Teachers’ guidance of students’ focus toward lesson objectives: how does a competent teacher make decisions in the key interactions?

Abstract In this paper we describe how a teacher makes decisions during interaction with students in order to guide their focus towards the lesson’s objectives that the teacher has in mind. In particular, in the paper we examine how a mathematics teacher’s knowledge connects with the teacher’s noticing skill and interactive action. We present the case of a competent Japanese teacher, Mr. T, during a series of nine lessons on comparing fractions in a fifth-grade classroom. We first look at how Mr. T structured the lessons and interactions to help the students shift their focus from the procedural aspects to the quantitative aspects, when generating their explanations concerning how to compare fractions. Then, we analyze how Mr. T interpreted the students’ responses and made decisions about his interactive actions in the two lessons. The results show that Mr. T structured the entire lessons by repeatedly eliciting students’ ideas and focusing on the object of examination. Detailed analysis of three vignettes shows Mr. T’s constant reference to the lesson objectives when attending to and interpreting the students’ thinking both in verbal and written form. Furthermore, he strove to adjust his initial decisions according to the students’ reactions. These processes of noticing the students’ mathematical thinking were made possible by his extensive content knowledge and pedagogical content knowledge; in particular, his knowledge of figural representation had a significant influence on his decision-making.