Observing Change In Students’ Attitudes Towards Mathematics: Contrasting Quantitative And Qualitative Approaches

A student’s attitude towards mathematics affects how they learn and perform in mathematics. What exactly is meant by attitude and how this interacts with mathematics education is a current debate in the mathematics education research community. Regardless, practitioners often acknowledge a consideration of improving students’ attitudes towards mathematics in their course design. This creates an impetus to study attitudes towards mathematics in a way that lends itself to observing changes over a course in mathematics. The current study draws on two approaches to observing and measuring attitudes towards mathematics in an effort to contrast disparate approaches and deepen an investigation of students’ changes in attitudes. Results indicate there is no superior approach; that the multi-dimensional nature of attitude defies a succinct description, but methods exist to allow us to get a handle on this construct, nonetheless

Changes In Attitudes Revealed Through Students’ Writing About Mathematics

The ways in which a student relates to mathematics is known to affect how they learn and perform in mathematics: anxiety may be compensated with avoidance; enjoyment with engagement. Therefore, there is a need to understand students’ relationships with mathematics and to see how these are affected by mathematics education. This paper presents results from the early stages of a mixed-methods study aimed at assessing changes in students’ attitudes towards mathematics as revealed in their writings about mathematics. In contrast to existing survey instruments on attitudes towards mathematics, the methods and discussion presented here have the potential to inform the analysis of more idiosyncratic, personal, and diverse relationships with mathematics in authentic, large-scale educational settings

Instructors\u27 Perceptions of their Students\u27 Conceptions: The Case in Undergraduate Mathematics

How a student conceives the nature of a subject they study affects the approach they take to that study and ultimately their learning outcome. This conception is shaped by prior experience with the subject and has a lasting impact on the student\u27s learning. For subsequent education to be effective, an instructor must link the current topic to the student\u27s prior knowledge. Short of assessing their students, an instructor relies on their subjective experience, intuitions, and perceptions about this prior knowledge. These perceptions shape the educational experience. The current study explores, in the context of undergraduate mathematics, the alignment of instructors\u27 perceptions of student conceptions of mathematics and the students\u27 actual conceptions. Using a version of the Conceptions of Mathematics Questionnaire, instructors of lower-year courses were found to have overestimated, while upper-year course instructors underestimated, their students\u27 fragmented conceptions of mathematics. Instructors across all years underestimate their students\u27 cohesive conceptions. This misalignment of perspectives may have profound implications for practice, some of which are discussed

Mathematical Knowledge as Memories of Mathematics

I propose that an understanding of a mathematical concept is comprised of both a conceptual understanding of, and recollections of working with that concept. That is, a mathematical concept may not be immediately distilled in its abstract form from lived experience, didactical or otherwise, and this milleu is brought along in subsequent recollections of the concept. In an effort to balance pedagogical recommendations for increased conceptual teaching/understanding, I propose that memories of encountering a mathematical concept improve its utility in novel problem situations. I support this claim by drawing on the literature on episodic future thinking and on our developing understanding of how users of mathematics perform in authentic mathematical situations

A College-Level Foundational Mathematics Course: Evaluation, Challenges, and Future Directions

Recently in Ontario, Canada, the College Math Project brought to light startling data on the achievement of students in Ontario\u27s College of Applied Arts and Technology System related to their performance in first-year mathematics courses: one-third of the students had failed their first-year mathematics course or were at risk of not completing their program because of their performance in such a course. Here I present the results of an attempt to address the findings of the College Math Project. A foundational mathematics course, based on the JUMP Math program, was designed and implemented at a college in Toronto, Ontario. Although the students who took this program made appreciable gains in their achievement, it is difficult to assert its effectiveness over other programs because of the absence of studies profiling college math education practices either in Canada or internationally. The intention of this article is to help establish a datum for research into specific college math education programs

The Siren Call of Calculus A Review of Steven Strogatz’s Infinite Powers: How Calculus Reveals the Secrets of the Universe

I hate calculus. Which is a lie: I secretly love it. I enjoy teaching it, drawing intricate diagrams of where the definition of the derivative comes from, stumping my students on convoluted trigonometric integrals with solutions dependent on partial fractions, hammering mnemonics for the derivative rules—all the joys of teaching calculus. And I enjoyed learning it, too. Well, not failing it the first time, but after that. I long for my undergraduate time spent in the reading room of Rutherford South re-arranging integrals à la Fubini’s Theorem, the massive lecture halls of anxious engineering students copying every stroke of chalk from the front, and the arithmetic errors costing me scores of marks from my tests. A calculus course presents the liturgy of undergraduate mathematics: students and instructors alike gather, willfully or otherwise, to engage in the ritualistic celebration of the mysteries of the infinite

Peer Motivation: Getting Through Math Together

Students have a complex relationship with mathematics. Some love it, but more often than not, the feelings are less favorable. These feelings can lead to decreased motivation which makes it difficult for students to engage with the subject as the semester progresses. Instructors also have difficulty addressing this waning motivation. In this paper, we claim peers are better able to connect with the students and this can be leveraged to better motivate students. We present an approach to having peers motivate their students. These peer interactions integrated with a mandatory mathematics course might improve students’ motivation