Abstract:
In this study, I investigated eleven mathematics teacher educators’ subject matter knowledge for teaching regarding the informal line of best fit. I specifically examined what conceptions and placement criteria for the informal line of best fit teacher educators had and what and how they used slope conceptualizations regarding the informal line of best fit. Basic qualitative research design was used in this study. I conducted approximately one hour long task-based interviews to understand teacher educators’ conceptualizations. Results showed that five of the teacher educators had representer, four had predictor and two had signal as their dominant conceptions. Particularly, while teacher educators having the representer conception interpreted the informal line of best fit visually focusing on the data points particular to the situation at hand, the ones having the predictor conception additionally considered the predicted values. Further, the teacher educators having the signal conception focused on the data points particular to the situation, the predicted values on the best fit line and the residuals simultaneously and holistically. These results implied for the informal line of best fit that signal conception reflect and include the ideas of both representer and predictor conceptions. Results also indicated that seven teacher educators used closest, five of them referred to the sum deviation and two teacher educators also used ellipse & area criterion dominantly for placement of informal line of best fit. In addition, results regarding the slope conceptualizations, all teacher educators had behaviour indicator and real world situation conceptions of slope. Besides these conceptions of slope, participants holding representer conception had also linear constant and parametric coefficient, participants with predictor conception also had the functional property; and, participants having the signal conception were also able to interpret the slope as the functional property, algebraic ratio and parametric coefficient dominantly. Results altogether implied that although having all the aforementioned dominant conceptions are necessarily important to understand the reasoning behind the line of best fit, signal conception seems to be vital for teachers and teacher educators to have.
