Table 3 The ACS rubric format.

From: Enhancing secondary-school mathematics teachers’ ability to notice argumentation through an argumentation classroom situations-based course

Noticing skill

Levels of noticing

Attending to structural aspectsa

1. s ≤ \(\frac{1}{4}\) X

2. \(\frac{1}{4}\) X < s ≤ \(\frac{3}{4}\) X

3. s > \(\frac{3}{4}\) X

Attending to dialogic aspectsb

1. Paid no attention to the dialogic aspect.

2. Paid attention to the dialogic aspect, lacking or general description of how the aspect is manifested in a given situation.

3. Paid attention to the dialogic aspect, with a detailed description of how the aspect is manifested in a given situation.

Interpretingc

1. Did not address the factor.

2. Addressed the factor with a largely descriptive or evaluative response and little or no use of evidence to support claims.

3. Addressed the factor, with some evidence to support claims (based on the ACS/theoretical perspectives/teaching experience)

4. Addressed the factor, with robust evidence to support claims (based on the ACS/theoretical perspectives/teaching experience)

  1. as represents the score for attending to the structural aspects; X denotes the number of arguments presented in the ACS. For more details, see the section “Data analysis” for Stage 1 of RQ1.
  2. bFor each of the four dialogic aspects (collaborating on constructing arguments, critiquing arguments, mutual respect, and working toward consensus building).
  3. cFor each of the five factors (task characteristics, teaching strategies, cognitive and affective student characteristics, socio-cultural characteristics) (Note that we did not find reference to additional factors in the teachers’ reports).
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