Teachers' Reported Characterizations and Supports for Students in Mathematics

• In Event: Effects of District Efforts to Improve Quality and Coherence of Pre-K–2 Math Instruction

Abstract

To differentiate instruction teachers need to know what their students know. This presentation investigates whether teachers in kindergarten through second grade characterized their students mathematically in ways that would enable them to take up the details of their students’ mathematical ideas. Knowing what students know mathematically is seen as an essential component of productively engaging students in learning mathematics (Sowder, 2007, Franke, Kazemi & Battey, 2007) and leads to more effective teaching practices (Franke et al., 2001; Jacobsen and Lehrer, 2000). Getting to know students in mathematically specific ways also enables coherence from the perspective of the student as teachers take up and use what students know to make instructional decisions.

Through annual fall teacher interviews we investigated how well the teachers could detail their students’ mathematical thinking and how the teachers conceived of supporting the students in their classroom practice. The 61 participating teachers included kindergarten (23), first- (22), and second- (16) grade teachers. Approximately two months into the school year we asked teachers to describe two students mathematically and how they supported these and other students in math class. The students were selected to represent different levels of mathematical skills. The majority of teachers talked in general ways about students in mathematics (e.g., he can count); many fewer teachers made specific comments related to math skills (e.g., she can use one-to-one correspondence when counting to 15). Both specific and general math comments were less common as teachers’ grade level increased (i.e., 30.4% of kindergarten, 13.6% of 1st-, and 12.5% of 2nd-grade teachers shared specific comments). Conversely, non-math descriptions (e.g., cannot focus, does not speak enough English, slow worker) increased as grade level increased, from 8.7% of kindergarten- to 50% of 2nd-grade teachers.

When asked how they supported their students a majority of teachers reported that they responded to students’ needs by either giving general help or by ability grouping. Many fewer teachers, especially in the higher grades, reported making specific moves related to their student’s thinking or to pose a problem in the moment. Teachers who shared supporting their students in ways that deepened or extended their thinking were most often the teachers who described their students in mathematically specific ways.

In summary, we saw an increase across both districts in non-math characterizations in higher grade levels, as well as more general practices being utilized, such as ability grouping, to support students. This raises questions about what is shaping teachers’ descriptions of students, as well as how those characterizations relate to the types of support students are offered as they progress through the grades. The finding that so many teachers across the two districts shared the same non-math details about their students and named the same practices to support students (i.e., grouping) shows how ubiquitous these ideas are and most likely explains why so little differentiated instruction was seen in the classroom observations. The findings suggest that for differentiated instruction to occur teachers need to learn how to pay attention to their students’ thinking.

Authors

• Megan L. Franke, University of California - Los Angeles

• Juliet Lee, Westfield State University

• Christine Roberts, University of California - Los Angeles