the cable on the ride.

I introduced what we were about to do as very different than what we did before. Before, we were shopping around for ideas, experiences, arguments, and that it was kind of OK to change our mind. But now I wanted us to stop letting our minds think whatever we want. I want to find out not “what we think”, but what our different ideas imply. I asked students to go back to their groups and draw 3 diagrams:

A free-body Diagram (just before the ring is pulled away), based on whether you think the forces are “inward only”, “balance in and out”, or “also around the circle”

A free-body Diagram (just after the ring is pulled away), based on what forces should disappear when the ring disappears.

We agreed that each diagram should be very clear about whether something is a force or a velocity, but that it was OK to not specify exactly what the outward force might be, since we were still not sure. We also agreed that the object of interest for our diagrams was the ball, and that only forces that act on the ball should be included.

The last diagram was to show a path about where the ball goes. I spent a lot of time telling them that this was not where “you think” the ball should go, but rather what the diagram has to say about where the ball should go based on a rules:

  • No Net Force -> Constant Velocity
  • Force in Direction of Velocity –> Speeding Up
  • Constant Forces in 2D –> Curved trajectory

Groups split up and worked on their diagrams, and then we circulated around looking at different diagrams. Several groups went in the direction of “inward only”, one group did balanced in and out, and another group did balanced in and out (with maybe force in the direction of motion).

We concluded that a balanced forces implies that the loss of ring would leave the ball with only an outward force… and that this would mean the ball curves slightly outward as it leaves the circle.

We concluded that the inward forces only idea implies that ball will go off tangentially, moving not only straight but with constant velocity. This is because since the only force was the inward normal force from the ring, once this force is gone, the particle is subject to zero net force.

I sent students off to make the observations at their tables.. Because it’s hard to see, students spend a fair amount of time on this. In small groups, I talked about “confirmation bias” and whether or not they think it was possible to see whatever you want, like those that want to see it as straight can see it that, and those that don’t, can claim they see a slight curve.

Step 8: Help students connect what they observed to what it means

Good thing we have the slow motion camera:

I did some summarizing here (should have made them do more of that work), and connected what we were learning to textbook notes and diagrams. This is also something I should have them do. I should have had them open their textbooks to the passages and diagrams, and ask them to do this work. This is like in my previous post about discourse, where I took too much responsibility for discourse 2 and 3, where I should have been the one to support them in engaging in the discourse.

Step 9: Practice Applying the Idea in progressively more challenging situations

The way I did it was ask them to engage somewhat in the 3rd type of discourse was by getting practice with applying the ideas, which is better than nothing. We did a few clicker questions about identifying the “force” that plays the role of the centripetal force. We did free body diagrams for penny on a turntable, the swingers on the ride, and then finally free body diagram at the bottom of pendulum swing.

Students did fairly well with the first two. I emphasized how in the first case we might think of just one force (friction) as playing the role of a (net) centripetal force, and how in the second we needed to think of the just the horizontal component of tension as playing that role. But the third one was a really interesting trouble spot.

In the pendulum swing, students had to decide which of the two individual forces was larger, weight or tension. Maybe one or two students said weight would be stronger than tension (probably focused on “outward throw” still), but most groups picked that tension and weight would be equal. What was interesting is that many of the people who said that tension and weight would be equal were the also the ones who were most adamant for the inner force only in the previous activity. I thought that was interesting because now they were saying that balances forces were needed. Some of these students even argued that if the T were greater than the weight than the mass would like “rise up” at the bottom (making a smaller circle). Essentially, the spiral in argument resurfaced, but not from the same students. It made me wonder if “having the right” idea the whole time made them more vulnerable to being tricked later.

Anyway, the situation is hard for several reasons (one it’s not uniform circular motion, vertical forces are involved, and there are two forces in the radial direction). I think a lot of students reasoning was actually trying to borrow from “independence of motions in projectile motion”… Something like Like the velocity is horizontal, and so it should have no impact on the forces vertical. Thus the vertical forces should be balanced. It’s an interesting case of saying “no velocity vertical” means “no vertical force”.. which is “force~velocity” reasoning just resurfacing with knowledge of components.

In discussion, however, groups were able to be pretty convincing that the tension should be larger than the weight. Groups did a good job of making it clear that what we had talked about, seen, and learned today was the basis for saying that the forces cannot be balanced if it’s moving in a circle, and that rather a surplus of force pointing upward toward the center of the circle was needed. I’m glad the class did this (without my help), but I could have done a better of job of pushing questions in small groups, like… “How did you apply what we learned today to help inform your answer?” or “How is your answer consistent with what we learned about the forces necessary to keep an object moving in a circle?” I might have even asked a question like, “So any time you have velocity that is purely horizontal, the forces vertically must be balanced?” The conversation was good, but I definitely see ways I could have been a better at “pressing for disciplinary connections” toward the end of the lesson.

We ended the day by observing the force sensor data. With five minutes left in class, I asked students to take some time to reflect, write, summarize what they learned today. This is also a practice I need to use more, using the last 5 minutes for reflection. All and all a good day. On Friday, we get more quantitative with “how much force exactly is needed” –> this will build off nicely from the spiral in /out question… we want just the right amount of force to keep the circle (not let it widen or tighten)… We will investigate what factors are involved.

 

Connecting: Lesson Design Structures, Instructional Discourse Patterns, and Teacher Talk Moves.

April 4, 2017

In teaching of physics this semester, we did an activity of sorting many question into three categories of discourse:

  1. Eliciting students’ initial ideas (questions that help us identify our /their thinking)
  2. Supporting changes to their thinking (questions that make one consider how what one is doing relates to our ideas and other activities)
  3. Pressing for disciplinary connections (questions that direct students to draw explicit connections between what they are currently doing (and/or what they have done) with specific concepts and/or practices from the discipline.

This categorization is basically from the Ambitious Science Teaching folks, but we’ve been adopting this framework to describe the instructional flow to most instructional frameworks we have talked about, whether it’s

  • Elicit Confront Resolve (Described here by Wenning with the additional steps of identify and reinforce)
  • Bridging Analogies (Described here by Clement), flow is Anchor –> Bridges –> Target
  • Learning Cycle in ISLE (e.g., observation experiments –> testing experiments)
  • Invention Tasks (i.e., based on preparation for future learning), and here as well.

as well as others.

One of points I’ve been trying to drive home is how these curricular structures have certain design “features” that make them effective, but ultimately it’s about the discourse that happens during instruction– what talking and thinking are students engaged in during each phase. For the appropriate discourse to happen, teacher talk moves need to shift from “eliciting” to “supporting change” to “pressing for disciplinary” connections. Previously, we had also talked about discourse at the level of “talk moves”- probing, re-voicing, pressing for reasoning, etc.

Our activity today was to try to link the two: what sort of talk moves support what kind of instructional discourse?

Here are the list of questions we considered.

  • You said_____, but why do you think that?
  • What connections are you seeing between  ____ and ____?
  • What do you think will happen when____
  • Can say more about that?
  • How is your thinking about __ different now after ____?
  • Who else has ideas about what might happen?
  • Do you agree or disagree, and why?
  • Who would like to add on to what ___ said ?
  • So you seem to be saying ___?
  • What do you all think about that idea?
  • How did you come up with that?
  • Can you describe what happened when___?
  • What evidence supports the idea that ___?
  • Is there a specific example you are thinking about?
  • What does this passage mean in your own words?
  • How do we know that ____ ?
  • Can you say why you agree with ____
  • How can you check your answer?
  • How are you making sense of that?
  • How is this observation different than your prediction?
  • What do you think these results imply about ____?
  • What can you say now that you couldn’t before?
  • Does this agree or disagree with your prediction?
  • How is this situation different than ___?
  • What reasoning justifies this ___?
  • What assumptions did you have to make in order to ____?
  • What does this observation tell us about ___?
  • What are some tools we have used to ____  ?
  • What are some things you notice?
  • What does this tell us about ___?
  • Do you think this supports or refutes the idea about __?
  • Explain to us what your thinking when you say ___
  • What made this particular situation difficult?
  • What do you think causes that to happen?
  • What do you think that tells us about the data?
  • What do the rest of you think?
  • How have your ideas changed at all?
  • What makes you think that will happen?
  • Does the explanation here describe what you discussed?
  • What patterns did we notice?
  • How did you decide to ___?
  • How did you know you had made a mistake?
  • How did you reach that conclusion?
  • What did you notice happening when ___?
  • Can you tell us how you came up with that?
  • How do you think ___ applies to this scenario?
  • How might we revise our thinking after seeing ___
  • Can you tell us why you think that’s not longer true?
  • How does your work here reflect what we’ve learned about ______?

For each, we talked about the context or contexts in which it might make sense to ask this question, and worked toward a consensus model of what type of discourse this question would most likely support. We talked a lot in class about how traditional instruction spends too much time in the 3rd kind of discourse, skipping the 1st and 2nd kinds. We also talked about how unsuccessful inquiry often fails to make the turn into the 3rd type of discourse, or perhaps fails to even do much of the 2nd (students just go through activities without ever thinking about them).

It was a good day. I feel like I learned a lot and so did the students.