Abstract:

Teacher professional noticing skills, which have a vital role for effective mathematics teaching, require attending to students’ strategies, interpreting students’ understanding, and making in-the-moment decisions to enhance students’ learning (Jacobs, Lamb, & Philipp, 2010). Thus, this study aims to investigate the middle school mathematics teachers’ professional noticing of children’s mathematical thinking regarding the representation of fractions on the number line. In particular, the current study focuses on clarifying the following research questions:
- How do middle school mathematics teachers attend to the student’s solution regarding the representation of fractions on the number line and interpret the underlying mathematical understanding of the student based on the solution?
- What is the nature of teachers’ responses to students based on their understanding of fraction representation on the number line?

The study was conducted with twenty-eight middle school mathematics teachers with teaching experience of fewer than 15 years who work in public schools in seven different provinces of Turkey. As part of the large-scale professional development study, the present case study was carried out at the end of the first year of the study. The data was gathered using the video on a student’s representation of fractions on the number line. In this regard, written responses of teachers describing how they attend, interpret, and respond to the student’s thinking in this context were obtained.The data were examined using the “Professional Noticing of Children's Mathematical Thinking” framework developed by Jacobs et al. (2010). A coding table was developed to assess the data collected from the teachers’ responses for the noticing skills. Based on the table, the attending skills to the student’s solution were classified into three categories: lack, limited and robust of evidence. Also, the interpreting skills were categorized as lack, limited, substantial, and robust of evidence. As a final classification, the responding skills were divided into five categories: unanswered, ignorance, questioning, challenging, and responding to child and incorporating.

The findings of this study revealed that 12 (42,9 %) teachers’ attending skills were mostly characterized as limited and 9 (32,1 %) as lack. However, 7 of them (25 %) demonstrated robust evidence of attending to the mathematical details of the student’s strategies. When the interpreting skills of teachers were considered, 11 of them (39,3 %) displayed substantial evidence, 9 (32,1%) displayed lack evidence, and 8 (28,6 %) displayed limited evidence to interpret the student’s mathematical understanding. None of the teachers provided robust evidence regarding the interpretation of the student’s mathematical understanding. In addition, their responding skills were mostly (7 teachers, 71,4 %) at the questioning level. As for the other categories of responding, 3 of them (10,7 %) presented clarification, and 5 of them (17,9 %) presented challenging evidence. None of the teachers’ responding skills was categorized under the lowest and highest level of responding. In other words, the teachers provided no evidence of ignorance and responding to the child and incorporating level regarding the student’s mathematical understanding when deciding how to respond. Therefore, there is a need for more studies to support the interpretation and responding dimensions of teachers’ professional noticing skills.

Keywords:

Fractions, mathematics teachers, middle school, noticing skills.