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Abstract
The purpose of this descriptive research study was to identify key mathematics competencies first-time college students need to succeed in entry-level college mathematics courses. The study was conducted at a large, urban public, research university where between 20-31 percent of its new incoming freshmen were placed in developmental mathematics from 2010 through 2013. In the initial part of the research (Phase 1), a pilot study was conducted utilizing historical student data from mathematics placement tests (MPT). Participants in the pilot were new entering freshmen completing the MPT during student orientation in the summer preceding their entrance in the university. Students’ performance on the MPT test questions were used to identify mathematical competencies differentiating students’ placements in the various entry-level mathematics courses, hence depicting their level of mathematics readiness. Demographic data and incoming characteristics were also considered. Pilot study data demonstrated deficiencies in questions requiring operations with rational numbers and rational expressions. On average, less than 50 percent of the students placing in Developmental Mathematics, College Algebra, or Precalculus answered those questions correctly. A follow-up study was conducted to confirm the results obtained in Phase 1 through observations and artifacts examination of an entry-level mathematics class. Results from Phase 2 confirmed the results from Phase 1 and identified operations with negative numbers as an important concept affecting student preparedness. This study extends the mathematics education research by providing specific mathematics competencies affecting students’ mathematics preparedness entering a 4-year institution.