College students' perceptions of their mathematical process models while enrolled in elementary algebra

This educational action research study contributes to the understanding of college student perceptions of mathematical process models and how students used those models with familiar and unfamiliar problem solving situations. It provides information about the steps students include as part of their mathematical process and compares these steps to those included in general cognitive process models.;This bounded qualitative case study focused on students enrolled in an elementary mathematics course at a single institution. Data collection included mathematical autobiographies, pictogram drawings, reflective and descriptive writing generated by the students enrolled in two sections of Algebra 1. Protocols, additional pictograms, and interviews were collected from selected students. Data analysis was ongoing throughout the study, following the tenets of educational action research. Discussion of the data occurred in two sections. The first section involved the development of the mathematical process models as generated by the students. The second section involved the application of the mathematical process models with familiar and unfamiliar problems. The latter section was framed by Schoenfeld's four problem solving behaviors (1985).;The following statements represent the major arguments of this study. (1) The mathematical process model should include the environment within which the students are working. Outside resources that form part of that environment would include the mathematics tutors or family members who provide assistance to the students while they are doing their mathematics. (2) Students had difficulty articulating a mathematical process model, regardless of the communicative medium used. They possessed the rudiments of a process model that guided their work on familiar problems, but they did not have a model that would guide their solution attempts on unfamiliar problems. (3) Control decisions, the metacognitive actions that shape the direction of the mathematical process itself, are determined by problem solving experience as well as usable knowledge of multiple problem solving strategies. This study showed that control was an issue only when there are various resources and strategies from which to choose.