Abstract:

Introduction:
The purpose of this study is to investigate middle school mathematics teachers’ noticing of student’s mathematical understanding about interpreting of slope and writing linear equation of graph. In order to achieve this aim, following research questions are examined:
1.How do middle school mathematics teachers attend to student’s solution about interpreting of slope and writing linear equation of graph and interpret student’s mathematical understanding based on his solution?
2. What is the nature of the decisions that teachers make to respond to student based on his understanding of interpreting of slope and writing linear equation of graph?

Method:
In order to conduct this study, qualitative case study research method was used. Thirty-five middle school mathematics teachers from seven cities in Turkey participated in this study. The data collected through student’s written solution about the interpreting of the slope and writing linear equation of the graph which was adapted from Cho & Nagle (2017). Teachers were asked to attend to student’s solution, interpret student’s mathematical understanding and decide how to respond to student with such solution. The teachers’ responses were coded based on the framework of Jacobs, Lamb and Philipp (2010). After that, according to teachers’ responses, some changes in the codes were made; new codes were added; some categories were divided into subcategories. As a consequence, in this study, the attending to student’ solution was coded under three categories: robust, limited and lack of evidence. Moreover, interpreting student’s mathematical understanding was coded as robust, substantial, limited and lack of evidence. Finally, teachers’ responses were categorized as ignorance, clarification, questioning, challenging and responding to child and incorporating.

Findings:
Although 9 (%25,7) teachers attended to student’s solution with robust evidence, many teachers provided limited 12 (%34,3) and lack of evidence 13 (%37,1) to attend to student’s solution. However, they had more difficulty in interpreting student’s mathematical understanding with respect to attending skill. For this reason, none of the teachers’ interpretation was coded as substantial evidence and only 1 (%2,9) teacher’s interpretation was coded as robust evidence of interpreting. Moreover, 16 (%45,6) and 17 (%48,6) teachers provided limited evidence and lack of evidence to interpret student’s mathematical understanding, respectively. The responses that were proposed by more than half of the teachers (68,6%) did not provide any opportunities for students to enhance their mathematical understanding. Only 10 (%28,6) teachers asked challenging problems to make further student’s mathematical understanding. However, there is no teacher’s response in the level of responding to child and incorporating. Consequently, similar to the study of Jacobs et al. (2010), teachers in this study had more difficulty in interpreting than attending. Apart from the study of Jacobs et al. (2010), teachers offered a wider variety of response types in this study.

References:
[1] Cho, P. & Nagle, C. (2017). Procedural and conceptual difficulties with slope: An analysis of students‟ mistakes on routine tasks. International Journal of Research in Education and Science (IJRES), 3(1), 135-150.
[2] Jacobs, V. R., Lamb, L. L., & Philipp, R. A. (2010). Professional noticing of children's mathematical thinking. Journal for Research in Mathematics Education, 169-202

Keywords:

Teacher noticing skill, student's mathematical understanding, slope, linear equation of the graph.