The impact of middle school teachers' conceptions of functions on student achievement

This study addressed the question, do the limits of teacher content knowledge impede student ability to meet criteria implicit in the “standards” requirement. A quantitative investigation was used to determine if there was a relationship between teachers' knowledge of the concept of a function and student academic achievement as measured by the Virginia Standards of Learning (SOL) 8th grade mathematics test. Understanding of the function concept was measured using a test developed by Dr. Brian O'Callaghan.; Approximately three percent of the variance of student achievement as measured by the SOL test was accounted for by teacher performance on the test of understanding of the function concept. There was not a significant difference in the means of student scores based on grouping teachers by “rich” and “not rich” understanding of functions as measured by the O'Callaghan test.; Contrary to previous research, this study found no relationship between teaching experience, college major or teacher score on a function test with student achievement, as measured by the SOL test in mathematics or the Stanford 9 test in reading or mathematics. The moderate relationship found between teacher score on the function test and the percentage of students on free or reduced lunch was counter-intuitive; i.e. the higher the score on the function test, the higher the percentage of students on free or reduced lunch.; The study has heuristic values in the questions that it raises. For example, were the teachers with the rich understanding of functions overcompensating for the schools with the higher rates of students on free or reduced lunch? Are the teachers currently teaching prepared to teach the mathematics being tested today? Why was the percentage of teachers in the rich understanding of functions group higher for teachers under age 40? Why was there such a difference in the percentage of teachers in the rich understanding of functions group from suburban and urban schools? Answers to these and other questions will help us develop policies that support quality learning in middle school mathematics.