^{a}

The present study investigated the moderating effect of self-confidence in one’s ability to learn mathematics on the relation between beliefs about its usefulness and performance. The study was conducted using a sample of college students from an urban college in the Eastern US (N = 306). Moderation was tested using hierarchical regressions as well as the Johnson-Neyman Technique. The results indicate that performance and beliefs about the usefulness of mathematics were not statistically related amongst individuals with high self-confidence, and negatively related for participants with low self-confidence. The findings suggest that teaching approaches aiming to improve student performance in mathematics by enhancing student beliefs about its usefulness, would likely be more effective if they primarily focused on increasing student self-confidence in their mathematics ability.

According to results from the latest report by the National Assessment of Educational Progress, performance in mathematics among college-ready students has remained low and stagnant for decades (

In particular, scholars have examined student beliefs regarding their ability to learn mathematics, and how these beliefs influence their performance. The evidence unquestionably indicates a positive relation (

According to

Data for this study were collected between the years 2015 and 2016. Participation was voluntary, and all questionnaires were completed in a research lab.

Undergraduate students at 4-year public university in the Northeastern US, who at the time were taking at least one mathematics class, were recruited for this study. Students were asked to fill out a survey including demographic questions (e.g., gender, age, major, etc.) as well as items from psychometric scales measuring perceptions about the usefulness of mathematics in their lives, and self-confidence in their ability to learn mathematics. Participants were also asked to provide consent for the researcher to contact their course instructors at the end of the term to obtain their final course grades.

Respondents (

Participants completed the Confidence in Learning Mathematics, and the Mathematics Usefulness scales of the Fennema-Sherman Mathematics Attitudes Scales (FSMAS) (

The outcome variable of interest was student performance in mathematics, which was measured on a numeric scale representing the students’ average score in the class (e.g., 78%). Average scores were obtained at the end of the term from course instructors.

Summary statistics for each scale, as well as Pearson and partial correlations are reported in

Measure | 1 | 2 | _{p} |
||
---|---|---|---|---|---|

1. Class Performance | — | 78.57 | 16.75 | ||

2. Self-Confidence scale | .22*** | — | .29*** | 47.15 | 8.83 |

3. Usefulness scale | -.09 | .42*** | -.21*** | 50.95 | 7.61 |

_{p}) between performance with each scale are presented in the third column. Means and standard deviations are presented in the last two columns. For Confidence and Usefulness scales higher scores imply higher self-confidence in mathematics ability and beliefs about mathematics as useful.

***

Although the correlation between the Usefulness scale and performance was not significant, the partial correlation, controlling for the effect of self-confidence, was negative and significant as indicated in the third column of

The moderating effect of self-confidence was gauged using hierarchical regressions as suggested in the literature (

Step and predictor variable | β | Δ^{2} |
^{2} |
|||
---|---|---|---|---|---|---|

Step 1^{a} |
.10*** | .10*** | ||||

Male | -3.6 | 1.90 | -.10 | -1.89 | ||

Self-Confidence | 0.63*** | 0.12 | .33 | 5.41 | ||

Usefulness of Mathematics | -0.48*** | 0.15 | -.22 | -3.26 | ||

Step 2^{b} |
.01* | .11*** | ||||

Self-Confidence*Usefulness | 0.02* | 0.01 | .83 | 3.66 |

^{2} = ^{2} change. Females constituted the comparison group for gender. Continuous variables were mean-centered.

^{a}^{b}^{2}

*

As shown, the first step of the regression confirmed the correlations presented in ^{2}_{p} = .10). In contrast, the relation between perceived usefulness of mathematics and performance, holding all else constant, was negative, but the effect size was small (η^{2}_{p} = .04). A Wald test confirmed a significant difference between these estimates (^{2} were statistically significant.

For each regression, the assumption of normality of residuals was verified using cutoff values of 2 for skewness and 7 for kurtosis as suggested by

The Johnson-Neyman (J-N) technique (

According to

This study analyzed the relation between perceptions about the usefulness of mathematics and performance, moderated by self-confidence in mathematics ability. Hierarchical regressions, followed by the Johnson-Neyman technique, were conducted using data from 306 undergraduate students at a 4-year college in the Northeastern US. The relation between performance and beliefs about the usefulness of mathematics was negative for individuals with low levels of self-confidence. For individuals with high levels of self-confidence, said relation was not significant. The effect sizes found were small, and the results may have been influenced by intricacies of the sample. Therefore, these analyses should be verified through replication in future studies. In addition, future studies should consider mathematics anxiety and motivation, two prevalent affective factors that are related to performance (

The practical effect of this study however, is potentially large as it relates to the use of affective approaches to teaching mathematics. Mathematics instructors are often advised to highlight the usefulness of the material (

The author has no funding to report.

The author would like to acknowledge support from staff of the Spielman Lab at The City College of New York for their assistance with data collection.

The author has declared that no competing interests exist.

This study and all associated procedures were approved by the Institutional Review Board of the university, and written informed consent was obtained from all participants.