Investigating middle school students' ability to draw and interpret line graphs by mathematics teachers: Teacher noticing skills

In this study, it was aimed to determine the level of middle school students' ability in drawing and interpreting line graphs, the common mistakes that they made and the difficulties that they experienced, and to determine the level of teachers' noticing skills through these identified situations. As a research design for this aim, the case study which constitutes as one of the qualitative research methods was selected. In the first phase of the research how students performed at the questions that required them to read the data, to read between the data and to read beyond the data, which constituted among the question types related to line graph interpretation was investigated. It was also aimed to determine what mistakes that the students made and what difficulties that they experienced in the questions of creating line graphs in this phase. In the second phase, teachers' levels of attention, interpretation and deciding how to respond to the students, which constituted the sub-dimensions of noticing skills, were investigated. The participants of the study consisted of 55 eighth grade students studying in three 8th grade classes and 5 mathematics teachers working in the same school. The "Line Graph Creation and Interpretation Test" consisting of two parts was used to collect data for the purpose in the first stage of the study. In the first part of the test, there are a total of sixteen sub-questions related to the interpretation of the line graph, and a total of nine questions, including the sub-questions for creating a line graph in the second part. In the first phase of the study, a test was applied to fifty-five students and semi-structured interviews were conducted with 10 students selected from these students. These interviews were video recorded. In the second phase of the study, the responses given by the students to these questions and drawings were presented to the math teachers and semi-structured interviews were conducted. These interviews were video-recorded. The test results of the students, the semi-structured interview records with the students and the semi-structured interview records with the teachers formed the data of the study. In the analysis of the data, the descriptive analysis method, one of the qualitative data analysis methods, was used. As a result of the data analysis, it was determined that the success of the students in the line graph interpretation was higher. In the questions of creating a line graph, it was determined that the students made typical mistakes such as not being able to draw the appropriate graph curve, not starting the graph from the appropriate place, not creating the appropriate scale for the data, perceiving the graph as a picture and not labeling the axes, making mistakes in data entry, and making mistakes in connecting the points. It also determined that the teachers' attention, interpretation and deciding how to respond skills remained at a limited level of evidence in all of them, and the success among these skills increased from the ability to pay attention to the ability to decide how to respond. Considering this situation, although it is known that the skill of paying attention is an effective skill on interpreting and deciding how to respond, it has been concluded that it is not a completely prerequisite skill. Keywords: Graph Drawing, Graph Interpretation, Line Graph, Noticing.