In My Class Today · Teaching Methods

Day 2: Thinking about Relationships

Day 1 I run a HUGE physics smorgy: 11-15 demos/lab set ups with minimal directions. Students are told to play, investigate, explore, PAY ATTENTION and ask lots of questions. This is my hook into the class for the year. I’m able to observe the students, act ridiculous and ease the MASSIVE anxiety they walk into this class with.

The next four days we actually spend working with data and relationships. Specifically to build the skills necessary to analyze data on a graph and straighten it when needed. I have a reading I ask students to do ahead of time and then we go through the straightening process. These brilliant students (half of whom are in AP Calc) are completely flabbergasted by the straightening process. It just doesn’t. make. sense to them.

I decided to try something different today on the fly, and it brought about some great conversations. First I put up blank sketches of graphs depicting a linear, squared, inverse and square root function. I asked them to put the graphs on their white boards and write the relationships. The answers consisted of the following:

  • “linear, squared, inverse and square root”
  • y=x, y=x^2 (etc)
  • y∝x y∝x^2 (etc)

This kicked off some great conversations. Are we in agreement, generally, about which is which? (yes). Are the equations really representative of the sketches? (We don’t know, there are no labels or numbers on the axes)

Next, I gave students four statements

  1. “Momentum is proportional to velocity”
  2. “A spring loaded gun is fired upward. The height of the bullet is proportional to the compression squared”
  3. “Velocity is inversely proportional to mass”
  4. “The period squared is proportional to the length of a simple pendulum”

I asked them to label the axes of their graphs with the physical quantities to match the statements. Here’s where the fun began. Students took a lot longer than I had originally anticipated completing this task. Here were the great conversations to be had:

  • In science, we usually put the independent and dependent variables on the x and y axis. With these statements, is it obvious which is which?
  • Since it’s not obvious, are answers where the axis are flipped wrong? (Not if they picked the appropriate shape!)
  • So, we often are going to use slope to talk about relationships. Like, say, if we plotted distance on the y and time on the x what would we get? (speed…minds are blown)  The cool thing is if you plot the graph “wrong” you can look at the units,  and decide if they need to flip because you’d have seconds per meter or something. The important thing is whatever you tell me the relationship is, needs to match your graph.
  • Then, of course, I let them in on the secret: we always list the y thing first. Literally all we are doing in these sentences is taking the math proportions, like y∝x^2 and saying, instead, height ∝ compression^2. It’s like the hugest lightbulb moment for students ever.

Now that they have that substitution thing in their brain, explaining how to straighten graphs is a snap. I was really pleased with the lack of frustrated and confused faces. Last year, I sadly, lost several kids during this unit. I wanted to cry so hard because we hadn’t even started physics and seriously questioned my lesson plans.

Tomorrow they finish their pendulum labs, so we’ll see how this all goes.

Meanwhile, AP Physics C is dabbling in computational physics for kinematics. More on that later.

 

In My Class Today · Teaching Methods

I did something I would NEVER do in most classrooms

Anyone I have spoken to one on one knows that my group of AP Physics C students is truly a unique group. They are the kind of group that comes around once every few years and makes your teacher heart soar…so you bring them up with you and cast them off and they fly higher than even you could have imagined.

So I thought I’d try something radical. Work on a skill that was far greater than their ability to do physics. I wanted them to focus on the learning process.

We are starting the Biot-Savart Law. Students need to do the derivations for a line, ring and ring segment of current. The reality is that the math skills are no different from anything they haven’t already seen before. But as we know, often times when students are presented with a new application it’s like everything they’ve learned is back to zero. The reality, of course, is that they lack the experience and mastry to be able to make those connections as we do as teachers. So I assigned the reading several nights ago. I asked students to take particular note of the three examples, and then I assigned the students in groups to one of the three examples.

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The paper they received, however, was not a carbon copy of the book’s example. Because we know what students do when we ask them to read. They skim. They decide they can understand how the author got from step 1 to step end and they move on. But we know if we asked them to do a similar problem they would barely know where to start. I wanted them to actively engage in the material in the text. So I told them they had to prepare their assigned problem to teach to the class, instead of me teaching it.

Students had 2 nights to prepare plus 30 minutes to discuss in their groups the day before. Today was presentation day.

Imagine your first year teaching and that lesson you thought you’d be fine at, so you didn’t quite prepare it the way you should have. That’s what happened. But it was ok because I knew that all of my students would be ok. They challenged each other, they forced the students presenting to slow down, they asked the necessary clarification questions that required the presenters to really think about what they were doing rather than regurgitating text.

After the group had come to the end, I stepped in. I asked the group to step back for a moment so we could summarize (because we all know what happens when we get lost in the details and the mistakes…) I asked the students to explain why we did each step and connected it to what they had seen before. If notes or annotations needed to be added to the board, we added them. Once we were certain everyone was securely on the same page we moved on.

At the end I explained my goals of this exercise  to my students. Not only do I want them actively engaging and learning (and seeing you CAN learn) from the text, the reality is that since they are ALL pursuing STEM majors there is a VERY REAL possibility that they will each be in a teaching assistantship in the next 3-5 years. They are going to need to learn how to teach what they are comfortable with, what they may not have been comfortable with, or something they learned 4-5 years ago. These teaching and communication skills are so valuable and go well beyond the world of academia.

I almost backtracked on this assignment and took over today, but I’m really glad I didn’t. My students once again rose way above and beyond what I expected. Working with a group of gifted AP Physics C students can be really challenging because finding the sweet spot of struggle vs overwhelming is a lot higher than one might anticipate, and in this course I think that sweet spot is higher than even the students realize. But that sweet spot is where the largest amount of growth happens, and I think we hit it today.

Concept Modeling · In My Class Today · Teaching Methods

Pass Along – Modeling Waves

The pass along activity is one I developed shortly after attending a Kelly OShea workshop. I wanted to combine modeling with the strengths of white board speed dating and board walks. At the time I didn’t have the large whiteboards and for this particular activity I decided a piece of paper would work best.

Students have already done a reading on waves ahead of time (hopefully).

Part I: I ask students to draw in a pictorial representation of what a longitudinal and a transverse wave might look like.

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This is inevitably the most common drawing. Students obviously did the reading, but struggle with a pictorial representation

Students are then told to pass along their paper. I predetermine groups randomly for this activity. Three is best, but if I don’t have a factor of 3 then I put the stragglers into groups of 4. It looks like this:

Student 1 -> Student 2 -> Student 3 -> Student 1

Part II: After students have passed along, they are required to look at the work done by their peer and explain, in words, why that person drew what they drew. Much like speed dating, this requires each of the students to get in the minds of their peers, but without the opportunity for their peers to explain.

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Students then pass along again.

The third person takes a look at the previous two answers and then has to think of a way to model each wave type with their bodies.

After the three pass alongs, students get into groups, at this point each paper has been touched by the same persons. They discuss their answers and then they have to get up in front of the class and model with their bodies each wave type.

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The physical modeling is great in that the kids are up and moving, but it also provides an opportunity to have a discussion about the model. 7th hour we had a discussion about whether or not doing the worm accurately models a wave (nope, the particle is moving across the room). Similarly, I had a few groups move their whole line down the room which brought up the discussion point about what a wave transfers and doesn’t transfer.

Afterwards, we will go out as a whole class and model transverse and longitudinal waves using an 8-step count.

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A unique representation of a longitudinal wave I hadn’t seen before
Teaching Methods

AP Physics C in the Accelerated Classroom: Addressing the Needs of the Gifted and Talented in Physics

Gifted and accelerated learners have specific needs in the classroom that frequently go unmet. It is a grievous error to assume that just because a student is gifted they will be successful. Differentiation is often viewed as incredibly labor-intensive on the part of the teacher with difficulty in grading different products fairly. This is of particular challenge in the current Advanced Placement (AP) Physics C program since, under the college board recommendations, many physics C students already have a strong foundation in mechanics from AP Physics 1 (algebra-based). This paper will share a particular example used in the lab in an AP Physics C gifted classroom and how the products are easily differentiated and scored in a fair manner.

 

Introduction to Gifted and Talented Learners

The first thing that must be noted is that gifted learners exist in every classroom. The second thing that must be noted is that gifted and talented looks different on each individual. Additionally, when students are put through an identification process, minority and English language learner students are overwhelmingly unidentified.

Identification of gifted and talented students is immensely important because research has shown that in the absence of the ability to nurture student talents, many of these students will, in fact, underperform. Students are either placed in environments that lack rigor and challenge and so they disengage because they are bored, or if the teacher identifies the student as “smart” the teacher often does not recognize specific markers of giftedness that contribute to student behavior in the classroom, prohibiting the teacher from allowing appropriate accommodations.

It is important that every classroom teacher become aware of giftedness so that they can best address their students. Much in the same way that we will readily allow a student with ADHD to stand during class, or use a fidget, we must also recognize that gifted and talented students have their own set of needs to be challenged and to grow.

Although there is no one blanket description for students who are gifted and talented, there are some unique markers. Much like a student who may be diagnosed with a special need, gifted and talented students’ brains are physiologically different. They have a thicker pre-frontal cortex that develops differently from their peers and they, in fact, have more and stronger neural pathways than their peers2. Not only do they think differently, they perceive the world in a different manner. In the absence of development of talent, gifted individuals can lose the strength of their pathways, rather than expanding them.

One of the most clear differences in gifted students is that they exhibit one or more over excitabilities. Overexcitabilities describe a series of traits and/or behaviors that gifted individuals feel on a level that is far more intense than the general population. These include the following: intellectual, emotional, psychomotor, sensory and imaginational. Intellectual is what people are most familiar with when they think of giftedness: avid readers, love of learning, independent thinking etc. Emotional are the students who often have an overwhelming sense of empathy for their friends and family. Due to this they are often the ones who will take up causes for advocacy. They also may exhibit extremely intense anxieties. Individuals with psychomotor over excitabilities are often misdiagnosed as having ADHD, they may talk fast, act impulsively and seem to run on little sleep. Sensory have a heightened sense in the five senses, they are often extremely interested in the arts and have a depth of interest in aesthetics. They may also, however, be unusually sensitive to smells and tastes. Individuals with imaginational overexcitabilities are the ones who are constantly daydreaming, visualizing, Males tend to score higher on the intellectual and psychomotor areas while females tend to score higher on the emotional and sensual over excitabilities3

AP Physics C for the Gifted and Talented

Acknowledging these needs for gifted students, what is a teacher to do? Two of the most important tools are acceleration and differentiation.

We often think of acceleration as grade skipping. While this is useful for many students, it is not in our grasp as classroom teachers. We should, however, not prohibit say, a sophomore, from enrolling in physics if they have met the appropriate math pre-requisites. Surprisingly, acceleration at the grade level has shown to somewhat close the gender gap in publication and salary for female students4. At the classroom level, where we have control, this means compaction of curriculum. I lean most heavily on this for my students.

Since the students in my class have all taken AP Physics 1, they have an incredible depth of conceptual foundation as it relates to mechanics. This was, indeed, the goal of the revised course. The challenge now, however, is to make AP Physics C exciting, interesting and challenging. At the same time the goal of any high school teacher should be to equip their students with the foundation for the skills needed in college.

For any STEM field, we know well that lab skills are indispensible. At the same time, we also know that creating a genuine lab experience when students have little to no lab experiences is extremely challenging. There is a certain level of base knowledge needed to have a valid lab experience from start to finish. Fortunately, students in AP Physics C have already obtained that base knowledge. The only difference is that now my students are required to incorporate calculus.

 

The Flipped Accelerated Classroom

I operate on the premise that first, the majority of the physics concepts should be review, and second, the lab experience is the most important experience in my classroom. While it is not imperative to student success that they be able to determine an obscure moment of inertia, it is imperative that they enter college with a basic skill set that includes troubleshooting, use of basic equipment, creativity, critical thinking and problem solving strategies. On the first day of school I gave my students the following assignment: design a product that demonstrates to me that you have mastery over all of the AP learning objectives for kinematics.

Immediately this assignment is differentiated: students have almost endless choice. They have full access to all lab equipment plus anything else they would like to use or bring in. This is, at first, an extremely challenging prospect to students. They are not used to having so much choice, their activities have more or less been dictated by the goal and/or equipment available. This is not true of real research; in that case you must select a project, investigate, and produce results.

We recently did the same with momentum. Since this topic is much more in-depth than kinematics, I assigned nightly homework sets and provided solutions the following day. The homework was not collected or scored as I am leaving it in the student’s hands to determine how much repetition is necessary for themselves. In this unit they were asked to design a lab in which all of the objectives are present. Since this project would inevitably include many other topics within mechanics I provided a little bit more guidance, encouraging students to start with a question. Within the first class period I had a group investigating a buoyant object dropped into a container of water (Fig 1)

and analyzing with Vernier VideoPhysics, another group analyzing the deflation of a balloon attached to a string with a straw, a third looking at spring pendulum, and a fourth examing a dynamics car attached to a spring on a horizontal surface. Each of these involved a varying force (not a requirement, but an option for the exemplary plus mark) and in the case of two of the experiments, students needed to study topics they had not yet covered as it related to their problem.

Student Products, Evaluation and Presentation

Student products vary n terms of level of complexity and interest, but they have always been exciting to grade. The first challenge, naturally, is scoring the product in a way that is fair for all students, given the large variety. To this end, I grade the products based on how well they meet each of the objectives, from Exemplary to Unsatisfactory. In order to permit students who are more mathematically advanced or who would like to go for the challenge, I include an exemplary plus category. At the beginning of the year this category was for any correct application of calculus, once the year progressed this category needed modification to ensure the same level of challenge.

Students are also expected to present their results and provide feedback to their peers. We do a type of poster presentation session. Students put their procedure, lab design and results on a large whiteboard. (Figure 2) , one partner circulates the room while the other remains at the board to present to their peers. During this time period students are to ask one another questions, whether it be for clarification, or as a way to offer a suggestion. (Figure 3) After students have moved through the room, original partners move together. The partner who circulated initially now must explain each board to their partner. As they do so, they are asked to leave feedback on a smaller board. At the end of this exercise, groups return to their boards and review the feedback. I then give students another few days to make adjustments and corrections before turning in the lab.

Applications for the Mixed Classroom

Allowing student choice and differentiation for gifted students is just as important as allowing other students extra time on exams or the ability to use a fidget. The reality is that just as our classrooms often will have students with special needs due to a disability, we likely also have a non-zero number of gifted students as well, who’s needs must also be met. In a mixed classroom, this might mean generating both the guided and open-ended lab. The modeling curriculum works very well for all students, but the differentiation component is key. Gifted learners should be permitted to do less repetition as long as they can prove mastery. They should be permitted to work together in class sometimes (ability-based grouping), rather than always grouped with the struggling students so they have the opportunity to flourish with like minds, much as we appreciate upon entering college.

 

Conclusions and Benefits

This type of activity and assessment has served multiple purposes. First, it allows for differentiation within the gifted classroom. Students have the ability to make their products as simple or complex as they determine, while still meeting the learning objectives. Secondly, it requires students to make a variety of considerations and assumptions such as which equipment will be best, how to control for a variety of variables, and which variables can be simplified due to assumptions or uncertainty measurements. (For example, in my group that examined the deflating balloon, they massed the weighted balloon on an extremely precise scale and noted it was loosing mass, even while tied. ) Students are using and improving on lab skills and techniques. Lastly, students are learning the importance of clear communication and critical evaluation. In a time where even undergraduates are expected to produce publishable research, communicating, evaluating and responding to evaluations become ever more important skills. By focusing on these at the high school level, students become better equipped for whatever their future holds.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

In My Class Today · Teaching Methods

A Spin on Energy

Last week I ran a pretty straightforward lab:

  1. Put 120cm of hot wheel track into a design of your choosing
  2. Run a ball down the track
  3. Record velocity with a photogate
  4. Repeat at 10-12 locations
  5. Plot the energy curves.
  6. Plot Translational vs Rotational Kinetic energies and find the rotational inertia constant.

 

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Sample track set up

 

Students should see a transfer of kinetic and potential energy which makes sense. Of course, students should also expect to see a decreasing total energy curve because of friction constantly taking energy from the system.

I had two fun surprises I got to incorporate:

  1. The shape of the TME curve

Inevitably this curve had a particularly sharp drop off at one moment in time. I had students sketch their tracks on their whiteboards in addition to their lab results. IMG-2087IMG-2088Do you notice anything? The largest drop off in TME corresponds to the moment where the ball is at the bottom of the hill. This serves as a great review of work and circular motion. Frictional force, as we know, is dependant on normal force. The normal force of the track changes and corresponds with its shape. We can actually predict the drop-offs in TME based on shape and even determine the work done by friction.

  1. A group with “bad” data.

Their data wasn’t actually bad, they obviously had forgotten something when they set up their formulas in the spreadsheet. But was there a way to find this without redoing the whole data spread? Absolutely. After creating a large circle to share whiteboards, we honed in on the group where the TME curve was mirroring the potential energy curve. The rest of the data seemed good…there was an obvious trade-off of PE and KE…although the curves weren’t as high as they should have been. So what was the problem? I selected a student to draw in where the energy curve should be, based on the shape of their track and everyone else’s data. She drew in the curve. Next, I asked students to note where this curve was and where the PE curve began. It was at 0.3 J with PE starting at 0.6 J Then I asked them to note where the KE curves were at… they were at 0.03 J. Notice anything??? They were off by a factor a 10! Where could a factor of 10 be? Did they forget a 9.8? Did they convert grams to kilograms properly? cm to m? Upon examination of their equations, they found the missing 10 and…TA-DA! Fantastic results.

I think it’s really important to note the value of both exercises. The lab itself was relatively simplistic, but it lent itself to fairly complex conversations.  I think this is especially true for the group with the “bad” results. How often do our students present with this and either (1) Default to “well my data must be bad” or (2) Start from scratch, rather than locating the mistake? In this way, students were able to critically analyze, strategize and problem-solve. It turned out to be a really easy fix.

Oh and the slope of the translational vs rotational KE? Yea that came out to 2/5….exactly. That’s super exciting!

Teaching Methods

Radical Renovations: The iOLab

I visited my alma mater today. The entirety of Green Street on campus is closed to traffic due to all of the construction. Buildings have gone down and come up and I half expected time to still be frozen in the year 1967 in the physics building.

When I walked in I found quite the opposite. Not only newly renovated rooms, but there is actually a women’s bathroom on the fourth floor. (This was always a running joke)

The reason I spent 6 hours in my car today, however, was to visit the Physics 101 class. iolab_remotes_redMy former adviser, Mats Selen, has been working on a new project: the iOLab. The concept is simple, it’s a multisensor system in a box. And it can do everything your $10,000 of Vernier equipment can do… for a little over $100. It connects wirelessly to your computer and runs with free, opensource software that does all of the analysis our expensive programs run.

On the other side of the coin, however, is a radical change in how the introductory level classes are being taught. When students walked into the lab, they had done a pre-lab experiment earlier…..at home…..with their iOLabs. Quite simply, they made a stack of books, put another book on top by its edge and then looked to see how the force changed with the iOLab as it was placed at different distances from the book stack. Data were submitted ahead of time for credit. Students discussed the results at the beginning of the lab and then were given their task. It’s the classic peg-board demo, however, students had to find a way to relate the force to the placement of the probe if the pivot was located in the top corner.

This was the sum total of the direction given to students.

Within about 20 minutes all students were taking measurements. Some were looking only horizontally, others were looking both horizontally and vertically. Questions arose about the approach: if we change the angle at which we hold the probe the force will change. Are we supposed to do this with a horiztontal force too? I think that’s impossible.

They were told it’d be great if they came up with a mathematical relationship, but they’re just looking for the trends.

Within an hour students were plotting their data, recognizing it was an inverse relationship and running the curve.

One group really wanted to get the formula.

Another group recognized the torques should be equal and started calculating all of the torques. Percent uncertainty was one of the objectives focused on, so I wanted to see how well they were grasping that concept. I looked at the torques and noticed the values were .14, .14, .14, .15, .16. So I asked them how they were going to decide that those were constant and not increasing. They responded that they would have to determine their percent uncertainty and compare what was acceptable to those values.

Now, clearly there are major differences between high school junior and seniors and pre-med juniors and seniors, but at the same time, it was still remarkable how they were approaching the lab, developing their experiment and writing up their labs. It is something that very much excites me about the potential use in the high school classroom (and online classrooms, and college classrooms etc)

I also asked students about their previous physics experiences. About half reported they had taken physics in high school, ranging from regular level to AP Physics 1. ALL students reported that they felt they had a FAR BETTER grasp of physics now in this course, compared to their high school course. Several students who said this felt the need to insist they still had a great high school teacher 🙂

The message, however, is clear: we need to give our students the opportunity to design and evaluate their experiments.

Also, the iOLab is a very exciting new piece of equipment. Morten Lundsgaard, currently the Coordinator of Physics Teacher Development
Instructor, is hoping to run workshops and/or a camp for high school teachers. If you are interested you should contact him!

Concept Modeling · Teaching Methods

Slicing a Cylinder for Moment of Inertia Integration

Guys….we’re in the throws of rotation. And at least one of my poor students has calculus immediately preceding AP Physics C. I feel so bad for her. The day we started she had made up a calc quiz, came to day 1 of rotational inertia, then went to calculus. Oh did I feel her pain.

Arguably the most difficult part of deriving rotational inertia is the visualization of how to go about the integration. I mean, let’s be honest, once we find how to express dm the integration is always an easy one.

Part of the problem is getting students to understand what it means to say things like dm, dV, dA, etc. They understand the definition linguistically, but it’s really hard to think of it practically. Tell them that dr^2 is zero and their minds are blown and bothered.

Day 1 of cylinders did not go well. Arguably, in part, because we were short on time. But also because the what why how was overwhelming.

I remembered a demo someone had shown where they 3D printed their objects to roll down the incline. They had actually made nesting cylinders, which then served as a great way to discuss integration.

I’m trying to think of a way to visualize each of the d-steps of the cylinder integration for my students with materials I have on hand. As I’m digging through the closet I notice the slinky coil. It’s nearly perfect!!!

Ideally, I wish I had one with nice thick coils so we could take about the cylinder with R1 and R2, but this will suffice for the most challenging part.

So imagine you have a cylinder of length L, and inner radius R1 and outer radius R2 and would like to determine the moment of inertia about its center…

IMG-2037 (1)

First, as always let’s define rho, but we have to find dm in terms of r. So how do we do that?

Well, let’s take some horizontal slices, where each slice is dm… now we can see that dm = rho*dV…but wait… what is dV?

Well, if we make those slices infinitely small…is there really a volume left?

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Ah! so dV is really dA, and we are looking at it across the length of the slinky, so dm = dA*L!

Conveniently, I know that A=pi*r^2, so dA = 2*pi*r dr

And the rest is substitution!