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Articles 1681 - 1710 of 4438

Full-Text Articles in Science and Mathematics Education

The Art Gallery Question, Vicki Sorensen Jul 2006

The Art Gallery Question, Vicki Sorensen

Department of Mathematics: Master 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.)

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Factors That Influence Mathematics Attitudes, Natalie Jenkins Jul 2006

Factors That Influence Mathematics Attitudes, Natalie Jenkins

Department of Teaching, Learning, and Teacher Education: Master of Arts in Teaching, Summative Projects

In this action research study conducted within my sixth grade High Ability Learner (HAL) classroom, I investigated the current mathematics attitudes of my students and how these attitudes correlated to personal mathematics achievement and identified intelligence domains. I discovered that most of my nineteen students held a negative attitude toward the subject of mathematics. Consistent low ratings were also found in the logical/mathematical domain of most of my students’ ALPS Multiple Intelligence Profiles. Regardless of this dominant affective data (indicating little mathematics interest or potential from student perspectives) surprisingly, most of my sixth grade HAL students scored above the 90th …

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Discourse And Cooperative Learning In The Math Classroom, Karen Hillen Jul 2006

Discourse And Cooperative Learning In The Math Classroom, Karen Hillen

Department of Teaching, Learning, and Teacher Education: Master 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 …

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The Effects Of Self-Assessment On Student Learning, Darla Rae Kelberlau-Berks Jul 2006

The Effects Of Self-Assessment On Student Learning, Darla Rae Kelberlau-Berks

Action Research Projects

In this action research study of my 7th and 8th grade mathematics classes, I investigated self-assessment and goal setting. Students set goals at the beginning of the chapter. Students rated themselves at the end of each lesson in several different areas. Those ratings were used to help students know what areas to focus on when preparing for a test. I discovered that students were realistic with their goals. I discovered that the 7th grade Pre-Algebra classes were accurate with their self-ratings and that those ratings helped students with test preparation. I also discovered that students were positive about the experience …

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Using Math Vocabulary Building To Increase Problem Solving Abilities In A 5th Grade Classroom, Julane Amen Jul 2006

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 …

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How To Better Prepare For Assessment And Create A More Technologically Advanced Classroom, Kyle Lannin Poore Jul 2006

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 …

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Student Transition To College, Doug Glasshoff Jul 2006

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 …

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Daily Problem-Solving Warm-Ups: Harboring Mathematical Thinking In The Middle School Classroom, Diana French Jul 2006

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 …

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Cooperative Learning Groups In The Eighth Grade Math Classroom, Dean J. Davis Jul 2006

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 …

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Departmentalization In The 5th Grade Classroom: Re-Thinking The Elementary School Model, Delise Andrews Jul 2006

Departmentalization In The 5th Grade Classroom: Re-Thinking The Elementary School Model, Delise Andrews

Action Research Projects

In this action research study of my 5th grade classroom, I investigated the benefits of a modified block schedule and departmentalization. The research consisted of dividing the 5th grade curriculum into three blocks. Each block consisted of two primary subject areas: Mathematics was paired with Social Studies, Reading was paired with Health, and Writing was paired with Science. These groupings were designed to accommodate district time-allotment requirements and the strengths of each teacher within the 5th grade team. Thus, one teacher taught all of the Mathematics and Social Studies, another all of the Reading and Health, and another all of …

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Cooperative Learning Groups In The Middle School Mathematics Classroom, Sandra S. Snyder Jul 2006

Cooperative Learning Groups In The Middle School Mathematics Classroom, Sandra S. Snyder

Action Research Projects

In this action research study of my classroom of 8th grade mathematics, I investigated the inclusion of cooperative learning groups. Data was collected to see how cooperative learning groups affected oral and written communication, math scores, and attitudes toward mathematics. On the one hand, I discovered that many students enjoyed the opportunity to work within a group. On the other hand, there continues to be a handful of students who would rather work alone. The benefits outweigh the demands. Overall, students benefitted from the inclusion of cooperative learning groups. Oral explanations of solutions and methods improved during the study. Written …

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Motivating Middle School Mathematics Students, Vicki Sorensen Jul 2006

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 …

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Bad Medicine: Homework Or Headache? Responsibility And Accountability For Middle Level Mathematics Students, Shawn Mousel Jul 2006

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 …

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Farey Sequences, Ford Circles And Pick's Theorem, Julane Amen Jul 2006

Farey Sequences, Ford Circles And Pick's Theorem, Julane Amen

Department of Mathematics: Master 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 …

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Symmetry Of Scale Expository Paper, Darla R. Kelberlau-Berks Jul 2006

Symmetry Of Scale Expository Paper, Darla R. Kelberlau-Berks

Department of Mathematics: Master 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.

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The Vigenére Cipher Expository Paper, Virginia L. Clark Jul 2006

The Vigenére Cipher Expository Paper, Virginia L. Clark

Department of Mathematics: Master 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.

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The Game Of Nim, Dean J. Davis Jul 2006

The Game Of Nim, Dean J. Davis

Department of Mathematics: Master 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.

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Taylor Polynomials, Doug Glasshoff Jul 2006

Taylor Polynomials, Doug Glasshoff

Department of Mathematics: Master 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, …

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Heron, Brahmagupta, Pythagoras, And The Law Of Cosines, Kristin K. Johnson Jul 2006

Heron, Brahmagupta, Pythagoras, And The Law Of Cosines, Kristin K. Johnson

Department of Mathematics: Master 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.

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Comparing Infinite Sets, Julie M. Kreizel Jul 2006

Comparing Infinite Sets, Julie M. Kreizel

Department of Mathematics: Master 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 …

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Fractals And The Chaos Game, Stacie Lefler Jul 2006

Fractals And The Chaos Game, Stacie Lefler

Department of Mathematics: Master 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.

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Triangulation, Jim Pfeiffer Jul 2006

Triangulation, Jim Pfeiffer

Department of Mathematics: Master 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 …

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Taxicab Geometry, Kyle Lannin Poore Jul 2006

Taxicab Geometry, Kyle Lannin Poore

Department of Mathematics: Master 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 …

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Fractals And The Collage Theorem, Sandra S. Snyder Jul 2006

Fractals And The Collage Theorem, Sandra S. Snyder

Department of Mathematics: Master 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.

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An In-Depth Study Of Student Engagement, Laura Parn Jul 2006

An In-Depth Study Of Student Engagement, Laura Parn

Department of Teaching, Learning, and Teacher Education: Master 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 …

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The Role Of Habits-Of-Mind Problems, Student Self-Assessments And Self Reflections In A 6th Grade Math Class, Garold J. Furse Jul 2006

The Role Of Habits-Of-Mind Problems, Student Self-Assessments And Self Reflections In A 6th Grade Math Class, Garold J. Furse

Department of Teaching, Learning, and Teacher Education: Master 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 …

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Student Problem Solving, Michael A. Cobelens Jul 2006

Student Problem Solving, Michael A. Cobelens

Department of Teaching, Learning, and Teacher Education: Master 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 …

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Improving Mathematics Problem Solving Through Written Explanations, Janet Schlattmann Jul 2006

Improving Mathematics Problem Solving Through Written Explanations, Janet Schlattmann

Department of Teaching, Learning, and Teacher Education: Master 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 …

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Math Anxiety: What Can Teachers Do To Help Their Students Overcome The Feeling?, Danielle Swanson Jul 2006

Math Anxiety: What Can Teachers Do To Help Their Students Overcome The Feeling?, Danielle Swanson

Department of Teaching, Learning, and Teacher Education: Master of Arts in Teaching, Summative Projects

In this action research study of my classroom of 7th and 8th grade mathematics, I investigated how math anxiety relates to the student work and behavior in the classroom, and how this can affect the student’s overall relationship to mathematics. I discovered that the harder the work, the more math anxiety was displayed. The harder I pushed students to think more deeply, the fewer responses to my questions I received. I noticed difference in the students’ body language and overall behavior. As a result of this research, I plan to help my students try to overcome the feeling of math …

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Writing In A Mathematics Classroom: A Form Of Communication And Reflection, Stacie Lefler Jun 2006

Writing In A Mathematics Classroom: A Form Of Communication And Reflection, Stacie Lefler

Action Research Projects

In this action research study, I investigated the use of journaling in my seventh grade mathematics classroom. I discovered that journaling can be a very rewarding and beneficial experience for me and for my students. Through journaling, my students became more adept at using correct mathematical terminology in writing and in speaking. The students also believed that they learned the content more deeply and retained it better. Additionally, implementing mathematical journals caused me to emphasize the use of correct terminology and thorough explanations of mathematical thinking in classroom discussions. As a result of this research, I plan to refine my …

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