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Full-Text Articles in Physical Sciences and Mathematics
Traveling Wave Solutions For Two Species Competitive Chemotaxis Systems, T. B. Issa, R. B. Salako, W. Shen
Traveling Wave Solutions For Two Species Competitive Chemotaxis Systems, T. B. Issa, R. B. Salako, W. Shen
Faculty Research, Scholarly, and Creative Activity
In this paper, we consider two species chemotaxis systems with Lotka–Volterra competition reaction terms. Under appropriate conditions on the parameters in such a system, we establish the existence of traveling wave solutions of the system connecting two spatially homogeneous equilibrium solutions with wave speed greater than some critical number c∗. We also show the non-existence of such traveling waves with speed less than some critical number c∗0 , which is independent of the chemotaxis. Moreover, under suitable hypotheses on the coefficients of the reaction terms, we obtain explicit range for the chemotaxis sensitivity coefficients ensuring c∗ = c∗0 , which …
Peer Motivation: Getting Through Math Together, Jessica Mean, Wes Maciejewski
Peer Motivation: Getting Through Math Together, Jessica Mean, Wes Maciejewski
Faculty Research, Scholarly, and Creative Activity
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.
Observing Change In Students’ Attitudes Towards Mathematics: Contrasting Quantitative And Qualitative Approaches, Wes Maciejewski
Observing Change In Students’ Attitudes Towards Mathematics: Contrasting Quantitative And Qualitative Approaches, Wes Maciejewski
Faculty Research, Scholarly, and Creative Activity
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 …
Changes In Attitudes Revealed Through Students’ Writing About Mathematics, Wes Maciejewski
Changes In Attitudes Revealed Through Students’ Writing About Mathematics, Wes Maciejewski
Faculty Research, Scholarly, and Creative Activity
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 …
Mathematical Knowledge As Memories Of Mathematics, Wes Maciejewski
Mathematical Knowledge As Memories Of Mathematics, Wes Maciejewski
Faculty Research, Scholarly, and Creative Activity
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 …
Mathematical Foresight: Thinking In The Future To Work In The Present, Wes Maciejewski, Bill Barton
Mathematical Foresight: Thinking In The Future To Work In The Present, Wes Maciejewski, Bill Barton
Faculty Research, Scholarly, and Creative Activity
Originating from interviews with mathematics colleagues, written accounts of mathematicians engaging with mathematics, and Wes's reflections on his own mathematical work, we describe a process that we call mathematical foresight: the imagining of a resolution to a mathematical situation and a path to that resolution. In a sense, mathematical foresight is the process of imagining a not-yet-experienced mathematical event—the solution to a problem solving scenario, or the creation of a mathematical model for a biological system, for examples that could occur in the future. This future thinking process guides the mathematician's present mathematical activity, motivates them, and bolsters persistence.
Research Mathematicians & Mathematics Educators: Collaborations For Change, Greg Oates, Wes Maciejewski
Research Mathematicians & Mathematics Educators: Collaborations For Change, Greg Oates, Wes Maciejewski
Faculty Research, Scholarly, and Creative Activity
No abstract provided.
Episodic Future Thinking In Mathematical Situations, Wes Maciejewski, Reece Roberts, Donna Rose Addis
Episodic Future Thinking In Mathematical Situations, Wes Maciejewski, Reece Roberts, Donna Rose Addis
Faculty Research, Scholarly, and Creative Activity
Episodic future thinking is a process of mentally projecting one's self into a future event, allowing the event to be experienced before it actually occurs (Atance & O'Neill, 2001). The current study explores the possibility that students engage in episodic future thinking while solving mathematical tasks. Participating students were given mathematical situations and verbalized thoughts that emerged as they planned resolutions to the situations. All participants exhibited episodic future thinking and we present a categorization of these thoughts. Given extant results on the positive influence episodic future thinking has on general problem-solving ability, we propose that a similar influence might …
Instructors' Perceptions Of Their Students' Conceptions: The Case In Undergraduate Mathematics, Wes Maciejewski
Instructors' Perceptions Of Their Students' Conceptions: The Case In Undergraduate Mathematics, Wes Maciejewski
Faculty Research, Scholarly, and Creative Activity
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's learning. For subsequent education to be effective, an instructor must link the current topic to the student's 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' …
Evolutionary Game Dynamics In Populations With Heterogenous Structures, Wes Maciejewski, Feng Fu, Christoph Hauert
Evolutionary Game Dynamics In Populations With Heterogenous Structures, Wes Maciejewski, Feng Fu, Christoph Hauert
Faculty Research, Scholarly, and Creative Activity
Evolutionary graph theory is a well established framework for modelling the evolution of social behaviours in structured populations. An emerging consensus in this field is that graphs that exhibit heterogeneity in the number of connections between individuals are more conducive to the spread of cooperative behaviours. In this article we show that such a conclusion largely depends on the individual-level interactions that take place. In particular, averaging payoffs garnered through game interactions rather than accumulating the payoffs can altogether remove the cooperative advantage of heterogeneous graphs while such a difference does not affect the outcome on homogeneous structures. In addition, …
A College-Level Foundational Mathematics Course: Evaluation, Challenges, And Future Directions, Wes Maciejewski
A College-Level Foundational Mathematics Course: Evaluation, Challenges, And Future Directions, Wes Maciejewski
Faculty Research, Scholarly, and Creative Activity
Recently in Ontario, Canada, the College Math Project brought to light startling data on the achievement of students in Ontario's 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 …
Multiple Visions Of Teachers' Understandings Of Mathematics, Ann Kajander, Ralph Mason, Peter Taylor, Edward Doolittle, Tom Boland, Dan Jarvis, Wes Maciejewski
Multiple Visions Of Teachers' Understandings Of Mathematics, Ann Kajander, Ralph Mason, Peter Taylor, Edward Doolittle, Tom Boland, Dan Jarvis, Wes Maciejewski
Faculty Research, Scholarly, and Creative Activity
In this dialog, the notion of mathematical understanding as might be needed by classroom teachers is critically examined by mathematics educators, mathematicians, and a classroom teacher, based on the outcomes of recent work with expert classroom teachers. Terminology, assumptions and examples are discussed and analysed from a number of points of view. Ultimately, the goal is to construct common ground from which appropriate mathematics courses for future teachers might be developed and taught. The need for common terminology and a unifying framework from which to work becomes apparent as multiple interpretations and visions are discussed.