Science and Mathematics Education Commons^™

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 …

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 …

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 …

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 …

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 …

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.

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.

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.

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, …

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.

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 …

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.

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 …

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 …

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.

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 …

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 …

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 …

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 …

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 …

Lake Mead National Recreation Area Sensitive Wildlife Species Monitoring And Analysis: Quarterly Progress Report, Period Ending June 30, 2006, Margaret N. Rees

Wildlife Monitoring

• Tortoise and tortoise habitat monitoring was conducted on the Northshore Road construction project, on the Southern Nevada Water Authority intake pipe project, the Frontier Telephone-Willow Beach project and the movie film at Temple Bar.
• A total of 25 tortoise education classes were given to 90 individuals.
• Evaluation of 3 potential sites for relict leopard frog translocations conducted but sites were not recommended.
• Head-starting and translocation efforts for relict leopard frogs continued. 1183 animals translocated so far this year.
• Relict Leopard Frog Conservation Team meeting held and yearly report completed.
• Continuation of data management and QA of GPS collar information from …

Red Rock Desert Learning Center: Evaluation Of Curriculum: Final Report, Lori Olafson, Gregory Schraw

Reports (RRLC)

The UNLV Center for Evaluation and Assessment developed an assessment instrument to evaluate curriculum for the proposed Red Rock Desert Learning Center science school’s fifth grade program. A 25-item Likert-type scale was created and administered before and after 68 pre-service and in-service teachers participated in each of five curriculum pilot sessions. The survey consisted of questions related to knowledge, pedagogy, and attitudes. Two open-ended questions were included on the post-survey.

Findings revealed significant gains in knowledge, pedagogy, and attitudes in each of five events from pre- to post-test. Gains over time were greatest for knowledge. Some events were rated more …

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 …

Elliptical Coordinates, Carl W. David

Chemistry Education Materials

This offering contains the transformation equations between Cartesian and elliptical coordinate systems appropriate for treating the hydrogem molecule ion's quantum mechanics.

The Effects Of Teaching Problem Solving Strategies To Low Achieving Students, Kristin Johnson, Anne Schmidt

Action Research Projects

In this action research study of an eighth grade Math Intervention class, we investigated the following:

• the direct teaching of problem-solving strategies to low achieving students;
• the effect the academic achievement has on these students; and
• students’ perceptions of themselves as problem solvers.

We discovered that students tended to have a positive experience with problem-solving activities when given direct instruction on a variety of strategies. Through the use of a four-point rubric, students’ written responses tended to be more comprehensive about their understanding of the problem. Over a span of four weeks during the spring semester in …

Does Changing The Definition Of Science Solve The Establishment Clause Problem For Teaching Intelligent Design As Science In Public Schools? Doing An End-Run Around The Constitution, Ann Marie Lofaso

The University of New Hampshire Law Review

[Excerpt] "When Charles Darwin published On the Origin of Species By Means of Natural Selection in 1859, it sparked some of the most contentious debates in American intellectual history, debates that continue to rage today. Although these debates have numerous political ramifications, the question posed in this paper is narrow: Does the Establishment Clause permit a particular assessment of current evolutionary theory – intelligent design (“ID”) – to be taught as science in American elementary and secondary public schools? This article shows that it does not.

To understand current disputes over whether and how to teach the origins of life …

Self-Directed Learning In The Middle School Classroom, Jim Pfeiffer

Action Research Projects

The action research project took place in my seventh grade mathematics classroom and involved the study of how student directed learning impacts the ability of students in the middle level to learn mathematics. This research project uncovered issues in student learning and self-discipline of the students, as well as classroom management skills that were not readily apparent in a teacher-centered middle level mathematics classroom. As a result of this action research project, my future seventh grade mathematics students will continue to have an increased role in the educational process to which they are an audience. The student-centered learning environment seems …

Learning To Use Innovative Pedagogy: The Experience Of A Primary Science Teacher In Pakistan, Nelofer Halai

Institute for Educational Development, Karachi

This study examined the experiences of primary science teachers when they weThis study examined the experiences of primary science teachers when they were exposed to a new and innovative teaching strategy and the process that they followed in using the strategy in the class- room for the first time. Four primary science teachers, among the 22 participants of an 8-week Certificate in Education (Science) in Karachi, were observed and interviewed after the four-day teaching session where they were instructed how to use "Discrepant Events" to teach science content. Only the case of Farhana Batool, a teacher in a private school, …

Reverse-Traditional/Hands-On: An Alternative Method Of Teaching Statistics, Aliakbar M. Haghighi, Roozbeh Vakil, Johnson K. Wetiba

Applications and Applied Mathematics: An International Journal (AAM)

This paper presents a method for teaching statistics called the Reverse-Traditional/Hands-On (RT/HO) method. The method includes student-generated data, use of a statistical computing package such as MINITAB to introduce statistical terms and methods, and a statistical research component. An analytic comparison of students’ successes in courses using the Traditional and RT/HO methods is presented.

Education In The Environment: A Hands-On Student Research And Outdoor Learning Experience: Quarterly Progress Report, Period Ending May 31, 2006, Margaret N. Rees

Reports (PLI Education)

During the past three months, the focus of the university’s efforts has included the following highlights:

• Forever Earth was scheduled for 18 days and benefited more than 400 individuals.
• Curricula for 5th, 6th, and 7th grades were created for the Forever Earth program; pre- and post-trip activities were also written.
• Activities for 5th and 6th grades were field tested on 7 Forever Earth trips.
• A 1000-gallon fuel donation was contributed to the Forever Earth program by Overland Petroleum Company, St. George, Utah.
• The Forever Earth marketing plan was completed.
• 12 Discover Mojave Outdoor World events were conducted for 104 participants; …