The goal of learning analytics is to optimize learning and the environments in which it occurs. Since 2011, when learning analytics was defined as a separate and distinct area of academic inquiry, the literature has identified a need for research that presents evidence of effective learning analytics, as well as, learning analytics research that…

The purpose of this article is to elaborate Cottrill et al.'s (1996) conceptual framework of limit, an explanatory model of how students might come to understand the limit concept. Drawing on a retrospective analysis of 2 teaching experiments, we propose 2 theoretical constructs to account for the students' success in formulating and understanding…

Considers examples of aspects of the infinitely small and large as they unfolded in the history of calculus from the 17th through the 20th centuries. Presents didactic observations at relevant places in the historical account. (Author/MM)

Examines first-year university students' (n=630) understanding of fundamental calculus concepts at three South African universities. Identifies several misconceptions underlying students' understanding of calculus concepts. Addresses some of the common errors and misconceptions related to students' understanding of 'limit of a function' and…

Assesses the ability of university students enrolled in an introductory calculus course to solve related-rates problems set in geometric contexts. Indicates that overall performance on the geometric related-rates problems was poor and the poorest performance was on steps linked to conceptual understanding. (Contains 34 references.) (Author/ASK)

Most presentations of mathematical ideas are suggested as being backwards from the way they evolved. Two alternatives are discussed, both emphasizing mathematical processes. (MP)

Examines the possibility that at times imagery might be a disadvantage in certain tasks. For example, the notion of a persistent image may be so vivid as to actually block other creative thought. Describes one calculus student's images supporting high levels of mathematical functioning which occasionally became so powerful as to obscure more than…

Examines the views of proof held by university-level mathematics students and teachers. Develops a framework for characterizing people's views of proof based on a distinction between public and private aspects of proof and the key ideas that link these two domains. (Author/KHR)

Rate of change has its basis in everyday experience like growth and motion and is a fundamental organizing idea for relationships between varying quantities. In this paper three types of rate of change knowledge for functions are discussed: global, interval, and point-wise. Each of these types of rate of change knowledge can be examined using…

Presents a study to describe and understand the thinking processes of students in a computer environment while undertaking mathematical tasks related to the differentiation of functions defined on real numbers. Describes two different approaches, the visual and the algebraic approach, in the thinking processes of calculus students. (Contains 19…

Results from a large-scale study of sixth-form and college students' understanding of elementary calculus and mathematical ideas underlying calculus are presented. Difficulties with speed, tables, linear graphs, curves and differences, the tangent as the limit, and the average rate of change are each discussed. (MNS)

A number of general ideas intended to be helpful in analyzing differences in concept images among individuals are formulated. These ideas are applied to the specific concepts of continuity and limits, as taught in the secondary school and university. (MP)

Problem solving in mathematics incorporates abstract thinking skills, number logic skills, and a nearly endless list of other factors. One problem-solving task required in university-level mathematics courses is integration. This study investigated instructor presentation of a specific problem-solving strategy and whether it impacted performance…

Examines students' beliefs about knowledge, and their motivation, learning strategies, and academic performance in two instructional contexts in introductory Calculus classes. Sophistication of epistemological beliefs was positively correlated with motivation, self-efficacy, self-regulation, and grades. Students in the more active, cooperative…

Abstracts of 12 mathematics education research reports and critical comments (by the abstractors) about the reports are provided in this issue of Investigations in Mathematics Education. The reports are: "More Precisely Defining and Measuring the Order-Irrelevance Principle" (Arthur Baroody); "Children's Relative Number Judgments:…