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…

As part of a study on the effects of teaching with a Modified Moore Method (MMM), a survey containing 20 items from Schoenfeld's (1989) investigation of attitudes and beliefs about mathematics was administered to students in undergraduate precalculus classes. The study included one section of precalculus taught with an MMM, a student-centered and…

Diversity and differentiation within our classrooms, at all levels of education, is nowadays a fact. It has been one of the biggest challenges for educators to respond to the needs of all students in such a mixed-ability classroom. Teachers' inability to deal with students with different levels of readiness in a different way leads to school…

Assessments and student expectations can drive learning: students selectively study and learn the content and skills they believe critical to passing an exam in a given subject. Evaluating the nature of assessments in undergraduate science education can, therefore, provide substantial insight into student learning. We characterized and compared…

Purpose: The purpose of this study was to examine differences between boys and girls in their performance on STEM related AP exams. Specifically, gender differences were examined for the following STEM related AP exams: Calculus AB, Calculus BC, Physics B, Physics C: Electricity and Magnetism, Physics C: Mechanics, Chemistry, and Computer Science…

This paper asks whether placement recommendations for a developmental math course at an elite public institution impact students' future academic performance, course-taking, and college outcomes. Researchers use these specific outcomes to measure whether developmental courses help students develop the skills necessary to succeed in college,…

Colleges and universities remain attentive to developing and supporting ways to foster student academic success. These efforts have taken on more importance as student success, commonly measured by student learning achievement, has failed to meet expectations. For colleges and universities, the flipped classroom represents a student-centered…

This paper describes a system for research on the behaviour of students taking online drills. The system is accessible and free to use for anyone with web access. Based on open source software, the teaching material is licensed under a Creative Commons License. The system has been used for computer-assisted education in statistics, mathematics and…

This paper presents instructive interdisciplinary applications of constrained mechanics calculus in economics on a level appropriate for undergraduate physics education. The aim of the paper is (i) to meet the demand for illustrative examples suitable for presenting the background of the highly expanding research field of econophysics even at the…

Although nowadays there are mythbusting teams ready to empirically confirm or deny advertising claims that may seem too good to be true, it is often economically prohibitive to perform the kinds of experiments that are called for. It is therefore sometimes more sensible and efficacious to perform a thought experiment instead, especially if the…

For almost all students, what happens when they push buttons on their calculators is essentially magic, and the techniques used are seemingly pure wizardry. In this article, the author draws back the curtain to expose some of the mathematics behind computational wizardry and introduces some fundamental ideas that are accessible to precalculus…

Freely rising air bubbles in water sometimes assume the shape of a spherical cap, a shape also known as the "big bubble". Is it possible to find some objective function involving a combination of a bubble's attributes for which the big bubble is the optimal shape? Following the basic idea of the definite integral, we define a bubble's surface as…

In this paper, we explore the development of two grounded theories. One theory is mathematical and grounded in the work of university calculus students' collaborative development of mathematical methods for finding the volume of a solid of revolution, in response to mathematical necessity in problem solving, without prior instruction on solution…

This article examines the question of finding the best quadratic function to approximate a given function on an interval. The prototypical function considered is f(x) = e[superscript x]. Two approaches are considered, one based on Taylor polynomial approximations at various points in the interval under consideration, the other based on the fact…

We discuss the need for devoting time in differential equations courses to modelling and the completion of the modelling process with efforts to estimate the parameters in the models using data. We estimate the parameters present in several differential equation models of chemical reactions of order n, where n = 0, 1, 2, and apply more general…