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Articles 1 - 13 of 13
Full-Text Articles in Education
Calculus Problems, Joshua N. Cooper
Calculus Problems, Joshua N. Cooper
Journal of Humanistic Mathematics
No abstract provided.
A Truly Beautiful Theorem: Demonstrating The Magnificence Of The Fundamental Theorem Of Calculus, Dan Mcquillan, Darlene M. Olsen
A Truly Beautiful Theorem: Demonstrating The Magnificence Of The Fundamental Theorem Of Calculus, Dan Mcquillan, Darlene M. Olsen
Journal of Humanistic Mathematics
In standard treatments of calculus, the Fundamental Theorem of Calculus is often presented as a computational method to evaluate definite integrals, with such powerful utility that one is tempted to overlook its beauty. To improve students' appreciation for the first part of the Fundamental Theorem of Calculus, we suggest a few classroom examples focusing on the accumulation function, to be introduced early and often throughout an introductory calculus course. These examples are small enough that they would not necessarily result in changes to a typical course schedule; yet we believe their contribution to student understanding can be significant. Furthermore, such …
Stop Ruining Math! Reasons And Remedies For The Maladies Of Mathematics Education, Rachel M. Steinig
Stop Ruining Math! Reasons And Remedies For The Maladies Of Mathematics Education, Rachel M. Steinig
Journal of Humanistic Mathematics
Did you love math as a kid? Or was it ruined for you? Sadly, many people have had math ruined for them for various reasons. Some might say that it was because of not understanding what was going on, being bored in class, parental or societal pressure to achieve in math, not seeing a point in learning math, wrong amount of homework, grades, curriculum, physical concerns, mean teachers, or any number of things. This article delves into the many common reasons why math is ruined for so many kids, and offers solutions so that math can be enjoyable for everyone. …
What Has An Impact On Grades? Instructor-Made Videos, Communication, And Timing In An Online Statistics Course, Regina Aragon, Indika P. Wickramasinghe
What Has An Impact On Grades? Instructor-Made Videos, Communication, And Timing In An Online Statistics Course, Regina Aragon, Indika P. Wickramasinghe
Journal of Humanistic Mathematics
This study investigates student success in an online introductory statistics class. We examine the impact of several variables: amount of time that a student watches instructor-made videos (IMV), the nature of communication between the student and the instructor, and the amount of time spent on completing the online assignments and exams on student grades in an introductory level online statistics course. Findings suggest that IMVs of short dur ation, the subject- related communication between the student and the instructor, and homework completion time have significant association with student performance. Though the average time spent on online exams does not show …
Bringing Students Back To Mathematics: Classroom Knowledge And Motivation, Giang-Nguyen T. Nguyen, Joel B. Goodin
Bringing Students Back To Mathematics: Classroom Knowledge And Motivation, Giang-Nguyen T. Nguyen, Joel B. Goodin
Journal of Humanistic Mathematics
This paper reports part of a larger research study that investigated how teachers motivate students to learn mathematics at the college level. Findings from the study indicated that teachers have the power to influence and reinvigorate students who had given up learning mathematics. In the framework of Self-Determination Theory (SDT), the researchers analyzed five students’ motivational levels based on intrinsic and extrinsic motivation to see how each student was motivated by their teacher. Findings from the study could provide some directions for future research on students’ motivation to learn mathematics.
Using Ibl In A History Of Mathematics Course: A Skeptic’S Success, Michael E. Matthews, Angela M. Hodge
Using Ibl In A History Of Mathematics Course: A Skeptic’S Success, Michael E. Matthews, Angela M. Hodge
Journal of Humanistic Mathematics
A college professor, who is highly skeptical of change, but sensing a need for teaching in a more inspiring and engaging way, implements an inquiry-based learning (IBL) approach to teaching the history of mathematics. The first author (Matthews) worked with an experienced IBL colleague mentor (Hodge) on the course. Some student data was collected to document the effects of the class on the students. The approach taken for the course is described in detail including how the students of the course learned about and used IBL in key peer-to-peer teaching about historical mathematics (with a primary focus on the mathemat- …
Humanizing Mathematics Through Ethnomodelling, Milton Rosa, Daniel Clark Orey
Humanizing Mathematics Through Ethnomodelling, Milton Rosa, Daniel Clark Orey
Journal of Humanistic Mathematics
Ethnomathematical techniques and modelling tools allow us to examine systems taken from the real world and offer us insight into forms of mathematics performed in holistic contexts [3]. A pedagogical approach that connects a diversity of cultural forms of mathematics can be implemented by the use of ethnomodelling, a process of translation and elaboration of problems and questions taken from non-academic systems. Here, we offer examples of studies conducted in Brazil and in the United States that explore this pedagogical approach. Our goal is to broaden the discussion of possibilities for ethnomathematics and associated ethnomodelling perspectives that respect the …
Jay Leno And Abstract Algebra, Adam Glesser, Martin Bonsangue
Jay Leno And Abstract Algebra, Adam Glesser, Martin Bonsangue
Journal of Humanistic Mathematics
The Jay Leno skit Jaywalking, showing ordinary people struggling to answer basic questions, is both entertaining and applicable to teaching. This article describes how an instructor can strengthen students' conceptual understanding by creating an element of confusion, or "cognitive dissonance," in the students' minds using Jaywalking-style interactions in the classroom.
Dramathizing Functions: Building Connections Between Mathematics And Arts, Gunhan Caglayan
Dramathizing Functions: Building Connections Between Mathematics And Arts, Gunhan Caglayan
Journal of Humanistic Mathematics
This article focuses on connections between mathematics and performance arts (drama). More specifically we offer an exposition of a segment of college algebra mathematics (an introduction to functions), with an approach primarily emphasizing the aesthetic aspects of mathematical learning, teaching, and performing.
What If?: Mathematics, Creative Writing, And Play, Emily Clader
What If?: Mathematics, Creative Writing, And Play, Emily Clader
Journal of Humanistic Mathematics
Mathematics can inform creative writing by suggesting structures for it to follow, as well as by providing the imaginative impetus for common rules to be broken. In a workshop co-taught by the author, a class of sixth-grade students explored this interplay as they produced fractal-inspired poetry and geometry-inspired fiction. This article describes the form and results of the workshop in the context of a broader discussion of the influence of mathematics upon literature.
The Importance Of Surprise In Mathematical Beauty, V. Rani Satyam
The Importance Of Surprise In Mathematical Beauty, V. Rani Satyam
Journal of Humanistic Mathematics
Mathematicians, mathematics education researchers, and philosophers have written about mathematical beauty and many of the qualities commonly associated with it, such as simplicity, brevity, enlightenment, etc. One key theme that underlies many of these qualities is surprise or the unexpected. In this article, I discuss the integral role surprise plays in mathematical beauty. Through examples, I argue that simplicity alone is oftentimes not enough for a piece of mathematics to be considered beautiful, but rather it is unexpected simplicity that we seek. I propose, moreover, that surprise is necessary for enlightenment. The paper also reports results from an activity designed …
The Role Of Sequence In The Experience Of Mathematical Beauty, Leslie Dietiker
The Role Of Sequence In The Experience Of Mathematical Beauty, Leslie Dietiker
Journal of Humanistic Mathematics
In this article, I analyze the aesthetic dimensions of a sequence of mathematical events found in an unusual first grade lesson in order to demonstrate how sequencing may affect an individual’s experience of mathematical beauty. By approaching aesthetic as a sense or felt quality of an experience in context (Sinclair, 2001, 2011), this analysis explains how sequence can affect the way mathematical objects or actions are experienced by an individual. Thus, rather than questioning whether or in what ways a set of mathematical objects are beautiful or not, this paper addresses under what conditions is the mathematics in play beautiful. …
Surprise And The Aesthetic Experience Of University Students: A Design Experiment, Ofer Marmur, Boris Koichu
Surprise And The Aesthetic Experience Of University Students: A Design Experiment, Ofer Marmur, Boris Koichu
Journal of Humanistic Mathematics
Little is known about instructional means by which the aesthetic experience of mathematics can be enhanced for undergraduate learners. This paper presents and discusses an iterative lesson design process towards creating an opportunity for students to appreciate the beauty of an unexpected solution to a challenging calculus problem. The lesson design draws on insights from both mathematics education research on aesthetics and research on aesthetic appreciation in music. The data were collected over the course of five lessons with different groups of calculus students in which the intended problem was presented in two different ways. In addition, stimulated-recall interviews were …