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1. The Algebra Concept Inventory for college students

   Wladis, C; Offenholley, K; Sencindiver, B; Myszkowski, N; Aly, G (November 2024, Proceedings of the 46th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Kent State University.)

   Kosko, K; Caniglia, J; Courtney, S; Zolfaghari, M; Morris, G (Ed.)

   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. 

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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. The multiple usages of Thinking With Algebra

   Feikes, D; McCathey, N; Oppland-Cordell, S; Walker, WS; Sorge, BH (January 2024, Proceedings of the ninth annual Indiana STEM Education Conference. Purdue University: Purdue e-Pubs. https://docs.lib.purdue.edu/instemed/2024/briefs/4)

   Walker, WS; Bryan, LA; Guzey, E (Ed.)

   Thinking With Algebra (TWA) is a National Science Foundation Project (DUE 2021414) to develop a post-secondary curriculum for intermediate algebra. TWA focuses on six elements that align with building algebraic fluency with conceptual understanding, a mixed review approach, small-group work, and whole-class discussion (Feikes, et al., 2021). Using an equity lens (Oppland-Cordell et al., 2024), TWA is designed for students, including underrepresented students, who need additional mathematical supports at the college level. Seventeen college math instructors attended a workshop on the lessons and pedagogy in order to use TWA in their college courses. Feedback from instructors participating in the TWA first-year faculty workshop indicated that the curriculum was used in many different ways to help prepare students for college algebra and other STEM courses. 

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4. When Am I (N)ever Going to Use This? How Engineers Use Algebra

   Istas, Brooke; Walkington, Candace; Leyva, Elizabeth (July 2021, 2021 ASEE Virtual Annual Conference)

   Mathematics is an important tool in engineering practice, as mathematical rules govern many designed systems (e.g., Nathan et al., 2013; Nathan et al., 2017). Investigations of structural engineers suggest that mathematical modelling is ubiquitous in their work, but the nature of the tasks they confront is not well-represented in the K-12 classroom (e.g., Gainsburg, 2006). This follows a larger literature base suggesting that school mathematics is often inauthentic and does represent how mathematics is used in practice. At the same time, algebra is a persistent gatekeeper to careers in engineering (e.g., Harackiewicz et al., 2012; Olson & Riordan, 2012). In the present study, we interviewed 12 engineers, asking them a series of questions about how they use specific kinds of algebraic function (e.g., linear, exponential, quadratic) in their work. The purpose of these interviews was to use the responses to create mathematical scenarios for College Algebra activities that would be personalized to community college students’ career interests. This curriculum would represent how algebra is used in practice by STEM professionals. However, our results were not what we expected. In this paper, we discuss three major themes that arose from qualitative analyses of the interviews. First, we found that engineers resoundingly endorsed the importance of College Algebra concepts for their day-to-day work, and uniformly stated that math was vital to engineering. However, the second theme was that the engineers struggled to describe how they used functions more complex than linear (i.e., y=mx+b) in their work. Students typically learn about linear functions prior to College Algebra, and in College Algebra explore more complex functions like polynomial, logarithmic, and exponential. Third, we found that engineers rarely use the explicit algebraic form of an algebraic function (e.g., y=3x+5), and instead rely on tables, graphs, informal arithmetic, and computerized computation systems where the equation is invisible. This was surprising, given that the bulk of the College Algebra course involves learning how to use and manipulate these formal expressions, learning skills like factoring, simplifying, solving, and interpreting parameters. We also found that these trends for engineers followed trends we saw in our larger sample where we interviewed professionals from across STEM fields. This study calls into question the gatekeeping role of formal algebraic courses like College Algebra for STEM careers. If engineers don’t actually use 75% of the content in these courses, why are they required? One reason might be that the courses are simply outdated, or arguments might be made that learning mathematics builds more general modelling and problem-solving skills. However, research from educational psychology on the difficulty of transfer would strongly refute this point – people tend to learn things that are very specific. Another reason to consider is that formal mathematics courses like advanced algebra have emerged as a very convenient mechanism to filter people by race, gender, and socioeconomic background, and to promote the maintenance of the “status quo” inequality in STEM fields. This is a critical issue to investigate for the future of the field of engineering as a whole. 

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5. Work-in-Progress Paper: Creating and Validating the Conceptual Assessment for Sedimentology courses

   Stepanova, Anna; Anwar, Saira; Laya, Juan Carlos; Alvarez-Zarikian, Carlos; Hammond, Tracy (October 2024, IEEE)

   Contribution: In this work-in-progress paper we describe the process of creating and validating a conceptual assessment in the field of sedimentology for undergraduate geoscience courses. The mechanism can aid future geoscience educators and researchers in the process of academic assessment development aligned with learning objectives in these courses. Background: Prior literature review supports the benefits of using active learning tools in STEM (Science, Technology, Engineering, and Mathematics) courses. This paper is part of a larger project to develop and incorporate research-based active learning software in sedimentology and other geoscience courses to improve grade point average (GPA) and time to graduation for Hispanic students at Texas A&M University. To evaluate the novel tool, we designed and validated the conceptual assessment instrument presented in this work. Research Question: What is the process to develop and validate a conceptual assessment for sedimentology? Methodology: This paper follows quantitative analysis and the assessment triangle approach and focuses on cognition, observation, and interpretation to design and evaluate the conceptual assessment. In the cognition element of the triangle, we explain the mechanism for creating the assessment instrument using students' learning objectives. The observation element explains the mechanism of data collection and the instrument revision. The interpretation element explains the results of the validation process using item response theory and reliability measures. We collected the conceptual assessment data from 17 participants enrolled in two courses where sedimentology topics are taught. Participants were geology majors in one of the courses and engineering majors in the other. Findings: The team developed a conceptual assessment that included eight multiple-choice (MCQ) and four open-ended response questions. The results of the design process described the conceptualization of questions and their validation. Also, the validity of created rubrics was established using inter-rater reliability measures, which showed good agreement between raters. Additionally, the results of the validation process indicated that the conceptual assessment was designed for students with average abilities. 

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