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Elementary Students’ Mathematics Identity: Findings from a Longitudinal Study in an Out-of-School Setting


This study presents findings from a randomized controlled trial of an afterschool program intended to develop mathematics identity for students from grades 4 and 5 in groups underrepresented in STEM. Mathematics identity refers to the ways that students think about themselves in relation to mathematics and the extent to which they have developed a commitment to, and have come to see value in, mathematics. While the impact analyses showed no effects of the intervention on mathematics identity or achievement, the exploration of the longitudinal data collected over 2 years provided several insights. On average, student mathematics identity remained constant over the study period; however, the overall averages mask large variations in individual students and sites. Some students saw improvement in mathematics identity, while others saw decreases. Counter to findings in previous literature, we found no overall differences by gender suggesting that boys and girls report similar mathematics identity. Importantly, we found a positive relationship between mathematics identity and achievement. This finding holds in both directions and suggests that boosting mathematics identity could lead to improving mathematics achievement and vice versa. This study contributes to our understanding of mathematics identity, how it is measured, how it evolves over time, what relationship it has to mathematics achievement, and what its potential for development in afterschool environments could be.

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  1. The student longitudinal panel is unbalanced; 458 students (or 33.7% of our student sample) provided only a single mathematics identity measure at some point in the study, while 901 students (66.3%) provided us with two or more measures of mathematics identity. In the analysis in Section 4, we estimate our growth models in the presence of such partially missing data. Following Curran et al. (2010), we fit our models via maximum likelihood, which helps to weight observations with large number of data points more heavily than observations with a smaller number of data points.

  2. Equivalence results indicated no significant differences in site, student, or educator characteristics between treatment and control groups except for educator gender. The percentage of female treatment educators was significantly higher than the percentage of female control educators (p < .05).

  3. Three factors were selected to rotate based on the scree test. Factor 2 consisted of negatively worded items and, after further analyses, was determined to be a method factor and was not interpreted substantively. Factor 3 included items referring to mathematics in relation to “my future” and the pattern of item loading appeared related primarily to the specific wording of the items. After further investigation, we focused on factor 1 as the measure of mathematics identity. Based on the output from the CFA, we further dropped 2 items without harming the factor structure. The goodness of fit of the final 16-item one-factor model was satisfactory, meeting all established criteria: AGFI = .92, CFI = .98, RMSEA = .05, SRMR = .03. The chi-square was 145.76 (df = 67, p < .001).

  4. Data from the 63 responses from the theme 3 educator survey administration were used in the maximum likelihood factor analysis. Based on the scree plot, 4 factors were rotated with a direct oblimin oblique procedure. We retained three distinct factors, while the fourth factor contained only negatively worded items and was not interpreted substantively.

  5. Growth curve models are also referred to as latent trajectory models or latent growth curve models. This approach to longitudinal modeling explicitly models the shape of trajectories of individuals over time and how these trajectories vary both systematically due to subject-level covariates as well as randomly. In the study here, both the shape of the trajectories and the degree of variability in growth among students are of interest. With random intercept, we allow each site and student to start their trajectory at a different initial level of mathematics identity; and with random slope, we allow the mathematics identity of each site and student to grow at different rates.

  6. Time can also be seen as semesters, since each theme takes roughly one semester to be implemented.

  7. We did not introduce educator mathematics identity as a covariate in the main impact growth model for two reasons. First, educator mathematics identity may have also been affected by the ASM + intervention, and as an endogenous time-varying covariate, it would have required additional assumptions to be estimated. Second, educator mathematics identity measures were collected at the end of each theme but not at baseline, which would have resulted in missing baseline data.

  8. A latent variable is not directly observed but rather inferred through statistical modeling from other observed variables.

  9. There were some missing data in student characteristics (4–6% of students were missing gender, ethnicity, or grade level) and in math achievement scores (37–39% for academic years 2016/2017 and 2017/2018; 64% for academic year 2015/2016, mainly because they were too young to be tested that year). The models were also estimated with simple missing data imputation leading to similar results.

  10. Random effects are not estimated and presented in Table 1; however, we can assign hypothetical values to them and present overall findings visually.

  11. All fixed effects are presented in Table 1.

  12. The random effects represent unobservable characteristics that are relevant and important but not measured by the researchers. They can include things such as educator motivation, parental support, and financial resources.


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This research was supported by Award #1515586 from the National Science Foundation.

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Correspondence to Michaela Gulemetova.

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Gulemetova, M., Beesley, A.D., Fancsali, C. et al. Elementary Students’ Mathematics Identity: Findings from a Longitudinal Study in an Out-of-School Setting. Journal for STEM Educ Res (2022).

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  • Mathematics identity
  • Growth curve model
  • Afterschool
  • Extended learning