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In addition, this analysis also generates various quantitative data that represent certain characteristics of the classroom discourse, i.e., length of dialog and the number of reasoning components used.

While Ben's average number of reasoning components used in his dialog is 1.05 and his average length of dialogs are less than 3 (M = 2.38).

Cory's average number of reasoning components used in a dialog is 1.40 that is relatively high, and her average LOD are longer than 4 (M = 4.15).

For example, Ann's average number of reasoning components used in a dialog is 1.46, which is higher than that of the other two teachers, so is her average length of dialogs (M = 4.69).

But the solution is presented in the context of an ambitious general project in nonmonotonic logic that not only develops properties of the preferred model approach and shows how to apply it to a number of reasoning problems, but that relates nonmonotonic logic to probabilities, using ideas deriving from Adams 1975.

While Ben and Ann's discourse level were evaluated overall as level 1.3 and 1.8 by the two coaches, Ben's CDAT discourse patterns (Fig. 5) showed limited number of reasoning components and simple IRE discourse patterns which might be consistent with this evaluation.

Similar(54)

Table 5 shows the numbers of each teacher's dialogs coded, average dialog time, average numbers of reasoning components used in a dialog, and average LOD.

Table 5 Comparison of each teacher's discourse patterns   Total no. of dialogs Average time per dialog Average numbers of reasoning components Average length of dialogs (LOD) Ann 59 0:41 1.46 4.69 Cory 91 0:45 1.40 4.15 Ben 109 0:35 1095 2.38.

Second, with the quantitative data produced by CDAT analysis (i.e., LOD, the numbers of reasoning components used, levels of teacher feedback), various relationships between teachers' discourse patterns and other intended outcomes in a PD project.

Ben's communication level rated by TIR is level 1.5 (between pre-inquiry and developing inquiry) that is consistent with CDAT coding results (Fig. 5) with extremely limited numbers of reasoning components and simple IRE discourse patterns.

"When we voted on Beijing, I was surprised at the number of different reasoning processes that people went through".

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