Abstract
This article examines how a coding scheme for mathematics classroom discussion that was created to highlight how teachers negotiate student responses during whole-class discussion around high-level, cognitively demanding tasks was used to help teachers shift what they notice when analyzing classroom discourse. Data from an intervention that trained teachers how to use the coding scheme and then provided them opportunities to use the scheme to code transcripts of classroom discussion are presented. Results suggest that teachers’ ability to notice interactions between teacher and students when analyzing classroom discussion (as opposed to focusing on one actor or the other) can be increased and that teachers can learn to identify specific discourse moves teachers use to negotiate student responses. However, teachers’ capacity to identify how students’ opportunities to learn are related to teacher discourse moves did not change as a result of the intervention. The article goes on to examine how discussion during the intervention itself may have contributed to what teachers learned to notice. This research contributes to the body of work on teachers’ noticing by examining the feasibility and efficacy of using transcripts and a coding scheme to foster teachers’ ability to notice how they can increase their students’ opportunities to learn through mathematics discourse.
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Notes
The coding scheme was developed at the University of Pittsburgh, Learning Research and Development Center by Kevin Ashley, Richard Correnti, Moddy McKeown, Peg Smith, Mary Kay Stein, James Chisholm, and Jimmy Scherrer.
Power Analysis was conducted using G*Power 3.1 with the following parameters F test, ANOVA: repeated measures, within-between interaction with the following inputs: effect size = .25, alpha = .05, Power = .8, two groups, two measurements, correlation between measurements = .85.
Following the advice of several researchers (Putnam and Borko 2000; Rodgers 2002), the intervention was designed to have teachers take an interpretive stance when coding transcripts rather than an evaluative stance. That is, the purpose of the coding activities was to determine what type of question a teacher was asking and how s/he used the student responses to that question; it was not to decide if the initial question and follow-up moves were “good” or “poor.” Although it is an open question that we have not tested, we hypothesize the evaluative stance would require a more “expert” coder.
There were a few decision points that included only a participant uttering a code. Hence, a few decision points had a length of 1 line.
Since the purpose of this intervention was to help participants understand that there are different moves that can be used to negotiate student responses (not to demonstrate that certain moves may be associated with student outcomes), some codes from the original ATM were collapsed. For example, the original ATM includes two codes named Pushback and Uptake. Both of these codes use student responses in an attempt to further the discussion. The only difference is that Pushback implicitly challenges the student to rethink her contribution. Participants in pilot studies had difficulty distinguishing the two. Although future empirical testing may indeed associate different student outcomes with use of these two codes, the primary investigator of this study felt that the laborious attempts of participants in this particular intervention to come to consensus on whether a move was either Pushback or Uptake would not be a productive use of time when attempting to move the group toward the goals of the intervention.
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Appendices
Appendix 1
ATMjr Footnote 5
Moves that begin a discussion
launch: open-ended question that invites student thinking
reinitiate: repeating or rephrasing a question that has already been asked
Moves that elaborate or deepen students’ knowledge by furthering the discussion
uptake: an open-ended question that uses a student response to extend or deepen the discussion
connection: linking ideas by comparing responses, solutions, or representations
Moves that elicit information
literal: a bounded question (i.e., not open-ended)
collecting: gathering additional responses to a question
Other moves
provides information: giving or telling information (including hints) to students
think aloud: modeling a thought process
lot: acknowledging that a response will be discussed later
terminal: ignoring or discontinuing a response
repeat: echoing a student response
NC; turn cannot be categorized using one of the codes above
Appendix 2
The illustration makes salient the conceptual space that could represent the territory of a fourth-grade discussion on quadrilaterals. Although the graphic itself would not be displayed, the example Launch below could be used to start a discussion that might eventually lead to the student creation of such an illustration.
Example: The teacher draws the following shape on the board 
See Table 3.
Appendix 3
See Table 4.
Appendix 4
General coding rules for ATM
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When assigning multiple codes to a single turn, assign codes in the order in which the words appear in the transcripts.
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Code according to the transcript (not according to what you think happened in the class).
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Do not apply more than one code to the same set of words.
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When assigning codes, you need to take into account the previous student’s response. You may take into account other students’ responses/contributions that have been up to that point in the lesson.
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Do not consider any responses that follow a teacher turn in order to code the teacher turn.
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Use the most specific code as possible when coding (e.g., code for uptake instead of launch when an open-ended question is asked based on a student contribution).
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Clarifying questions such as, “Does everybody understand?” should be coded as literal.
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Only code “NC” if no other codes are applicable to the turn.
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Code “Okay,” “Ah ha,” or other habits of speech as NC if it constitutes the entire turn.
Appendix 5
Pre-and post-test questions
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1.
What did you pay attention to while watching this piece of discussion?
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2.
What else did you notice during the discussion?
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3.
How would you rate this piece of discussion on a 1–10 scale, with 1 reflecting a low-level discussion and a 10 reflecting a high-level discussion?
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4.
What about this discussion made you give it a score of ______?
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5.
What do you feel the teacher did well?
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6.
What are some ways the teacher could have altered students’ opportunities to learn?
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7.
How might the teacher have been able to improve the discussion?
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8.
What are some explicit moves you saw the teacher do?
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9.
Additional thoughts about the discussion.
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10.
What question would you ask next if you were the teacher? Why?
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Scherrer, J., Stein, M.K. Effects of a coding intervention on what teachers learn to notice during whole-group discussion. J Math Teacher Educ 16, 105–124 (2013). https://doi.org/10.1007/s10857-012-9207-2
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DOI: https://doi.org/10.1007/s10857-012-9207-2