A couple of years ago, I gave a presentation to a group of secondary-school girls who were attending a workshop at a community college. The workshop's purpose was to encourage the girls to keep taking mathematics courses while in high school and beyond, in order to increase their future opportunities. The presentation was titled, "Where Can I Find…

Although proof comprehension is fundamental in advanced undergraduate mathematics courses, there has been limited research on what it means to understand a mathematical proof at this level and how such understanding can be assessed. In this paper, we address these issues by presenting a multidimensional model for assessing proof comprehension in…

This study was conducted with 93 freshmen and 82 senior prospective mathematicians and mathematics teachers in order to investigate how they construct and evaluate proofs and whether there are any significant differences in their proof construction (with respect to department and grade) and proof evaluation (with respect to department)…

Higher education in the United States is facing a failure-rate crisis in entry-level mathematics courses. In this article, the authors describe an innovative, technology-enhanced hybrid course model that has significantly improved course completion and content mastery outcomes in general education (GE) mathematics courses. The model relies on five…

Ever had a roommate? Then you know that it can be difficult to share housekeeping duties. This article uses game theory to analyze situations in which there is a task to be done and two people who might do it. We then use our analysis to consider what game theory tells us about the gendered division of household labor.

Videos have been used in classrooms for decades, but student-produced video has recently become a viable, economical option to enhance learning. Students were asked to create videos to be used for their exam review in two different undergraduate mathematics courses: Differential Equation and Complex Analysis. Students were then surveyed about…

This article explores learning opportunities offered by students' written reflections as they learn through writing an action research proposal. From tapping into students' reported struggles, I analysed data using three stages of qualitative data analysis: data reduction, data display, and conclusion drawing (Miles and Huberman 1994). It emerged…

A mixed-method study was conducted during the Fall 2008 semester to better understand the experiences of students participating in computer-aided instruction of College Algebra using the software MyMathLab. The learning environment included a computer learning system for the majority of the instruction, a support system via focus groups (weekly…

In this article, the author suggests a cross-curricular idea that can link with PE, dance, music and history. Teacher David Schmitz, a maths teacher in Illinois who was also a square dance caller, had developed a maths course that used the standard square dance syllabus to teach mathematical principles. He presents an intensive, two-week course…

A procedure modelling ideal classical and quantum gases is discussed. The proposed approach is mainly based on the idea that modelling and algorithm analysis can provide a deeper understanding of particularly complex physical systems. Appropriate representations and physical models able to mimic possible pseudo-mechanisms of functioning and having…

The mathematical sciences are part of nearly all aspects of everyday life--the discipline has underpinned such beneficial modern capabilities as Internet search, medical imaging, computer animation, numerical weather predictions, and all types of digital communications. "The Mathematical Sciences in 2025" examines the current state of the…

Literature in mathematics has been found to foster positive improvements in mathematics learning. This manuscript reports on a mathematics teacher educator's use of literature via literature circles with 11 prospective secondary mathematics teachers in a mathematics content course. Using survey and reflection data, the author found that…

The last ten years have seen an explosion of research in the zero-divisor graphs of commutative rings--by professional mathematicians "and" undergraduates. The objective is to find algebraic information within the geometry of these graphs. This topic is approachable by anyone with one or two semesters of abstract algebra. This article gives the…

Based on the results of a prior case-study analysis of mathematics placement at one university, the mathematics department developed and piloted a mathematics placement test. This article describes the implementation process for a mathematics placement test and further analyzes the test results for the pilot group. As an unexpected result, the…

Teaching and learning of mathematics is challenging when lecturer and students are separated geographically. While student engagement and interaction with the course, with other students and with the lecturer is vital to mathematics learning, it is difficult to facilitate this electronically, because of the nature of mathematics. With tablet…