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Articles 31 - 60 of 213
Full-Text Articles in Education
Ethnomathematics, Chad Larson
Ethnomathematics, Chad Larson
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
When asked to think about a foreign country the first thing that comes to my mind is the language barrier and the customs that accompany that specific country. The culture of the citizens and how it differs from my culture are also things which peak my interest. Things which I view as “normal” may seem very odd to someone who lives thousands of miles away, and likewise, traditions that have been past down from generations of people from distant lands may seem peculiar to me. These customs and cultures of which I speak are also the things that make this …
How To Graphically Interpret The Complex Roots Of A Quadratic Equation, Carmen Melliger
How To Graphically Interpret The Complex Roots Of A Quadratic Equation, Carmen Melliger
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
As a secondary math teacher I have taught my students to find the roots of a quadratic equation in several ways. One of these ways is to graphically look at the quadratic and see were it crosses the x-axis. For example, the equation of y = x2 – x – 2, as shown in Figure 1, has roots at x = -1 and x = 2. These are the two places in which the sketched graph crosses the x-axis.
Experimentation With Two Formulas By Ramanujan, Daniel Schaben
Experimentation With Two Formulas By Ramanujan, Daniel Schaben
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
Srinivasa Ramanujan was a brilliant mathematician, considered by George Hardy to be in the same class as Euler, Gauss, and Jacobi. His short life, marred by illness and tragic educational events, was unique in the history of mathematics. Mathematical discoveries are still being gleaned from his personal notebooks. Paper was a hard commodity to come by so his notebooks were a cluttered mix of pen over pencil mathematical hieroglyphics. The following highlights Ramanujan’s life in connection with Hardy, his work with ellipses, and his work with the partition function.
Master Of Arts In Teaching (Mat), Josh Severin
Master Of Arts In Teaching (Mat), Josh Severin
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
The number zero is a very powerful tool in mathematics that has many different applications and rules. An interesting fact about the number zero is that according to our calendar (the Gregorian calendar), there is no “year zero” in our history. There is also no “zeroth” century as time is recorded from centuries B.C. to the 1st century A.D. However, certain calendars do have a year zero. In the astronomical year numbering system year zero is defined as year 1 BC. Buddhist and Hindu lunar calendars also have a year zero. In this paper I am going to discuss many …
Simple Statements, Large Numbers, Shana Streeks
Simple Statements, Large Numbers, Shana Streeks
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
Large numbers are numbers that are significantly larger than those ordinarily used in everyday life, as defined by Wikipedia (2007). Large numbers typically refer to large positive integers, or more generally, large positive real numbers, but may also be used in other contexts. Very large numbers often occur in fields such as mathematics, cosmology, and cryptography. Sometimes people refer to numbers as being “astronomically large”. However, it is easy to mathematically define numbers that are much larger than those even in astronomy. We are familiar with the large magnitudes, such as million or billion. In mathematics, we may know a …
Perimeter And Area Of Inscribed And Circumscribed Polygons, Lindsey Thompson
Perimeter And Area Of Inscribed And Circumscribed Polygons, Lindsey Thompson
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
This paper looks at comparing the perimeter and area of inscribed and circumscribed regular polygons. All constructions will be made with circles of radius equal to 1 unit. To begin this exploration, I created a circle with a radius of 1(for my purposes I used 1 inch as my unit of measure). I chose my first construction to contain the most basic regular polygon, an equilateral triangle. A regular polygon implies that all sides of the figure are equal and all interior angles of the figure are congruent. My first construction shows an equilateral triangle inscribed in a circle (see …
The Four Numbers Game, Tina Thompson
The Four Numbers Game, Tina Thompson
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
The Four Numbers Game is a fun way to work with subtraction and ordering of numbers. While trying to find an end to a game that is played with whole numbers, there are several items that will be investigated along the way. First, we offer an introduction to how the game is played. Second, rotations and reflections of a square will be presented which will create a generalized form. Third, we explain how even and odd number combinations will always end in even numbers within four subtraction rounds. Fourth, we argue that the length of the game does not change …
Order Of Operations And Rpn, Greg Vanderbeek
Order Of Operations And Rpn, Greg Vanderbeek
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
There is not a wealth of information regarding the history of the notations and procedures associated with what is now called the “order of operations”. There is evidence that some agreed upon order existed from the beginning of mathematical study. The grammar used in the earliest mathematical writings, before mathematical notation existed, supports the notion of computational order (Peterson, 2000). It is clear that one person did not invent the rules but rather current practices have grown gradually over several centuries and are still evolving.
Connections Between Communication And Math Abilities, Rachelle Mayo
Connections Between Communication And Math Abilities, Rachelle Mayo
Departament of Teaching, Learning, and Teacher Education: Master's of Arts in Teaching, Summative Projects
In this action research study of my Class I School’s 5th and 8th grade mathematics, I investigated students’ connections between communication of math skills and their math abilities. I discovered that students can increase their math abilities with the opportunities to discuss their thinking as well as evaluate thinking and strategies of other students. Electronic communication can be a valuable source for students to communicate further to other students.
Pre-Reading Mathematics Empowers Students, Stacey Aldag
Pre-Reading Mathematics Empowers Students, Stacey Aldag
Action Research Projects
In this action research study of my 8th grade mathematics classroom, I investigated the improvement of mathematical communication via assigning pre-reading material and requiring students to take notes prior to class discussions. I discovered that students became more active participants during classroom discussions and were able to produce work which illustrated their mathematical understanding. Teacher observations and improved quiz scores provide quantitative evidence, and student survey responses validate student communication. As a result of this research, I plan to assign pre-reading tasks and require students to take notes prior to class discussions with the goal to change classroom presentation from …
Generating Interest In Mathematics Using Discussion In The Middle School Classroom, Jessica Fricke
Generating Interest In Mathematics Using Discussion In The Middle School Classroom, Jessica Fricke
Action Research Projects
In this action research study of my classroom of 8th grade algebra, I investigated students’ discussion of mathematics and how it relates to interest in the subject. Discussion is a powerful tool in the classroom. By relying too heavily on drill and practice, a teacher may lose any individual student insight into the learning process. However, in order for the discussion to be effective, students must be provided with structure and purpose. It is unrealistic to expect middle school age students to provide their own structure and purpose; a packet was constructed that would allow the students to both show …
“Let’S Review.” A Look At The Effects Of Re-Teaching Basic Mathematic Skills, Thomas J. Harrington
“Let’S Review.” A Look At The Effects Of Re-Teaching Basic Mathematic Skills, Thomas J. Harrington
Action Research Projects
In this action research study of my classroom of 8th grade mathematics, I investigated the effect of reviewing basic fraction and decimal skills on student achievement and student readiness for freshman Algebra. I also investigated the effect on the quality of student work, with regards to legibility by having students grade each other’s work anonymously. I discovered that students need basic skill review with fractions and decimals, and by the end of the research their scores improved. However, their handwriting had not. At the end of the research, a majority of the students felt the review was important, and they …
Improving Student Engagement And Verbal Behavior Through Cooperative Learning, Daniel Schaben
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 …
Do Students Progress If They Self-Assess? A Study In Small-Group Work, Cindy Steinkruger
Do Students Progress If They Self-Assess? A Study In Small-Group Work, Cindy Steinkruger
Action Research Projects
In this action research study of my classroom of 8th grade mathematics, I investigated the effects of self-assessment on student group work. Data was collected to see how self-assessment affected small-group work, usage of precise mathematical vocabulary, and student attitudes toward mathematics. Self-assessment allowed the students to periodically evaluate their own learning and their involvement in math class. I discovered that the vast majority of students enjoy working in small-groups, and they feel they are good group members. Evidence in regard to use of precise mathematical vocabulary showed an increased awareness in the importance of its usage. Student attitudes toward …
Why Are We Writing? This Is Math Class!, Shana Streeks
Why Are We Writing? This Is Math Class!, Shana Streeks
Action Research Projects
In this action research study of my classroom of 8th grade mathematics, I investigated writing in the content area. I have realized how important it is for students to be able to communicate mathematical thoughts to help gain a deeper understanding of the content. As a result of this research, I plan to enforce the use of writing thoughts and ideas regarding math problems. Writers develop skills and generate new thoughts and ideas every time they sit down to write. Writing evolves and grows with ongoing practice, and that means thinking skills mature along with it. Writing is a classroom …
The Challenge: Magazine Of The Center For Gifted Studies (No. 19, Summer 2007), Center For Gifted Studies, Tracy Inman Editor
The Challenge: Magazine Of The Center For Gifted Studies (No. 19, Summer 2007), Center For Gifted Studies, Tracy Inman Editor
Gifted Studies Publications
No abstract provided.
A Monte Carlo Simulation Of The Birthday Problem, Stacey Aldag
A Monte Carlo Simulation Of The Birthday Problem, Stacey Aldag
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
Question, how many people would you need in a group in order for there to be a 50-50 chance that at least two people will share a birthday? Answer, 23 people. But how can this be? There are 365 days in a year and half of that would be 182, so why wouldn’t you need at least 182 people to have a 50-50 chance? Strangely enough the answer to this question is only 23 people are necessary to have a 50% chance at least two people in the group will share a birthday. This situation, where the answer is counter …
Extending A Finite Sequence, Jessica Fricke
Extending A Finite Sequence, Jessica Fricke
Department of Mathematics: Master's of Arts in Teaching, Exam Expository Papers
One of the most common mistakes in school mathematics is to list a few terms of a sequence and ask “What term comes next?” For example, a teacher may write: 1 2 4 … and ask what term comes next? The best answer is “almost anything could be the next term.” But people often find that answer unsatisfying. It helps, instead, to give an example. Perhaps, one might respond by saying: “The next number might be 8, but then again, it might be 7.” This answer might, of course, result in an angry teacher, so you need to be prepared …
Hyperbolic Geometry, Christina L. Sheets
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
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
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
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
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
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
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
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
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
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
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
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 …