This paper reports on the experience of STEM and mathematics faculty at four different institutions working collaboratively to integrate learning theory with curriculum development in a core undergraduate linear algebra context. The faculty formed a Professional Learning Community (PLC) with a focus on learning theories in mathematics and…

Two first-year engineering mathematics courses used computer-aided assessment (CAA) to provide students with opportunities for formative assessment via a series of weekly quizzes. Most students used the assessment until they achieved very high (>90%) quiz scores. Although there is a positive correlation between these quiz marks and the final…

This article investigates the numbers [image omitted], originally studied by Catalan. We re-confirm that they are indeed integers. Using the close relationship between them and the Catalan numbers C[subscript n], we develop some divisibility properties for C[subscript n]. In particular, we establish that [image omitted], where f[subscript k]…

In a previous study, the onto-semiotic approach was employed to analyse the mathematical notion of different coordinate systems, as well as some situations and university students' actions related to these coordinate systems in the context of multivariate calculus. This study approaches different coordinate systems through the process of change of…

Issues arising in the transition from secondary school to tertiary mathematics study are increasingly coming under scrutiny. In this paper, we analyse two practical aspects of the school-tertiary interface: teaching style; and assessment. We present some of the findings arising from a 2-year national project in New Zealand titled "Analysing…

Passing through remedial and required math classes poses a significant barrier to success for many community college students. This study uses random assignment to investigate the impact of a "light-touch" intervention, where an individual visited math classes a few times during the semester, for a few minutes each time, to inform…

This paper reports on a qualitative study focusing on engineers' point of view in regard to university mathematics and mathematics education. An individual interview was conducted with three electrical and two mechanical engineers between the ages of 25-40, all engaged in successful careers. The subjects were requested to reflect upon themselves…

We report on our analysis of data from a dataset of 26 videotapes of university students working in groups of 2 and 3 on different proving problems. Our aim is to understand the role of example generation in the proving process, focusing on deliberate changes in representation and symbol manipulation. We suggest and illustrate four aspects of…

We present an analysis of students' formal constructions in mathematics regarding to syntactic, semantic and pragmatic aspects. The analyzed tasks correspond to students of the Course of Mathematics for the admission to the university. Our study was qualitative, consisted in the identification, analysis and interpretation, focused in logic…

After providing some background on change ringing, this paper introduces a question that arises in the systematic ringing of church bells and uses group theory to solve it.

Using a simple trigonometric limit, we provide an intuitive geometric proof of the Singular Value Decomposition of an arbitrary matrix.

Maximal ideals in the ring of continuous functions on the closed interval [0, 1] are not finitely generated. This is well-known. What is not as well-known, but perhaps should be, is the fact that these ideals are not countably generated although the proof is not harder! We prove this here and use the result to produce some non-prime ideals in the…

This paper describes how the author's students (in-service and pre-service secondary mathematics teachers) enrolled in college geometry courses use the Geometers' Sketchpad (GSP) to gain insight to formulate, confirm, test, and refine conjectures to solve the classical airport problem for triangles. The students are then provided with strategic…

The Common Core State Standards (CCSS) provide teachers with the expectations and requirements that are meant to prepare K-12 students for college and the workforce (CCSSI 2010b). The Common Core State Standards for Mathematical Practice (SMPs) emphasize the development of skills and conceptual understanding for students to become proficient in…

This study analyzed the effect of mathematics courses on a cohort of students at a 4-year university in order to compare the effect of mathematics on adult students, those 25 and older, and traditional-age students. The transcripts of the 118 adult students and the 3,747 traditional-age students who were freshmen in the fall of 1999 were compared.…