Day 30 – Graphical Solutions to Kinematics Problems

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Physics 11 – Another mostly successful day. Students were able to solve a variety of kinematics problems without having seen any kinematic equations yet. I really encourage this type of work for a few reasons.  First, I think it’s important to sketch a v-t graph regardless of the calculations because the graph clarifies the object’s motion.  Second, it keeps students away from blindly applying an equation and the dreaded statement, “I get confused on which equation to use.”  However, some problems are more easily solved with using equations directly.

Day 27 – Graphical Representations of Acceleration

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Physics 11 – Students worked in groups and made different graphical representations of uniform acceleration.  With only a little bit of nudging, kids were able to mostly do things correctly.  I had the whole class work on the same problems, so when we did our whiteboard meetings I had the students find similarities and differences between the different groups.

Day 24 – Whiteboarding Acceleration Lab

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Physics 11 – Students presented their whiteboards after completing all of their lab work.  Lots of kids got the equation of a line for the v-t graphs, which was nice to see.  They also started showing appropriate thinking such as, “I know that our spool was accelerating faster because the line is steeper.”

One issue is creeping up in the work though. Students are getting confused on when to use a Best Fit Line, and when their graphs are supposed to be discontinuous. I tried to emphasize that BFL are used when the motion is uniform (a ball rolling down the ramp, a buggy driving along the floor), and the discontinuous graphs are for graphs that tell the story of objects that change the motion (starts moving forward, slows down, turns around, etc).   There was a lot of head nodding but I’m not convinced that all students really get the difference.

Day 20 – Acceleration Lab

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Physics 11 – Today the students starting working on the modeling paradigm lab for constant acceleration.  Most students used the track and spools that I had made, which have a nice slow acceleration. Others tried using a steel ball rolling down the rails.  The ball is difficult to use because it goes pretty fast. However, students started to use the video on their phones to capture position and clock readings.  At first they thought they’d use the video timer, but that doesn’t work (I think they’re using slow motion video but the timer doesn’t convert).  However, kids started to figure out that they could place a second phone/timer in the video.  Smart!

Day 28: Solving CA Problems with Graphs

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Physics 11 I decided to have the kids jump right into solving problems with little guidance from me.  8 questions and 8 groups later, we were off to the races.  I was a bit surprised to see most groups first try to hunt and find equations to work with.  Lots of kids were pulling out their agendas, where they had seen a page with physics formulas on it.  I pretty much had to stop the work and point out that all we’ve used in the past few weeks are graphs, and that graphs would be the smart path forward for this task.

In groups the students were pretty good with negotiating with slope and velocities.  Most groups needed some prodding to recall that the area under the curve on a velocity-time graph was displacement.  The 2nd photo above was a good example of students working through the issue of displacement.  The bottom photo, the group needed more prompting to get through their problem.  They were getting stuck with mixing up pythagorean theorem and the meaning of slope.  This was a good example of how changing the context of the question (instead of asking a graphing question, they were asked a kinematics word problem) can easily change how students apply their understanding.

The top photo shows how a few groups were approaching displacement.  When working with constant velocity, the area under the graph is calculated by finding the area of the rectangle.  When given increasing velocity, they no longer had a rectangle to work with.  Instead, they decided to break the triangle into smaller rectangular regions. I like seeing things like this because it shows problem solving skills, and I get to say that they are doing the same thing as calculus.  The group in the top photo initially started doing the problem by applying a formula, but when they got to displacement, they weren’t sure what to do.  So they decided to make a graph to see what they could find out.

Next day they will have a quiz, so I’m not sure how much time we’ll have to expand on problem solving.  I may just derive some formulas from their graphs, and model how I would expect a graph to be annotated as a means for demonstrating understanding.

Day 26: Working with CA Graphs

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Physics 11 Today was spent working through graphs of objects moving with constant acceleration.  The majority of students got it ok, but almost everyone needed a few corrections or challenges.  A few students were starting to hit the wall on clearly understanding how these graphical descriptions fit together.

The students that had problems reminded me a lot of what I saw when teaching Math 10 last year.  They would show understanding but then a few minutes later would get stuck. And I mean really stuck.  I think this is a perfect example of cognitive overload.  Cognitive Load Theory (CLT) informs us that when a person’s cognition is taxed to its limit, the brain is no longer able to transfer knowledge from short term memory to long term memory (that’s my lay person’s explanation). I believe this is what I see with a few students in physics.

I believe that the best way to deal with these situations is to first try and recognize that it’s happening.  If a kid is getting stuck, telling them to go home and do more practice probably won’t help a ton. In the particular situation of CA graphs, I offered three strategies for students to use to help them work through confusion.

Strategy 1

I encouraged them to break each part of the position-time graph into separate sections.  For each section, they then write in words what the object is doing.  All the kids can do this (moves forward, moves backwards, moves faster, etc).  For each section, I then have them explain how the motion affects velocity (constant, getting faster, getting slower, etc).  Now they graph what they wrote down for velocity

The above may seem formulaic, and it is.  However, it is a series of steps that doesn’t dance around conceptual understanding.  It’s a way for students to verbalize their guide to the motion.

Strategy 2

The next strategy I suggested was to take the position-time graph and sketch tangents on it.  As long as the student understands the correlation between slope of the tangent line and velocity, they can build the velocity-time graph. Again, the strategy still depends on a conceptual understanding and is not just a series of steps.

Strategy 3

The third strategy I proposed was… oh who am I kidding. I can’t remember what the third strategy was.  It seemed like a good idea at the time. If I remember it later I’ll update this post.

Day 24: Graphing Constant Acceleration

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Physics 11 Today we finally graphed data from our constant acceleration lab. There were several hurdles to overcome, most notably the kids getting their head around what a tangent line is.  We finally had some really good discussion with the whiteboards, with students really challenging each other.

Some common pre-conceptions encountered:

  • the velocity time graph should have horizontal lines (like before)
  • points on the graph should be connected with a line
  • a faster starting push on the object should make the v-t graph steeper because it’s going faster

I’m not sure yet how I will deal with the quadratic relationship. If I go over curve straightening, it will certainly be a bit hand-wavy.