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Posts

July 28, 2014

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4:13 AM | Parallelogram Proof- Open Middle Problem
Is this figure a parallelogram?  Explain how you know.   Draw a diagonal of your parallelogram.  Using  2 Transformations (Rotations, Reflections or Translations), explain how triangle 1 is congruent to triangle 2.Filed under: Geometry, Open Middle
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3:37 AM | Meeting the Community
I am just home from Twitter Math Camp (yes, that’s a thing). I’d like to share an overview, aimed more at people from Canada who don’t know what this is than for the people who were actually there. Twitter Math Camp bills itself as “Professional Development By Teachers, For Teachers.” Last week, 150 teachers, mostly […]
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3:18 AM | stop or i’ll say stop again
http://kitchentablemath.blogspot.com/2014/07/elizabeth-green-is-funded-by-bill-gates.html
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3:18 AM | This Month: Wedding, Honeymoon, and the gentle drift back to reality
So it’s been a solid month since I posted here, and a brief synopsis of what I’ve been doing should be in order. The school year ended very abruptly as our school community had to figure out how to deal with the loss of our amazing art teacher the same week that all the final […]
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3:00 AM | Monday Puzzle: Nigeria’s Sex Ratio
Today’s problem comes from a recent issue of The Economist. The article is Fertility and son-preference in Nigeria and it refers to a recent study about sex preference. Families in Nigeria have a preference for boys over girls. If they have a girl or two girls, they will try to have another child to get […]
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2:57 AM | A Job Ad OR Mathematics in Context at Pitzer College
No summary available for this post.
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2:57 AM | JHM Contents Word Puzzle
This is a word-search puzzle based on the contents page of the previous (Volume 4 Issue 1-January 2014) issue of the Journal of Humanistic Mathematics.
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2:57 AM | The Physicist's Basement
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2:57 AM | The Math of Achilles
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2:57 AM | Computational Compulsions
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2:57 AM | Jeffery's Equation
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2:57 AM | The Discipline of History and the “Modern Consensus in the Historiography of Mathematics”
Teachers and students of mathematics often view history of mathematics as just mathematics as they know it, but in another form. This view is based on a misunderstanding of the nature of history of mathematics and the kind of knowledge it attempts to acquire. Unfortunately, it can also lead to a deep sense of disappointment with the history of mathematics itself, and, ultimately, a misunderstanding of the historical nature of mathematics. This kind of misunderstanding and the disappointment […]
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2:57 AM | A Critique of the Modern Consensus in the Historiography of Mathematics
The history of mathematics is nowadays practiced primarily by professional historians rather than mathematicians, as was the norm a few decades ago. There is a strong consensus among these historians that the old-fashioned style of history is “obsolete,” and that “the gains in historical understanding are incomparably greater” in the more “historically sensitive” works of today. I maintain that this self-congratulatory attitude is ill-founded, and that the alleged superiority of […]
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2:57 AM | Nine Mathematical Ways of Watching a Baseball Game
Whatever its other flaws or merits as a game, baseball gives us plenty of time to think. (How else to spend the 2 hours, 50 minutes when nothing in particular is happening?) In the long gaps between pitches, my own thoughts veer towards mathematics. Are statistics really changing the game? Can any sense emerge from baseball's symmetries and odd patterns? Is it now a sport of science, or as ever one of superstition? And the aesthetic question that arises from all of this:\ In a human pursuit […]
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2:57 AM | How Do I Love Thee? Let Me Count the Ways for Syllabic Variation in Certain Poetic Forms
The Dekaaz poetic form, similar to haiku with its constrained syllable counts per line, invites a connection between poetry and mathematics. Determining the number of possible Dekaaz variations leads to some interesting counting observations. We discuss two different ways to count the number of possible Dekaaz variations, one using a binary framework and the other approaching the count as an occupancy problem. The counting methods described are generalized to also count variations of other […]
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2:57 AM | Fields in Math and Farming
A young woman’s search for a a contemplative, insightful experience leads her from farming to mathematics.
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2:57 AM | Being Reasonable: Using Brainteasers to Develop Reasoning Ability in Humanistic Mathematics Courses
Developing reasoning ability is often cited as one of the principal justifications of a mathematics requirement for liberal arts undergraduates. Humanistic math courses have become recognized as a paradigm for liberal arts mathematics, but such courses may not provide the opportunity to develop reasoning ability. The author describes his procedure for using brainteasers to promote reasoning in a humanistic math course for liberal arts undergraduates.
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2:57 AM | Joining ``the mathematician's delirium to the poet's logic'': Mathematical Literature and Literary Mathematics
This paper describes our team-taught interdisciplinary mathematics and literature course, Mathematical Literature and Literary Mathematics, which invites students to consider Raymond Queneau's challenge: "Why shouldn't one demand a certain effort on the reader's part? Everything is always explained to him. He must eventually tire of being treated with such contempt.'' We study works by Berge, Borges, Calvino, Perec, Queneau, Robbe-Grillet and Stoppard, among others. From a literary critical […]
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2:57 AM | A Subjective Comparison Between a Historical and a Contemporary Textbook on Geometry
In order to investigate how a 19th century mathematical textbook (in contrast to a contemporary one) would be experienced by a novice reader, we embarked on the following project: In the summer of 2013, a student with no previous training in college-level mathematics (the first author) set out to learn projective geometry from Pasch's 1882 textbook Lectures on Modern Geometry. Afterwards, he studied the same material from Coxeter's 1994 popular undergraduate textbook Projective Geometry. We […]
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2:57 AM | Religion and Language as Cultural Carriers and Barriers in Mathematics Education--Revisited
Here we revisit a paper which examined two theses regarding the roles of religion and language of instruction in mathematics education. The first thesis states that if values of mathematics education are incompatible with the value system of the mother culture, then mathematics will be ``appended'' to the culture as a ``technology'' rather than assimilated as a ``mode of thinking''. The second thesis states that as soon as mathematics is applied in problems and situations, the language of […]
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2:57 AM | Loxodromic Spirals in M. C. Escher's Sphere Surface
Loxodromic spirals are the analogues in spherical geometry of logarithmic spirals on the plane. M.C. Escher's 1958 woodcut Sphere Surface is an image of black and white fish arranged along eight spiral paths on the surface of a sphere. By connecting the plane and spherical models of the complex numbers, we show that Sphere Surface is the conformal image on the sphere of a tessellation of fish on the plane, and that the spirals running through the fish are indeed loxodromic spirals to a high […]
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2:57 AM | Some Effects of the Human Genome Project on the Erdős Collaboration Graph
The Human Genome Project introduced large-scale collaborations involving dozens to hundreds of scientists into biology. It also created a pressing need to solve discrete mathematics problems involving tens of thousands of elements. In this paper, we use minimal path lengths in the Erdős Collaboration Graph between prominent individual researchers as a measure of the distance between disciplines, and we show that the Human Genome Project brought laboratory biology as a whole closer to […]
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2:57 AM | Mathematical Perspectives
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2:57 AM | Front Matter
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2:43 AM | #July2014Challenge: My Exeter PD Day 1
About 10 years ago I was invited by my district to attend a week long summer institute led by the instructors of a private school on the east coast called Phillips Exeter Academy.  Each day we spent about six hours doing math problems from the curriculum that students use in these courses.  Sometimes we would work on problems alone, sometimes together, with lots of presentations as well as integration of technology.  What a fantastic week!  I attended the same institute the […]
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1:50 AM | The Change Problem and the Gap between Recreational and Serious Mathematics
In a prior post (here)I discussed the change problem: given a dollar, how many ways can you make change using pennies, nickels, dimes, and quarters (and generalize to n cents). Scouring the web I found either programs for it, the answer   (242), and answers like `is the coefficient of x^100 in ... . What I didn't find is a  formula for n cents. So I derived one using recurrences and wrote this up with some other things about the change problem, and I posted it on arXiv. (I have […]
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1:27 AM | NY Times obsesses about math again; every kid loses
NY Times obsesses about math again; every kid loses: Roger Schank: I have a confession to make. I did graduate admissions in computer science for more than 25 years. The first thing I looked for was the applicant’s math GRE score. I eliminated anyone under 96th percentile. (Also, to add to my confession. I majored in Mathematics in college.)  [source: mme rss]
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1:20 AM | Mr. Honner does it again
Patrick Honner has several blog articles about poor problems (sometimes outright mistakes) on some of the exams that New York state requires for students. Since I don’t live in NY I’m not super familiar with these exams, though Mr. Honner’s … Continue reading →
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1:09 AM | Hoeken en afstanden
voorkennishoeken bij lijnen en vlakkenafstanden in de ruimtevergelijkingen van vlakkenhoeken en vectorenOp basis van het hoofdstuk 'hoeken en afstanden' van VWO 4 wiskunde D is de HAVO-versie snel gemaat. Laat 'kruisende lijnen' en 'het uitproduct' weg en je bent er al bijna. Nog wel iets toegevoeg over 'ribben in een kubus' en 'evenwijdige vlakken in een kubus', maar uiteindelijk snel gemaakt.Het volgende hoofdstuk gaat over de normale verdeling. Ook leuk:-)
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12:36 AM | Algebra 1 plans, post TMC14
I am working pretty hard this summer in my never ending quest to make my Algebra 1 class a place where all students can learn. In 2014/2015, I will be using SBG for the second time and I will be using the second edition of the book I am writing on ck12.org. YouTube videos of my teaching will also be available online. This will also be the second year of our new Common Core Alg 1 curriculum, I don't think I did a great job teaching the 8 Mathematical Practices while I was trying the new […]
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