Helping Mathematics Teachers Develop Noticing Skills: Utilizing Smartphone Technology for One-on-One Teacher/Student Interviews.

Teaching mathematics for understanding requires listening to each student’s mathematical thinking, best elicited in a one-on-one interview. Interviews are difficult to enact in a teacher’s busy schedule, however. In this study, the authors utilize smartphone technology to help mathematics teachers interview a student in a virtual one-on-one setting. Free from physical constraints and preconceived biases, teachers can concentrate on building questioning, listening, and responding skills when noticing student mathematical thinking. Teachers engaged in four communication types when working with students through this technology: clarification, verification, and either extension or redirection. Modern day mathematics teaching focuses heavily on inquiry. This sort of mathematics teaching, often labeled as reform-oriented or inquiry-oriented mathematics teaching, emphasizes conceptual understanding and procedural fluency as opposed to speed and recall (National Council of Teachers of Mathematics (2000). Teachers’ instruction, therefore, revolves around understanding how students think, specifically the strategies that students create when trying to solve problems for the first time. Contemporary Issues in Technology and Teacher Education, 16(1) 23 For instance, suppose a teacher is interested in how students solve a proportional reasoning problem, such as follows: “Teddy read 30 pages of a book in 45 minutes. How many pages should he be able to read in 120 minutes?” A general teaching flow for this type of problem might involve a proportion with an unknown variable, 30/45 = x/120, and then teaching cross-multiplication to form the equation 45x = (30)(120). This approach, while efficient, limits students’ understanding of why the teacher converted the proportion to an equation or how the procedure connects to the number of pages Teddy has read. Inquiry-oriented teaching, on the other hand, requires students to explore this problem on their own, to attempt to understand what is being asked, and to formulate a strategy. Then, the teacher can connect each student’s strategies to other strategies in the class and, perhaps, to a general strategy. Understanding exactly how a student solved a problem, unraveling the layers of steps and missteps a student took, however, requires a patience and attention aimed at individual students. This understanding does not happen when a student writes and explains a quick explanation on the board. Nor does it happen when a teacher circulates around the room, hovering over students as they work. Rather, the most effective way to understand and listen to the way a student thinks mathematically is through a one-on-one investigative interview between teacher and student, a technique honed by Piaget and referred to as aclinical interview (Ginsburg, 1997) or diagnostic interview (Huff & Goodman, 2007). Teachers rarely engage in these one-on-one interviews for a number of reasons (Zazkis & Hazzan, 1998). First, teachers seldom have time in a busy school day to sit with a student for a one-on-one interview (Hunting, 1997). Second, learning how to question, listen, and respond to a student are highly refined teaching skills that do not simply manifest without organized support (Jacobs, Lamb, & Philipp, 2010). Yet, few teachers have access to support that helps them focus on noticing mathematical thinking. Third, whenever teachers work with students, certain student attributes affect their disposition toward that student (Dunn, 2004). That is, teachers cannot help but notice certain student characteristics, such as gender, ethnicity, familiarity with mathematical vocabulary, or even the clothes a student is wearing. These factors consciously and subconsciously affect how a teacher hears what a student is saying, inevitably creating prejudices that reify a teacher’s perception of a student and obstruct an opportunity to focus on active listening of a student’s mathematical thinking. Additionally, providing spaces for teachers to practice listening to children’s mathematical thinking, particularly children they might not know or work with regularly, focuses teachers’ attention completely on the child’s thinking rather than subconsciously evaluating a student’s physical attributes. We attempt to address these problems by introducing an idea formulated in a current technology tool that brings the teacher-to-student interview into the modern era and helps to develop a teacher’s mathematical noticing skills. We have built technology that allows teachers and students to interact without having to be physically next to each other, helping to mitigate pre-conceived biases so teachers can focus on building their skill in noticing student thinking. In our study, we asked the research question: When using smartphone technology for a one-on-one teacher/student mathematics interviews, what is revealed about how mathematics teachers notice through the way they question, listen to, and respond to student mathematical thinking? Contemporary Issues in Technology and Teacher Education, 16(1) 24 Literature Review Recent research on teaching mathematics (Jacobs et al., 2010; Smith & Stein, 2011) as well as the Common Core State Standards for Mathematics Teaching Practices (National Governors Association Center for Best Practices and Council of Chief State School Officers, 2010) have outlined the importance of a particular set of teacher skills: the ability to question, listen to, and respond to a students’ mathematical thinking. We refer to the termnoticing, particularly, mathematics teacher noticing, to encompass these constructs. While the act of noticing often refers to the ways a teacher attends to, interprets, and responds to students’ thinking within a classroom environment (Jacobs et al., 2010), we apply the construct of noticing to a one-on-one interview environment.