Ohio Journal of School Mathematics: Number 62 (Fall 2010)

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Front Matter
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If Mathematics Were a Color ...
Özgün-Koca, S. Asli pp. 5-10
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Eratosthenes Meets the GPS
Cooper, Linda pp. 11-16
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Maximizing the Area of a Sector With Fixed Perimeter
Adabor, James K; Foley, Gregory D. pp. 17-22
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Writing Mathematical Nursery Rhymes
Hrina-Treharn, Terri pp. 24-26
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The Middle Path
Gerhardinger, Joseph pp. 27-34
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The Book as a Hook: Literature and Exponential Functions
Kaplan, Gail; Rice, Lynn Anne pp. 35-39
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Exploring Exponential Functions
Kaplan, Gail pp. 40-43
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The Name Game: An Integer Activity
Krach, R. Michael p. 44
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Circular Table Seating: An Application of the Fundamental Principle of Counting
Duncan, David R.; Litwiller, Bonnie H. pp. 45-47
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Those Darn Exponents: Fifty Challenging True-False Questions
Tilton, Tim p. 48
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Graphing the Grand Canyon
Kim, Taik H. pp. 49-53
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Contest Corner: Common Core Standards Emphasize Problem Solving
Flick, Michael; Kuchey, Debbie pp. 54-57
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Back Matter
pp. 58-60
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    Front Matter (Number 62, Fall 2010)
    (Ohio Council of Teachers of Mathematics, 2010)
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    If Mathematics Were a Color ...
    (Ohio Council of Teachers of Mathematics, 2010) Özgün-Koca, S. Asli
    Students' beliefs, attitudes, emotions, and values toward a subject not only influence their interests and achievement, but also their actions such as their choices of course work, major, and career. In this study, middle school, high school, and college students' affective responses and perspectives toward mathematics were observed by using metaphors. The outcomes of the use of metaphors to learn about students' affective domains not only revealed the nature of students' affective domains regarding mathematics, but also students' justifications for those affective perceptions. Therefore, another aim of this paper is to model how teachers and researchers might categorize and interpret students' responses to reflect on not only the nature of students' affective tendencies, but also the reasoning behind them.
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    Eratosthenes Meets the GPS
    (Ohio Council of Teachers of Mathematics, 2010) Cooper, Linda
    Multiple representations of a problem encourage students to make and strengthen connections across mathematics. This article presents three solution methods that students can use to estimate the Earth's circumference. All solution methods involve proportional reasoning, require physical measurements, and draw upon basic concepts of geography, notably longitude and latitude. They range from a geometric representation first proposed by ancient Eratosthenes using simple measuring devices of meter sticks and protractors (with and without use of trigonometry) to the use of modern Global Positioning System (GPS) units.
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    Maximizing the Area of a Sector With Fixed Perimeter
    (Ohio Council of Teachers of Mathematics, 2010) Adabor, James K.; Foley, Gregory D.
    Historically, many maxima and minima were found long before Newton and Leibniz developed calculus. Ivan Niven's (1981) classic Maxima and Minima Without Calculus provides a systematic and thorough account of solving extreme-value problems using elementary algebra, geometry, and trigonometry. Niven devotes a chapter to isoperimetric problems: problems that ask "for the region of largest area in a given class of regions ... of a specified perimeter" (p. 77). We use technology as a tool to solve the isoperimetric problem for the sector of a circle—an investigation inspired by a project in Farrell and Boyd (2007).
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    Writing Mathematical Nursery Rhymes
    (Ohio Council of Teachers of Mathematics, 2010) Hrina-Treharn, Terri
    Students take ownership of their learning by becoming authors and illustrators of their own work. Students employ a writing technique, copy change, which provides a framework to guide their mathematical writing. The following demonstrates how students can be engaged and thinking about mathematics while constructing their own text.
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    The Middle Path
    (Ohio Council of Teachers of Mathematics, 2010) Gerhardinger, Joseph
    Both traditional and integrated high school mathematics curricula have their strengths and weaknesses, and the author describes a middle path which is a hybrid of the two, offering the best of both systems. Each branch of math is studied in each year, but all the algebra is grouped together, then the geometry, then probability and statistics. The author and fellow teachers wrote their school's own electronic texts. Designed for classroom interactive whiteboards, the texts are available to students electronically and online. Issues in writing, implementing, and evaluating the texts are discussed.
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    The Book as a Hook: Literature and Exponential Functions
    (Ohio Council of Teachers of Mathematics, 2010) Kaplan, Gail; Rice, Lynn Anne
    Playing with rice provides a concrete representation of exponential functions. The math-literature connection provides a "hook" to generate interest in exponential functions. Subsequent investigations provide the opportunity to analyze and understand how the functions can be used to represent real world situations. Students create their own story containing a situation whose resolution requires exponentials. The classroom comes alive as students actively pursue mathematical understanding.
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    Exploring Exponential Functions
    (Ohio Council of Teachers of Mathematics, 2010) Kaplan, Gail
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    The Name Game: An Integer Activity
    (Ohio Council of Teachers of Mathematics, 2010) Krach, R. Michael
  • Item
    Circular Table Seating: An Application of the Fundamental Principle of Counting
    (Ohio Council of Teachers of Mathematics, 2010) Duncan, David R.; Litwiller, Bonnie H.
  • Item
    Those Darn Exponents: Fifty Challenging True-False Questions
    (Ohio Council of Teachers of Mathematics, 2010) Tilton, Tim
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    Graphing the Grand Canyon
    (Ohio Council of Teachers of Mathematics, 2010) Kim, Taik H.
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    Contest Corner: Common Core Standards Emphasize Problem Solving
    (Ohio Council of Teachers of Mathematics, 2010) Flick, Michael; Kuchey, Debbie
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    Back Matter (Number 62, Fall 2010)
    (Ohio Council of Teachers of Mathematics, 2010)