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<title>Journal of Humanistic Mathematics</title>
<copyright>Copyright (c) 2013 Claremont Colleges All rights reserved.</copyright>
<link>http://scholarship.claremont.edu/jhm</link>
<description>Recent documents in Journal of Humanistic Mathematics</description>
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<lastBuildDate>Fri, 24 May 2013 15:06:16 PDT</lastBuildDate>
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<title>Three Poems: The Lorenz Transformations, Rotating the Strange Attractor to Find the Principal Components, The Sieve of Eratosthenes</title>
<link>http://scholarship.claremont.edu/jhm/vol3/iss1/15</link>
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<pubDate>Wed, 30 Jan 2013 23:11:03 PST</pubDate>
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<author>Robin Chapman</author>


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<title>Some Contributions to the Sociology of Numbers</title>
<link>http://scholarship.claremont.edu/jhm/vol3/iss1/16</link>
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<pubDate>Wed, 30 Jan 2013 23:11:03 PST</pubDate>
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	<p>Those who work with numbers eventually realize that they all have different personalities (the word "numbers" can of course be replaced by any number of other nouns here.) Here is one view of the issue.</p>

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<author>Robert Dawson</author>


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<title>Outlier, Or A Statistical Explanation of Fear</title>
<link>http://scholarship.claremont.edu/jhm/vol3/iss1/14</link>
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<pubDate>Wed, 30 Jan 2013 23:11:02 PST</pubDate>
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	<p><em>Postscript</em></p>
<p>As a seventh grader, I would sit in algebra class thinking I understood what my teacher had explained -- the order of operations or how to factor a polynomial -- but I would get home, try to do my homework, and my “knowledge” was gone. I had a vague idea that these formulas were about complicated relationships: the division and commonalities of beings. But just as I didn’t have the experience to allow me to discern the true nature of the human relationships these abstract concepts could represent, I didn’t know how to apply these new calculations to anything practical so they would make sense. I’d go home and cry over my homework each evening as if it were a lover with whom I couldn’t communicate. And, in a way, it was.</p>
<p>Many years later, after beginning to overcome my subsequent math fear and having had the privilege of receiving a copy of a math poem by a Nobel Laureate economist, I felt that my instinct was vindicated. Indeed, I was on the track for deeper understanding, and it’s good to see that math instruction these days may be heading toward helping students understand “why,” not just “what.”</p>
<p>In the back of my mind, all these years, math-inspired poems of various sorts have been forming. Though most are based in calculus, this particular poem related more to statistics. I’m slowly working on creating an online, hyperlinked math-inspired chapbook in which the hyperlinked words come together to make up, ultimately, an “equation” that holds the whole work together and can be read as a piece unto themselves.</p>

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<author>Erika Dyquisto</author>


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<title>Poetic Reactions</title>
<link>http://scholarship.claremont.edu/jhm/vol3/iss1/13</link>
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<pubDate>Wed, 30 Jan 2013 23:11:01 PST</pubDate>
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	<p>This trio of poems helps illustrate some of the many ways mathematics, poetry, and life integrate and inspire each other.</p>

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<author>Lawrence M. Lesser</author>


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<title>At The Gate Of Discovery</title>
<link>http://scholarship.claremont.edu/jhm/vol3/iss1/12</link>
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<pubDate>Wed, 30 Jan 2013 23:11:01 PST</pubDate>
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	<p>This is the story of how a mathematical problem was discovered. Although it was never solved, it gave great joy to the discoverer.</p>

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<author>Jan Nordgreen</author>


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<title>Developing a Healthy Scepticism About Technology in Mathematics Teaching</title>
<link>http://scholarship.claremont.edu/jhm/vol3/iss1/11</link>
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<pubDate>Wed, 30 Jan 2013 23:11:00 PST</pubDate>
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	<p>A reflective account is presented of experiences which took place alongside a research project and caused a change in approach to be more sceptical about implementation of learning technology. A critical evaluation is given of a previous e-assessment research project, undertaken from a position of naive enthusiasm for learning technology. Experiences of teaching classes and designing assessment tasks lead to doubts regarding the extent to which the previous project encouraged deep learning and contributed to graduate skills development. Investigations of the benefits of another technology – in-class response systems – lead to revelations about learning technology: its enthusiastic introduction in isolation cannot be expected to produce educational benefit; instead it must address some pedagogic need and should be evaluated against this. Overall, these experiences contribute to a shift away from a naive enthusiasm to an approach based on careful consideration of educational need before technology implementation.</p>

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<author>Peter J. Rowlett</author>


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<title>Wandering About: Analogy, Ambiguity and Humanistic Mathematics</title>
<link>http://scholarship.claremont.edu/jhm/vol3/iss1/10</link>
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<pubDate>Wed, 30 Jan 2013 23:10:59 PST</pubDate>
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	<p>This article concerns the relationship between mathematics and language, emphasizing the role of analogy both as an expression of a mathematical property and as a source of productive ambiguity in mathematics. An historical discussion is given of the interplay between the notions of logos, litotes, and limit that has implications for our understanding and teaching of Dedekind cuts and, more generally, for a humanistic notion of the role of mathematics within liberal education.</p>

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<author>William M. Priestley</author>


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<title>How to Cook Up a Math Poem in n Easy Steps</title>
<link>http://scholarship.claremont.edu/jhm/vol3/iss1/9</link>
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<pubDate>Wed, 30 Jan 2013 23:10:58 PST</pubDate>
<description>
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	<p>A mathematical poem attempts to distill a mathematical concept and present it in a literary or visually compelling way. This paper presents an outline of my own personal method of composing such poetry. The outline is elucidated via an extended meditation on the composition of one particular poem.</p>

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<author>Caleb Emmons</author>


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<title>Incorporating Pólya’s Problem Solving Method in Remedial Math</title>
<link>http://scholarship.claremont.edu/jhm/vol3/iss1/8</link>
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<pubDate>Wed, 30 Jan 2013 23:10:57 PST</pubDate>
<description>
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	<p>György Pólya’s problem solving method has influenced generations of mathematicians and non-mathematicians alike. Though almost all math teachers have come across Pólya’s problem solving method, his ideas are not regularly implemented in the classroom. Few studies have examined the effectiveness of his approach in teaching remedial math. In this article we revisit this once well-known teaching method and show how it can be used in basic skills math classes to ease student fears of math, and potentially change their common misconceptions of the subject.</p>

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<author>Shenglan Yuan</author>


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<title>On Contemplation in Mathematics</title>
<link>http://scholarship.claremont.edu/jhm/vol3/iss1/7</link>
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<pubDate>Wed, 30 Jan 2013 23:10:56 PST</pubDate>
<description>
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	<p>In a section about research, we make the case that intentional, structured reflection on the mathematical research process, by mathematical researchers themselves, would result in better mathematicians doing better mathematics. As supporting evidence, we describe the <em>Flavors and Seasons</em> project. In a section about teaching, we describe the contemplative education movement and share personal experiences using meditation in the math classroom. We conclude with an explicit proposal for elucidating the experiential context of mathematics, in both research and teaching environments.</p>

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<author>Frank Lucas Wolcott</author>


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<title>Teaching the Complex Numbers: What History and Philosophy of Mathematics Suggest</title>
<link>http://scholarship.claremont.edu/jhm/vol3/iss1/6</link>
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<pubDate>Wed, 30 Jan 2013 23:10:55 PST</pubDate>
<description>
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	<p>The narrative about the nineteenth century favored by many philosophers of mathematics strongly influenced by either logic or algebra, is that geometric intuition led real and complex analysis astray until Cauchy and Kronecker in one sense and Dedekind in another guided mathematicians out of the labyrinth through the arithmetization of analysis. Yet the use of geometry in most cases in nineteenth century mathematics was <em>not</em> misleading and was often key to important developments. Thus the geometrization of complex numbers was essential to their acceptance and to the development of complex analysis; geometry provided the canonical examples that led to the formulation of group theory; and geometry, transformed by Riemann, lay at the heart of topology, which in turn transformed much of modern mathematics. Using complex numbers as my case study, I argue that the best way to teach students mathematics is through a repertoire of modes of representation, which is also the best way to make mathematical discoveries.</p>

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<author>Emily R. Grosholz</author>


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<title>Humanistic Mathematics Network Newsletter: A Bibliographic Report</title>
<link>http://scholarship.claremont.edu/jhm/vol3/iss1/5</link>
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<pubDate>Wed, 30 Jan 2013 23:10:54 PST</pubDate>
<description>
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	<p>The <em>Humanistic Mathematics Network Newsletter</em> (HMNN) was founded by Alvin White in the summer of 1987 to address a difficult question about mathematics instruction: How can we teach mathematics humanistically? The <em>Newsletter</em> had six issues, before it was renamed <em>The Humanistic Mathematics Network Journal</em> (HMNJ). In this report, we provide an introduction to and brief comments on each of the articles that appeared in the six issues of <em>HMNN</em>. We hope that this report will serve as a guide that can help readers preview the variety of articles published in <em>HMNN</em> and choose the ones they would like to read.</p>

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<author>Claire Skrivanos et al.</author>


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<title>Changing the Order of Mathematics Test Items: Helping or Hindering Student Performance?</title>
<link>http://scholarship.claremont.edu/jhm/vol3/iss1/4</link>
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<pubDate>Wed, 30 Jan 2013 23:10:54 PST</pubDate>
<description>
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	<p>This paper recounts an experiment by a mathematics professor who primarily teaches mathematics majors. The main question explored is whether the ordering of the questions makes a difference as to how students perform in a test. More specifically we focus here on the following research questions:\ (1) <em>Does arranging a math test with easy-to-hard items versus hard-to-easy items impact student performance?</em> and (2) <em>If so, does item order impact male and female mathematics majors and non-majors in unique ways?</em> We examine data collected over multiple semesters with several different classes. We find that for most of the mathematics students who were examined, the ordering of the questions on a test did not impact performance. However, female majors performed better on classroom exams when the test was arranged with the more difficult questions presented first. Readers who are interested in teaching mathematics, educational psychology, or gender issues in the classroom may find our results intriguing.</p>

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<author>Kristin T. Kennedy et al.</author>


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<title>Sloane’s Gap: Do Mathematical and Social Factors Explain the Distribution of Numbers in the OEIS?</title>
<link>http://scholarship.claremont.edu/jhm/vol3/iss1/3</link>
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<pubDate>Wed, 30 Jan 2013 23:10:53 PST</pubDate>
<description>
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	<p>The Online Encyclopedia of Integer Sequences (OEIS) is a catalog of integer sequences. We are particularly interested in the number of occurrences of N(n) of an integer n in the database. This number N(n) marks the importance of n and it varies noticeably from one number to another, and from one number to the next in a series. “Importance” can be mathematically objective (2^10 is an example of an “important” number in this sense) or as the result of a shared mathematical culture (10^9 is more important than 9^10 because we use a decimal notation). The concept of algorithmic complexity (also known as Kolmogorov or Kolmogorov-Chaitin complexity) will be used to explain the curve shape as an “objective” measure. However, the observed curve does not conform to the curve predicted by an analysis based on algorithmic complexity because of a clear gap separating the distribution into two clouds of points. We shall call this phenomenon “Sloane’s gap”.</p>

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<author>Nicolas J.-P. Gauvrit et al.</author>


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<title>Math: That Thing You Do</title>
<link>http://scholarship.claremont.edu/jhm/vol3/iss1/2</link>
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<pubDate>Wed, 30 Jan 2013 23:10:52 PST</pubDate>
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<author>Mark Huber et al.</author>


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<title>Front Matter</title>
<link>http://scholarship.claremont.edu/jhm/vol3/iss1/1</link>
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<pubDate>Wed, 30 Jan 2013 23:10:51 PST</pubDate>
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<title>The Mathematical Cultures Network Project</title>
<link>http://scholarship.claremont.edu/jhm/vol2/iss2/17</link>
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<pubDate>Tue, 31 Jul 2012 16:50:40 PDT</pubDate>
<description>
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	<p>The UK Arts and Humanities Research Council has agreed to fund a series of three meetings with associated publications on mathematical cultures. This note describes the project.</p>

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<author>Brendan P. Larvor</author>


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<title>On The Occasion Of Your Graduation</title>
<link>http://scholarship.claremont.edu/jhm/vol2/iss2/16</link>
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<pubDate>Tue, 31 Jul 2012 16:50:39 PDT</pubDate>
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	<p>A letter from an absent supervisor to a doctoral student about to graduate reveals a terrible secret.</p>

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<author>Robert Dawson</author>


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<title>Math Moment</title>
<link>http://scholarship.claremont.edu/jhm/vol2/iss2/15</link>
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<pubDate>Tue, 31 Jul 2012 16:50:37 PDT</pubDate>
<description>
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	<p>A short poem comparing Exponential and Logistic functions.</p>

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<author>Paige S. Orland</author>


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<title>Confidence Interval</title>
<link>http://scholarship.claremont.edu/jhm/vol2/iss2/14</link>
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<pubDate>Tue, 31 Jul 2012 16:50:36 PDT</pubDate>
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	<p>A poem about estimating probabilities.</p>

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<author>Ursula Whitcher</author>


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