We did the Whiteboard Mistakes Game as a way of reviewing our constant acceleration unit in 1st year physics. Specifically, I chose problems from a worksheet where students “translated” between position vs. time, velocity vs. time, and acceleration vs. time graphs, and also from a worksheet involving word problems. This went okay. I still have a ways to go with developing a culture where all students feel comfortable participating in whole group conversations and where large amounts of students volunteer to ask questions (not just a few).
The best discussions occurred when teams created the whiteboards in the beginning. I had them start by discussing, agreeing, and creating a “correct” solution, and then modifying it to add the mistake. I heard quite a few groups who were happy when they found out that one of their peers had a different solution or idea, they usually used that idea as the mistake.
The best whole groups discussions were about the graphs, especially scenarios where an object was speeding up while moving in the negative direction.
I am really liking the short partner tasks that I have been creating and giving students in AP C. The one for today took students about 15 minutes and helped them consider how to determine acceleration and force for “two body” systems by thinking about the whole system, and not setting up systems of equations (which we did last class). I started doing these last year in our E&M Unit (my first was on determining electric flux) and have been using them on a regular basis (once or twice per week) in AP Physics so far this year. In general, these are based of my experience with Physics by Inquiry, and Tutorials in Introductory Physics. However, instead of being 1 hour lessons, I am tailoring them to be 10-15 minute discussion worthy tasks with a partner.
Here’s the general process: 1) These typically fall after a topic has been introduced, but before students have thought about this particular skill/idea in detail. For example, the one that I had students do to analyze forces on an incline plane came after reading notes that included incline plane examples, and after a lab where students split forces acting at angles into components, but before we had discussed inclined planes in class. 2) Have students “stand up, hand up, pair up” to find a partner not in their current lab group, 3) Each pair of students gets one handout and goes to the lab tables in the back to discusses the prompts/questions on the handout together and writes their responses on the handout, 4) as each pair finishes, they check with another pair of students to check their answers and reasoning, and resolve any differences and then return to their original seats, 5) if the two partners can’t resolve differences, they check with another group, and then with me.
There are a few clear benefits that I’ve seen with this process: 1) Students talk time is at about 50%. Since students are working with a partner and are either sharing their ideas or listening to another students ideas, all of the time. 2) It develops a sense of independence. The more I have done these, the less I am having students come to me to ask if they have “the right answers.” Instead, I am encouraging them to trust themselves. If they apply the rules, processes, and ideas from class and agree with their partner, and then check with another pair of students, they should feel confident in the results. This frees me up to spend more time listening and focusing my time on pairs of students who are having more difficulty with that particular task. 3) There is a specific goal that can be accomplished in a relatively short period of time. Many of the tasks themselves come from longer guided inquiry lessons, which have a place (like the Newton’s 2nd and 3rd Law from my last post), but aren’t necessarily appropriate or desirable for every lesson. The tasks range from 5 minutes to 15 minutes, depending on the task. The movement and change of location plays into this to. Students go to a location to complete a task, and then return to their seats when the task is done.
The two examples below are from today (2 Body systems) and last week (Forces on an incline). I am sharing the original Google Docs of each in case you are interested in trying or modifying them.
The second half of today’s lesson was the 2 Body System Challenge Lab. The challenge had 2 parts: 1) determine the time it will take the cart to travel a 50cm distance up the incline, and 2) determine the tension in the string as the cart accelerates up the incline. This required setting up and solving systems of equations (our goal last class).
Students in AP C were introduced to the topic of “2-body systems” today with a tutorial from Tutorials in Introductory Physics. In the tutorial, students draw forces diagrams for each object in a two-body system and are lead through a series of questions to help them identify and realize how Newton’s 3rd Law can help them identify and compare forces in this force diagram, and how other rules (Newton’s 2nd and how friction works) can be used to help them rank the forces involved. Almost everyone “misses” one of the 3rd law pair forces acting between the two objects and incorrectly identifies equal and opposite forces as Newton’s 3rd Law force pairs, until prompted by questions in the Tutorial. This set us up to be able to determine the value of these internal forces and the acceleration of a system in situations where two objects are interacting and accelerating together.
Two strategies from today that worked great. Today was the second large problem set of traditional word problems that students have been asked to solve this year, and the first time students saw and used all of the kinematic equations. Today’s warm up was to work with a partner to categorize small excerpts from word problems as one of the variables listed in the kinematic equations (xi, xf, vi, vf, a, or t). Then, after sorting these cards, compare their sort with another set of partners and resolve differences. The best discussions were around “starts from rest,” “comes to a stop” and “10 mi/hr/sec.”
The main cooperative strategy that we used in the lesson was a variation of Rally Coach (thanks for the idea Tony Cacciola!). Students worked through the problem set on a big whiteboard with a partner. For each problem, partner A made a list of variables, partner B chose the equation(s), partner A substituted variables in, and partner B solved the equation. We modeled this with 2 students at the front of the class and then let students work on the problem set this way for 25 minutes. Students were really engaged and followed the process. Whatever they did together, they took pictures of, and did the rest for homework.
Pictures of some of the whiteboards that students created for our post-lab discussion of the ramp lab. The most interesting points of discussion were what caused groups to have different y-intercepts, and what the slope of the graph represented.
Today was a great day in AP C! After a vibrant reading notes discussion students worked in pairs on a “5 Minute POGIL” that actually took about 15-20 minutes where students followed instructions to draw a force diagram for an object at rest on a ramp, split the force of gravity into components parallel to and perpendicular to the ramp (our first time doing this), proving the values of the angles in the triangle, and then using it to calculate values for the Normal Force and Friction. This came up in the textbook, but without a full treatment. It was fun to see students wrestle with the ideas involved and get to a point where they understood it. I structured the POGIL in a way where the instructions told them the outcomes of what they needed to do, but not exactly how to do it.
After the POGIL, students solved two “mini-challenge labs.” The first was to find the amount of weight (suspended inside a box) that must be hung from a pulley to keep a cart at rest on a track inclined at a specific angle (see picture below). The second challenge to determine the angle at which a ramp must be inclined in order for a weight of known mass to keep a cart from moving up or down the ramp, when connected by a string (not shown). Inclined plane problems were difficult for this class in general last year, I’m hopeful that the discovery aspect of today’s lesson will engender deeper understanding of the available tools that can be used to analyze these types of situations.
Today was an awesome day in 1st year Physics! We started the constant acceleration unit with the ramp lab from the modeling curriculum. In the past, I have done this with the same spinners that I used in the Day 1 Challenge Lab for AP Physics. That was a good lab set-up, but the spinners are so easy to break and tricky to make. This is the same lab, but with the accelerated object as a battery, section of PVC, round weight, or other cylindrical object rolling down a lab table that is made into a ramp by putting something small (I used workbooks for half of the classroom and small chunks of 3/4″ plywood for the other half). Students placed a strip of butcher paper along the length of the table and then marked the position of the object at the beginning of its motion, and then at 1 second time intervals as a metronome at 60 bpm played over the speakers in the classroom. Data was quick and easy for students to collect, and they easily made the connection that this was a real-life “motion diagram,” just like the ones we created in the constant velocity unit. Thanks to Amanda Powell for sharing this idea with me.
The best part of the lab, however, was the focus and discussion on today’s Essential Question, which was “How can we determine the speed of an object at an instant, even if the speed of the object is changing (not constant)?” After students crated a position vs. time graph, we had prompts to help them think about how to calculate speeds from their data, and to think about at what time that speed actually occurs. I did a Physics by Inquiry “check out” style discussion with each team, before they worked on a worksheet with similar questions that asked them to apply our operational definition of Instantaneous Velocity (finding the average velocity over a time interval where the instant in question is in the middle). Next class the focus will be on the velocity vs. time graphs with a post-lab whiteboard discussion comparing the graphs, equations, and written representations from each team.
We used the two demonstrations below to practice solving problems with forces acting an an angle where one or two values are unknown. This was our first real practice solving systems of equations, which we will be using to analyze two-body systems in the upcoming week. In the first demonstration, paper covered the spring scales in the top right and left which we uncovered after calculating what the values should be. In the second, there is an unknown amount of weight suspended on the left and right, inside each of the two boxes. I got this years ago from Aaron Debbink.
Last spring our physics team started adding lab skill questions to a couple of our tests in 1st year Physics. We plan to add them to more of our tests this year. The goal is for students to demonstrate actual lab skills as part of the test, and use this as an avenue to assess understanding of physics in lab situations. For this test, students interacted with a Position vs. Time graph that describes the motion of two objects before and after a collision. The prompts asked students to identify information on the graph, make measurements on the graph (use the slope tool to calculate velocity) and to make a claim about a conceptual question and support this claim with data.