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There are currently no large-scale assessments to measure algebraic conceptual understanding, particularly among college students with no more than an elementary algebra, or Algebra I, background. Here we describe the creation and validation of the Algebra Concept Inventory (ACI), which was developed for use with college students enrolled in elementary algebra or above. We describe how items on the ACI were administered and tested for validity and reliability. Analysis suggests that the instrument has reasonable validity and reliability. These results could inform researchers and practitioners on what conceptual understanding in algebra might look like and how it might be assessed. 

In college, taking algebra can prevent degree completion. One reason for this is that algebra courses in college tend to focus on procedures disconnected from meaning-making (e.g., Goldrick-Rab, 2007). It is critical to connect procedural fluency with conceptual understanding (Kilpatrick, et al., 2001). Several instruments test algebraic proficiency, however, none were designed to test a large body of algebraic conceptions and concepts. We address this gap by developing the Algebra Concept Inventory (ACI), to test college students’ conceptual understanding in algebra. A total of 402 items were developed and tested in eight waves from spring 2019 to fall 2022, administered to 18,234 students enrolled in non-arithmetic based mathematics classes at a large urban community college in the US. Data collection followed a common-item random groups equating design. Retrospective think-aloud interviews were conducted with 135 students to assess construct validity of the items. 2PL IRT models were run on all waves; 63.4% of items (253) have at least moderate, and roughly one-third have high or very high discrimination. In all waves, peak instrument values have excellent reliability ( R ≥ 0.9 ). Convergent validity was explored through the relationship between scores on the ACI and mathematics course level. Students in “mid”-level courses scored on average 0.35 SD higher than those in “low”-level courses; students in “high”-level courses scored on average 0.35 SD higher than those in “mid”-level courses, providing strong evidence of convergent validity. There was no consistent evidence of differential item functioning (DIF) related to examinee characteristics: race/ethnicity, gender, and English-language-learner status. Results suggest that algebraic conceptual understanding, conceptualized by the ACI, is measurable. The final ACI is likely to differentiate between students of various mathematical levels, without conflating characteristics such as race, gender, etc. 

Even though algebraic conceptual understanding is recognized as a critical skill, existing larger scale validated algebra assessments consist mostly of computational tasks, or only assess a very narrow range of conceptions in a smaller focused domain. Further, few instruments have been validated for use with college students. In this paper, we describe the creation and validation of an algebra concept inventory for college students. We describe how items were administered, revised, and tested for validity and reliability. Results suggest that algebraic conceptual understanding is a measurable construct, and that the instrument has reasonable validity and reliability. Revision and validation is ongoing; however, lessons learned thus far provide information about what conceptual understanding in algebra might look like and how it might be assessed.