Posted at Oct 22/2018 01:28PM by Stu 4:
Hackenberg repeatedly references "subjective vitality" as a major construct in her article. She defines it at the bottom of the first page as "the level of positive energy that a person experiences as available to the self." She then spends the bulk of the article analyzing the subjective vitality of several students and herself.

In the spirit of Pat's definition of a quantity, I'm curious about the metric she is using to measure "subjective vitality." The student is the object, subjective vitality is the attribute, but how is she measuring it?

The best I can get is that she is measuring subjective vitality through verbal and non-verbal clues that the students exhibit while working through math problems.

Furthermore, is the metric used to measure one's personal subjective vitality (Hackenberg repeatedly refers to her own subjective vitality) identical to the metric used to measure another's subjective vitality? My gut says no on this one...

Posted at Oct 22/2018 07:37PM by Stu 9:
From the paper by J. Proulx,

at the bottom of page 311, top of page 312, "So obviously, when one does not know, it is difficult to expect him to display this knowledge."

Is it a difficult expectation, or is this an impossible expectation? How can we expect students to demonstrate knowledge they do not possess? Am I taking this out of context or misunderstanding the author's vignette?

Posted at Oct 22/2018 07:38PM by Stu 5:
Hm. That's a good question, Stu 4.

I think you're right that subjective vitality is determined using verbal and non-verbal cues in the conversation. But, I'm not sure if that can count as a measurement since recognizing those cues is subjective.

Maybe if someone developed a coding system (which I assume they did) for rating subjective vitality then it could be measurable. This could be an exciting thing to look at with a more concrete way of measuring it. But, as it is, I'm not sure how to interpret subjective vitality other than by instinct which does not feel like good research...

Posted at Oct 22/2018 07:56PM:
Pat: Stu 4, Stu 9, and Stu 5 address two important issues:

  1. The extent to which Amy's notion of "subjective vitality" is a theoretical construct, and
  2. How one might measure it.

The issue of psychometric measurement is nontrivial. But we do it all the time with tests of various sorts. We'll talk about this tomorrow (Tuesday).

Posted at Oct 23/2018 08:47AM by Stu 1:
Building off of what both Stu 5 and Stu 4 have mentioned, I think it is important to point out that Hackenburg states “First, in this study I used qualitative methods to examine the development of student-teacher relationships over an extended period of time, trying to understand how such relationships form.” I think it is important to point out that she this is a qualitative research study not a quantitative research study. From my understanding of pg 246-247 it seems as though she used a complex coding scheme to analyze the data. Thus, even though she is using verbal and non-verbal cues to determine subjective vitality, I do not feel this is a subjective process. Rather, the clear distinctions and definitions the author used for each code (made to analyze these verbal and non-verbal cues) makes this analysis objective. Below is an example where the author described this process: "I coded students’ and the teacher’s body language, facial expressions, verbal expressions, and verbal tone, to develop a more fine-grained picture of when students and the teacher seemed to experience enhancement or depletion of subjective vitality in our interactions. For example, when coding a particular chain of interaction, the body language code putting hand to head for a student was often accompanied by codes such as verbal expression of bafflement, teacher challenging students’ thinking and/or activity, and teacher searching for a task to pose. Any one of these four codes could indicate that the student was experiencing depletion during that segment of our interaction, and that the teacher may have been as well. All four of them together strengthened the conclusion about the student’s energy level in relation to my activity and energy level as a teacher. Based on these codes, I wrote analytic memos that would serve as the foundation for telling a story of MCRs from the data" (Hackenberg, 2010).

Posted at Oct 23/2018 10:45AM by Stu 2:
@ Stu 9, I want to add onto what you stated within J. Proulx article.

I want to build off our discussion in class, on last Tuesday, about students conceiving a quantity within the context of a problem entailing how a grain explosion can occur. Also, taking into consideration Proulx’s statement on pg 315:

"We do not "choose" or "take" problems as if they were lying "out there, " objective and independent of our actions: we bring them forth, we pose them, we specify the problems that we encounter because of our structure, which enables us to act and recognize things in specific ways."

I do not believe that you (Stu 9h) are taking her statement out of context. When we first pose a problem to students in pathways, how can we have this expectation of them to have “knowledge” pertaining to the context of certain problems. Even with Pat’s discussion on the grain explosion. That type of problem can be given to students in our pathways class, but we cannot expect everyone to have the knowledge needed to conceive an appropriate image for this particular problem. Thus, students’ attributes play a big role in solving mathematical problems. It is difficult, but not impossible to fix. That is how I took this statement.

Posted at Oct 23/2018 11:32AM by Stu 7:
For the Hackenberg paper, It's really interesting to see how both a teacher and a student experience subjective vitality. It's also noteworthy to observe how the student's and teacher's subjective vitality can come from the each others responses. For example, on page 253-254 she describes how Michael's energy is related to Amy's Energy. "Another reason for this change could have stemmed from my responses and the responses of the witness–researcher during the continuation of Excerpt 1. From our verbal praise as well as our pleased and somewhat surprised attitudes, Michael seemed to be able to tell that what he was doing was impressive to us and that we held a high opinion of his work. The experience that his work was deemed impressive likely enhanced his subjective vitality, since he seemed pleased that he was doing well in our eyes. In short, he demonstrated a more obvious sense of enjoyment and perhaps a more aroused state than “calm” implies (Pekrun, 2006). His manner still supports the inference that he was experiencing subjective vitality in the interaction."(Hackenberg,2010).

Posted at Oct 23/2018 01:38PM by Stu 8:
I find the concept of perturbation defined by Hackenberg to be interesting. I imagine perturbations can be very helpful for overcoming obstacles in working through problems subsequent growth in thinking, but then, too much prolonged perturbation seems risky because it could result in reduced motivation to solve problems.

This makes me think it is important to consider when a challenge (in a problem posed to students) is good and when it is too much. Also in reference to subjective vitality, Hackenberg seems to use her conjectures of enhancement and depletion of students' subjective vitality to gauge whether a problem is too easy, challenging enough, or too challenging.

This reminds me of when we talked about the level of challenge various teachers presented to their students in The Teaching Gap. We judged that Japanese students are often presented far more challenging problems than American students, which might lead one to conclude that Japanese students experience a higher level of perturbation in their math classes. A couple of questions I have about this: Might the level of perturbation and length of a perturbation experience (according to Hackenberg's definition) for a Japanese student sometimes be high enough that his subjective vitality has been depleted for too long and he is no longer motivated to think about a problem? Do the autonomy students have in a classroom (as opposed to in a one-on-one or one-on-two experimental lesson) and the potentially increased time students have to work on specific problems reduce the level of perturbation Japanese students experience and their resultant depletion of subjective vitality when they are thinking through challenging problems?

Posted at Oct 23/2018 01:39PM by Stu 8:
Now sure how I made that link; I don't think I bracketed anything.

Posted at Oct 23/2018 02:18PM by Stu 6:
At the beginning of the semester we talked about a theoretical construct as an idea, defined precisely, central to a system of ideas used to explain observations. And, you are as precise as possible with known information. Hackenberg develops a coding system to identify energy responses in observations of physical behaviors and the teacher's personal reflections. However, it is possible that the same physical cues could be observed and it does not necessarily indicate subjective vitality. For any observation of a student using speed lengths we can explain their mathematical understanding. Hackenberg chose not to explicitly ask the students about their energetic responses which limited the measurement of subjective vitality. Often people feel an emotion and do not express it physically. A student that does not respond in a positive way to a mathematical task may be a emotional response to a stimulus other than the task or the teacher.

Posted at Oct 23/2018 03:42PM by Stu 3:
I had previously read articles that discussed the affective realm and the potential impact on student learning. None of the previous articles discussed it from the teachers perspective, nor the interplay between the teacher and student experiences. It was very interesting to read about how the interactions between student and teacher affected both.

Both articles seem to be pointing to the complexity of understanding student’s strategies for problem solving. The Proulx article describes that the student strategies are influenced by the students previous experiences as well as the problem itself (and how the student perceived the problem). Also that the strategies are emergent (and adjusting) as the student interacts with the problem. The Hackenberg article also talks about how student reasoning is impacted by factors outside the problem (such as in the caring relationship between student and teacher).