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Garrett Eastman

Mondrian Meets Euclid: An Eccentric Victorian Mathematician's Masterwork of Art and Sci... - 6 views

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    Profile of a reissue of Elements of Euclid with colored designs and graphics by Oliver Byrne, 19th century engineer and mathematician
Garrett Eastman

Interlocked Coins Form Complex Geometric Sculptures - 3 views

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    Several photos of Robert Wexler's work, also featured in the recent Money issue of the New Yorker.
Garrett Eastman

Core foundations of abstract geometry - 4 views

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    Abstract: "Human adults from diverse cultures share intuitions about the points, lines, and figures of Euclidean geometry. Do children develop these intuitions by drawing on phylogenetically ancient and developmentally precocious geometric representations that guide their navigation and their analysis of object shape? In what way might these early-arising representations support later-developing Euclidean intuitions? To approach these questions, we investigated the relations among young children's use of geometry in tasks assessing: navigation; visual form analysis; and the interpretation of symbolic, purely geometric maps. Children's navigation depended on the distance and directional relations of the surface layout and predicted their use of a symbolic map with targets designated by surface distances. In contrast, children's analysis of visual forms depended on the size-invariant shape relations of objects and predicted their use of the same map but with targets designated by corner angles. Even though the two map tasks used identical instructions and map displays, children's performance on these tasks showed no evidence of integrated representations of distance and angle. Instead, young children flexibly recruited geometric representations of either navigable layouts or objects to interpret the same spatial symbols. These findings reveal a link between the early-arising geometric representations that humans share with diverse animals and the flexible geometric intuitions that give rise to human knowledge at its highest reaches. Although young children do not appear to integrate core geometric representations, children's use of the abstract geometry in spatial symbols such as maps may provide the earliest clues to the later construction of Euclidean geometry. "
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Garrett Eastman

King of Infinite Space: Euclid and His Elements - 1 views

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    by David Berlinski, published January 2013. "In The King of Infinite Space, renowned mathematics writer David Berlinski provides a concise homage to this elusive mathematician and his staggering achievements. Berlinski shows that, for centuries, scientists and thinkers from Copernicus to Newton to Einstein have relied on Euclid's axiomatic system, a method of proof still taught in classrooms around the world. Euclid's use of elemental logic-and the mathematical statements he and others built from it-have dramatically expanded the frontiers of human knowledge. The King of Infinite Space presents a rich, accessible treatment of Euclid and his beautifully simple geometric system, which continues to shape the way we see the world."
Garrett Eastman

Measurement - Paul Lockhart | Harvard University Press - 5 views

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    "Measurement explains how math should be done. With plain English and pictures, [Lockhart] makes complex ideas about shape and motion intuitive and graspable, and offers a solution to math phobia by introducing us to math as an artful way of thinking and living."
Garrett Eastman

Measurement: Exploring the Whimsical World of Mathematical Reality through Playful Patt... - 4 views

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    A review of Paul Lockhart's new book with a focus on mathematical reasoning and geometry, with a video of the author.
Garrett Eastman

Archives | BetterExplained - 9 views

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    This site features a math category, math concepts explained informed by the principle that "math is no about equations than poetry is about spelling .. .[but exist] to convey an idea."
Garrett Eastman

MISCONCEPTIONS IN GEOMETRY AND SUGGESTED SOLUTIONS FOR SEVENTH GRADE STUDENTS - 5 views

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    Abstract: "The principal aim of this study is to find the weaknesses of secondary school students at geometry questions of measures ,
    angles and shapes , transformations and construction and 3-D shapes. The year 7 curriculum contains 4 geometry topics out
    of 17 mathematics topics. In addition to this , this study aims to find out the mistakes, 28 , 7th grade students made in the last
    4 exams including two midterms and two final exams.To collect data, students were tested on two midterms and two final
    exams using open-ended questions on geometry to analyze their problem solving skills and to test how much they acquired
    during the year.Frequency tables were used in data analysis.To fulfill this aim in the first midterm exam the subject measures
    were tested.In the first final exam which followed the first midterm exam in addition to measures and angles shapes skills
    were also tested. Following these tests , in the second midterm we tested the students on transformation and construction. A
    descriptive methodology and student interview were used in the study to analyze and interpret the results. The results from
    this study revealed that 7th grade secondary school students have a number of misconceptions, lack of background
    knowledge, reasoning and basic operation mistakes at the topics mentioned above."
Garrett Eastman

Middle East Peace Potential through Dynamics in Spherical Geometry - 2 views

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    "This is an exploration of the hypothesis that unique belief systems depend for their coherence on distinctive patterns typically embodied in geometrical symbols in two dimensions. On the basis of that assumption, the case tentatively explored here is that of the "incommensurability" of the 5-fold Star of Islam and the 6-fold Star of David of Judaism -- both symbols appearing on flags of the nations having those distinct faiths. ... The approach taken here explores the possibility that the "pieces" only fit together on a three-dimensional surface, namely a sphere. It is the spherical geometry that then merits consideration, together with the challenge of how to get from any "mis-fitting" two-dimensional layout to a three-dimensional form. Of course, two-dimensional layouts are far more readily comprehensible. Hence the focus on them. However the three-dimensional layout has the potential of rendering comprehensible a far more elegant layout which may well exemplify intuitions characteristic of the faiths so dramatically opposed.

    The approach follows from various earlier explorations of the potential of mathematics to offer a new perspectives on these issues" ....
Garrett Eastman

Through the History Glass - 3 views

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    by John Yoo, Yuba Community College, a series of columns on math history, written for the CMC3 newsletter
Garrett Eastman

The Views of High School Geometry Teachers regarding the Effect of Technology on Studen... - 9 views

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    From the abstract: "The purpose of this study was to find out from current high school math teachers, of geometry specifically, what their views of technology are. The goal of the study was to ask these teachers which technologies they use and whether they believe technology has beneficial effects on student learning. Data was collected for the survey by asking teachers to take brief electronic surveys and conduct in-person interviews. All questions in both the survey and interviews were focused on the effects of technology that they see in their classrooms. The scope of the participants was restricted to Columbus, Ohio, and thus, generalizations for any classroom or any school building cannot be made. However, this study did find a consensus among the participants as to which technologies they felt were the most beneficial in their classrooms, as well as those that might not be needed at all in a classroom. The three technologies that these teachers claimed to be the most beneficial were SMART boards, TI-nspire calculators and Geometer's Sketchpad/GeoGebra. Again, this study cannot make solid conclusions, but it is safe to say that this study gives insight into teachers' viewpoints, which, in a sense, are more important than those of outside researchers. The teachers agreed on a few technologies that are the most beneficial and thus future studies should focus on really studying the effects of these technologies as well as focus on getting a wider range of teachers' opinions on this topic."
Garrett Eastman

Math for the Frightened: Facing Scary Symbols and Everything Else That Freaks You Out a... - 5 views

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    "Some people love math, some hate it, and some are scared of it. Math for the Frightened provides a trauma-free entry into the world of numeracy, written by someone who is on your side. It even gives away the big secret: math really is useful"
Garrett Eastman

Icons of Mathematics - 2 views

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    "This book explores 20 geometric diagrams that play crucial roles in visualizing mathematical proofs."
Garrett Eastman

Exploring quadrilaterals in a small group computing environment - 2 views

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    From the abstract (full text requires subscription or purchase): "Though cooperative learning has been a topic of considerable interest in educational research, there has been little study specific to learning in the mathematics content area of geometry. This paper seeks to address that gap through a design experiment featuring a novel small-group computing environment for supporting student learning about quadrilaterals. In this design, each student controls a unique point in a shared geometric space, and those points are linked such that a group of four students collectively forms a quadrilateral. We first present results from pre- and post-measures to show how the students learned from the activities and developed in terms of geometric reasoning. We then present three episodes, elaborated with the notion of appropriation, to explain how students took up ways of using the technological tools and of talking about geometric concepts from one another in the interactive environment. Our study found that students achieved learning gains in this novel environment, that the environment provided rich opportunities for peer interaction around geometric objects, and that student learning opportunities and interactions were characterized by processes of appropriating ways of talking about and using software features."
Garrett Eastman

Processing mathematics through digital technologies: The primary years - 4 views

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    "This book provides insights into how mathematical understanding emerged for primary-aged children (5-13 years) when they investigated mathematical tasks through digital media."
Garrett Eastman

Kill Math - 12 views

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    "Kill Math is my umbrella project for techniques that enable people to model and solve meaningful problems of quantity using concrete representations and intuition-guided exploration. In the long term, I hope to develop a widely-usable, insight-generating alternative to symbolic math."
Garrett Eastman

Annalisa Crannell Combines "Math and Art" at MAA Distinguished Lecture - 5 views

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    Lecture from 2010 ""Mathematics and Art: The Good, the Bad, and the Pretty," "use of mathematics to create realistic art"
Garrett Eastman

LOVING GEOMETRIC GARLANDS - 18 views

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    Do-it-yourself designs
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