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This article reports on a study designed to estimate the effect of high school coursetaking in the algebra-calculus pipeline on the likelihood of placing out of postsecondary remedial mathematics. A nonparametric variant of propensity score analysis was used on a nationally representative data set to remove selection bias and test for an effect among all comparable students and among students least likely to enroll in precalculus, trigonometry, or calculus. The effect failed to reach practical significance among all comparable students and was particularly weak among students least likely to take precalculus, trigonometry, or calculus. These findings suggest that the regression-based results that factor strongly into discussions on high school graduation requirements for mathematics coursetaking contain substantial selection bias. [ABSTRACT FROM PUBLISHER]

The article presents an abbreviated version of the methodologies and musings experienced by mathematics educators through a genuine problem-solving investigation. It investigates dimensions of an algebraic concept known to many high school students. It also shows how these dimensions lead to an intuitive understanding of the limit in calculus. It is stated that the readers of the article will experience and come to a deeper understanding of the Process Standards and experience the necessity of using multiple representations to make and solve mathematical conjectures. The article also describes a chronological development of mathematical ideas.

This study reports on basic, mostly pre-senior mathematical skills, as measured by a multiple choice questionnaire, of 566 students enrolled in a first year introductory data analysis subject within a science or broadly scientific degree programme. Most students had previously undertaken a senior high-school algebra and calculus based mathematics subject. Rasch analysis was used to validate the questionnaire and assist in the description of levels of skill. General linear models demonstrated that a student's skills score depended on the result obtained in senior mathematics, whether or not the student was a mathematics student, gender, whether or not higher level mathematics had been studied, self-efficacy and year. It is concluded that in order to have full and confident use of basic, pre-senior mathematical skills, algebra-based mathematics needs to be studied beyond this level. [ABSTRACT FROM AUTHOR]

The author reflects on the important role of mathematics teachers in bridging the gap in algebra and calculus learning. She cites her experience in helping students develop an intuitive understanding in the subjects by framing questions within a real-world context. It also suggests the advantage of the process since it develops understanding through real-world scenario and bolster the student's confidence as they work with a concept essential to calculus.