A complex system analysis of practitioners' discourse about research

Focus on Learning Problems in Mathematics, Wntr, 2008 by Randall E. Groth

The first message in thread 3 was intended to extend the conversation that had begun in thread 1. I sought to prompt the participants to reflect on the extent to which their statistics instruction consisted of rote teaching of procedures as opposed to engaging students in authentic data analysis as envisioned by NCTM (2000). The hope was that this sort of reflection would move some participants beyond "blaming the students" for lack of understanding of mean, median, and mode. With the sixth post to the discussion board, I wrote,

    Consider the following two word problems. They are similar, but the
    first one is a typical textbook problem, while the second one is
    not:
    (1) Seven 100-point tests were given during the Fall Semester.
    Erika's scores on the tests were: 76, 82, 82, 79, 85, 25, 83. Find
    Erika's mean score.
    (2) Seven 100-point tests were given during the Fall Semester.
    Erika's scores on the tests were: 76, 82, 82, 79, 85, 25, 83. What
    grade should Erika receive for the semester? There is a world of
    difference between these two tasks. Which type of the two tasks is
    more prevalent in your instruction? How do you suppose the thinking
    that is triggered by the second task differs from the thinking
    triggered by the first task?

I hypothesized that this post would help prompt participants to re-examine their teaching practices and beliefs about the field of data analysis, since it had previously been used successfully with pre-service teachers for these purposes (Groth, 2006). It generated some sub-threads of conversation and some individual responses, as illustrated in Figure 4.

[FIGURE 4 OMITTED]

Maura promptly replied to my message with an observation about her current practices that led to a short exchange between her and Sarah G. With the seventh overall post to the board, Maura wrote,

    I have presented the second problem to students which makes them
    think about a grade. I have also given them a problem with a list of
    grades and asked which grade would you rather have; one figured by
    the mean or median and why. What I need to do is to have more
    classroom discussion as one of the earlier articles suggests. I need
    to have a classroom driven by student discussion and not teacher
    lecture. I am looking forward to trying this. Hopefully, meaningful
    discussion will lead to more understanding of the concept.

Sarah's reply to this message expressed agreement with Maura's decision to try to implement more discussion in her class. Maura's reply back to her simply re-affirmed their stated agreement. Hence, this short sub-thread of discourse did not push either individual to re-consider existing positions.

In addition to engaging in discourse with Maura L., Sarah G. responded directly to my post during this thread of conversation. With the eleventh overall post to the board, she answered one of the questions I posed in the first post in the thread, stating,

    The first task does not require higher-level thinking, but the
    second task does. In order to answer the second task, a student
    would have to know how to compute (at least) the mean and median,
    compare the varying results, and then justify his or her choice of
    the more appropriate measure of central tendency.