Using linked high school and college records for a national sample of students, I document the first college math courses that students take and examine how they compare with high school coursework. Detailed 12th-grade math assessment data and variation in college math course-taking allow me to estimate the extent of redundant college math…

Most any students can explain the meaning of "a[superscript b]", for "a" [element-of] [set of real numbers] and for "b" [element-of] [set of integers]. And some students may be able to explain the meaning of "(a + bi)[superscript c]," for "a, b" [element-of] [set of real numbers] and for…

As it is already observed by mathematicians and educators, there is a discrepancy between the formal techniques of mathematical logic and the informal techniques of mathematics in regards to proof. We examine some of the reasons behind this discrepancy and to what degree it affects doing, teaching and learning mathematics in college. We also…

This paper reports on mathematics remediation efforts at a public 4-year institution. Specifically, it describes redesign efforts that led to the implementation of co-requisite mathematics remediation. Data on this program were collected and analyzed with respect to completion rates, length of time to earn college mathematics credit, and factors…

In light of rising college student debt, many states now offer multiple options for students to earn college credit while still in high school. Concurrent enrollment programs, which allow qualified high school teachers to teach college credit-bearing classes in the high school, are one such option. Because concurrent enrollment classes teach…

For many mature-aged students, there can be a considerable gap between finishing formal study and beginning university. They are often required to draw on qualifications and skills, including mathematics, which are dated, but necessary for success. Most universities offer several pathways that prospective students can take to enter university:…

Across the nation, community colleges have expanded dual enrollment programs to increase college enrollment and completion, particularly among historically underserved populations. The California Community College system--the largest system in the nation--is no different and recently expanded its dual enrollment programming to include College and…

The California Community Colleges (CCC) began implementation of AB 705 in fall 2018, ensuring that most students started in transfer-level math rather than a developmental education sequence. The RP Group's Multiple Measures Assessment Project (MMAP) has found that for all student groups, dramatically increasing access to transfer-level math…

This qualitative narrative study examined high achieving college Black STEM students who enrolled in precalculus, calculus I and II, differential equations, linear algebra, and applied linear algebra courses at Rhowlin Bonsu University (RBU). RBU is located in the Midwestern region of the United States. This investigation used a semi-structured…

Critical to constructing and interpreting graphs is an individual's understanding of the underlying coordinate systems, yet coordinate systems are often overlooked or taken-for-granted in both mathematics education research and curricula. In this paper, we foreground coordinate systems and present a distinction between two uses of coordinate…

Following a line of inquiry regarding the exact number of real roots of a real polynomial, this investigation considers: Descartes' Rule of Signs, the Budan-Fourier Theorem, and versions of Sturm's Method in contrast with the approximate root count gleaned from graphing utilities. Online applets are provided to allow the reader to freely…

Should proof by induction be reserved for higher levels of mathematical instruction? How can teachers show students the nature of mathematics without first requiring that they master algebra and calculus? Proof by induction is one of the more difficult types of proof to teach, to learn, and to understand. Thus, this article delves deeper into…

The structure sense is a part that must be learned in order to help understand and construct connection in abstract algebra. This study aimed at building the pattern of a structure sense as a profile of the structure sense in group property. Using a qualitative study, the structure sense of group property was explored through lecturing activity of…

Many students enter community college underprepared in math and must take multiple semesters of developmental (remedial) classes. Far too few of these students ever enroll in -- let alone pass -- an introductory college-level math course, but without those credits, they cannot graduate. Among the many reforms practitioners are undertaking to try…

Researchers have been interested in students' transition to calculus since the early 1900s. One line of inquiry highlights students' understandings of high school mathematics as impeding or supporting their successful transition to university mathematics. This paper addresses an underlying question in this line of inquiry: does school mathematics…