Ohio Journal of School Mathematics: Number 65 (Spring 2012)

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https://kb.osu.edu/handle/1811/78126

Front Matter
pp. 1-5
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Multiple Representations Help Teachers and Students Understand a Geometry Problem
Uzan, Erol; Harkness, Shelly Sheats pp. 6-13
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The Interplay Between Theoretical and Experimental Probability: Beyond "Sample Size Matters"
Meagher, Michael pp. 14-20
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Making the Laws of Sines and Cosines a Splash for Students
Bolognese, Chris pp. 21-23
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Developing Real-World Math through Literacy
Hoover, Stephanie pp. 24-29
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Learning Measurement with Interactive Stations
Lee, Hea-Jin; Link, Rebecca pp. 30-39
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Helping Children Understand Measurement Using a Ruler
Christie, Gary pp. 40-44
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Assessment and Grading in a Differentiated Mathematics Classroom
Peshek, Sarah pp. 45-50
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Benford’s Law - Using Logarithms to Detect Fraud
Minor, Darrell pp. 52-57
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The History of the Abacus
Samoly, Kevin pp. 58-66
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A New 20 Minute Mathematics Contest: Practice For Competition
Flick, Michael; Kuchey, Debbie pp. 67-69
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Back Matter
pp. 70-72
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Now showing 1 - 12 of 12

Front Matter (Number 65, Spring 2012)
(Ohio Council of Teachers of Mathematics, 2012)
Multiple Representations Help Teachers and Students Understand a Geometry Problem
(Ohio Council of Teachers of Mathematics, 2012) Uzan, Erol; Harkness, Shelly Sheats
This narrative account begins in a high school classroom as we describe how students were mostly unengaged with a "Problem of the Week." As observers in this setting, we sat in the back of the classroom and attempted to solve the problem: Choose any three vertices of a cube at random.What is the probability that any three vertices will form a right triangle? Because of our different answers to the problem and the struggles we experienced as we attempted to visualize a cube with triangles on the faces and in the interior space we later created concrete and virtual manipulatives. Additionally, we posed this problem in a mathematics methods course with preservice high school teachers and then discussed the use of enactive (concrete), iconic (pictorial), and symbolic representations (Bruner, 1966). The significance of using concrete manipulatives for some mathematics problems cannot be overstated.
The Interplay Between Theoretical and Experimental Probability: Beyond "Sample Size Matters"
(Ohio Council of Teachers of Mathematics, 2012) Meagher, Michael
This article presents a series of class activities that develop an extended examination of the interplay between theoretical and experimental probability. In some cases an experiment can be used to confi rm a theory and in other instances it can be used to develop a theory. Examples include coin-tossing, a dice game, and cup dropping with Monte Carlo approaches to probability discussed. This set of activities could be used with preservice teachers to improve their content knowledge in the area of probability as well as provide both a model of inquiry-based approaches and a forum for discussing pedagogical techniques involving hands-on activities. They could also be used in middle school classrooms to help students experience the power of probability experiments in examining real-life phenomena.
Making the Laws of Sines and Cosines a Splash for Students
(Ohio Council of Teachers of Mathematics, 2012) Bolognese, Chris
The Laws of Sines and Cosines are tremendously powerful in solving application problems, but traditionally the use of these methods is reduced to solving static word problems out of a textbook. This article describes a way for students to apply these trigonometric methods to a very novel and motivating context of hitting their mathematics teacher with water balloon trajectories.
Developing Real-World Math through Literacy
(Ohio Council of Teachers of Mathematics, 2012) Hoover, Stephanie
The article depicts two mathematical lessons in a first grade classroom that incorporate literacy throughout to increase students’ knowledge and understanding of the mathematical concepts. The first lesson uses the book, The Doorbell Rang (1987) to introduce sharing and dividing, and the second lesson incorporate the book, The Penny Pot (1998) to reinforce counting money. In both lessons, the students explore mathematics through read-alouds, problem solving, classroom discussions, and manipulative use. The article presents the two different lessons in detail and includes classroom discussions to illustrate the students’ thinking process, understanding, and discovery of the two different mathematical concepts being taught in the classroom.
Learning Measurement with Interactive Stations
(Ohio Council of Teachers of Mathematics, 2012) Lee, Hea-Jin; Link, Rebecca
This paper shares seven interactive stations teaching measurement concepts and skills: Measuring Weights; Comparing Volumes of Cylinders; Comparing Volumes of Various Bottles; Measuring Areas of Irregular Shapes; Measuring Perimeters of Irregular Shapes; Comparing Volumes of Prisms and Pyramids; and Comparing Volume of Cone to Sphere. These stations engage students in measuring real life objects, using different measurement units and tools, and working with embedded problems. Authors describe the objective, main mathematical concepts, and possible extension ideas for each station.
Helping Children Understand Measurement Using a Ruler
(Ohio Council of Teachers of Mathematics, 2012) Christie, Gary
Two teachers incorporate research findings into helping a first grade class build the conceptual foundation of the ruler. Assessing students to identify common misconceptions and errors reported in the literature, the teachers design a lesson in which students effectively create their own rulers from square inch cardstock. By creating their rulers, students find similarities between their manufactured rulers and the classroom set. As a result students seem to better understand the "meaning" of the spaces between the numbers on a ruler, and use the ruler more accurately to measure.
Assessment and Grading in a Differentiated Mathematics Classroom
(Ohio Council of Teachers of Mathematics, 2012) Peshek, Sarah
Differentiated instruction provides a way for teachers to meet the needs of all students in a mathematics classroom. Some teachers, however, may be apprehensive about its implementation because of concerns related to assessment of student learning within this framework. This article explains how summative and formative assessments are both necessary and reasonable to perform within the differentiated mathematics classroom. The principles suggested are appropriate for any mathematics classroom, but a specific example is discussed in the area of fractions.
Benford’s Law - Using Logarithms to Detect Fraud
(Ohio Council of Teachers of Mathematics, 2012) Minor, Darrell
In 1881, Simon Newcomb made the simple observation that the beginning pages of books were more worn than the later pages of those books. From that routine observation, Newcomb and others developed a mathematical principle involving logarithms that can be observed in a wide variety of data, from birth and death rates, to lengths of rivers, to financial transactions. In this article, the author provides an example of how this principle can be used to detect fraud in a company’s accounts payable department. Suggestions for classroom activities are provided for additional exploration.
The History of the Abacus
(Ohio Council of Teachers of Mathematics, 2012) Samoly, Kevin
The abacus is a counting tool that has been used for thousands of years. Throughout history, calculating larger numbers has been problematic, especially for the common uneducated merchant. Out of this necessity, the idea of the abacus was born. Solving problems on an abacus is a quick mechanical process rivaling that of modern-day four-function calculators. After first addressing basic counting procedures and memorizing a few simple rules, students can use the abacus to solve a variety of problems. The abacus is a timeless computing tool that is still applicable in today’s classrooms.
Back Matter (Number 65, Spring 2012)
(Ohio Council of Teachers of Mathematics, 2012)
A New 20 Minute Mathematics Contest: Practice For Competition
(Ohio Council of Teachers of Mathematics, 2012) Flick, Michael; Kuchey, Debbie

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