Education Commons^™

Hyperbolic Geometry, Christina L. Sheets

Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers

In general, when one refers to geometry, he or she is referring to Euclidean geometry. Euclidean geometry is the geometry with which most people are familiar. It is the geometry taught in elementary and secondary school. Euclidean geometry can be attributed to the Greek mathematician Euclid of Alexandria. His work entitled The Elements was the first to systematically discuss geometry. Since approximately 600 B.C., mathematicians have used logical reasoning to deduce mathematical ideas, and Euclid was no exception. In his book, he started by assuming a small set of axioms and definitions, and was able to prove many other theorems. …

Pythagorean Triples, Diane Swartzlander

Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers

Who was Pythagoras after which the Pythagorean Theorem is named? Pythagoras was born between 580-572 BC and died between 500-490 BC. Pythagoras and his students believed that everything was related to mathematics and that numbers were the ultimate reality. Very little is known about Pythagoras because none of his writings have survived. Many of his accomplishments may actually have been the work of his colleagues and students. Pythagoras established a secret cult called the Pythagoreans. His cult was open to both females and males and they lived a structured life consisting of religious teaching, common meals, exercise, reading and philosophical …

Distance, Rate, Time And Beyond, Janet Timoney

Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers

In middle school mathematics, students learn to use the formula “distance equals rate times time,” usually expressed as d = r × t. Why not consider the formula distance = velocity × time? Does the term velocity mean something different than the term rate? We could also consider the variations of these formulas: distance ÷ time = rate, or distance ÷ rate = time. We can examine the definitions of these words and words which are very similar. After looking at the definitions of these words, maybe we will have a better understanding of how to use the formulas and …

Evaluating Polynomials, Thomas J. Harrington

Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers

Computers use algorithms to evaluate polynomials. This paper will study the efficiency of various algorithms for evaluating polynomials. We do this by counting the number of basic operations needed; since multiplication takes much more time to perform on a computer, we will count only multiplications. This paper addresses the following: a) How many multiplications does it take to evaluate the one-variable polynomial, Σ= + + + + = n i i i n n a a x a x a x a x 0 2 0 1 2 ... when the operations are performed as indicated? (Remember that powers are …

The Volume Of A Platonic Solid, Cindy Steinkruger

Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers

A regular tetrahedron and a regular octahedron are two of the five known Platonic Solids. These five “special” polyhedra look the same from any vertex, their faces are made of the same regular shape, and every edge is identical. The earliest known description of them as a group is found in Plato’s Timaeus, thus the name Platonic Solids. Plato theorized the classical elements were constructed from the regular solids. The tetrahedron was considered representative of fire, the hexahedron or cube represented earth, the octahedron stood for gas or air, the dodecahedron represented vacuum or ether (which is made up of …

Using Cooperative Learning To Promote A Problem-Solving Classroom, Amy Nebesniak

Departament of Teaching, Learning, and Teacher Education: Master's of Arts in Teaching, Summative Projects

In this action research study of my eighth grade mathematics classroom, I investigate the benefits of cooperative learning, the support structures needed to promote a cooperative learning environment, and students’ ability to transfer the cooperative learning skills into less structured problem solving situations. The data analysis reveals that cooperative learning increases students’ confidence level as well as their involvement in the learning process. In order to create successful teams, students require my providing support structures and modifying the support for each group of students. Finally, students are able to more effectively apply their cooperative skills in concrete situations as compared …

The Use Of Think-Aloud Strategies To Solve Word Problems, Lisa M. Henjes

Departament of Teaching, Learning, and Teacher Education: Master's of Arts in Teaching, Summative Projects

In this action research study of my sixth grade mathematics class, I investigated how students’ use of think-aloud strategies impacts their success in solving word problems. My research reveals that the use of think-aloud strategies can play an important role in the students’ abilities to understand and solve word problems. Direct instruction and modeling of think-aloud strategies increased my students’ confidence levels and the likelihood that they would use the strategies on their own. Providing students with a template to use as they solve a word problem helps students to better focus in on the think-aloud strategies I had been …

Writing In The Mathematics Classroom: Does It Have An Effect On Students’ Mathematical Reasoning?, Rachel Bunnett

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 investigate how to improve students’ written explanations to and reasoning of math problems. For this, I look at journal writing, dialogue, and collaborative grouping and its effects on students’ conceptual understanding of the mathematics. In particular, I look at its effects on students’ written explanations to various math problems throughout the semester. Throughout the study students worked on math problems in cooperative groups and then shared their solutions with classmates. Along with this I focus on the dialogue that occurred during these interactions and whether and how …

A Study Of The Role Of Mnemonics In Learning Mathematics, Kathy Delashmutt

Departament of Teaching, Learning, and Teacher Education: Master's of Arts in Teaching, Summative Projects

In this action research study of my fifth grade mathematics teaching, I investigated student engagement levels in the classroom, with a specific interest in the importance and effectiveness of mnemonics in learning mathematics for all learners. I defined mnemonic instruction as a strategy that provides a visual or verbal prompt for students who may have difficulty retaining information. It is a memory enhancing instructional strategy that involved teaching students to link new information that is taught to information they already know. I investigated mnemonics effectiveness in my classroom by using two student interviews, a teacher survey, two student surveys and …

A Study Of Written Communication: Showing Your Steps, Megan Kelly

Departament of Teaching, Learning, and Teacher Education: Master's of Arts in Teaching, Summative Projects

In this action research study of my teaching of sixth grade mathematics, I investigated the importance of showing work on daily assignments. I wanted to find out what happens when I ask students to show their work, specifically, whether it would improve students’ grades or not and whether I could help the students to understand the importance of showing their work. I discovered that students need to be shown the proper way to show their work, how to look at a problem and then how to show all of their steps to get to the answer. They need to be …

Increasing Student Confidence And Knowledge Through Student Presentations, Lori Ziemba

Departament of Teaching, Learning, and Teacher Education: Master's of Arts in Teaching, Summative Projects

In this action research study of a 9th grade Algebra classroom, I investigated the influence of having students present homework solutions and what effect it had on student learning and student confidence. Students were asked to present solutions to homework problems each day and were rated on how well they did. The students were also surveyed about their confidence and feelings about mathematics. Students were also observed for information about who they asked questions of when presented with a math problem they did not understand. In this classroom, two teachers were involved in instruction and this study examines what affect …

An Investigation Into Careless Errors Made By 7th Grade Mathematics Students, Andrea Wiens

Departament of Teaching, Learning, and Teacher Education: Master's of Arts in Teaching, Summative Projects

In this action research study, I investigated the careless errors made by my seventh-grade mathematics students on their homework and tests. Beyond analyzing the types of careless errors and the frequency at which they were made, I also analyzed my students’ attitudes toward reviewing their work before they turn it in and self-reflection about the quality of work that they were producing. I found that many students did not know how to review their test before turning it in; no one had ever taught them how to do so. However, when students were given tools to help them with this …

Here Is The Plan: So What Is The Question?, Dot Snesrud

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 students, I investigated their understanding of the mathematical operations by having them write problems to match given equations. I discovered that writing a story to match an equation does provide insight into a student’s understanding of mathematical concepts, however, reading comprehension is a factor in the understanding. Readers who struggle with comprehension do struggle with understanding and writing math story problems. The discussion that follows the writing of a math story problem and the solving of the written problems helps to strengthen the students’ mathematical abilities as well …

Improving The Effectiveness Of Independent Practice With Corrective Feedback, Greg Vanderbeek

Action Research Projects

In this action research study of my 8th grade Algebra class, I investigated the effects of teacher-to-student written corrective feedback on student performance and attitude toward mathematics. The corrective feedback was given on solutions for selected independent practice problems assigned as homework. Each problem being assessed was given a score based on a 3- point rubric and additional comments were written. I discovered that providing teacher-to-student written corrective feedback for independent practice problems was beneficial for both students and teachers. The feedback positively affected the attitudes of students and teacher toward independent practice work resulting in an improved quality of …

Increasing Conceptual Learning Through Student Participation, Janet Timoney

Action Research Projects

In this action research study of my 9th grade Algebra I classroom, I investigated the idea of presenting problems at the beginning of class. Data was collected to determine if presenting problems at the beginning of class would have an effect on students’ conceptual learning, verbal communication and confidence. It was also my intention that this project would have a positive impact on my students both academically and mentally with increasing their confidence with mathematical problems. I discovered that presenting problems at the beginning of class did impact my students’ overall abilities and achievement. It seemed to improve their volunteerism …

Increasing Teacher Involvement With Other Teachers Through Reflective Interaction, Tina Thompson

Action Research Projects

In this action research study of a district’s mathematics teachers, the researcher investigated how teachers interact with other teachers in their building and throughout the district. The researcher wanted to know how deeply teachers thought about teaching mathematics, and if they use other teachers in the district as a resource to help with unknown math problems. The researcher discovered that some teachers are willing to interact with others, but would like to have time supplied to them during the school year’s staff development meetings. The teachers involved were able to observe each other teaching and take valuable strategies back to …

Improving Student Engagement And Verbal Behavior Through Cooperative Learning, Daniel Schaben

Action Research Projects

In this action research study of my classroom of 10th grade Algebra II students, I investigated three related areas. First, I looked at how heterogeneous cooperative groups, where students in the group are responsible to present material, increase the number of students on task and the time on task when compared to individual practice. I noticed that their time on task might have been about the same, but they were communicating with each other mathematically. The second area I examined was the effect heterogeneous cooperative groups had on the teacher’s and the students’ verbal and nonverbal problem solving skills and …

Writing For Understanding In Math Class, Linda Moore

Action Research Projects

In this action research study of my classroom of 10th grade geometry students, I investigated how students learn to communicate mathematics in a written form. The purpose of the study is to encourage students to express their mathematical thinking clearly by developing their communication skills.

I discovered that although students struggled with the writing assignments, they were more comfortable with making comments, writing questions and offering suggestions through their journal rather than vocally in class. I have utilized teaching strategies for English Language Learners, but I had never asked the students if these strategies actually improved their learning. I have …

The Importance Of Vocabulary Instruction In Everyday Mathematics, Chad Larson

Action Research Projects

In this action research study of my 6th grade math students I try to answer the question of how mathematical vocabulary plays an integral role in the understanding and learning of middle level mathematics. It is my belief that mathematics is a language, and to be fluent in that language one must be able to use and understand vocabulary. With the use of vocabulary quizzes and mathematically-centered vocabulary activities, student scores and understanding of math concepts can be increased. I discovered that many of the students had never been exposed to consistent mathematical terminology in their elementary education, which led …

Cooperative Learning As An Effective Way To Interact, Gary Eisenhauer

Action Research Projects

In this action research study of my classroom of 8th grade mathematics, I investigated the effects of students’ interactions while cooperatively learning in groups. I discovered that in order to be cooperative, a lesson must be well-defined, open for discussion, and have positive face-toface interaction. The cooperative learning groups should be teacher generated rather than student-selected. When done correctly, cooperative learning tends to promote student relationships, more positive attitudes toward mathematics and the teacher, and greater self-confidence in a student’s mathematics abilities. As a result of this research, I plan to better incorporate cooperative learning into the classroom. Students will …

Algebraic Geometric Codes On Anticanonical Surfaces, Jennifer A. Davis

Department of Mathematics: Dissertations, Theses, and Student Research

Algebraic geometric codes (or AG codes) provide a way to correct errors that occur during the transmission of digital information. AG codes on curves have been studied extensively, but much less work has been done for AG codes on higher dimensional varieties. In particular, we seek good bounds for the minimum distance.

We study AG codes on anticanonical surfaces coming from blow-ups of P² at points on a line and points on a conic. We can compute the dimension of such codes exactly due to known results. For certain families of these codes, we prove an exact result on …

Two Problems In Extremal Set Theory, Joshua Brown Kramer

Department of Mathematics: Dissertations, Theses, and Student Research

The focus of this dissertation is on two problems in extremal set theory, which is a branch of extremal combinatorics. The general problem in extremal set theory is to start with all collections of subsets of an underlying ground set, apply restrictions, and then ask how large or small some property can be under those restrictions. We give a brief introduction to extremal combinatorics and consider two open questions.

One open question we consider is an extremal problem under “dimension constraints.” We give a brief account of the history of this subject and we consider the open problem of determining …

Toward Common Nomenclature And Definitions For Natural Science Professional Collections-Related Positions, Paisley S. Cato, Hugh H. Genoways

University of Nebraska State Museum: Programs Information

Analysis of recent literature and experience with professional positions in several institutions provided the basis for proposing a basic grouping of titles for positions relating to the natural sciences collections profession. Six groups ore proposed with recommendations for education, experience, knowledge, and skills to support the key responsibilities of the positions. Discussions and critiques of these groupings ore anticipated to refine and ultimately result in a standardized nomenclature for natural science collections-related positions.

Planning The Future Workforce Of Natural Science Research Collections: A Review Of Graduate Academic Programs In The United States, Stephen L. Williams, Hugh H. Genoways

University of Nebraska State Museum: Programs Information

Selected literature and Internet sites were used to identify universities that provide graduate academic degrees relevant to the management and care of natural science research collections. Twelve universities with degree programs not dedicated to the arts or humanity fields were selected for closer evaluation. By analyzing the courses offered in museology and the natural sciences at each university, seven universities were identified as currently in a position to provide some level of education and training needed by the future workforce of natural science research collections. However, only two universities stood out as being in the best position to serve most …

Promoting Undergraduate Research In Mathematics At The University Of Nebraska – Lincoln, Judy L. Walker, Glenn Ledder, Richard Rebarber, Gordon S. Woodward

Department of Mathematics: Faculty Publications

The Department of Mathematics at the University of Nebraska – Lincoln (UNL) has several programs which promote undergraduate research in a variety of ways. Two of these are summer programs which draw from a national applicant pool: The Nebraska REU in Applied Mathematics (Section 1) is a traditional NSF-funded REU site, and Nebraska IMMERSE (Section 2) offers a summer “bridge” program (with a research bent) for students about to start graduate school in mathematics. IMMERSE is a relatively new program, started in 2004 as part of the department’s Mentoring through Critical Transition Points (MCTP) grant from NSF. The MCTP grant …

Nebraska Earth Systems Education Network – Winter 2006/07

Nebraska Earth Systems Education Network

Content:

Second Lab Earth Course to Study Natural Resources by Karen Pietsch

Teacher Spotlight: Bob Fuerer By Karen Pietsch

Carbon Offsets Offer Environmental Penance, Promotion By Karen Pietsch

Lab Earth Concepts Carried into Classrooms By Karen Pietsch

‘Advanced Scholars’ Helps High School- College Transition By Karen Pietsch

New Masters of Arts Option Focuses on Applied Science by Karen Pietsch

Nebraska Summary: S683 New Holland T6040 Elite As, Nebraska Tractor Test Lab

Nebraska Tractor Tests

ABOUT THE TEST REPORT AND USE OF THE DATA The test data contained in this report are a tabulation of the results of a series of tests. Due to the restricted format of these pages, only a limited amount of data and not all of the tractor specifications are included. The full OECD report contains usually about 30 pages of data and specifications. The test data were obtained for each tractor under similar conditions and therefore, provide a means of comparison of performance based on a limited set of reported data. EXPLANATION OF THE TEST PROCEDURES Purpose The purpose of …

Nebraska Summary: S688 New Holland T6020 Plus, Nebraska Tractor Test Lab

Nebraska Tractor Tests

ABOUT THE TEST REPORT AND USE OF THE DATA The test data contained in this report are a tabulation of the results of a series of tests. Due to the restricted format of these pages, only a limited amount of data and not all of the tractor specifications are included. The full OECD report contains usually about 30 pages of data and specifications. The test data were obtained for each tractor under similar conditions and therefore, provide a means of comparison of performance based on a limited set of reported data. EXPLANATION OF THE TEST PROCEDURES Purpose The purpose of …

Nebraska Summary: S689 New Holland T6030 Plus, Nebraska Tractor Test Lab

Nebraska Tractor Tests

ABOUT THE TEST REPORT AND USE OF THE DATA The test data contained in this report are a tabulation of the results of a series of tests. Due to the restricted format of these pages, only a limited amount of data and not all of the tractor specifications are included. The full OECD report contains usually about 30 pages of data and specifications. The test data were obtained for each tractor under similar conditions and therefore, provide a means of comparison of performance based on a limited set of reported data. EXPLANATION OF THE TEST PROCEDURES Purpose The purpose of …

Test 1904: Agco Rt 120a Powrmaxx Diesel, Nebraska Tractor Test Lab

Nebraska Tractor Tests

ABOUT THE TEST REPORT AND USE OF THE DATA

The test data contained in this report are a tabulation of the results of a series of tests. Due to the restricted format of these pages, only a limited amount of data and not all of the tractor specifications are included. The full OECD report contains usually about 30 pages of data and specifications. The test data were obtained for each tractor under similar conditions and therefore, provide a means of comparison of performance based on a limited set of reported data.

EXPLANATION OF THE TEST PROCEDURES

Purpose

The purpose of …