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Preparing Students for College and Careers: The Causal Role of Algebra II

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Abstract

In educational research and policy circles, college and career readiness is generating great interest. States are adopting various policy initiatives, such as rigorous curricular requirements, to increase students’ preparedness for life after high school. Implicit in many of these initiatives is the idea that college readiness and career readiness are essentially the same thing. This assumption has persisted, largely untested. Our paper explores this assumption in greater depth. Using two national datasets and an instrumental variables approach to mitigate selection bias, we evaluated the effects of completing Algebra II in high school on subsequent college and career outcomes (i.e., persistence and graduation as well as wages and career advancement). Results suggest Algebra II matters more for college outcomes than career outcomes and more for students completing Algebra II in the early 1990s than in the mid-2000s. Study limitations are discussed along with directions for future research, such as evaluating the opportunity cost associated with taking Algebra II for students seeking careers upon high school completion.

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Notes

  1. Almost half of the states in the United States currently mandate that students complete Algebra II in order to earn a high school diploma (Achieve 2011).

  2. Among students who entered the workforce immediately after high school, 22 % later attended college and earned a GPA. Our sub-sampling rules eliminated these students from the career track and included them instead in the college track. Reasonable arguments can be made for including these “late-arrivers” in both the career and college tracks, but as we note in the Results section, including late-arrivers in both tracks would not substantively change our findings.

  3. Tests of the null hypothesis that Algebra II is exogenous were easily rejected in all the NELS models, but for the ELS models the null was not rejected.

  4. For some models both instruments were included, for others only the age 16 in 10th grade instrument was used. This determination was based on tests of instrument redundancy available in Stata’s ivreg2 command. In some cases the unemployment instrument did not add to the model, above and beyond the age 16 instrument. Inclusion of redundant instruments in over-identified models, such as those that include more IVs (e.g., unemployment rate and age 16) than endogenous regressors (e.g., Algebra II) will tend to bias point estimates relative to a just identified model (e.g., one including age 16 only; see Angrist and Pischke 2009, for details).

  5. For college GPA, Sargan χ2 (1) = 0.134 (p = 0.714), and for graduation, Sargan χ2 (1) = 469 (p = 0.494).

  6. For both NELS and ELS models, results from endogeneity, over-identification, weak ID, and first-stage F-tests are included in the Online Resource.

  7. We also bootstrapped the entire two-stage process to account for the estimation of the residuals in stage one and address uncertainty introduced by this estimation process. For example, estimating the two-stage structure in a single iteration would not account for these sources of uncertainty and may lead to underestimates of the standard errors and overestimates of the significance of the regressors, potentially leading to incorrect inferences about their effects on our outcomes.

  8. We chose the control function approach because the method of control functions (CF) is more robust than alternatives, such as using propensity scores (predicted values only) as controls in the outcome equation. The CF approach allows any unobservables affecting the dependent variable (Y) to be dependent on X (Algebra II) while controlling for both the covariates (Z) and any instrumental variables. Importantly, the CF approach explicitly models this dependence whereas alternative methods fail to incorporate such dependence (see Heckman and Vytlacil 2004, for details).

  9. In ELS, hourly, weekly, or monthly wages were rescaled to annual earnings. In NELS, reported earnings over the six months that immediately followed high school were multiplied by two.

  10. Wage change metrics span a longer time period in NELS than in ELS. Specifically, “initial wage” in NELS was collected in 1992, while “current wage” was collected in 2000. By contrast, “initial wage” in ELS was collected in 2004, while “current wage” was collected in 2006.

  11. Initial earnings results are similar whether or not late-arrivers (students who enter the workforce immediately after high school but eventually enroll in college and earn a GPA) are included in career models. If late-arrivers are included in the career track in NELS, the estimated Algebra II effect changes from −$3,255 to −$3,478.

  12. First-year retention is measured by a student’s postsecondary status (enrolled or not) in the fall of their second year (1993 in NELS; 2005 in ELS). Second-year retention focuses on enrollment in the beginning of a student’s third year.

  13. ELS data extend only 2 years beyond high school exit, so college graduation is reported only for NELS students.

  14. O*NET Job Zones are not reported explicitly in NELS. Rather, separate NCES-specific job categories were matched to the ELS dataset, where O*NET job categories are provided. To impute O*NET Job Zones in NELS, we chose the modal Job Zone in ELS associated with the job categories both datasets have in common. To test the impact of this imputation, observed O*NET Job Zones in ELS were converted to imputed Job Zones using this modal-mapping technique. Occupational prestige models in ELS were re-estimated, and Algebra II effects remained stable.

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Correspondence to Matthew N. Gaertner.

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Gaertner, M.N., Kim, J., DesJardins, S.L. et al. Preparing Students for College and Careers: The Causal Role of Algebra II. Res High Educ 55, 143–165 (2014). https://doi.org/10.1007/s11162-013-9322-7

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