Preservice Teachers’ Learning to Respond on the Basis of Children’s Mathematical Understanding

Table 1

Summary of prompts used in the two assignments.

Component skill	Inquiry into Student Thinking	Tutoring assignment
Attending to children’s strategy	(i) Choose one of the four students from the case study and trace their responses and learning through the study.	What does each student know, think, and understand about number, operations, and problem solving?
	(ii) Summarize what you think they knew or understood at the end of the study that they did not know or understand in the beginning
	(iii) Choose 2 examples of this student’s responses as evidence for your claim from part (1) and explain how they support your claim about this student’s learning.
Interpreting children’s mathematical understanding	(i) Summarize what you think they knew or understood at the end of the study that they did not know or understand in the beginning	How will what you learned in the interviews influence how you work with the children during the next sessions?
	(ii) Choose 2 examples of this student’s responses as evidence for your claim from part and explain how they support your claim about this student’s learning.
Respond based on children’s mathematical understanding	(i) If you were to teach the next lesson to this group of students, write one problem that you could give them and explain why you think this would be a good problem for this group	How are these tasks intended to build on what you know about your students’ understanding and misunderstanding?