In mathematics education research paradoxes of infinity have been used in the investigation of students' conceptions of infinity. We analyze one such paradox--the Painter's Paradox--and examine the struggles of a group of Calculus students in an attempt to resolve it. The Painter's Paradox is based on the fact that Gabriel's horn has infinite…

We discuss a decade of initiatives to improve the teaching and learning of calculus at The Ohio State University. Calculus at OSU is taught in lecture/recitation format with large lectures and is tightly coordinated, so all innovations had to occur within that framework. We show how many smaller projects built upon one another to create a larger…

This study examined outcomes for AP® Calculus and AP Physics students on the 2015 Trends in International Math and Science Study (TIMSS) relative to other participating countries and other advanced math and science students in the United States. Compared to other countries in the study, AP Calculus BC and AP Physics C: EM students outperformed all…

The purpose of this study is to investigate whether or not students' understanding of mathematical content typically covered in calculus courses is enhanced by using the TINspire CAS instead of the TI-89. The study was conducted over two phases at a mid-size university in the northeastern United States in Calculus I and Accelerated Calculus I. In…

In the abstract for "Calculus for a New Century: A Pump, Not a Filter," Lynn Steen wrote: "The authors agree on the forces that are reshaping calculus, but disagree on how to respond to these forces. They agree that the current course is not satisfactory, yet disagree about new content emphases. They agree that the neglect of…

Summer break sets students in grades K-12 back by at least one month of instruction and has the strongest impact on mathematics retention. This study investigates whether there is evidence of the summer gap effect at the university level for engineering students enrolled in the introductory calculus course sequence, and possible demographic…

The correct use of visual perspective is one of the main reasons that virtual reality environments and realistic works of art look lifelike. Geometric construction techniques used by artists to achieve an accurate perspective effect were developed during the Renaissance. With the rise of computer graphics, translating the geometric ideas of 600…

Although national interest has been focused on increasing STEM graduates, calculus courses still pose a challenge for most STEM major students. As recent statistics show, only half of the students are successful in calculus courses. Many times, students in these courses do not see the relevancy of the material to their future careers and this…

The Multiple Measures Assessment Project (MMAP) research team has conducted this study in order to examine whether student completion of a transfer-level course in math or English within one year varies by students' participation in either the Extended Opportunities Programs and Services (EOPS) program or the Disabled Students Programs and…

String art can be easily used in introductory calculus to capture the interest of students, to motivate mathematical investigations, and to deepen mathematical understanding.

The staircase and fractional part functions are basic examples of real functions. They can be applied in several parts of mathematics, such as analysis, number theory, formulas for primes, and so on; in computer programming, the floor and ceiling functions are provided by a significant number of programming languages--they have some basic uses in…

In this study, we examined five limit lessons using Mathematical Tasks Framework to understand students' opportunities to learn cognitively challenging tasks and maintain cognitive demand during limit lessons. Our analysis of Dr A's five lessons shows that students rarely had opportunities to maintain or increase cognitive demand. There are two…

Learning progressions (LPs) describe the development of domain-specific knowledge, skills, and understanding. Each level of an LP characterizes a phase of student thinking en route to a target performance. The rationale behind LP development is to provide road maps that can be used to guide student thinking from one level to the next. The validity…

This paper reports the results of a research exploring the mathematical connections of pre-university students while they solving tasks which involving rates of change. We assume mathematical connections as a cognitive process through which a person finds real relationships between two or more ideas, concepts, definitions, theorems, procedures,…

One of the key steps when developing pathways between baccalaureate and diploma programs is comparing learning goals between the programs. This paper presents application of a seven-dimensional framework (cognitive process, transferability, depth of analysis, interdependence, question novelty, scaffolding and communication) to analyze the implicit…