Definitions are fundamental to any mathematics classroom. We consider how definitions are presented in textbooks and instructors' lecture notes, and whether students are positioned to gain a full understanding of new terms. Four textbooks, covering precalculus, calculus, and analysis, as well as three professors' Calculus I lecture notes are…

We discuss an innovative course model used in first-year calculus courses at a large North American research university, which we refer to as the "Blended Model." We argue that our model takes the best features of lectures, flipped classrooms, and traditional recitations, and gathers them into a cohesive, robust structure that benefits…

Although lecture is the traditional method of university mathematics instruction, there has been little empirical research that describes the general structure of lectures. In this paper, we adapt ideas from narrative analysis and apply them to an upper-level mathematics lecture. We develop a framework that enables us to conceptualize the lecture…

This paper outlines the experience of a university professor who implemented flipped learning in two sections of college algebra courses for two semesters. It details how the courses were flipped, what technology was used, advantages, challenges, and results. It explains what students do outside of class, what they do inside class, and discusses…

In this paper, we examine the benefits of employing an inverted or "flipped" class design in a Transition-to-Proof course for second-year mathematics majors. The issues concomitant with such courses, particularly student acquisition of "sociomathematical norms" and self-regulated learning strategies, are discussed along with…

Real Analysis is a required class for most undergraduate mathematics majors, but it is also one of the most difficult classes they will take. In this article, the author compares two approaches to teaching in the two analysis classes she has taught. The first one was taught in a traditional lecture-homework-exam format, while the second was taught…

This article presents the importance of using multimedia in the math classes by an example of multimedia lesson about definite integral and the results of the research carried out among the students of the first years of faculty, divided into two groups of 25. One group had the traditional lecture about the definite integral, while the other one…

Lectures have been widely criticized as a method of teaching, but remain a standard component of most university mathematics courses. Does this necessarily harm students' education? This critical review contends that many arguments against lecturing are misconceived, at least when applied to mathematics. The effectiveness of lectures in carrying…

The purpose of this study was to examine the effects of the educational software "Frizbi Mathematics 4" on 4th grade student's mathematics achievement, retention, attitudes toward mathematics and attitude toward computer assisted learning. Two groups (experimental and control) of students from the state primary school in Gazimagusa,…

Lab-centric instruction emphasizes supervised, hands-on activities by substituting lab for lecture time. It combines a multitude of pedagogical techniques into the format of an extended, structured closed lab. We discuss the range of benefits for students, including increased staff interaction, frequent and varied self-assessments, integrated…

This paper reports on a quasi-experimental study comparing a "productive failure" instructional design (Kapur in Cognition and Instruction 26(3):379-424, 2008) with a traditional "lecture and practice" instructional design for a 2-week curricular unit on rate and speed. Seventy-five, 7th-grade mathematics students from a…

According to "Standards of Excellence in Teaching Mathematics in Australian Schools," excellent teachers of mathematics need to create "an environment that maximises students' learning opportunities"; so that they can encourage self-directed learning, "model mathematical thinking and reasoning," and provide…

At the University of Toronto at Scarborough, we provide enhanced flexibility to our students using a blended-learning approach (i.e., the webOption) whereby students can attend lectures live, watch them online at their convenience, or both. The current research examines the use of pause and seeks features afforded by the webOption interface and…

This study examines the timing using computer-enriched instruction (CEI), before or after a traditional lecture to determine cross-over effect, period effect, and learning effect arising from sequencing of instruction. A 2 x 2 cross-over design was used with CEI to teach central limit theorem (CLT). Two sequences of graduate students in nursing…

It has been reported that the students' level of mathematics when entering university has changed in recent years. A surprising number of students struggle with mathematics or have a mathematics anxiety. Although this was widely reported within the UK, there was some uncertainty if colleagues in other countries were experiencing the same…