Beliefs and Their Influence on Mathematical Performance

Abstract

Recent research in mathematics education has shown that success or failure in solving mathematics problems often depends on much more than the knowledge of requisite mathematical content. Knowing appropriate facts, algorithms, and procedures is not sufficient to guarantee success. Other factors, such as the decisions one makes and the strategies one uses in connect ion with the control and regulation of one's actions (e.g., deciding to analyze the conditions of a problem, planning a course of action, assessing progress), the emotions one fee ls while working on a mathematical task (e.g., anxiety, frustration, enjoyment), and the beliefs one holds relevant to performance on mathematical tasks, influence the direction and outcome of one's performance (Garofalo and Lester 1985; Schoenfe ld 1985; McLeod 1988). These other factors, although not explicitly addressed in typical mathematics instruction, are nonetheless important aspects of mathematical behavior.

Epistemic climate and epistemic change: Instruction designed to change students' beliefs and learning strategies and improve achievement.

“…We argue that perhaps the use of rehearsal strategies is deeply rooted in students' repertoire of learning strategies for learning statistics. As previous research has shown (Garofalo, 1989;Muis, 2004;Schoenfeld, 1989), even at the graduate level of education, students rely heavily on rehearsal strategies when learning mathematics and statistics. To explain this result, following Alexander, Murphy, Woods, Duhon, and Parker (1997) and Lind and Sandmann (2003), we argue that students' low prior knowledge in statistics (as evidence by their low prior knowledge scores) can influence the types of strategies they use and the extent to which they use them.…”

“…As such, we also examined whether students' approaches to learning and their levels of motivation (e.g., self-efficacy) shifted as a function of the epistemic climate. We implemented the intervention in a graduate-level introductory social sciences statistics class, as research has shown that students at all levels of education typically espouse less constructivist beliefs in this domain (Muis, 2004), that students' learning strategies are based primarily on rote memorization of formulas (Garofalo, 1989; Schoenfeld, 1989), and that students experience low levels of motivation (Garofalo, 1989; Muis, 2004; Schoenfeld, 1989).…”

Flipped-OCN Method in Mathematics Learning to Analyze the Attitudes of Pre-Service Teachers

“…As it is shown, in the OCN method, there was not a sole manner to solve the calculations and it could propose various paths to get the same answer. Here, this method could highlight the flexibility aspect, which this new OCN method had no necessitates a priori indication for where the PSTs had to initiate resolving the basic calculations to achieve in answering them [26,27]. This OCN intervention was comprised of mathematics difficulties indicated by the PSTs because of teachers' expectations.…”

“…Along with the OCN methodology, instructors can apply it in the context of flipped learning presented by Bergmann and Sams, which has advanced a consideration as an alternative and active instruction method to ratify the concept and contents of the OCN in mathematics education [4,[23][24][25]. Therefore, this methodology specifies an effective attitude improvement towards mathematics that can be prolonged [26], which is placed to develop mathematical competence and foster mathematical reasoning for students in order to increase their attention [27].…”

Creencias de los estudiantes de matemáticas. La influencia del contexto de clase

“…Esta autora señala que muchos de estos estudios han sido unidireccionales. Por ejemplo, investigaciones que examinan el impacto de creencias en el logro y aprendizaje de los estudiantes centrándose sólo en estrategias de aprendizaje o en procesos cognitivos o en factores motivacionales (Frank, 1988;Garofalo, 1989y Schoenfeld, 1985a. Todas las investigaciones sobre cambios de creencias implícita o explícitamente proponen una modifi cación de las estrategias de aprendizaje.…”