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"Precalculus"
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Characteristics of Precalculus Through Calculus 2 Programs: Insights From a National Census Survey
The authors present findings from a recently completed census survey of all mathematics departments in the United States that offer a graduate degree in mathematics. The authors
report the viewpoints of departments about characteristics shown to support students’ success as well as the extent to which these characteristics are being implemented in programs
across the country.
Journal Article
Pre-calculus
Pre-calculus courses have become increasingly popular with 35 percent of students in the U.S. taking the course in middle or high school. Often, completion of such a course is a prerequisite for calculus and other upper level mathematics courses. Pre-Calculus For Dummies is an invaluable resource for students enrolled in pre-calculus courses. By presenting the essential topics in a clear and concise manner, the book helps students improve their understanding of pre-calculus and become prepared for upper level math courses.
Book
Opportunities to Learn Reasoning and Proof in High School Mathematics Textbooks
The nature and extent of reasoning and proof in the written (i.e., intended) curriculum of 20 contemporary high school mathematics textbooks were explored. Both the narrative and exercise sets in lessons dealing with the topics of exponents, logarithms, and polynomials were examined. The extent of proof-related reasoning varied by topic and textbook. Overall, about 50% of the identified properties in the 3 topic areas were justified, with about 30% of the addressed properties justified with a general argument and about 20% justified with an argument about a specific case.
Journal Article
Quantitative Reasoning and the Sine Function: The Case of Zac
A growing body of literature has identified quantitative and covariational reasoning as critical for secondary and undergraduate student learning, particularly for topics that require students to make sense of relationships between quantities. The present study extends this body of literature by characterizing an undergraduate precalculus student's progress during a teaching experiment exploring angle measure and trigonometric functions.
Journal Article
The Path to College Calculus: The Impact of High School Mathematics Coursework
This study addresses a longstanding question among high school mathematics teachers and college mathematics professors: Which is the best preparation for college calculus—(a) a high level of mastery of mathematics considered preparatory for calculus (algebra, geometry, precalculus) or (b) taking calculus itself in high school? Mastery of the mathematics considered preparatory for calculus was found to have more than double the impact of taking a high school calculus course on students' later performance in college calculus, on average. However, students with weaker mathematics preparation gained the most from taking high school calculus.
Journal Article