We all agreed that worksheet 5 does a great job of helping clarify the relationship between motion maps and and the other tools for modeling. One thing someone mentioned is that they might have the students make basic, qualitative equations to bring that aspect into the fold. Jon, while agreeing, also cautioned that we need to remember that motion maps are pseudo-quantitative at best. Don't get too bogged down in the limits of the constant velocity model (what happens to the speed at the last instant shown on the graph?). Chris mentioned that we need to make sure that the motion map does correctly depict the motion shown. He illustrated this poignantly when one group had 3 points for their motion map. One while it was moving away from the origin at constant speed, one while it was at rest, and a third while it was moving at constant speed toward the origin. While at first trying to model to us how to lead the group with Socratic questioning, he saw the group presenting wasn't getting what he was selling. However, he kept at it and led the group to realize that they needed more than one point for each segment of the graph to show that the velocity was constant in a given section.

They also pointed out that a good convention to use is to put each type/segment of motion on a "different line," meaning if the object changes from one constant speed to another (stopping would constitute a new constant speed), put the first dot for the new motion slightly above (or below) the first set of points. They also clarified to work from the displacement vector away (i.e.: if drawing above said reference, each segment is place higher).

To finish up the unit, Jon and Chris again elicited feedback. We said we liked worksheet 5 (converting between the different tools of modeling), having students enact the motion shown in motion maps or velocity-time graphs, and the motion mapping activity with the vernier motion sensors.

From there, we moved onto summarizing our HW from the night before. We were asked to read the first half of Arons text "Teaching Introductory Physics." Each group was asked to whiteboard a summary of one part of the reading. (

*We did a similar activity yesterday for ch 1. I left it out since, to me, it enhances the workshop and the mindset of modeling, but I would recommend reading it for yourself. However, one member from my group had to leave so I'm including it here for her.*)

Section 2.1 is the introduction to the chapter on Rectilinear Kinematics (not sure why he can't just call it 1D Kinematics, but who am I to criticize). One of the main things the group said that jumped out at me was to remember that mankind's development of this concept/model took of 1500 years, so it's OK if our students struggle a little. Some of the greatest minds in history couldn't understand it.

Sect. 2.2: In this section, Arons begins to explain why there is so much difficulty with understanding 1D motion. He says part of the difficulty is that we, the teachers, aren't consistent with our terminology when we teach it. Instead of focusing on time and distance, we need say "instantaneous time" for clock reading, "time interval" for elapsed time, and position. In doing this, we will more easily flow into the more complicated concepts found later in the course.

Sect. 2.3: One of those concepts that we need to begin to foreshadow is that of "event." By focusing on position and clock reading as truly instantaneous, the concept of "event" will make more sense when reference frames come up in relativity later in the year. It also is important that we have our students verbalize these terms, and explain them, not just us use them over and over.

Sect. 2.4: This section build on the last to develop the concept of instantaneous position. One other important idea is to say some happened

**a moment in time, not**

*at***a moment of time, as the latter suggest a time interval.**

*for*Sect. 2.5: This section began discussing average velocity, by say that we should not use the term "average velocity" until after the students have been exposed to several experiences with motion. By using the term

*our students often think that we mean "not complicated" and can become discouraged when they struggle with the "simple" concept. Instead we should focus on the ratio of $\frac {\Delta s}{\Delta t}$ over the name (*

**average**,*Arons uses $s$ to represent any direction instead of the more common $x$ more commonly used today)*. Have the students verbalize that this represents how fast the object is moving: higher ratio, quicker motion. Also to have students explain the inverse ratio $\frac {\Delta t}{\Delta s}$ to represent the slowness of the motion.

Sect. 2.6 Discusses graphs of position vs clock readings. The keys points from the group we that to understand motion, we need to make sure that the students are relating the graphs to actual motion. By having the students show the motion depicted in a graph with their hands, both the teacher and the student will insure that the concept is understood. One other point they made was to tell the students to think of the motion activity, especially when trying to comprehend motion maps. They said to think of the origin as the motion detector itself. One other suggestion that came up was to modify the motion mapping activity by slowing the sampling rate and then showing the data points instead of the line connecting the points. They thought this might help students connect the graphs they were creating with their motion.

From there, we moved on to Unit III, and began the "Cart on an Incline Plane Lab." After talking to Jon and Chris about Brian Frank's Blog during our lunch break, Jon and Chris altered the first question to begin the cycle by asking "What do you see/notice?" Again, we moved through "What can you measure?" and "What can you manipulate?" before arriving at the purpose: "to determine the mathematical and graphical relationships between position and time for a cart on an incline plane at a fixed angle. As a group, we seemed to struggle with this process this time. I'm not sure if we are taking our role in "student mode" too seriously and confusing ourselves in the process. We didn't seem satisfied to look at this relationship and many wanted to add more quantities such as mass and angle into the procedure. One good suggestion was to focus the students back on the first question, "What do you see?" By using what is already on the board, we can steer the students to the necessary target of this unit. I might add that we should include some help to our students to focus on the actual demonstration we are doing (cart rolling down a fixed ramp) and try to dissuade them from altering the set up. Possibly reminding them that our job is to create the experience that will teach them the necessary component of physics, and we chose this exact one for a reason.

After we were settle on the debate, Jon told us to use the motion detector to acquire "clean data" for the cart. When asked what he meant, he said, "You'll see what I mean." He put on the board for us to then manually calculate 10 values of "average speed" over the range of our data (he originally put instantaneous, but later corrected it). He also remembered later that he usually has the file "01a Graph matching.cmbl" from the physics file loaded onto the computers, so that the velocity will not be automatically calculated for the students. For the average velocity, he tells the students to use the position and clock readings from just before and after the point we are using to calculate the average velocity. Jon also mentioned that during the acquisition of data, and the subsequent creation of the whiteboards, he would talk to the groups about the significance of the data produced (if you started the cart after the motion detector, what do the initial data points mean? points after the cart hit the bottom of the track?).

At the end of the day, most of the groups had presented their whiteboards, with 1 or 2 left for tomorrow.

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