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1. The Algebra Concept Inventory: Creation and Validation with Students Across a Range of Math Courses in College

   Wladis, C; Offenholley, K; Sencindiver, B; Myszkowski, N; Aly, G (February 2024, Proceedings of the 26th Annual Conference on Research in Undergraduate Mathematics Education)

   Cook, S; Infante, N (Ed.)

   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. 

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2. Creation and validation of the Algebra Concept Inventory in the tertiary context.

   Wladis, C; Offenholley, K; Sencindiver, B; Myszkowski, N; Aly, G (July 2024, Proceedings of the 47th Conference of the International Group for the Psychology of Mathematics Education)

   Evans, T; Marmur, O; Hunter, J; Leach, G (Ed.)

   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. 

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3. Developing Algebraic Conceptual Understanding: Can procedural knowledge get in the way?

   Wladis, C.; Verkuilen, J.; McCluskey, S.; Offenholley, K.; Licwinko, S.; Lee, J. K.; Dawes, D. (January 2019, Proceedings of the 22nd Annual Conference on Research in Undergraduate Mathematics Education)

   In this study we use latent class analysis, distractor analysis, and qualitative analysis of cognitive interviews of student responses to questions on an algebra concept inventory, in order to generate theories about how students’ selections of specific answer choices may reflect different stages or types of algebraic conceptual understanding. Our analysis reveals three groups of students in elementary algebra courses, which we label as “mostly random guessing”, “some procedural fluency with key misconceptions”, and “procedural fluency with emergent conceptual understanding”. Student responses also revealed high rates of misconceptions that stem from misuse or misunderstanding of procedures, and whose prevalence often correlates with higher levels of procedural fluency. 

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4. For Good Measure: Identifying Student Measurement Estimation Strategies Through Actions, Language, and Gesture

   Harrison, A. (January 2020, Proceedings of the International Conference on the Learning Sciences)

   Measurement informs our actions and decisions well beyond school, necessitating that students develop a conceptual understanding of measurement alongside the procedural ability to measure objects. We present a first attempt to explore how students express their understanding of measurement by analyzing the behavior of college and elementary students as they completed measurement estimation tasks. We clustered observable student behavior to identify six profiles of behavioral strategies which may indicate different levels of conceptual understanding. 

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5. For good measure: Identifying student measurement estimation strategies through actions, language, and gesture.

   Harrison, A. (January 2020, Proceedings of the International Conference on the Learning Sciences)

   Measurement informs our actions and decisions well beyond school, necessitating that students develop a conceptual understanding of measurement alongside the procedural ability to measure objects. We present a first attempt to explore how students express their understanding of measurement by analyzing the behavior of college and elementary students as they completed measurement estimation tasks. We clustered observable student behavior to identify six profiles of behavioral strategies which may indicate different levels of conceptual understanding. 

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