Student rating of the usefulness of teacher-provided strategies for simplifying expressions and solving equations : how might student understanding of equals and equivalence be impacted by these strategies?

Almost twenty years ago Texas implemented a functions-based approach (FBA) to teaching algebra. This approach emphasized the use of nearly all multiple representations, use of a graphing calculator to explore graphs, and modeling of linear and quadratic functions. This interpretation of FBA in conjunction with curriculum placing the teaching of simplifying expressions and solving equations close in sequence may contribute to student confounding of the rules for simplifying and solving. The purpose of this exploratory qualitative study was to explore student rating of the usefulness of teacher-provided and function-based approach (FBA) strategies for simplifying expressions and solving equations in Algebra. The subjects of this study were two algebra teachers and their respective algebra students. The teachers, who taught both Algebra 1 and Algebra 2, were at a high school campus located in an urban district. A researcher created survey based on teacher-provided strategies used by participating teachers was administered to 100 students and 22 teachers. The teacher survey results were used as a professional basis for comparing students' results. Descriptive statistics were used to create graphical representations of students by course groups and identify students who confounded rules. Student FBA preferences and course groups were used to identify 18 student interviewees. Student and teacher interviews were used to corroborate survey results. Participating teachers identified and commented on areas of concern from the survey results. Both teachers approved of the low percentages of students rating FBA strategies as useful but were concerned about higher percentages of students (30% or greater) confounding rules or not realizing the usefulness of relevant sub-strategies. Neither teachers nor students were aware of benefits of graphing calculator use in simplifying. Students, regardless of course group or FBA preference, justified the use of teacher-provided strategies with symbolic manipulation and changed FBA ratings to less likely. There were few student references to equivalence and equality that were supported by FBA. These results are important for algebraic instruction in Texas. Texas has mandated use of graphing calculator on 8th grade Mathematics STAAR exam. Recognizing the benefits of a complete FBA along with effective use of graphing technology may prevent this type of confounding.