Sinead Breen

An investigation of the mathematical literacy of first year third-level students in the Republic of Ireland

This article reports on a study carried out to measure the mathematical literacy of a selection of students entering third-level education in Ireland. The study investigates how such students performed when confronted with mathematical tasks, which, though commensurate with their level of education, may not have been familiar to them, and to identify the factors influencing their performance. Moreover, the relationship between the skills measured by the test of mathematical literacy administered and those measured by state examinations was explored, as was the question of whether or not the concept of mathematical literacy is a useful one for third-level educators.

A Year of Engaging with the Discipline of Noticing: Five Mathematics Lecturers' Reflections.

In September 2010, five mathematics lecturers set out on a professional development project with the following aim: to reflect on teaching practice using John Masons Discipline of Noticing. At the end of the academic year, each lecturer considered her experiences of engaging with the process. In this paper, we describe the observations made and discuss the benefits and challenges of engaging with the Discipline of Noticing, namely, the benefits of a collaborative approach; the challenges of ‘noticing in the moment’ and the advantages of and difficulties with, writing brief-but-vivid accounts.

Designing Mathematical Thinking Tasks

Abstract Research has shown that the types of tasks assigned to students affect their learning. Various authors have described desirable features of mathematical tasks or of the activity they initiate. Others have suggested task taxonomies that might be used in classifying mathematical tasks. Drawing on this literature, we propose a set of task types that are deemed appropriate for undergraduate students and which foster mathematical habits of mind. These are: generating examples; analyzing reasoning; evaluating mathematical statements; conjecturing and/or generalizing; visualizing; and using definitions. We give rationales for our choices and examples of each type of task suitable for use in an introductory calculus course.

Threshold Concepts and Undergraduate Mathematics Teaching

Abstract Traditionally, many undergraduate mathematics courses have been defined in terms of mathematical content and the techniques in which students should become proficient or theorems they should be able to prove. This can result in a reliance on shallow or rote learning by students, despite the fact that the main goal of a mathematics lecturer1 is usually to foster mathematical understanding in their students. In contrast, it is suggested that placing an emphasis on the threshold concepts involved in a course can enable teachers and students to focus on what is fundamental to the study and mastery of their subject.