Last Friday brought more, unexpected drama into my life as a student teacher, mostly a result of differences in perspective and backgrounds between my CT and myself. In a broader sense, I believe the drama is a result of several factors to include: a) working with a master teacher (my CT) who has not had a student teacher before, b) this is my first time as a student teacher, c) I’m not the typical first time student teacher (I have 25 years work experience using math in many fields and applications) so I bring lots of different perspectives to situations, d) I am not familiar with AP tests, standard practices, techniques, etc whereas my CT is very familiar, and e) both my CT and I are similar in a couple of ways: seeking understanding and being doggedly persistent.
Anyways, as mentioned in an earlier post, Friday was a very active day with quizzes abounding. In P3, the AP stats students took a quiz which my CT gave to me a bit later in the period to convert into an answer key. So, I jumped into the problems on the quiz. It took me a bit longer to compute mean and standard deviation of the data set since I am not a TI calculator wizard, but I got there with ease.
The next problem provided a bunch of background text leading to the following figure and the statements below.
The standard deviation of ratings for the control group is 2.141. Explain how this value summarizes variability in the control group.
My answer for this part simply included a statement that s.d. was a measure of spread about the mean which is the sqrt(s^2) since variance measured variability, by definition. When I handed in my answer key, my CT did not like my answer and showed me the rubric for a complete answer. It said something like “S.D. measures the “typical” or “average” distance from the mean. So the control group had a discoloration rating which deviated from the mean by 2.141.” I said I did not like the rubric’s answer since it stated “typical,” “average” and “distance.” I went on to say that I viewed s.d. as more of a measure of tightness of data around a mean (e.g. spread), and in comparison to other data’s mean & s.d., allows selection of better processes, treatments, etc. I also said something like the rubric’s answer, while academically correct, had little info of value from which to make a decision relative to the treatment group; it would have been better to include the s.d. for the treatment group and ask a different question. [NB: I also said that both the rubric’s and my answers were very similar in one way in that spread is essentially a measure of distance from a mean. This did not appease my CT’s desire to understand my reasoning.]
My statements led to a lengthy discussion, in chunks of time, throughout the morning and into lunch. My CT was trying to understand my position, which while admirable may not have been possible without us setting aside dedicated time so I could speak, draw, etc to elaborate rather than attempt to communicate in small packets of time as they randomly became available.
The whole discussion felt a little awkward to me since it kept going and going and my CT would not let it go. She even said something I do not believe she picked up on but it surprised me when she asked if I thought I could explain standard deviation to someone who did not know statistics. I simply said yes and let it go for the time being; but it hurt a bit. I finally asked if there was anything I needed to do to help out the current situation and she said “no, that she just wanted to understand what I said to make sure she was teaching the material correctly, and admitted that she wrote that question” which I thought she took from a prior AP Stats test – ooops, for speaking too soon there…
I’m curious if she will bring this up tomorrow. Regardless, I still enjoy working with her and I admire her wish to seek understanding. It just gets a little uncomfortable when you say something, and someone else, who I view as an expert BTW, does not get your perspective and nothing you say helps.
We’re still working on figuring each other out. And I am taking it verrryyyy slowly since I do not want a repeat of my experience with CT #1. This pace should help me insure everything is OK but it still is unnerving when you feel as if you are not meshing as quickly as you might prefer, not on a personality level BTW, since I feel we are very similar, just on an “ability to understand one another” but that just takes time, and patience.
My CT did bring this issue up this morning. She apologized for how she essentially tossed the quiz to me without any setup which led to our overly lengthy discussion. I accepted and my view of her increased a few notches. Later in the day, she also mentioned that she was having a tough time letting go in class. I said “Its OK and expected” and all is good. She rose another few notches in my mind. While it’s a challenge for both of us to settle into our respective roles, it’s happening and like life, has a few bumps along the way.