MORE THAN MOTIVATION: The Combined Effects of Critical Motivational Variables on Middle School Mathematics Achievement

The role of mathematical interest, identity, utility, self-efficacy, and effort was examined as a set of interdependent factors leading to students' mathematics achievement. A structural equations model, testing a hypothesized structure of motivation variables and their impact on middle school mathematics achievement was developed utilizing the High School Longitudinal Study of 2009 (National Center for Education Statistics, 2011). Results support the theory developed by Middleton Leavy, and Leader (in press), emphasizing the central role of interests in determining effort, utility and self-efficacy. However, the relatively small amount of variance accounted for by the model in predicting mathematics achievement indicates that other, unresearched intervening variables must be acting on the system. Implications for research on motivation and design of interventions are discussed.INTRODUCTIONThe importance of motivation in shaping the mathematical experiences of children has been well established for some time. Over the years researchers have focused on students' feelings about their own success in mathematics, their ability beliefs and self-efficacy, aspects of tasks that foster intrinsic and extrinsic motivation, and on the social nature of motivations in context (Middleton & Jansen, 2011 ; Middleton & Spanias, 1999). Each of these theoretical perspectives1 has characterized the beliefs, values and goals of students trying to navigate the educational landscape, and the effects of these beliefs, values and goals on their decisions to put forth effort, persist in difficult tasks, and on their choices of academic and vocational pursuits.In the grand scheme of things, it can be said that, along with mathematical knowledge, students' motivations are the most direct predic* tors of Student performance and achievement in which teaching, learning, and school organization can have an impact (Eccles & Wigfield, 2002). This is due to the fact that they are themselves influenced by a variety of these psychological, social, and cultural determinants, which interact in the life of the learner. It can be argued, therefore, that motivations serve as a lynchpin, connecting the psychosocial baggage carried by the learner, with the instructional environment, enabling to a great extent the potential future directions that he or she may take (Husman & Lens, 1999).The purpose of the study reported in this manuscript was to test a model of this interaction, utilizing a small set of important motivational factors that have been found to be influential in the literature on student academic performance. Instead of exploring their impact individually, and separately, I analyze their mutual influence using structural equations modeling, a statistical technique that allows for analyzing the relationships among variables, some of which display direct effects one upon the other, and some of which show indirect and combined effects. The logic of, and problems associated with, these techniques are reviewed later in the Methods section. For the present, I review the theory behind each of the variables shown to impact student learning and achievement, arguing how they constitute a single hypothetical structure that as a composite provides explanatory power for students' mathematical decisions and subsequent performance. In the present study, partly due to the nature of the data set employed (the High School Longitudinal Study of2009), I focus on middle-level motivations-those that relate to (1) the utility of courses and course-taking, (2) interest in mathematical pursuits as a general orientation, (3) mathematics self-efficacy, (4) the degree to which students maintain an identity as a "mathematics person," and (5) the effort students are willing to expend in the service of mathematical performance. Each of these motivational domains is reviewed separately, but I attempt to show that they each support the other in creating a reasonably robust attitude in students that assists them in predicting the potential value of mathematical engagement. …