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The Algebra Concept Inventory (ACI) is the first large-scale instrument validated to measure the foundational algebraic conceptual understanding of college students. This study uses ACI scores to conduct the first quantitative analysis on the relationship between algebraic conceptual understanding and college outcomes, thus exploring the predictive validity of the ACI. Specifically, we investigate whether ACI scores predict: (1) math course grades; (2) subsequent completion of math courses required for STEM majors; (3) completion of STEM versus non-STEM degrees; and (4) the extent that differences in these outcomes by race/ethnicity or gender are explained by ACI scores. Results indicate that ACI scores significantly predict math course outcomes and STEM versus non-STEM degree completion, as well as significant proportions of differences in these outcomes by race/ethnicity and gender. This illustrates the importance of providing every student instruction that supports development of the kinds of foundational algebraic conceptual understanding measured by the ACI. 

Algebraic conceptual understanding is a critical mathematical skill. However, until recently, larger-scale validated assessments in algebra consisted mostly of computational tasks, or only assessed a narrow range of conceptions in a focused domain. Moreover, few instruments had been validated for college students. In this paper, we explore the predictive validity of the recently-validated Algebra Concept Inventory (ACI); in particular, whether college students’ ACI scores predict math course grades, STEM-major math course completion, and STEM vs. non-STEM degree attainment. We also explore whether the ACI score explains outcome differences by race/ethnicity/gender. 

Algebra has been found to be a barrier to college and STEM-major completion, and a contributing factor to unequal access to STEM fields. Conceptual understanding has often been discussed as an important component of mathematics learning; yet more marginalized students often have less access to rich mathematics instruction and to algebra learning opportunities. However, to date no research has investigated the relationship between conceptual understanding and math or STEM outcomes in college. In this research, we explore the predictive validity of the recently validated Algebra Concept Inventory (ACI) to determine whether college students’ ACI scores predict math course grades, STEM-major math course completion, and STEM vs. non-STEM degree attainment as well as whether ACI score explains outcome differences by race/ethnicity/gender. 

Algebraic conceptual understanding is a critical mathematical skill. However, until recently, larger-scale validated assessments in algebra consisted mostly of computational tasks, or only assessed a narrow range of conceptions in a focused domain. Moreover, few instruments had been validated for college students. In this research, we explore the predictive validity of the recently-validated Algebra Concept Inventory (ACI); in particular, whether college students’ ACI scores predict math course grades, STEM-major math course completion, and STEM vs. non-STEM degree attainment. We also explore whether the ACI score explains outcome differences by race/ethnicity/gender. The ACI was designed to assess student conceptions of core mathematics concepts that are critical for algebra, such as variable, equivalence, and function. Items were designed to be accessible to students with all levels of algebra experience, starting with students who have taken or are currently enrolled in elementary algebra in college (or who have prior experience with Algebra I in secondary school). Data for students enrolled in any mathematics course at or above elementary algebra at the largest community college at the City University of New York (CUNY) were collected and merged with an existing dataset of ACI scores (based on 2pl IRT models). Regression as well as mediation analysis using the KHB method were used in order to explore predictive relationships between ACI score and subsequent academic outcomes. On average, one standard deviation (SD) increase in ACI score correlated with a 0.4 increase in grade points for a student’s enrolled mathematics course. ACI scores also significantly predicted whether a student would complete each of the five core STEM major mathematics requirements, given their current course level. For every one SD increase in ACI score, students were also 5.1 percentage points more likely to complete a STEM vs. non-STEM degree when controlling for current course level. ACI score predicted STEM degree completion more strongly than course grade alone. ACI scores also explained a significant portion of differences in math course grade by race/ethnicity, illustrating the importance of instruction in algebraic conceptual understanding for equitable learning and course outcomes. 

Abstract A first synthesis of available data for the period of Rome’s expansion in Italy (about 400–29 b.c.e.) shows the role of climate and environment in early Roman imperialism. Although global indices suggest a warmer phase with relatively few short-term climate events occuring around the same time as the expansion, local data emphasize the highly variable timing and expression of these trends. This variability casts doubt on ideas of a unitary, historically consequential “Roman Warm Period.” The historical importance of climate and environment to socioeconomic development merits emphasis, but should be understood in terms of evolving, contingent forms of resilience and risk-mitigating behavior by Italian communities during Roman expansion.