This dissertation reports three studies of students' and teachers' meanings for quotient, fraction, measure, rate, and rate of change functions. Each study investigated individual's schemes (or meanings) for foundational mathematical ideas. Conceptual analysis of what constitutes strong meanings for fraction, measure, and rate of change is…

In this paper the author investigates how the one-year math throughput rate of community college students varies according to the highest level of math completed in high school, with a particular focus on the implications of successfully completing Algebra 2 while in high school. Community college math throughput rates for students with different…

Lexical ambiguities exist when two different meanings are ascribed to the same word. Such lexical ambiguities can be particularly problematic for learning material with technical words that have everyday meanings that are not the same as the technical meaning. This study reports on lexical ambiguities in six statistical words germane to statistics…

We explore the transition from school to university through a commognitive (Sfard 2008) analysis of twenty-two students' examination scripts from the end of year examination of a first year, year-long module on Sets, Numbers, Proofs and Probability in a UK mathematics department. Our analysis of the scripts relies on a preliminary analysis of the…

Students who attend two-year institutions are not always academically prepared for the level of work that is required to be successful. Two-year institutions determine students' readiness for college-level mathematics courses using one of three placement methods. However, few empirical studies have investigated which placement methods are most…

Advanced-level (A-level) mathematics is a high-profile qualification taken by many school leavers in England, Wales, Northern Ireland and around the world as preparation for university study. Concern has been expressed in these countries that standards in A-level mathematics have declined over time, and that school leavers enter university or the…

Developmental mathematics, which is designed to prepare students for college-level mathematics courses, can be a barrier to students' success. In the United States, the majority of students placed into developmental mathematics courses fail to complete the developmental sequence. Alternative mathematics pathways offer some benefits when integrated…

To address under-preparation of students for college-level course-work, Texas House Bill 5 (HB5) introduced a number of substantive changes to the state high school curriculum and graduation requirements. Among its provisions, HB5 created a requirement that school districts offer a college preparatory mathematics course for students not meeting…

The paper argues that mathematical modeling is the essence of computational thinking. Learning a computer language is a valuable assistance in learning logical thinking but of less assistance when learning problem-solving skills. The paper is third in a series and presents some examples of mathematical modeling using spreadsheets at an advanced…

The focus of the current proposal is to examine the effect of two dynamic simulations on the participants' conceptions of rate of change. Conceptions of rate of change were measured according to Carlson et al.'s (2002) Mental Actions framework and how the participants related the physical simulations to the graphical representations (Heid, et al.,…

Statewide policies can impact enrollment patterns of students. At one Texas University, 11th-grade Texas Assessment of Knowledge and Skills scores were predictive of success in students' first college-level mathematics course, but many students--those most at risk of failure--seem to have avoided taking a mathematics course in their first year at…

This article describes a sequence of design research projects, some exploratory others more formal, on the teaching of modelling and the analysis of modelling skills. The initial motivation was the author's observation that the teaching of applied mathematics in UK high schools and universities involved no active modelling by students, but was…

This study examined the extent to which student- and teacher-level characteristics in high school and college are associated empirically with high school students' college readiness and success in American Samoa. More specifically, multilevel ordinal logistic regressions were employed to understand the extent to which these characteristics predict…

Mathematics is not only a subject but it is also a language consisting of many different symbols and relations. Taught as a compulsory subject up the 10th class, students are then able to choose whether or not to study mathematics as a main subject. The present paper discusses mathematical modeling in mathematics education. The article provides…

The phenomenon in which students enter university under-prepared for the mathematical demands of their undergraduate courses, regularly referred to as the 'Maths Problem', has been widely reported in Ireland, UK, Australia, and the US. This issue has been of particular concern in Ireland recently, with beginning undergraduates' performance of…