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Spherical Geometry, Linda Moore
Spherical Geometry, Linda Moore
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
Spherical geometry was studied in ancient times as a subset of Euclidian three-dimensional space. It was a logical outcome as the earth is a sphere. The word geometry literally means the measure of the earth. However, the undefined terms, axioms and postulates of Euclidian geometry take on a new meaning when studied on a sphere.
Project Fulcrum 2006-2007 Handbook
Project Fulcrum 2006-2007 Handbook
Project Fulcrum: Materials
About Project Fulcrum LogisticsPFAssessment and ResearchFor Scientists: Working in K-12 SchoolsWorking in the Lincoln Public SchoolsMisc Information Resources
Pf 2006-2007 Case Study Exercises
Database Handbook 2006-2007
Project Fulcrum: Materials
INTRODUCTION MAIN WEBSITE OVERVIEW LOGGING IN INFO REPORTING RESOURCES
Cooperative Learning Groups In The Eighth Grade Math Classroom, Dean J. Davis
Cooperative Learning Groups In The Eighth Grade Math Classroom, Dean J. Davis
Action Research Projects
In this action research study of my classroom of 8th grade mathematics students, I investigated whether cooperative learning would lead to a better understanding of the mathematical concepts and thus more success for the students. I used my three eighth grade classes with two using cooperative groups and the third not. I discovered that the students who wanted to work in cooperative groups were more successful than they had been. I also discovered that the grouping itself has a great effect on how the group works together. The wrong grouping of students can lead to disaster and many headaches for …
Using Math Vocabulary Building To Increase Problem Solving Abilities In A 5th Grade Classroom, Julane Amen
Using Math Vocabulary Building To Increase Problem Solving Abilities In A 5th Grade Classroom, Julane Amen
Action Research Projects
In this action research study of my 5th grade mathematics class, I investigated how students’ understanding of math vocabulary impacts their understanding of the curriculum. I discovered math vocabulary plays an important role in a student’s ability to understand daily lessons, complete homework, discuss ideas in groups, take tests and be successful on achievement tests. A student’s ability to understand the words around him (or her) in math class seem very related to his or her ability to solve word problems. Word problems are what our national assessments are all about. I also discovered that direct instruction and support of …
How To Better Prepare For Assessment And Create A More Technologically Advanced Classroom, Kyle Lannin Poore
How To Better Prepare For Assessment And Create A More Technologically Advanced Classroom, Kyle Lannin Poore
Action Research Projects
In this action research study of my classroom of 8th grade mathematics, I investigated how to better prepare these students for quizzes and how technology can be used in the classroom. I discovered that there are many different ways to challenge students and help them prepare for assessments. There are also many ways to use technology in the classroom if one has the opportunities to use some of the tools, such as Power Point and Algebra Tiles. As a result of this research, I plan to increase the scores on state standards while also allowing the students to enjoy technology …
The Role Of Habits-Of-Mind Problems, Student Self-Assessments And Self Reflections In A 6th Grade Math Class, Garold J. Furse
The Role Of Habits-Of-Mind Problems, Student Self-Assessments And Self Reflections In A 6th Grade Math Class, Garold J. Furse
Departament of Teaching, Learning, and Teacher Education: Master's of Arts in Teaching, Summative Projects
The focus of my action research is to study the impact of student self-assessment and reflection on my 6th grade math students’ abilities to solve deep-thinking math problems, herein referred to as habits-of-mind, or HOM, problems. I investigated the way informal self-assessments and self-reflections impact student learning and motivation. I discovered that students are seldom stimulated to think about their own learning. When they are encouraged to do so, student self-assessments give students ownership of their own learning and provide them with a means for evaluating their growth. Students’ assessments of their work also gives teachers a meaningful indication of …
Discourse And Cooperative Learning In The Math Classroom, Karen Hillen
Discourse And Cooperative Learning In The Math Classroom, Karen Hillen
Departament of Teaching, Learning, and Teacher Education: Master's of Arts in Teaching, Summative Projects
In this action research study of my 6th grade math classroom I investigated the effects of increased student discourse and cooperative learning on the students’ ability to explain and understand math concepts and problem solving, as well as its effects on their use of vocabulary and written explanations. I also investigated how it affected students’ attitudes. I discovered that increased student discourse and cooperative learning resulted in positive changes in students’ attitudes about their ability to explain and understand math, as well as their actual ability to explain and understand math concepts. Evidence in regard to use of vocabulary and …
Student Problem Solving, Michael A. Cobelens
Student Problem Solving, Michael A. Cobelens
Departament of Teaching, Learning, and Teacher Education: Master's of Arts in Teaching, Summative Projects
The purpose of this study is to determine if students solve math problems using addition, subtraction, multiplication, and division consistently and whether students transfer these skills to other mathematical situations and solutions. In this action research study, a classroom of 6th grade mathematics students was used to investigate how students solve word problems and how they determine which mathematical approach to use to solve a problem. It was discovered that many of the students read and re-read a question before they try to find an answer. Most students will check their answer to determine if it is correct and makes …
Improving Mathematics Problem Solving Through Written Explanations, Janet Schlattmann
Improving Mathematics Problem Solving Through Written Explanations, Janet Schlattmann
Departament of Teaching, Learning, and Teacher Education: Master's of Arts in Teaching, Summative Projects
In this action research study of two classrooms of 7th grade mathematics, I investigated how requiring written explanations of problem solving would affect students ability to problem solve, their ability to write good explanations, and how it would affect their attitudes toward mathematics and problem solving. I studied a regular 7th grade mathematics class and a lower ability 7th grade class to see if there would be any difference in what was gained by each group or any group. I discovered that there were no large gains made in the short time period of my action research. Some gains were …
Symmetry Of Scale Expository Paper, Darla R. Kelberlau-Berks
Symmetry Of Scale Expository Paper, Darla R. Kelberlau-Berks
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
A checkerboard, a beehive, a brick wall and a mud flat dried in the sun all have something in common. They are all examples of tilings or tessellations. Although you may think of mosaics or other pieces of artwork when you hear these words, in actuality you should also think of mathematics and science. I will describe in more detail the mathematics involved with tessellations and tilings, and discuss specific tilings such as the Pinwheel Tiling and the Penrose Tiles.
Heron, Brahmagupta, Pythagoras, And The Law Of Cosines, Kristin K. Johnson
Heron, Brahmagupta, Pythagoras, And The Law Of Cosines, Kristin K. Johnson
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
The formula for the area of a triangle can be developed by making an exact copy of the triangle and rotating it 180°. Then join it to the given triangle along one side to obtain a parallelogram as shown above. To form a rectangle, cut off a small triangle along the right and join it at the other side of the parallelogram. Because the area of the rectangle is the product of base (b) and height (h), the area of the given triangle must be 1⁄2bh.
The Art Gallery Question, Vicki Sorensen
The Art Gallery Question, Vicki Sorensen
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
MAT question Suppose you have an arbitrary room in an art gallery with v corners, and you wanted to set up a security system consisting of cameras placed at some of the corners so that each point in the room can be seen by one of the cameras. How many cameras do we need? (See the example at right for a possible room with an interesting shape.)
Student Transition To College, Doug Glasshoff
Student Transition To College, Doug Glasshoff
Action Research Projects
In this action research study of recent graduates from my district, I investigated their level of readiness for college-level mathematics courses. I discovered that the students have a wide variety of experiences in college. There are many factors that determine success in college mathematics courses. These factors include size of college, private or public, university or community college. Other factors include students’ choice of major, maturity level, and work ethic. As a result of this research, I plan to raise the individual expectations in my classroom. It is our duty as high school educators to prepare the students for a …
Daily Problem-Solving Warm-Ups: Harboring Mathematical Thinking In The Middle School Classroom, Diana French
Daily Problem-Solving Warm-Ups: Harboring Mathematical Thinking In The Middle School Classroom, Diana French
Action Research Projects
In this action research study of my classroom of 8th grade mathematics, I investigated the use of daily warm-ups written in problem-solving format. Data was collected to determine if use of such warm-ups would have an effect on students’ abilities to problem solve, their overall attitudes regarding problem solving and whether such an activity could also enhance their readiness each day to learn new mathematics concepts. It was also my hope that this practice would have some positive impact on maximizing the amount of time I have with my students for math instruction. I discovered that daily exposure to problem-solving …
Bad Medicine: Homework Or Headache? Responsibility And Accountability For Middle Level Mathematics Students, Shawn Mousel
Bad Medicine: Homework Or Headache? Responsibility And Accountability For Middle Level Mathematics Students, Shawn Mousel
Action Research Projects
In this action research study of my 5th grade mathematics class, I investigated the issue of homework and its relationship with students and parents. I made some interesting observations and discovered that the majority of students and parents felt that the math homework that was given was fairly easy, yet issues of incomplete assignments and failing homework quizzes were notorious for some individuals. Comments were also made to make homework even easier and have shortened assignments despite the already indicated ease of the work. As a result of this research, I plan to look more closely at the history and …
Motivating Middle School Mathematics Students, Vicki Sorensen
Motivating Middle School Mathematics Students, Vicki Sorensen
Action Research Projects
In this action research study I examined the relationship between the teacher, the students and the types of motivation used in mathematics. I specifically studied the mathematic teachers at my school and my seventh grade mathematics students. Motivating middle school students is difficult and the types of motivation can be as numerous as the number of students studied. I discovered that the teachers used multiple motivating tactics from praise, to extra time spent with a student, to extra fun activities for the class. I also discovered that in many instances, the students’ perception of mathematics was predetermined or predetermined by …
The Vigenére Cipher Expository Paper, Virginia L. Clark
The Vigenére Cipher Expository Paper, Virginia L. Clark
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
French diplomat and cryptographer Blaise de Vigenére (1523-1596), developed the Vigenére Cipher in 16th century France in the mid-1580s. Vigenére was on the court of Henry III of France. Vigenére developed a polyalphabetic coding system in which one letter of plain text may be encrypted as different letters rather than one plain text letter represented as one cipher text letter throughout the encoded message.
The Game Of Nim, Dean J. Davis
The Game Of Nim, Dean J. Davis
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
The game of Nim is possibly one of the most frustrating games I have ever played. Just when I started to feel that I had figured the strategy out, my brother, who is a computer programmer, blew me out of the water. I should have known better than to take on a computer wizard.
Area And Perimeter Of Polygons, Bryan Engelker
Area And Perimeter Of Polygons, Bryan Engelker
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
A student comes to class excited. She tells you she has figured out a theory you never told the class. She says she has discovered that as the perimeter of a closed figure increases, the area also increases. She shows you two pictures to prove what she is doing. The first picture is of a 4 by 4 square. Of course, its perimeter is 16 and its area is 16. The second picture is of a 4 by 8 rectangle. Here the perimeter is 24 and the area is 32. What do you say to the student?
Just What Do You “Mean”?, Myrna L. Bornemeier
Just What Do You “Mean”?, Myrna L. Bornemeier
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
In Ancient Greece the Pythagoreans were interested in three means. The means were the arithmetic, geometric, and harmonic. The arithmetic mean played an important role in the observations of Galileo. Along with the arithmetic mean, the geometric and harmonic mean (formerly known as the subcontrary mean) are said to be instrumental in the development of the musical scale. As we explore the three Pythagorean Means we will discover their unique qualities and mathematical uses for helping us solve problems.
Farey Sequences, Ford Circles And Pick's Theorem, Julane Amen
Farey Sequences, Ford Circles And Pick's Theorem, Julane Amen
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
One of the ongoing themes through the Math in the Middle coursework has been the idea of identifying patterns. From our first course, Math as a Second Language, patterns have been useful to explain phenomena and determine future values. Some patterns are numerical but can be described using algebra. Some are visual or geometric and also can be described using numbers and symbols. Many of these patterns have resurfaced in different forms and at different times in new and interesting ways. It has been a humbling experience to see the interconnectedness of seemingly unconnected ideas. Pick’s Theorem, Farey Sequences and …
Fractals And The Chaos Game, Stacie Lefler
Fractals And The Chaos Game, Stacie Lefler
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
The idea of fractals is relatively new, but their roots date back to 19th century mathematics. A fractal is a mathematically generated pattern that is reproducible at any magnification or reduction and the reproduction looks just like the original, or at least has a similar structure. Georg Cantor (1845-1918) founded set theory and introduced the concept of infinite numbers with his discovery of cardinal numbers. He gave examples of subsets of the real line with unusual properties. These Cantor sets are now recognized as fractals, with the most famous being the Cantor Square.
Taylor Polynomials, Doug Glasshoff
Taylor Polynomials, Doug Glasshoff
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
Before the age of calculators, studying functions such as sin x, cos x , ex , and ln x was quite time consuming. The graphs of these functions are important when studying their characteristics. James Gregory, a Scottish mathematician in the 17th century, made an important discovery about these functions. Using calculus, he wrote a series of terms to approximate very closely the graph of the curve. His main focus was with the function ln x ; he was able to calculate any positive value of x using a polynomial series. Brook Taylor, an English mathematician, generalized the Maclaurin series, …
Comparing Infinite Sets, Julie M. Kreizel
Comparing Infinite Sets, Julie M. Kreizel
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
I have been assigned to explore the theorem stating that there is no largest (infinite) set as established and proven by Georg Cantor. To do this I need to start by defining what it means to say that a set is infinite. This can be quite difficult because the tendency might be to say that a set is infinite if it is not finite, and I don’t believe that grants us the clarity of definition we are looking for. When trying to understand the size of a given set, the number of objects (elements) in the set, we may not …
Triangulation, Jim Pfeiffer
Triangulation, Jim Pfeiffer
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
Map making has been a scientific endeavor for mankind since the beginning of recorded human history (ca. 5000 years ago) and it is today more sophisticated than ever before. In terms of trigonometric functions there is evidence that dates back to Babylonian times that angles and distances from points on a triangle were utilized in measurement with significant amounts of work in this field done by ancient Greeks, Indians, as well as Arabic mathematicians. For example the ancient Egyptians utilized the trigonometric functions for surveying properties in order to determine how much of their land had washed away when the …
Taxicab Geometry, Kyle Lannin Poore
Taxicab Geometry, Kyle Lannin Poore
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
Taxicab geometry was founded by a gentleman named Hermann Minkowski. Mr. Minkowski was one of the developers in “non-Euclidean” geometry, which led into Einstein’s theory of relativity. Minkowski and Einstein worked together a lot on this idea Mr. Minkowski wanted people to know that the side angle side axiom does not always hold true for all geometries. He wanted to prove this in the case that you can not always use the hypotenuse to find the shortest way from one spot to another. The best way to think of his idea is to think of a taxicab going from one …
Fractals And The Collage Theorem, Sandra S. Snyder
Fractals And The Collage Theorem, Sandra S. Snyder
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
The idea of fractals is relatively new, but their roots date back to 19th century mathematics. A fractal is a mathematically generated pattern that is reproducible at any magnification or reduction and the reproduction looks just like the original, or at least has a similar structure. Georg Cantor (1845-1918) founded set theory and introduced the concept of infinite numbers with his discovery of cardinal numbers. He gave examples of subsets of the real line with unusual properties. These Cantor sets are now recognized as fractals, with the most famous being the Cantor Square.
An In-Depth Study Of Student Engagement, Laura Parn
An In-Depth Study Of Student Engagement, Laura Parn
Departament of Teaching, Learning, and Teacher Education: Master's of Arts in Teaching, Summative Projects
In this action research study of my classroom of 5th grade mathematics, I investigated student engagement levels in the classroom, with a specific interest in how to raise the levels of engagement which students were demonstrating before the study began. I defined student engagement based on students’ posture, thinking, responsibility level, participation, and test readiness. Each day, students were given an engagement rubric where they would rate themselves on the previous five criteria. Students enjoyed the opportunity to grade themselves, and their engagement levels significantly improved over the course of the study. I discovered that giving students specific guidelines and …