## Day 38 – Concrete vs Abstract

Physics 11 – Students have a really hard time interpreting graphs like the one just above this text. Once they get good at the mechanics (procedure) of the interpretation, it can be done easily and quickly. My co-worker thinks students struggle because they don’t have a procedure or set of steps to do this type of task. I agree. We could give them a procedure, but what would be the point?

Today I quizzed my students on this learning objective again (graphing constant acceleration motion), using questions like the first photo above. This gives the students a concrete idea of what the motion is. It’s easier, and while I would hope that all my students can do the 2nd graphing task, I believe that it’s the first one that we really care about.

## Day 23 – Tangent Lines

Physics 11 – There was about 15 minutes of direct instruction in today’s lab. I wanted students to learn about tangent lines, so I worked through a set of arguments that would communicate how a tangent line on a position-time graph is the instantaneous velocity at that point.

So some kids get this pretty quick.  A lot of students, when asked to draw tangent lines on their position-time graphs, start drawing lines between two points. I really have no explanation for this.  While I can understand a student having a fuzzy idea of what a tangent line represents, it’s difficult to say why they would read the above and draw a line that crosses their curve in two points.

## Day 38 – BFL

Physics 11 – Today was another A-Ha! day for me. It became apparent to me that my physics students were utterly confused on when to draw a best fit line and when not to.  I had seen warnings of this, but today I found just how confused the kids were.

Starting with constant velocity, we used graphs to tell the story of an objects movement – moves forwards fast, slows down, stops, then moves forward again, etc.  When conducting experiments, we collect position and clock reading data, plot the data, and analyze using best fit lines on linear relationships.  To the kids, this is all lumped into the category of “graphing” and they’re not sure when to draw lines from point to point, and when to use a BFL.

I went over the topic, talking about constant motion vs story telling, but I don’t think many kids really got it.  There was a lot of head nodding, but still a lot of confusion I think.  This is also the time of year when we really need to move on.  It’s just not worth getting into an endless rut of graphing.

So the real question is, how to motivate students that don’t get it, to come in for extra help and get past any hurdles they are experiencing?

## Day 30 – Graphical Solutions to Kinematics Problems

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 24 – Whiteboarding Acceleration Lab

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 22 – Graphing Constant Acceleration

Physics 11 – Students continued to work on their constant acceleration lab, creating the position – time graph, and then using it to get velocity information.  I think there are some problems with this lab, where the students have to be told how to use the x-t graph to get velocity.  They get the idea but it involves a bit of hand waving.

## Day 4 – CV Buggies

Physics 11 – The day started with a ball drop activity before we moved on to using constant velocity buggies* to analyze motion and come up with a model for constant velocity.  To reinforce how “almost meaningless” the physics in Science 10 is (they do kinematics in science 10), most students perform this task as if they’ve never studied motion before.  This suits me fine, because we get to start from scratch with model building.

I got the “it depends” idea from Brian Frank and his excellent blog: https://teachbrianteach.wordpress.com/2015/08/26/day-3-launching-the-buggy-lab/

I also reviewed how to get an equation of a line using the slope-intercept form. I anticipate many battles over the next few weeks as kids are weened off of x and y, and start to view symbols as having a meaning and not just a placeholder for something that is solved for.

* My choice was either to use \$220 of my \$250 classroom budget for the year and buy the buggies through the school and their supplier, or spend \$100 of my own money and order the buggies myself (from the USA for less than 1/2 the price than the rip-off educational science stores).  I bought them myself.  That’s what we have to do in BC.

## Day 30: Problems with Graphs

Physics 11  Question and solution from last day’s quiz on constant acceleration.  The students were really starting to push back on the graphing.  One student spent the weekend with his tutor and had memorized d = vit + 1/2 a t^2.  He used it, although he wasn’t sure why it worked.  Another student had been researching the use of graphs, and explained to the class that at least 3 other high schools in our district used equations to solve problems.

My response that plugging numbers into formulas wasn’t much to aspire to, nor would it benefit them in university or in life.  Apparently tutors also disagreed with this, saying that they have degrees and used formulas in university.  Another student claimed that he just didn’t like graphing. Of course the real problem is that he still doesn’t properly understand how to construct and read a graph, which leads to him not liking them.

So that’s where we are.  Despite of the pushback, the lesson plan for the day was to use a v-t graph to develop some kinematic equations.  Developing the equations has dubious pedagogical reasoning behind it, but I like the idea of showing that the kinematic equations don’t automagically appear out of nothingness.  I’m ok with this rationale.

Oh, the above question… Very few students were able to recognize that the area under the v-t curve was displacement.  They had been practicing this concept but mostly qualitatively. Placing the graphs in the context of a word problem shifted their perspective. I had expected this, we were only into our 2nd day of dealing with word problems.

## Day 28: Solving CA Problems with Graphs

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.