A complex system analysis of practitioners' discourse about research

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

This post by Sarah did not ask for input from any other study participants and did not receive any further responses.

A post made by Terri K. in response to my original post did provoke a small sub-thread of discussion, although the sub-thread had little statistical or pedagogical substance. With the twelfth post to the discussion board, Terri wrote,

    Based on experience, I think that the first example is what has
    occurred in our classes. We have demonstrated to students what that
    25 does to the mean. (Oh, why obfuscate? We refer to it as an
    average.) ... What would you say if a student said that because both
    the median and the mode are 82, that grade reflects more of the
    student understanding than the mean? Anyone can have a bad day. How
    would you probe the student's thinking?

Kristin's response to this post simply expressed that she would be surprised to hear a student make such an argument about their grade, and also joked about Terri's use of the word "obfuscate." The responses of Yvonne and Terri back to Kristin simply acknowledged the joke.

The final two responses that were made directly to my initial post to start the thread did not lead to any sub-threads of conversation. Greg Z. and Charles M. each posted personal reflections on the questions I posed in the initial post. With the twenty-eighth overall post, Greg reflected,

    The second question obviously reflects higher level thinking when
    the student is posed with a choice, then you should discuss if you
    would determine the two answers differently and why. However, an
    average is an average. Should all students' work count? Or, should
    we just throw out the bad days? At my job, we are still accountable
    for the bad days.

In the fiftieth overall post, Charles stated,

    I would use the second example, because it is more of a real life
    problem and requires the student to do more than crunch some
    numbers. I think it is also important that the student know not just
    how to find the mean and median, but why we might need to know about
    the concept of central tendency.

Even though these posts did not generate further sub-threads of conversation, they did demonstrate that each individual had reflected to a degree on the difference between rote and reform-based conceptions of teaching data analysis.

Thread 4: Use of the Word "Average"

The fourth thread of conversation again began with a moderator post. With the thirteenth post to the discussion board, I wrote,

    Some textbooks use the word "average" exclusively for "arithmetic
    mean" (the "add-and-divide" algorithm). Others use the word
    "average" in connection with the mean, median, and mode. Which usage
    do you prefer? Why? Are there advantages or disadvantages in terms
    of students' learning?

The intent of this post was again to push participants to consider how their teaching practices might influence the degree of conceptual understanding exhibited by students. I hypothesized that this issue would be important for participants to consider in light of research illustrating the role that informal conceptions of the word "average" play in students' understanding (Watson & Moritz, 2000). The post generated a fairly lengthy thread, as shown in Figure 5.