Science and Mathematics Education Commons^™

Gsi: Geo Scene Investigation! Pre-Visit, Support Materials: Topographic And Geologic Maps (Grade 7), Discover Mojave: Forever Earth

Curriculum materials (FE)

Student worksheets for reading Lake Mead area topographic maps.

How A Master Teacher Uses Questioning Within A Mathematical Discourse Community, Omel Angel Contreras

Theses and Dissertations

Recent scholarly work in mathematics education has included a focus on learning mathematics with understanding (Hiebert & Carpenter, 1992; Hiebert et al., 1997; Fennema & Romberg, 1999; National Council of Teachers of Mathematics, 2000). Hiebert et al. (1997) discussed two processes that they suggested increase understanding and that are central to this study: reflection and communication. Learning mathematics with understanding requires that the students create a deeper knowledge of mathematics through reflection and communication. The environment in which such learning can take place must include patterns of behavior, known as social norms that promote deeper thinking. When the social norms …

Second Graders' Solution Strategies And Understanding Of A Combination Problem, Tiffany Marie Hessing

Theses and Dissertations

I inquire about second graders' capabilities of developing solution strategies and the original variety of strategies they bring forth while solving a combination problem. Based on analysis of the data presented in this paper, students developed five different general strategies. After analyzing what the second grade students were capable of developing, we can conclude that young children are capable of developing powerful systematic strategies grounded in their personal experiences. This research shows that even when the teacher does not foster personal agency, children will still exercise agency. The social interactions in the classroom helped students learn to propose mathematical ideas, …

The Nature And Frequency Of Mathematical Discussion During Lesson Study That Implemented The Cmi Framework, Andrew Ray Glaze

Theses and Dissertations

During a year-long professional development, the faculty members at an elementary school received instruction on mathematics and how to use the Comprehensive Mathematics Instruction framework. The instruction and the framework were consistent with the standards suggested by the National Council of Teacher of Mathematics (2000). This thesis analyzes the mathematical language used by three fifth-grade teachers who participated in lesson study to create a research lesson based upon the Comprehensive Mathematics Instruction framework.

Determining High School Geometry Students' Geometric Understanding Using Van Hiele Levels: Is There A Difference Between Standards-Based Curriculum Students And Nonstandards-Based Curriculum Students?, Rebekah Loraine Genz

Theses and Dissertations

Research has found that students are not adequately prepared to understand the concepts of geometry, as they are presented in a high school geometry course (e.g. Burger and Shaughnessy (1986), Usiskin (1982), van Hiele (1986)). Curricula based on the National Council of Teachers of Mathematics (NCTM) Standards (1989, 2000) have been developed and introduced into the middle grades to improve learning and concept development in mathematics. Research done by Rey, Reys, Lappan and Holliday (2003) showed that Standards-based curricula improve students' mathematical understanding and performance on standardized math exams. Using van Hiele levels, this study examines 20 ninth-grade students' levels …

Ua64/2 The Challenge: Magazine Of The Center For Gifted Studies (No. 17, Summer 2006), Center For Gifted Studies, Tracy Inman Editor

Gifted Studies Publications

No abstract provided.

Just What Do You “Mean”?, Myrna L. Bornemeier

Department of Mathematics: Master 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.

Area And Perimeter Of Polygons, Bryan Engelker

Department of Mathematics: Master 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?

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.)

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 …

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 …

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 …

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

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 …

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

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 …

Iowa Academy Of Science: The New Bulletin, V02n3, Summer 2006, Iowa Academy Of Science

New Bulletin

Inside This Issue:

--Message from the Executive Director

--InnoCentive

--Saylorville 2006 Weather Talk

--Jane Haugen receives Gold Star

--GLOBE ONE Posters go to Thailand

--Education and the Environment

--Upcoming Programs

Using Literature And Innovative Assessments To Ignite Interest And Cultivate Critical Thinking Skills In An Undergraduate Neuroscience Course, Eileen Lynd-Balta

Biology Faculty/Staff Publications

Science education reform initiatives emphasize 1) the value of concepts over facts; 2) the benefits of open-ended, inquiry-based problem-solving rather than protocols leading to a single correct answer; and 3) the importance of a multidisciplinary approach to teaching that is not confined by departmental boundaries. Neuroscientists should be at the forefront of this movement by the very nature of the discipline we study. Neuroscience is a relatively new field that integrates diverse subjects (anatomy, physiology, pharmacology, molecular biology, computer science, and psychology) and experimental advances are constantly changing and expanding our understanding of brain function. How can we convey this …

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 …

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 …