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…

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…

Many students are passively engaged in mathematics content across the United States because they are in classrooms that use traditional instruction methods (i.e. lecture and guided practice). Calculus is a struggle for students because of the critical thinking, conceptual understanding, and problem solving required. Active learning has been shown…

As part of a large-scale survey of over 4000 undergraduates at British universities, 238 economics students reported on their experiences of studying post-compulsory secondary mathematics qualifications (A-levels) and the preparation they provided for their degrees. Participants were positive about their experience of post-compulsory mathematics…

This study extends past research on students' understanding of slope by analyzing college students' mistakes on routine tasks involving slope. We conduct both quantitative and qualitative analysis of students' mistakes on common slope tasks to extract information regarding procedural proficiencies and conceptual underpinnings required in order for…

This study focuses on the mathematics department at a South African university and in particular on teaching of calculus to first year engineering students. The paper reports on a cause-effect analysis, often used for business improvement. The cause-effect analysis indicates that there are many factors that impact on secondary school teaching of…

Despite the efforts to confirm the effectiveness of writing in learning mathematics, analysis on common errors in mathematical writings has not received sufficient attention. This study aimed to provide an account of the students' procedural explanations in terms of their commonly committed errors in mathematical writing. Nine errors in…

The purpose of this study is to explore how an introductory real analysis (IRA) course can be designed to bridge a gap between students' intuition and mathematical rigor. In particular, we focus on a task, called the e-strip activity, designed for the convergence of a sequence. Data were collected from a larger study conducted as a classroom…

Many interventions have been proposed to improve the retention and graduation rates of engineering students. One such intervention is to use study groups for first-year college students; such groups provide a structured environment in which the students can learn course material from each other outside of class and can provide the students with a…