Date of Award
Summer 7-28-2016
Degree Type
Dissertation
Degree Name
Doctor of Education in Secondary Education
Department
Education
Committee Chair
Mei-Lin Chang
First Committee Member
Susan Stockdale
Second Committee Member
Wendy Sanchez
Abstract
Mathematical problem solving has received recent attention and been recognized as central to analysis and application in everyday life. Mathematical problem solving has often been characterized by traditional word problems. From the models-and-modeling perspective, students problem solve mathematically by engaging in conceptual development through interaction with communities of practice that produce artifacts that are continually under design. Productive problem-solving dispositions and beliefs mold students who are confident and willing to take on new tasks. Attitudes, feelings, dispositions, and beliefs are manipulatable, and thus individuals’ problem-solving identity is complex. To date, there are no empirical studies that have measured students’ levels of mathematical problem-solving dispositions and beliefs. This study describes the development and validation of a measure of mathematical problem-solving dispositions and beliefs (MPSDB), based on the models-and-modeling perspective of problem solving. An initial pool of 72 items represented six different dimensions of the model. Data were collected from 575 middle grade students to validate and examine the MPSDB scale. Through a series of phases including a pilot study, expert panel, and exploratory factor analysis, a final 40-item MPSDB scale was validated with strong reliability. The validation study showed that scores on the 40-item measure: (a) established construct validity as the MPSDB scores correlated with two of the theoretically related constructs, including math anxiety and self-efficacy and the usefulness of mathematics; (b) established content validity as there was a high degree of agreement between the expert panel’s review of items; (c) established criterion validity as MPSDB scores were positively correlated with GPA and mathematics class average; and (d) established incremental validity as the MPSDB added significant predictive capacity to the model.