The influence of self-efficacy and working memory capacity on problem-solving efficiency

Abstract

a b s t r a c tWe investigated the influence of self-efficacy beliefs and working memory capacity on mathematical problem-solving performance, response time, and efficiency (i.e., the ratio of problems solved correctly to time). Students completed a letter-recoding task (Experiment 1) or an operation span task (Experiment 2), rated their self-efficacy for solving mental multiplication problems, and then solved similar problems of varying complexity. We tested the motivational efficiency hypothesis, which predicted that motivational beliefs, such as self-efficacy, increase problem-solving efficiency through focused effort and strategy use. Experiments 1 and 2 reported a significant effect for self-efficacy on problem-solving performance and efficiency, but limited effects for time. A self-efficacy by working memory interaction occurred in Experiment 1, suggesting self-efficacy is beneficial as demands on working memory increase. These findings suggested that self-efficacy increased problem-solving efficiency through strategic performance rather than faster solution times, and were consistent with the motivational efficiency hypothesis.

Self-Regulation, Math Self-Efficacy, Math Interest and Mathematics Achievement

“…That is, the successful solving of specific problems and equations under testing conditions depends on the student's self-perceived ability to solve the tasks of different levels and types. This result is correlated with those of other researchers who showed that self-efficacy beliefs about mathematics have been found to be strongly associated with mathematics achievement (e.g., Hackett & Betz, 1989;Hoffman & Schraw, 2009;Pietsch, Walker & Chapman, 2003).…”

The Relationship between Mathematics Teachers’ Teaching Approaches and 9th Grade Students’ Mathematical Self

“…Researchers claim that it is more important than the overall ability of the human mind, gender, mathematics learning experience, mathematical anxiety, mathematical self-conception and beliefs about the usefulness of mathematics (Pajares & Miller, 1994;Stevens, Olivarez & Hamman, 2006). Students with higher mathematical self-efficacy are able to work longer on complex mathematical problems and have fewer mistakes in calculation (Collins, 1982;Hoffman & Schraw, 2009).…”

Cognitive efficiency: A conceptual and methodological comparison

“…The likelihood formula is consistent with studies of efficiency in other disciplines such as statistics and engineering that assesses rates and proportions in mathematics. Empirical studies in educational psychology have used the likelihood formula to test the superiority of different modalities in conjunction with pre-and post-task effort to investigate the cognitive efficiency of reading (Choi & Clark, 2006), in mathematics to determine the efficiency of performance under conditions of escalating complexity or restricted learning conditions (Hoffman & Schraw, 2009;Walczyk & Griffith-Ross, 2006), and the efficiency of strategy selection during problemsolving (Imbo & Vandierendonck, 2008).…”

“…Motivation has also been found to mediate CE (Hoffman & Schraw, 2009;Hummel, Paas, & Koper, 2004) and the amount of mental resources dedicated toward a task may be a function of a learner's level of motivation (Paas, Tuovinen, van Merriënboer, & Darabi, 2005). Self-efficacy, the belief in one's ability to execute courses of action to attain desired results (Bandura, 1986), is an important motivational component that has consistently been found to explain variance in mathematics problem-solving ability above and beyond background knowledge (Pajares, 2003;Pajares & Miller;.…”