Ohio Journal of School Mathematics: Number 65 (Spring 2012)
http://hdl.handle.net/1811/78126
Thu, 05 Aug 2021 18:57:23 GMT2021-08-05T18:57:23ZFront Matter (Number 65, Spring 2012)
http://hdl.handle.net/1811/78215
Front Matter (Number 65, Spring 2012)
Includes Errata for 2011 Fall Issue on page 4.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/1811/782152012-01-01T00:00:00ZMultiple Representations Help Teachers and Students Understand a Geometry Problem
http://hdl.handle.net/1811/78214
Multiple Representations Help Teachers and Students Understand a Geometry Problem
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.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/1811/782142012-01-01T00:00:00ZUzan, ErolHarkness, Shelly SheatsThe Interplay Between Theoretical and Experimental Probability: Beyond "Sample Size Matters"
http://hdl.handle.net/1811/78213
The Interplay Between Theoretical and Experimental Probability: Beyond "Sample Size Matters"
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.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/1811/782132012-01-01T00:00:00ZMeagher, MichaelMaking the Laws of Sines and Cosines a Splash for Students
http://hdl.handle.net/1811/78212
Making the Laws of Sines and Cosines a Splash for Students
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.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/1811/782122012-01-01T00:00:00ZBolognese, ChrisDeveloping Real-World Math through Literacy
http://hdl.handle.net/1811/78211
Developing Real-World Math through Literacy
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.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/1811/782112012-01-01T00:00:00ZHoover, StephanieLearning Measurement with Interactive Stations
http://hdl.handle.net/1811/78210
Learning Measurement with Interactive Stations
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.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/1811/782102012-01-01T00:00:00ZLee, Hea-JinLink, RebeccaHelping Children Understand Measurement Using a Ruler
http://hdl.handle.net/1811/78209
Helping Children Understand Measurement Using a Ruler
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.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/1811/782092012-01-01T00:00:00ZChristie, GaryAssessment and Grading in a Differentiated Mathematics Classroom
http://hdl.handle.net/1811/78208
Assessment and Grading in a Differentiated Mathematics Classroom
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.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/1811/782082012-01-01T00:00:00ZPeshek, SarahBenford’s Law - Using Logarithms to Detect Fraud
http://hdl.handle.net/1811/78207
Benford’s Law - Using Logarithms to Detect Fraud
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.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/1811/782072012-01-01T00:00:00ZMinor, DarrellThe History of the Abacus
http://hdl.handle.net/1811/78206
The History of the Abacus
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.
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/1811/782062012-01-01T00:00:00ZSamoly, KevinBack Matter (Number 65, Spring 2012)
http://hdl.handle.net/1811/78205
Back Matter (Number 65, Spring 2012)
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/1811/782052012-01-01T00:00:00ZA New 20 Minute Mathematics Contest: Practice For Competition
http://hdl.handle.net/1811/78204
A New 20 Minute Mathematics Contest: Practice For Competition
Flick, Michael; Kuchey, Debbie
Sun, 01 Jan 2012 00:00:00 GMThttp://hdl.handle.net/1811/782042012-01-01T00:00:00ZFlick, MichaelKuchey, Debbie