A new angle: a teacher’s transformation of mathematics teaching practice and engagement in quantitative reasoning

Figures & data

Figure 1. Three spinners: different sizes, same amount of “turn.”

Table 1. Six dimensions guiding account of practice sets.

1	Teachers’ vision of mathematics teaching
2	Teachers’ conceptual knowledge of the mathematical content they teach
3	Teachers’ assumptions of their students’ mathematical knowing
4	Teachers’ differentiation for cognitively and linguistically diverse students
5	Teachers’ rationale for their teaching moves
6	Teachers’ views of what constitutes evidence of mathematical learning

Table 2. Guiding questions and focus areas.

Pre-Interview	Guiding Questions: Tell me about the lesson you will teach. Show me the tasks/activities that students will do. o How did you decide on them? o How did you decide to sequence them? o Why did you include particular numbers/diagrams? (For the task that seems most central to the lesson) Can you give me an example of how you think three different students might make sense of this task? How does this lesson fit with what students have already learned? What math do you intend for students to learn in this lesson? o How will you help students to move from not knowing to knowing what you intend for them to learn? o How will you know that students learned what you intended for them to learn? How will you differentiate for students with different language needs?
Classroom Observation	Focus areas: Specific student responses to tasks/activities. Teacher questions/moves that relate to different students’ thinking Instances when the teacher deviates from the stated plan and/or makes real-time adjustments for students’ thinking.
Post-Interview	Guiding Questions: How did the lesson go? Was it how you expected? (For the task that seems most central to the lesson) How did different students work on the task? (Use examples from field notes) (For a question/move recorded in field notes, preferably related to the above task) Why did you ask that question/make that move? Why did you change your plan and/or make adjustments? Do you think students learned what you intended for them to learn today? How do you know?

Figure 2. Four key areas of each written account of practice.

Figure 3. Jen’s angle demonstration.

Figure 4. Mathematical Merry-Go-Round: circle transparency (left), student work (right).

Figure 5. How might students “see” angles?

Figure 6. Two different looking angles.

Figure 7. Angles: right (90°), acute (less than 90°), and obtuse (greater than 90°).