Posted at Sep 07/2018 09:25PM by Stu 6:
This comment has to do with how I analyze these videos and to illicit your feedback. I find that I cannot just watch the video and make suppositions about the thinking taking place. First I have to determine how I think about solving the problem. I have to separate my own thinking from those that I am observing. Also, I have to read the transcripts first, make some predictions about the thinking, and then watch to get more traction on my own thoughts about what I notice. How are you working through these video analysis? Same? Different?

Posted at Sep 07/2018 09:25PM by Stu 6:
I have only watched the first video. I think Ann is chunking out time based on distance chunks. To me finding the rate becomes difficult because she cannot measure the rate the same way she can measure the time. I need to watch video 2 to see if this comes out true.

Posted at Sep 07/2018 10:17PM by Stu 9:
Hey @Stu 6, I am not quite approaching the videos the same way you are, but I might try your approach. I have had to watch the same 2-3 minute sections a few times, read the transcript, write down what I think Bill and Ann are thinking. Then I annotate my own thoughts further. I have not been able to make it completely through the first video. My brain hurts.

I agree with your theory that Ann is chunking time based on distance. I also believe that Ann is struggling with developing the number sense required to realize why some of her calculations have been incorrect.

Posted at Sep 08/2018 10:37AM by Stu 1:
Stu 6, I am doing something very similar to you. I too think that Ann is chunking time based on distance. I also get the sense that she is unaware of what the quantities she is using/calculating represent. I find reading the script is very helpful. I have been watching portions of the video, then spending some time looking at the script for the corresponding portions. I think this has really helped me grasp what is happening in the video.

Posted at Sep 08/2018 10:43AM by Stu 4:
I will admit, I have given into the temptation to analyze the video based on my own personal experiences and bias. I think that this is one of the purposes of this assignment. Pat doesn't want us to know what the study was looking for yet. We're supposed to come up with our own personal frame of reference for what is going on.

I'll post a few things that I have noticed, just to get some discussion on specifics of the video going.

1) I am witnessing Bill, in real time, teach procedural math. There is very little discussion of the interplay between the quantities they are studying--most of the lesson seems to follow the assumption of "if you see these values, this is the operation you use." Bill seems to be trying to set a procedural foundation and then refers back to this later when Ann starts the worksheet. He keeps trying to frame this as "do the reverse of the process we were doing before." This will get Ann the right answer, but it doesn't get her to see the mathematics that are going on in the background.

2) In a similar but not precisely the same vein, I am astonished how infrequently Bill and Ann describe the quantities in the problem with units. With units, we could say "If the rabbit is running at 20 ft/sec, it will take him 5 seconds to travel 100 feet. Since 100 feet is half of the distance of the race (200 ft), you must double the amount of time it took to travel 100 feet in order to complete the race. Hence, doubling 5 seconds to travel 100 feet would give 10 seconds to travel 200 ft." Instead, we hear Bill teaching something like "If his speed is 20, then 20 times 5 is 100, and double that is 200. So doubling 5 gets you ten, so he finishes the race in 10." This lack of using units totally confuses Ann at times because she cannot keep track of (as Bill can) which quantities refer to which units and which operations are being performed on which units.

3) I think Bill could have saved himself a lot of trouble by spending an extra 2-3 minutes at the beginning considering more cases of rate of change, building the idea of dy = m dx, the proportional relationship between change in time and change in distance. This reveals my bias because this is what we are studying in MAT 270 right now... :)

Maybe I'll insert a link to post further comments on my post so that other people can post their ideas as well. At least, I think Pat said that brackets around words created a nested page....

Posted at Sep 08/2018 04:30PM by Stu 6:
@Stu 9, Yes! My brain hurts :-) . It is taking work to get out of my own head and understanding. And, it is difficult to focus on her understanding only using her words and written work. Also, trying to understand Bill's goal. What is he trying to illicit from Ann? He seems to be leading her to his understanding of how to calculate without realizing what she is thinking about. Rather how she understands/doesn't understand about rate.

Posted at Sep 08/2018 04:48PM by Stu 4:
One other thought I had while drafting my essay. I think Bill is just superficially checking for understanding with Ann. If she is able to reproduce the answer, he moves on. I would like to hear him ask her to express her answer in her own words. He does ask her to describe things a couple of times, but he seemed satisfied when she describes the procedure rather than the mathematical concept of one quantity varying proportionally with another quantity.

Posted at Sep 09/2018 12:36PM by Stu 7:
Stu 6 from you first comment, I did sosmething similar to you. At the beginning I thought I was going to take notes as I watched it, but after about 5 minutes I began reading the transcript writing notes about the transcript and trying to understand my own thoughts about the problem. Then when I felt ready, I watched the video and wrote anything else I felt was noteworthy.

Stu 4 I agree with your first point and even being in pathways for a few weeks I can see there is conceptual depth that I am looking for now when watching teachers give lessons. I ask myself first if I can conceptualize the ideas deeply, and then reflect on my own thought process. After I look to see if the ideas are embedded within the lesson.

Throughout both videos there are times where Bill will explain how the quantities are related at a surface level rather than letting her struggle and see how everything is related. Then towards the end of the second video we can see holes in her understanding because she was never pushed to find the relationships on her own. This is where procedural math alone can lead teachers to think that they understand the concepts because they can manipulate the numbers, however they don't know the reasoning behind it.

Posted at Sep 09/2018 01:32PM by Stu 2:
I am analyzing the way both  @Stu 9 & @Stu 6 are doing combined in a sense. I watch the video and stop every 3-4 minutes, then read the transcript and look at the worksheets that were given. I appreciate the transcript because it goes into detail of work that Ann is writing down, that sometime does not add up with what she is speaking.

Also, because of the mathematical work she is displaying, you see even more that the concept of rate of change is not forming and she is more into the procedural aspect of the scenario. Which leads to the misunderstanding of what she is actually calculating.

Another thing, @Stu 4 it is fitting to see that you are right about the affect of Bill not appropriately stating the units during discussion, takes away the understanding of what Ann should be looking for in each of her answers.

Posted at Sep 09/2018 02:23PM by Stu 7:
I completely agree, with both Stu 4 and Stu 2 about the units. If Bill would have emphasized the units when he was speaking along with when Ann is speaking, I believe its possible that she could have caught onto the quantities and their meaning a little better.

Posted at Sep 10/2018 09:49AM by Stu 3:
I think she isn’t thinking about a rate at all. I think she is thinking in distanced and has made an association of a chunk of distance is one unit of time. She is then counting chunks of distance. She seems to be applying this same strategy to trying to find the rate (by guessing at different rates and the counting chunks to see if it works (at least before deciding that strategy is wrong.

Posted at Sep 10/2018 01:31PM by Stu 1:
I would like to second what Stu 3 just said. I do not think Ann sees speed as a rate, rather I think she views it as chunks of distance that you can count to find time. Because I think this, I found myself pondering how Ann immediately knew to divide 100 by the speed at the beginning.

Posted at Sep 11/2018 11:20AM by Stu 8:
I think your idea @Stu 6, Stu 1, Stu 9, Stu 3 of chunking distance into units of time and counting the number of chunks is a good way to explain what I thought Ann was trying to do (but was having trouble articulating). I thought maybe Ann needed the distance traveled in one second as a point of reference for how long the turtle or rabbit takes to travel a specified distance given a distance-per-second value (rate), which might be viewed by Ann as a distance-ruler based on time, or, in this case, a time-ruler based on distance. To me, Ann does appear to have a basic understanding of how rate affects distance traveled in a given amount of time, but she has trouble understanding how rate can be analyzed with respect to distance and time or how rate changes according to the proportion between distance and time.

When viewing the videos, I was constantly switching back and forth between video and transcript to ensure I new everything that was going on with Ann's process and Bill's ideas in working with her. Sometimes I had to pause the video and stare at the transcript for a short while because I was not sure of the reason behind one of Ann's calculations. It is not always clear what she is thinking when she computes the value of an unknown in these problems.

Posted at Sep 11/2018 03:40PM by Stu 10:
@Stu 4 "I am witnessing Bill... teach procedural math" I disagree; I think there is a deeper lesson present in Over and Back and this lesson is NOT being taught procedurally. I think that the series of activities is leading toward a point where Bill will help Ann to reason from the set of patterns she's seen to a deeper understanding of proportional and inversely proportional relationships. (IE, v=d/t, d=v*t, and t=d/v). At least, I HOPE that's where the lesson is headed!

Posted at Sep 11/2018 03:42PM by Stu 10:
@Stu 6 I didn't notice anything illicit in this video. ;-P

Posted at Sep 11/2018 03:46PM by Stu 10:
@Derik, @Stu 2, @Stu 7: I noticed examples of Ann describing distances with time terms ("time yourself at an hour" to describe distance, 24), speed with time terms ("take him twenty to get back" to describe speed, 145), and speed with distance terms ("go that far" to describe distance, 40)