College-Prep Physics: Modeling Instruction’s standard lab practicum for the constant velocity unit is colliding buggies. Lab groups take data to determine the speed of their buggy, then the buggies are quarantined and groups are paired up. Each group pair is then given an initial separation distance for their buggies and are asked to predict the point were the buggies will collide. Once they calculate the answer, they are given their buggies back to test their prediction.
It’s fun, but there are some frustrations. Groups that have poor experimental design or data collection techniques won’t calculate the correct buggy speed, which means they won’t accurately predict the collision point. Also, since only the separation distance is given, there isn’t much focus on the position of the buggy and students are less likely to use a graphical method to find the collision point. They try all sorts of equations instead. In the end, one person in the group typically does the calculations while her partners just copy her work.
This year, I decided to shy away from the calculation aspects of the buggy collision lab and instead use the activity to get students more familiar with some of the digital tools we’ll be using throughout the year.
Logger Pro: Students used a motion detector and Logger Pro to find the speed of their buggies. They learned how to select portions of the graph and how apply a linear fit. This also reinforced the concept that the slope of a position graph represents velocity. They printed a copy of the graph and taped it into their lab notebooks. Then I quarantined the buggies.
Position, not distance: Pairs of groups were then assigned a starting position relative to an origin (marked on the floor) and a direction of motion. Careful advance planning let us have a variety of collision scenarios — some head on, some where a fast buggy catches up to a slow buggy moving in the same direction.
Desmos: Groups were then required to model the collision scenario in Desmos in order to determine the collision point. For me, the physics is in formulating the correct models to type into Desmos, not actually solving the set of simultaneous equations or graphing them by hand. Surprisingly, there were some interesting mistakes in this stage: Some groups didn’t use the proper sign for the slope to indicate a buggy heading north/south. Some groups just used the sign from their Logger Pro graph (positive or negative, depending on whether they made their buggy move towards or away from the motion detector). And still some groups used the y-intercept from their Logger Pro graph as their starting point instead of the starting point they were assigned. Once the mistakes were realized, it was a quick fix in Desmos — much less frustrating than reworking a set of simultaneous equations. Then they tested their predictions and included their Desmos graph in their notebooks.
It went well this way, and took about 40 minutes from start to finish. It was something that even students with weaker math/algebra skills could find accessible. Plus, there was more reasoning and discussion about what the slopes and intercepts mean and how to model the situation rather than a focus on solving equations.
NGSS Science and Engineering Practice 2: Developing and Using Models
College-Prep Physics: We had a great discussion/debate about the meaning of average velocity today. Rather than give students the definition, I simply asked them to determine the average velocity for the following position-time graph (thanks Kelly O’Shea):
Students generated 8 different possible ways to compute the average velocity and I wrote them on the board (see top pic):
- The average of the magnitudes of the non-zero slopes.
- The average of the non-zero slopes.
- The average of the magnitudes of all slopes.
- The average of all the slopes.
- A time-weighted average of all the magnitudes of all slopes.
- A time-weighted average of all the slopes.
- Total distance divided by time.
- Total displacement divided by time.
Then we calculated each one and saw we got mostly different answers.
Students: “Which one’s right?”
Me: “So, how do we find the velocity for part of the trip?”
Students: “It’s the slope of the position-time graph.”
Me: “So how about the whole trip?”
Students: “The slope from start to finish?”
Students: “That’s 6 m in 6 seconds, so 1 m/s north.”
Me: “Did any of your methods yield the same value?”
Students: “Methods 6 and 8.”
Me: “Can you see why?”
And so we discussed how those two methods and the “net slope” method of finding the average velocity are really all the same thing.
It was a really great discussion.
A copy of my handout (with Kelly’s graph) is here: WORKSHEET Interpreting Position Time Graphs 2015
NGSS Science and Engineering Practice 6: Constructing Explanations and Designing Solutions
AP Physics C: On Monday, AP students took an exam on most of the material in Chapter 2 of Matter and Interactions. Today, they took the same exam in groups. Open notes, open each other, open anything. Whatever they didn’t finish in class is tonight’s homework. (Note: They did not get Monday’s exam back yet.) I don’t know if I’ll keep doing it — that’s a lot of time to devote to assessment. But yet the conversations going during class today were so great. I think that is what has to keep them honest — hearing the discussion and the explaining and the learning. As soon as it turns into one kid telling all the other what to write down, or everyone working in silence as they all copy off the same kid, then we won’t continue any more.
In my SBG system this year, I’ve switched from last year’s binary system (✓ or ✗) to a traffic light system (green = mastery, yellow = partial mastery, red = no mastery). The binary system had led to a defeatist attitude in some students. Plus, I wanted students to feel some sense of accomplishment for understanding part of a learning objective. Having a partial mastery level also allows me to recognize students who understand the concepts but might need some help or prompting. Students that demonstrate mastery of a concept on a group assessment will score yellow/partial mastery.
Read more about 2-Stage Collaborative Exams here: “Collaborative Testing: Evidence of Learning in a Controlled In-Class Study of Undergraduate Students” by By Brett Hollis Gilley and Bridgette Clarkston.
College-Prep Physics: Today we whiteboarded the second run through the buggy lab, this time focusing on position, not distance. What’s similar about the graphs? What’s different? What does the slope mean? How are these different than the graphs from the first buggy lab?
NGSS Science and Engineering Practice 4: Analyzing and Interpreting Data
College-Prep Physics: Someone once said, “Any lab worth doing is worth doing twice.”
The traditional modeling physics materials have students do the buggy lab once, finding the relationship between position and time. I’ve found that kids don’t understand the difference between position and distance right away and end up taking distance data instead. So, for the first buggy lab, I just let them roll with their intuition and they take distance and time data for both fast and slow buggies.
Before we do the second buggy lab, I show them this picture and ask them to write down the position of each car in as many ways possible. (We haven’t formally discussed position yet, but I want them thinking on their own first.)
After they’ve shared answers, we look to see what qualities were common in all the positions they listed (distance, direction, and origin/reference point). NOW, we can define position and NOW we re-do the buggy lab, but in terms of position.
And unlike the first buggy lab, where everyone looked at the same situation (red and blue buggy distances), for the re-do each group investigates a different situation. I lay down a common origin in the hall (green tape), and groups get a red (fast) or blue (slow) buggy, each with a different starting position and travel direction:
- Blue heading south from 200 cm north
- Blue heading north from 150 cm north
- Red heading south from 100 cm north
- Red heading north from 50 cm north
- Red heading north from 50 cm south
- Red heading south from 100 cm south
- Blue heading north from 150 cm south
- Blue heading south from 200 cm south
Because they already did the first buggy lab in terms of the distance traveled, they are quick to see that the re-do is different and we’re tracking position relative to the green tape. On Monday, we’ll graph the data using Desmos and share results.
NGSS Science and Engineering Practice 3: Planning and Carrying Out Investigations
Astronomy: Clouds today prevented us from tracking the actual path of the sun outside. So we fired up Stellarium to track the azimuth and altitude of the sun. Each group was assigned a different month during which to track the sun on the 15th of that month. Groups had to find the time for sunrise on that day, and then track the sun for each hour after sunrise until the sunset. Tomorrow, we’ll graph our data in Desmos and look for similarities and differences between each group’s graph.
NGSS Science and Engineering Practice 3: Planning and Carrying Out Investigations.