Algebraic reasoning of first through third grade students solving systems of two linear equations with two variables

Thesis (Ed.D.)--Boston UniversityPLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you.The purpose of the study was to investigate the algebraic reasoning of first through third grade subjects solving systems of two linear equations with two variables. The population consisted of 60 subjects, 20 from each of the grades, 1, 2, and 3, in an elementary school in a suburban city in Massachusetts. To assess algebraic reasoning abilities, the Assessment of Students' Equation Solving Abilities (ASESA) instrument was developed, one version for each grade level. In ASESA, three types of systems of equations were presented in three contexts: pictures of animals, geometric figures, and letters to represent the variables for a total of nine problems. Variations by grade level were due to the magnitude of the values of the variables. A predetermined sequence of hints was developed to be used in the event that subjects could not solve the problems independently. The hints were of three types: 1) Look, that focused subjects on key information; 2) Record, that requested subjects to record given problem information; and 3) Solve, that led subjects to the algorithm for solving the problems. Hints were scored for each subject and each problem. Strategies used to solve the problems were coded as algebraic or arithmetic. Statistical analyses were performed to determine the effect of grade level, problem context, problem type, and solution strategy on solution success when the subjects solved problems independently as well as with assistance in the form of hints. Differences in the numbers of hints of each hint type were also identified and analyzed. When solving problems both independently and when hints were provided, grade level was a significant factor for solution success. Subjects in Grades 2 and 3 performed significantly better than did subjects in Grade 1. Problem context was not a significant factor for solution success. The type of problem was a significant factor for solution success. Type 3 problems, involving four solutions steps, posed the greatest difficulty for all subjects. Subjects who used algebraic strategies were significantly more successful solving problems of all types and in all contexts than were subjects who used arithmetic strategies.2031-01-0