Two New Types of Problems

As my students have been developing their understanding of uniform acceleration, my colleagues and I have come up with two problem types for student practice. Much appreciation to Brian Frank for his writing about multiple representations, as it was a big motivator for me to pull this together.

Deploying the Model from an Incomplete Representation

We asked students to fully deploy the model of uniform acceleration based on an incomplete chunk of info. (Background: for our students, to “fully deploy the model of uniform acceleration” means to create all the representations they know[1], filling in all the values at every step.) We’ve been practicing deploying our model on a bunch of scenarios. What you see below come from practice as well as our test.

For example, this data table:

Screen Shot 2018-12-12 at 10.27.01 PM

Students had to finish the table, then flesh out the model using a variety of representations.

Here’s another, starting with this mathematical representation:

Screen Shot 2018-12-12 at 10.28.15 PM

And finally, this velocity-time graph, which appeared on the test today:

Screen Shot 2018-12-12 at 10.28.38 PM.png

Here’s where we went from the above velocity-time graph. First, we asked for the initial conditions (position and velocity) as well as the acceleration. Most students did a decent job here. A design flaw in the graph we provided on the first version of the test (photo below) made it tough to read points and therefore calculate slopes. We updated for later classes and the screenshot above is the newer version.

Next, we asked about when the object reaches its starting position. I absolutely love the explanation from the student below.

Finally, we asked about the displacement of the object over some time interval. Again, check out the work below to see how this student applied her work from the previous question to make her job easier on this one. Brilliant!

20181212_224603

As y’all know, students are forever misreading velocity-time graphs as position-time graphs. Here’s a classic example of that mistake on this question:

20181212_225252

Or, in this student’s case, confusing position with displacement:

20181212_225459

Identifying Initial Conditions

Now, let’s back up from today’s test. Sort of late in the game, we realized kids who struggled with deploying the model on problems like those above were struggling to identify the initial conditions (velocity and position) and the uniform acceleration. That’s when we whipped up the “identifying the initial conditions” problems.

Again, these problems presented the students with a single representation (sometimes incomplete). Students almost unanimously agreed it was easiest to start with the mathematical representation:

Screen Shot 2018-12-12 at 10.35.26 PM

The verbal descriptions were also pretty simple:

Screen Shot 2018-12-12 at 10.35.10 PM

And for some reason, the motion maps continue to be a struggle. For this particular batch of kids and for this particular content timing, I opted to give them initial velocity, though it’s totally obtainable from this motion map:

Screen Shot 2018-12-12 at 10.34.54 PM

Parting Thoughts

Both the incomplete representations and the initial conditions problems proved super helpful. I mean, of course they did or I wouldn’t be writing about them here. I keep saying that I’ve never taught kinematics with so many open-ended problems. Most of the time, our students are modeling a scenario. Then sometimes, we throw in a pretty traditional question they need to answer with the model.

Oh, and though you don’t see it here, we did a little with free fall. Most kids realize that the acceleration acting on an object thrown up in the air is uniform, even at the apex of the throw. First time ever that so many kids get it. I credit velocity-time graphs and data tables for helping them see it.

I remain baffled at why so many students find the motion maps to be so difficult. These same kids love them some data tables, which have exactly the same information.

Finally, Brian Frank’s Primer on Problem Solving with Multiple Representations is a great follow up.


[1] Our students know motion maps, position-time graphs, velocity-time graphs, acceleration-time graphs, verbal descriptions, mathematical representations, data tables. In some circumstances, we might ask them to add computational models.

Advertisements

Free Fall: A Satisfying Board Meeting

Finally! A satisfying board meeting with students! It’s been a long fall with awkward board presentations around my room. Silence, constantly looking to me for affirmation, and boards that are total messes have been the hallmarks of the past few months.

I’m here today to say that with persistence, it’s possible to have a great discussion. First, a few whiteboards post-meeting:

Thursday: Free Fall Day 1

My rough outline of class goes as follows: Introduce that the topic today is free fall. Explain it’s a subset of the uniform acceleration model we’ve been studying. Drop a few objects and suggest which ones I think could probably be modeled with a free fall model and which can’t. Ask what they think free fall means, what it implies as far as a model.

Then I asked students to film a falling ball and perform video analysis. First time with this particular tool, so I taught it to them.

They then took the two graphs they got directly from Logger Pro (position-time and velocity-time) and used them to generate semi-quantitative versions of the other representations they know (acceleration-time graph, motion map, verbal description, and mathematical models).

No board meeting at the end of Thursday’s class. Instead, I wrapped with a definition along the lines of “an object in free fall experiences no air resistance, only the force due to gravity” and sent them on their way.

Friday: Free Fall Day 2

On Friday, a student and I launched a ball straight up (using a projectile launcher). From that observation, the students were asked to produce whiteboard models. I gave students 12-15 minutes working in pairs and brought them together for a board meeting after.

The first questions I got included:

  • But we don’t know any values, how are we supposed to create a data table or equation?
  • Should this be a qualitative or quantitative model?
  • Where is x = 0m?

Most boards came in with impeccable kinematics graphs.

When the graphs had mistakes, it was almost always on the velocity-time graph. Here are the two variations.

When confronted with these graphs, students had detailed discussions about how long the ball is at rest at the top of the motion. Does the ball pause for more than a moment? How do we know? Someone pointed to the acceleration graph at a constant a = -9.8 m/s/s as their proof — velocity must change by that amount every second.

This was my first board meeting where other students were able to explain the exact ways in which these are not a representation of the ball launched up. Kids were out there changing their whiteboards in the moment.

20181207_132227

Look at the data table in the center — this pair of students, bothered by not knowing v0, opted to make up a value and go from there.

models.001

Group 2 here got their graphs right. But if you look closely at their motion map, they believe the acceleration changes direction with the object. Also, they switched to thinking initial velocity is 0 m/s on the more concrete models in the second picture.

But We Still Need More Time

So, after the boards were correct, I had 5 minutes remaining in my last section of Physics 1, so I asked them “An object in free fall’s time in the air is represented by time, t. At what time would it reach the apex?” Though this kind of algebraic representation is new to my 9th graders, most said “1/2t” with confidence.

Yay! They get it! So I followed up with:

“For the launched ball you just modeled, does the ball spend more time going up or more time falling down?”

A variety of answers, no consensus, not a soul says “the times are equal.” I point out how it’s the same question I just asked them mathematically. They push back with all sorts of considerations. Very few students truly believe “the times are equal.”

Then the bell rang.

LGBT History Month: The Stonewall Rebellion

Below is the text of a presentation made by my school’s GSA leaders at school meeting in honor of October being LGBT History month.

stonewall_inn_2012_with_gay-pride_flags_and_banner

By Daniel Case [GFDL or CC BY-SA 3.0], from Wikimedia Commons

This is the Stonewall Inn, one of the most recognizable landmarks of the LGBT community. It’s located in Manhattan’s Greenwich Village. In June 1969, the Stonewall was a gay bar and was raided by police, touching off 3 days of rebellion and the start of the modern queer rights movement.

The Stonewall catered to mostly gay men between their upper teens and early thirties, transgender women, and butch lesbians. Patrons were about a third each white, Black, and Hispanic. Most were working class or poor.

In 1969, it was illegal for several reasons to be queer out in public — for one, bars were not allowed to serve LGBT patrons. For another, it was illegal to dress in the clothing for another gender. Under the excuse of enforcing these laws, in the early hours of June 28, police entered the bar and announced they were raiding it. Patrons found to be dressed illegally or dancing with a same sex partner were arrested, as were all the employees.

stonewall_inn_1969

By Diana Davies, copyright owned by New York Public Library (Contact us/Photo submission) [GFDL or CC-BY-SA-3.0], via Wikimedia Commons

This is the Stonewall Inn back in 1969.

Being arrested in a gay bar raid anywhere at the time was a humiliating experience because those arrested often had their names and photos published in the newspaper, which in turn got them fired from their jobs. Few LGBT people were out about their sexuality or gender identity. It was a shameful secret that caused many to seek the relative acceptance of Greenwich Village, even just for the evening.

At this point in the evening, police have escorted employees, transgender women, and lesbians dressed as men to the curb. While waiting for the police wagons to show up, those patrons who were not arrested gathered on the street out front, about 100 people in total. The crowd was uneasy.

The start of violence is a little fuzzy but three events stand out:

  • A woman in handcuffs kept breaking free of the 4 policemen escorting her.
  • Police struck a lesbian over the head with a baton after she complained that her handcuffs were too tight.
  • One of those detained looked to the crowd and shouted, “Why don’t you guys do something?”

The crowd responded. They threw coins, beer cans, and later, bricks at the police. 10 officers barricaded themselves and a few handcuffed detainees inside the bar.

Stonewall Inn nightclub raid. Crowd attempts to impede polic

New York Daily News Archive / Getty Images

Meanwhile, outside the Stonewall, the crowd included homeless, mostly gay youth, who lived in nearby Christopher Park. This is the only known photo taken the first night of the Stonewall Rebellion. It shows those youth scuffling with the police.

Writing about why the rebellion started, a contemporary account suggested the Stonewall Inn “catered largely to a group of people who are not welcome in, or cannot afford, other places of homosexual social gathering… The Stonewall became home to these kids. When it was raided, they fought for it. That, and the fact that they had nothing to lose other than the most tolerant and broadminded gay place in town, explains why.”

The rebellion continued for three nights.

Michael Fader, who was there, remembered “We all had a collective feeling like we’d had enough of this kind of shit. It wasn’t anything tangible anybody said to anyone else, it was just kind of like everything over the years had come to a head on that one particular night in the one particular place, and it was not an organized demonstration… Everyone in the crowd felt that we were never going to go back. It was like the last straw…There was something in the air, freedom a long time overdue, and we’re going to fight for it. It took different forms, but the bottom line was, we weren’t going to go away. And we didn’t.”

The Stonewall Rebellion led to annual Stonewall commemorations, and later LGBT Pride Parades.

b33e9f8d444cb802c790be90f96d0d4d3cbee3dd

Marsha Johnson and Sylvia Rivera (The Death and Life of Marsha P. Johnson)

Two of the most well-known faces of the Stonewall Rebellion are Marsha P Johnson at left and Sylvia Rivera at right. They were transgender women who were at the Stonewall.

Later, both were active through the 70s and 80s LGBT rights causes. Their most notable achievement was establishing STAR House in 1972. The house functioned as both home and chosen family for gay and trans street kids.

The LGBT community owes our struggle to many transgender women of color, including Marsha P. Johnson and Sylvia Rivera. They are heroes to the community.

Happy LGBT History Month!

Constant Velocity Card Sort

Autumn is here one day then gone the next on campus. We’ve had this odd up/down temperature fluctuation this week, which has made for many foggy days. Monday, as I walked home, I was struck by the fog rolling in over the nearby hill and enjoyed a high of 58°F. Today, it’s 80°F and sunny. Oh, and by the way, that building on the right is the dorm where I live.

20181008_162710

Ok, that’s enough rambling about autumn in the Pioneer Valley. Let’s look at some physics.

My colleagues and I created a card sort for our students and the results were wonderful. The students have been working with five different representations at this point and our card sort left out only the data table. Here’s one page from the sort:

Screen Shot 2018-10-10 at 4.08.33 PM

While sorting today, students chose to work together in so many different ways. My favorite was this group that turned their sort into a kind of Go Fish game — each kid took all the cards for one representation and read off important details to ask for that card from the others. For instance, “do you have one with a velocity of +6 m/s and a starting point of -3 m?”

20181010_084716

Many thanks to Kelly O’Shea and Brian Frank for sharing so many card sorts over the summer. Their work inspired us to create our own.

If you use and improve ours, would you let me know? Constant velocity card sort (on Google Slides).

A Cost-Effective Robotics Learning Platform

I’ve put together a basic two-wheeled Arduino robot platform that comes in just under $60.

I like that the chassis is aluminum so it’s reusable year-to-year. Alternatives I considered (here, here, and here) are laser cut plastic and are similarly-priced. This chassis is specifically designed to work with micro DC Motors, which are admittedly a weird size, but I love their compactness. I’m not sure how kids will attach the line sensors we’ll inevitably use at the start of the year to build a line-following robot.

The caster wheel makes for a simpler design than adding two more wheels. It’s easiest to start the kids with two-wheel drive so that the third point exists for balance only. Some robots use a swivel wheel but I find the robot sometimes get stuck with the wheel in an awkward position.

The Adafruit Motor Shield has been flexible for my entire year of robotics. We’ve also used the SparkFun Motor Driver Shield, which tops out at 2 DC motors.

Here’s the parts list:

Pololu Wheel 60×8mm Pair for FEETECH FS90R/FT90R Micro Servo – Black
Anodized Aluminum Metal Chasis for a Mini Robot Rover
Pololu Ball Caster with 3/8″ Plastic Ball
DC Motor in Micro Servo Body (x2)
Adafruit Motor/Stepper/Servo Shield for Arduino v2 Kit – v2.3
Adafruit METRO 328 Fully Assembled – Arduino IDE compatible – ATmega328

Do you have suggestions or improvements?

Most Fun Exam Ever? Robotics Class

Alternate title: Forget blue books, we’ve got heat guns

It’s time for the winter trimester exams. Given that robotics is a new prep for me, I’ve carefully considered what my exam should look like. My design goals were roughly as follows: 1) mirror the type of learning we’ve done this year, 2) but not rehash old material, 3) uphold my emphasis on deferring to the documentation, and 4) be achievable by a range of students in about 2 hours.

Below is the exam as I’ll give it to the students. At the end is a video demonstrating my thermometer (which will *not* be given to the students).

Objective

Create a thermometer that reads and displays the temperature.

Detailed requirements:

  • display the temperature on a physical scale in °C
  • distinguish temperatures to a resolution of 5°C (as in, the user should be able to tell 25°C from 30°C)
  • run a self-test on startup to show the thermometer’s possible range of values (as in, hit the lowest temp on your scale and the highest on startup)

Provided Equipment20180304_142436.jpg

  • servo motor
  • digital temperature sensor and pull-up resistor
  • breadboard with plenty of jumper wires
  • Arduino Uno compatible board with USB cable
  • paper, pen, ruler, scissors, tape
  • heat gun

Permitted Resources

  • You may use any resources of your choosing, with one exception — no consulting with live humans. This means internet searching is allowed but emailing a friend is not.
  • You may borrow sample code from the internet, so long as you cite it and link to the source.

Submission Guidelines

Please submit a Google Doc writeup of your finished product.

  • Introduction that explains the project and gives photos of the finished product (60% of the points) & a video (or link) in which you fully demonstrate the thermometer (10% of the points)
  • Describe how the digital temperature sensor works (in terms of the scientific principle it operates on) (10%)
  • Your commented code (15%)
  • Wiring diagram or description (5%)

Student Submissions

Open Thread: Teacher Pro-Tips

What’s your favorite, probably under-appreciated teacher advice?

Here’s mine:

Hole punch every paper you give students.

Copying a quiz? A class assignment? Whatever it is, put holes in it for their 3 ring binders before you hand it to the kids. Their organization will be miles better.

What’s yours? Put ’em in the comments.

hole punches.jpg