Journal of Humanistic MathematicsCopyright (c) 2016 Claremont Colleges All rights reserved.
http://scholarship.claremont.edu/jhm
Recent documents in Journal of Humanistic Mathematicsen-usSat, 27 Aug 2016 12:09:01 PDT3600Teaching Differential Equations Through a Modeling First Approach
http://scholarship.claremont.edu/jhm/vol6/iss2/22
http://scholarship.claremont.edu/jhm/vol6/iss2/22Sun, 31 Jul 2016 20:44:29 PDTBrian WinkelOur Lady, Queen of Undecidable Propositions
http://scholarship.claremont.edu/jhm/vol6/iss2/21
http://scholarship.claremont.edu/jhm/vol6/iss2/21Sun, 31 Jul 2016 20:44:25 PDT
Boundary systems take many forms: personal, historical, mathematical, and in the case of an elderly Jesuit and a young mathematician, a struggle to identify the larger boundary that both connects them and provides their separate identities. Their ragged conversation is couched in a pastiche of historical, popular, and personal notions of mathematics; however their language is simultaneously natural and mathematical so that it points to the irremediable gaps that the multitude of our languages attempt to "solve." Father McMann pages through his list of such incommensurables: female/male, young/old, parabola/limit, rational/surd and “all the other 88 asynchronies that plagued his dreams like a badly tuned piano.” Like the gap between Adam’s outstretched finger and the finger of the creator on the ceiling of the Sistine Chapel, these “gaps” are what motivate us, perplex us, and which lead to very strange arguments about the re-presentational nature of any language — mathematical or natural — between literary scholars and their mathematical friends.
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Hugh C. CulikAn Exercise on Limits
http://scholarship.claremont.edu/jhm/vol6/iss2/20
http://scholarship.claremont.edu/jhm/vol6/iss2/20Sun, 31 Jul 2016 20:44:22 PDTManya Raman-SundströmCalculus Problems
http://scholarship.claremont.edu/jhm/vol6/iss2/19
http://scholarship.claremont.edu/jhm/vol6/iss2/19Sun, 31 Jul 2016 20:44:18 PDTJoshua N. CooperMenger Sponge
http://scholarship.claremont.edu/jhm/vol6/iss2/18
http://scholarship.claremont.edu/jhm/vol6/iss2/18Sun, 31 Jul 2016 20:44:15 PDTE Laura GolbergQuantitative Literacy
http://scholarship.claremont.edu/jhm/vol6/iss2/17
http://scholarship.claremont.edu/jhm/vol6/iss2/17Sun, 31 Jul 2016 20:44:11 PDTThomas L. MooreThe Greatest Integer Function
http://scholarship.claremont.edu/jhm/vol6/iss2/16
http://scholarship.claremont.edu/jhm/vol6/iss2/16Sun, 31 Jul 2016 20:44:07 PDTAlanna RaeTeaching the Quandary of Statistical Jurisprudence: A Review-Essay on Math on Trial by Schneps and Colmez
http://scholarship.claremont.edu/jhm/vol6/iss2/15
http://scholarship.claremont.edu/jhm/vol6/iss2/15Sun, 31 Jul 2016 20:44:03 PDT
This review-essay on the mother-and-daughter collaboration Math on Trial stems from my recent experience using this book as the basis for a college freshman seminar on the interactions between math and law. I discuss the strengths and weaknesses of this book as an accessible introduction to this enigmatic yet deeply important topic. For those considering teaching from this text (a highly recommended endeavor) I offer some curricular suggestions.
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Noah GiansiracusaBook Review: A New Index for Predicting Catastrophes: Poems by Madhur Anand
http://scholarship.claremont.edu/jhm/vol6/iss2/14
http://scholarship.claremont.edu/jhm/vol6/iss2/14Sun, 31 Jul 2016 20:43:59 PDT
This review explores Madhur Anand’s recent poetry collection from several points of view. One involves consideration of mathematical concepts and imagery in her poems. A second viewpoint takes into consideration Anand’s own field – she is a professor of environmental science with a focus on ecology. A third view considers the poems as art objects – words building pictures that offer to readers both insights and pleasures.
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JoAnne GrowneySimple Tools with Nontrivial Implications for Assessment of Hypothesis-Evidence Relationships: The Interrogator’s Fallacy
http://scholarship.claremont.edu/jhm/vol6/iss2/13
http://scholarship.claremont.edu/jhm/vol6/iss2/13Sun, 31 Jul 2016 20:43:55 PDT
This paper takes a mathematical analysis technique derived from the Interrogator’s Fallacy (in a legal context), expands upon it to identify a set of three interrelated probabilistic tools with wide applicability, and demonstrates their ability to assess hypothesis-evidence relationships associated with important problems
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Justus R. RiekFuzzy Logic in Health Care Settings: Moral Math for Value-Laden Choices
http://scholarship.claremont.edu/jhm/vol6/iss2/12
http://scholarship.claremont.edu/jhm/vol6/iss2/12Sun, 31 Jul 2016 20:43:51 PDT
This essay is intended as an example of “moral math”, i.e., ideas culled from mathematics which can positively impact social behavior. Specifically, it combines fuzzy logic with the ethical decisions which hospital staff and others are sometimes forced to make about health care (e.g., euthanasia issues following Hurricane Katrina). The assumption is that such decisions involve value-laden choices which lend themselves to “fuzzy” or “smart” protocols. The article discusses the history of fuzzy logic – what it is, how it is used, and how it might be even better-used as a support basis for making difficult choices in the health care setting.
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Sarah VossA Truly Beautiful Theorem: Demonstrating the Magnificence of the Fundamental Theorem of Calculus
http://scholarship.claremont.edu/jhm/vol6/iss2/11
http://scholarship.claremont.edu/jhm/vol6/iss2/11Sun, 31 Jul 2016 20:43:47 PDT
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 examples might allow students to share more of the excitement that the pioneers of the subject surely experienced along the way.
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Dan McQuillan et al.Stop Ruining Math! Reasons and Remedies for the Maladies of Mathematics Education
http://scholarship.claremont.edu/jhm/vol6/iss2/10
http://scholarship.claremont.edu/jhm/vol6/iss2/10Sun, 31 Jul 2016 20:43:44 PDT
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. Some of the solutions include societal shifts, some are things that math teachers can do in the classroom, some are ways parents can shift their attitudes towards math, therefore creating a healthier home culture surrounding math, and, lastly, some are ways that students can change the way they participate in math class to get the most out of it.
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Rachel M. SteinigAl-Khwarizmı and the Hermeneutic Circle: Reflections on a Trip to Samarkand
http://scholarship.claremont.edu/jhm/vol6/iss2/9
http://scholarship.claremont.edu/jhm/vol6/iss2/9Sun, 31 Jul 2016 20:43:40 PDT
In this paper we discuss al-Khwarzmi's life and aspects of his work and suggest a possible hermeneutic avenue into his contribution to mathematics.
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Asuman G. AksoyPatterns Formed by Coins
http://scholarship.claremont.edu/jhm/vol6/iss2/8
http://scholarship.claremont.edu/jhm/vol6/iss2/8Sun, 31 Jul 2016 20:43:36 PDT
This article is a gentle introduction to the mathematical area known as circle packing, the study of the kinds of patterns that can be formed by configurations of non- overlapping circles. The first half of the article is an exposition of the two most important facts about circle packings, (1) that essentially whatever pattern we ask for, we may always arrange circles in that pattern, and (2) that under simple conditions on the pattern, there is an essentially unique arrangement of circles in that pattern. In the second half of the article, we consider related questions, but where we allow the circles to overlap. The article is written with the idea that no mathematical background should be required to read it.
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Andrey M. MishchenkoWhat has an Impact on Grades? Instructor-Made Videos, Communication, and Timing in An Online Statistics Course
http://scholarship.claremont.edu/jhm/vol6/iss2/7
http://scholarship.claremont.edu/jhm/vol6/iss2/7Sun, 31 Jul 2016 20:43:32 PDT
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 a statistical association with student grades, the results indicate that the students who complete the exam between two-to-four hours perform better than the students who spend less than two hours or more than four hours to complete the exam.
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Regina Aragon et al.Bringing Students Back to Mathematics: Classroom Knowledge and Motivation
http://scholarship.claremont.edu/jhm/vol6/iss2/6
http://scholarship.claremont.edu/jhm/vol6/iss2/6Sun, 31 Jul 2016 20:43:27 PDT
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.
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Giang-Nguyen T. Nguyen et al.Combinatorics of the Sonnet
http://scholarship.claremont.edu/jhm/vol6/iss2/5
http://scholarship.claremont.edu/jhm/vol6/iss2/5Sun, 31 Jul 2016 20:43:23 PDT
Using a definition of a sonnet, the number of basic rhyming schemes is enumerated. This is then used to discuss the 86 sonnets which appear in John Clare's The Rural Muse.
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Terry S. GriggsUsing IBL in a History of Mathematics Course: A Skeptic’s Success
http://scholarship.claremont.edu/jhm/vol6/iss2/4
http://scholarship.claremont.edu/jhm/vol6/iss2/4Sun, 31 Jul 2016 20:43:19 PDT
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- ics). An innovative rubric is described to evaluate IBL teaching. Results indicate that the students were engaged in the course and inspired about mathematics, seemingly more than previous semesters. The results also imply that the stu- dents learned at least as much mathematics and history as in previous semester. Finally, the students, most of which were future high school teachers, began to seriously reflect on their own teaching and appreciated the IBL approach.
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Michael E. Matthews et al.Humanizing Mathematics through Ethnomodelling
http://scholarship.claremont.edu/jhm/vol6/iss2/3
http://scholarship.claremont.edu/jhm/vol6/iss2/3Sun, 31 Jul 2016 20:43:14 PDT
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 social diversity of distinct cultural group members with guarantees for the development of understanding of the different ways of doing mathematics through dialogue and respect.
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Milton Rosa et al.