Algebraic reasoning in grades two through five: Effects of teacher practices, characteristics and professional development

Algebra is a gatekeeper (Moses & Cobb, 2001). Long before students enter an Algebra I course in the high school, the foundations for algebra are being developed in elementary school through algebraic reasoning. Research (Rowan, Chiang, and Miller, 1997) confirms a direct correlation ( r=.03, p=.05) between teachers\u27 content knowledge and student achievement in the learning and understanding of mathematics. The need for teachers to be well equipped to develop students\u27 algebraic reason is apparent (Lambdin, 1999, Ma, 2000). This study explores how teachers\u27 practices, characteristics, and professional development relate to student achievement and; thereby, gain greater understanding and awareness of the role algebraic reasoning performs in teaching and learning at the elementary school level. The following two research questions directed this study: (1) To what extent and in what manner can variation in student achievement on problems involving algebraic reasoning be explained by teacher practices, characteristics and professional development? (2) What teaching practices focused on algebraic reasoning have the greatest impact on student achievement? This study utilized a mixed method research design that examined classroom practices of Grades 2-6 elementary teachers, N=62, and their N=1550 students in 17 urban and suburban schools in Rhode Island. Data were gathered through a participant questionnaire utilizing a 1-5 point Likert-scale survey instrument developed by the researcher. Following the collection of the data, focus groups, n=18, were conducted with volunteer participants. The qualitative data obtained from the focus groups were analyzed by generating themes and patterns to describe the findings. Descriptive statistics (frequencies, percents, and means) were computed for each variable. Multiple regression analysis was use to determine the magnitude of the relationship between teaching practices and professional development related to student achievement. The findings of the study revealed the variables, teaching practices and professional development, used to calculate multiple regression (r=.055, p=.70) were not found to be significantly related. In addition, current professional development on algebraic reasoning is not meeting the needs of the teachers and the connections between teacher knowledge/practices and algebra content require strengthening. The findings emanated from the focus groups and from the open ended questions on the questionnaire suggested teachers are not equipped to teach algebraic reasoning. These findings have recently been collaborated in the National Math Panel Advisory Panel (2008) report. Recommendation are made as well as suggestions for additional future research specific to professional development and algebraic reasoning