A Psychometric Analysis of the Algebra and Precalculus Concept Readiness Assessment for Community Colleges

Yadira Peralta, Profesora Investigadora Titular Visitante del Programa de Estudios Longitudinales, Experimentos y Encuestas del CIDE, Nidhi Kohli, April Strom, Irene Duranczyk, Vilma Mesa y Laura Watkins escribieron el artículo A Psychometric Analysis of the Algebra and Precalculus Concept Readiness Assessment for Community Colleges  publicado en el Journal of Psychoeducational Assessment.

 

Abstract

 

Understanding students’ readiness for precalculus and calculus at the community college level is critical not only because of the key role community colleges play in higher education but also because calculus remains a gateway course for students in advancing to higher level mathematics. The Algebra and Precalculus Concept Readiness Assessment for Community Colleges (APCR-CC) was designed to investigate community college students’ quantitative reasoning abilities and conceptual understanding in algebra. The present study investigates the psychometric properties of the APCR-CC instrument using item response theory based on a sample of intermediate and college algebra students from six community colleges collected in a pretest (N = 1,131) and posttest (N = 772) setting. We examine unidimensionality, item fit, local item independence, measurement invariance, and sensitivity to instruction. Our findings suggest that the APCR-CC instrument is sufficiently characterized by one underlying construct, local dependence does not seem to be an issue, and 80% of the items in the APCR-CC instrument are sensitive to instruction.

 


 

Although the predominant focus of research in the field of mathematics education has been on K-12 and university settings, there is an abundance of information to be learned from both mathematics students and faculty in the community colleges. The role that the 982 public community colleges play in the United States is vital for both workforce development and educating students beyond high school. Community colleges in the United States provide an open access opportunity for students to complete various certificates and associate degrees or to complete college coursework prior to or during their university education. According to the National Center for Educational Statistics, there were just more than 14 million undergraduate students in postsecondary public institutions in the United States in the fall of 2015, with nearly 43% of them enrolled in community colleges (Snyder, de Brey, & Dillow, 2018). A report on the role of community colleges in postsecondary success from the National Student Clearinghouse Research Center (2017) showed that 46% of 4-year college graduates in 2013 to 2014 had attended a community college at some point in their past. The 2017 demographics of community colleges show a highly diverse student population: 62% of all community college students were enrolled part-time, 56% were female, 36% were the first in their family to attend college, 17% were single parents, and 22% of full-time students held full-time jobs, whereas 41% of part-time students held full-time jobs (American Association of Community Colleges, 2017). Certainly, the community colleges provide educational opportunities to a widely diverse student population with a variety of academic goals, and due to their demographics, the student population of community colleges is often very different from that of universities. Helping students realize their educational dreams and persevere through obstacles is the primary mission of the community colleges in the United States, and yet a major challenge, given the diversity of students.

In mathematics, community colleges serve an even more important role because they offer precollege coursework, also known as developmental mathematics, designed to enhance students’ preparedness for college-level mathematics (e.g., college algebra [CA] or precalculus). The 2015 College Board of the Mathematical Sciences survey reported that about 42% of all mathematics students enrolled in U.S. institutions of higher education were taking their mathematics courses at a public 2-year college (Blair, Kirkman, & Maxwell, 2018). Blair et al. (2018) also found that approximately 41% of all community college mathematics students in fall 2015 were enrolled in developmental mathematics courses. Although many students who enroll in community colleges have previously taken algebra in high school, the reality is that only 62% would have completed Algebra II for graduation and even fewer (18%) would have completed additional courses that prepare them for taking precalculus (e.g., trigonometry 16%; see Champion & Mesa, 2017). These statistics suggest that a significant proportion of high school students who want to pursue an advanced degree in science, technology, engineering, or mathematics will need more mathematical preparation after graduation, and that many of these students are likely to do so at a community college. In addition, as Sitomer et al. (2012) point out, “community college mathematics teachers are reteaching mathematical content that students have encountered in previous mathematics courses, yet little is known about how students arrive at understanding when they are reintroduced to the content” (p.35). The American Mathematical Association of Two-Year Colleges (AMATYC) has made it a priority to promote research on the teaching and learning of mathematics in the first 2 years of college and the organization has called for more research investigations “to understand how to best assist students in two-year colleges to succeed” (AMATYC, 2018, p. 94).

Students’ readiness for precalculus and calculus hinges upon the capacity of their prior algebra preparation to open doors to the possibility of earning a science, technology, engineering, and mathematics (STEM) degree or a non-STEM career that demands college-level mathematics skills. Yet, beyond commercially available placement assessments such as ALEKS, Accuplacer, and Compass that focus on students’ procedural skills rather than conceptual knowledge, the field does not have research-based instruments (e.g., concept inventories) that truly assess students’ precalculus readiness specifically at the community college level. In a research by Wladis, Offenholley, Licwinko, Dawes, and Lee (2018), they found that no validated assessments (such as concept inventories) existed to evaluate students’ conceptual understanding specifically in postsecondary elementary algebra. However, such concept inventories are extremely important for two reasons. First, they help assess students’ knowledge of fundamental disciplinary concepts (e.g., the Force Concept Inventory in physics, Hestenes, Wells, & Swackhamer, 1992; the Precalculus Concept Assessment [PCA] in mathematics, Carlson, Oehrtman, & Engelke, 2010), and second, when they are valid and reliable, they can be used to assess the impact of interventions that target teaching those fundamental concepts. Wladis et al. (2018) contend that not having access to validated assessments is a barrier for community college faculty because “instructors cannot systematically detect which incorrect or underdeveloped algebraic conceptions are impeding student progress, and thus they cannot target instruction to address these conceptions explicitly” (p. 1).

To address this barrier, the study presented in this article stems from a research project focused on understanding the precalculus knowledge of fundamental concepts that students possess while they are in algebra-intensive courses, such as intermediate algebra (IA) and CA, in the community college setting. The purpose of this article is to analyze and report on the psychometric properties of an assessment developed to assess community CA students’ quantitative reasoning abilities and conceptual understanding of fundamental algebraic ideas. This assessment, called the Algebra and Precalculus Concept Readiness Assessment for Community Colleges (APCR-CC), informs both our knowledge about students’ understanding of fundamental algebraic concepts and the impact of instruction on learning in algebra courses at the community college level.

 

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