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Science and Mathematics Education Commons™

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2007

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Articles 31 - 60 of 334

Full-Text Articles in Science and Mathematics Education

The Council On Undergraduate Research As A Resource For Mathematicians, Thomas Q. Sibley Aug 2007

The Council On Undergraduate Research As A Resource For Mathematicians, Thomas Q. Sibley

Mathematics Faculty Publications

No abstract provided.

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A New Framework For Grading, Kris H. Green, W. Allen Emerson Aug 2007

A New Framework For Grading, Kris H. Green, W. Allen Emerson

Mathematical and Computing Sciences Faculty/Staff Publications

Grading is one of the least liked, least understood and least considered aspects of teaching. After years of work, we have developed a grading system that is quite different from traditional and reformed approaches to grading and which meaningfully incorporates and integrates the collection of evidence, the evaluation of evidence, and the reporting of judgments about that evidence. This system satisfies the requirements of good grading system and answers many of the problems faced by more traditional methods by substantially changing the way in which grade information is aggregated, resulting in a final course grade that aligns qualitative evaluation with …

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A Rotating Panel Survey To Assess Quality Of Hunter College Education, Jennifer Sousa Brennan, William (Bill) H. Williams Aug 2007

A Rotating Panel Survey To Assess Quality Of Hunter College Education, Jennifer Sousa Brennan, William (Bill) H. Williams

Publications and Research

A rotating sample design is proposed to most accurately measure the perceived quality of a Hunter College education. A representative sample of Hunter College students will belong to one of six rotating panels. Students will be contacted during four rotation periods and report their assessment of the two most recent months. It is advantageous to use a rotating panel design as opposed to a fixed panel design in order to guard against the negative effects of a deteriorating response rate. Stratified sampling will help to ensure representation across major departments and academic year of study. Methods for sampling procedures, stratification, …

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An Investigation Of Successful And Unsuccessful Students’ Problem Solving In Stoichiometry, Ozcan Gulacar Aug 2007

An Investigation Of Successful And Unsuccessful Students’ Problem Solving In Stoichiometry, Ozcan Gulacar

Dissertations

In this study, I investigated how successful and unsuccessful students solve stoichiometry problems. I focus on three research questions: (1) To what extent do the difficulties in solving stoichiometry problems stem from poor understanding of pieces (domain-specific knowledge) versus students' inability to link those pieces together (conceptual knowledge)? (2) What are the differences between successful and unsuccessful students in knowledge, ability, and practice? (3) Is there a connection between students' (a) cognitive development levels, (b) formal (proportional) reasoning abilities, (c) working memory capacities, (d) conceptual understanding of particle nature of matter, (e) understanding of the mole concept, and their problem-solving …

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Discovering The Derivative Can Be "Invigorating:" Mark's Journey To Understanding Instantaneous Velocity, Charity Ann Gardner Hyer Jul 2007

Discovering The Derivative Can Be "Invigorating:" Mark's Journey To Understanding Instantaneous Velocity, Charity Ann Gardner Hyer

Theses and Dissertations

This is a case study using qualitative methods to analyze how a first semester calculus student named Mark makes sense of the derivative and the role of the classroom practice in his understanding. Mark is a bright yet fairly average student who successfully makes sense of the derivative and retains his knowledge and understanding. The study takes place within a collaborative, student-centered, task-based classroom where the students are given opportunity to explore mathematical ideas such as rate of change and accumulation. Mark's sense making of the derivative is analyzed in light of his use of physics, Mark as a visual …

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Probing For Reasons: Presentations, Questions, Phases, Kellyn Nicole Farlow Jul 2007

Probing For Reasons: Presentations, Questions, Phases, Kellyn Nicole Farlow

Theses and Dissertations

This thesis reports on a research study based on data from experimental teaching. Students were invited, through real-world problem tasks that raised central conceptual issues, to invent major ideas of calculus. This research focuses on work and thinking of the students, as they sought to build key ideas, representations and compelling lines of reasoning. This focus on the students' and their agency as learners has brought about a new development of the psychological and logical perspectives, as well as, highlighted students' choices in academic and social roles. Such choices facilitated continued learning among these students.

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The Main Challenges That A Teacher-In-Transition Faces When Teaching A High School Geometry Class, Greg Brough Henry Jul 2007

The Main Challenges That A Teacher-In-Transition Faces When Teaching A High School Geometry Class, Greg Brough Henry

Theses and Dissertations

During a semester-long action research study, the author attempted to implement a standards-based approach to teaching mathematics in a high school geometry class. Having previously taught according to a more traditional manner, there were many challenges involved as he made this transition. Some of the challenges were related to Geometry and others were related to the standards-based approach in general. The main challenges that the author encountered are identified and discussed. A plan of action for possible solutions to these challenges is then described.

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Applying Toulmin's Argumentation Framework To Explanations In A Reform Oriented Mathematics Class, Jennifer Alder Brinkerhoff Jul 2007

Applying Toulmin's Argumentation Framework To Explanations In A Reform Oriented Mathematics Class, Jennifer Alder Brinkerhoff

Theses and Dissertations

This study looks at conceptual explanations given in a reform-oriented mathematics class for preservice secondary mathematics teachers and extends Toulmin's argumentation framework to account for some of the complexities of the explanations given by these students. This study explains the complexities that arose in applying Toulmin's framework to explanations and extends the framework by accounting for the features of conceptual explanations. The complexities of these explanations are that they are made up of multiple arguments that build on each other to reach a final conclusion and that they are also dependant upon the social aspects of the class in which …

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Recycle Please: Teach Your School To Recycle, To Care, And To Help Solve The Climate Crisis, Ted Wells Jul 2007

Recycle Please: Teach Your School To Recycle, To Care, And To Help Solve The Climate Crisis, Ted Wells

Graduate Student Independent Studies

This Independent Study offers one developmentally-appropriate way in which the elementary school teacher can help alleviate the current global warming crisis by leading students to organize a school-wide recycling program carried out in the spirit of service learning. The reader will learn that this recycling work is two-pronged: the physical labor of recycling and the educational outreach to the school community through marketing, using posters, assemblies, videos, and more. A philosophy of education underlying this work is described in detail, as is the journey of the author in discovering this pedagogy that includes tapping into a personal environmental activism for …

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The Importance Of Vocabulary Instruction In Everyday Mathematics, Chad Larson Jul 2007

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 …

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A Monte Carlo Simulation Of The Birthday Problem, Stacey Aldag Jul 2007

A Monte Carlo Simulation Of The Birthday Problem, Stacey Aldag

Department of Mathematics: Master 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 …

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Calculators In The Classroom: Help Or Hindrance?, Christina L. Sheets Jul 2007

Calculators In The Classroom: Help Or Hindrance?, Christina L. Sheets

Action Research Projects

In a world where technology is ever present and ever changing, is too much technology at too young of an age detrimental to a child’s educational success? The purpose of this paper is to share the results of a four-month study that focused on the use of calculators in grade eight. This study was conducted in an eighth grade class, in a small kindergarten through twelfth grade school. This paper will share the findings of a study of a classroom in which calculator use was limited and mental computation was emphasized. The main focus of this study was whether or …

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Connections Between Communication And Math Abilities, Rachelle Mayo Jul 2007

Connections Between Communication And Math Abilities, Rachelle Mayo

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

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Evaluating Polynomials, Thomas J. Harrington Jul 2007

Evaluating Polynomials, Thomas J. Harrington

Department of Mathematics: Master 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 …

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How To Graphically Interpret The Complex Roots Of A Quadratic Equation, Carmen Melliger Jul 2007

How To Graphically Interpret The Complex Roots Of A Quadratic Equation, Carmen Melliger

Department of Mathematics: Master 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.

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Master Of Arts In Teaching (Mat), Josh Severin Jul 2007

Master Of Arts In Teaching (Mat), Josh Severin

Department of Mathematics: Master 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 …

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Hyperbolic Geometry, Christina L. Sheets Jul 2007

Hyperbolic Geometry, Christina L. Sheets

Department of Mathematics: Master 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. …

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Pythagorean Triples, Diane Swartzlander Jul 2007

Pythagorean Triples, Diane Swartzlander

Department of Mathematics: Master 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 …

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Perimeter And Area Of Inscribed And Circumscribed Polygons, Lindsey Thompson Jul 2007

Perimeter And Area Of Inscribed And Circumscribed Polygons, Lindsey Thompson

Department of Mathematics: Master 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 …

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The Volume Of A Platonic Solid, Cindy Steinkruger Jul 2007

The Volume Of A Platonic Solid, Cindy Steinkruger

Department of Mathematics: Master 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 …

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Using Cooperative Learning To Promote A Problem-Solving Classroom, Amy Nebesniak Jul 2007

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

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

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A Study Of The Role Of Mnemonics In Learning Mathematics, Kathy Delashmutt Jul 2007

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

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

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Increasing Conceptual Learning Through Student Participation, Janet Timoney Jul 2007

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 …

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The Effects Improving Student Discourse Has On Learning Mathematics, Lindsey Thompson Jul 2007

The Effects Improving Student Discourse Has On Learning Mathematics, Lindsey Thompson

Action Research Projects

In this action research study of my 8th grade mathematics classroom, I investigated how improving student discourse affects learning mathematics. I conducted this study because I wanted to give students more opportunities to develop and share their ideas with their peers as well as with me. My idea was to create a learning environment that encouraged students to voice their opinions. In order to do so, I needed to reassure and model with my students that they were in a classroom where it was safe to take risks, and they should feel comfortable sharing their ideas. By facilitating activities for …

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Improving Students’ Story Problem Solving Abilities, Josh Severin Jul 2007

Improving Students’ Story Problem Solving Abilities, Josh Severin

Action Research Projects

In this action research study of my classroom of 8th grade mathematics students, I investigated if learning different problem solving strategies helped students successfully solve problems. I also investigated if students’ knowledge of the topics involved in story problems had an impact on students’ success rates. I discovered that students were more successful after learning different problem solving strategies and when given problems with which they have experience. I also discovered that students put forth a greater effort when they approach the story problem like a game, instead of just being another math problem that they have to solve. An …

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Understanding The Mathematical Language, Carmen Melliger Jul 2007

Understanding The Mathematical Language, Carmen Melliger

Action Research Projects

In this action research study of my calculus classroom consisting of only 12th grade students, I investigated activities that would affect a student’s understanding of mathematical language. The goal in examining these activities in a systematic way was to see if a student’s deeper understanding of math terms and symbols resulted in a better understanding of the mathematical concepts being taught. I discovered that some students will rise to the challenge of understanding mathematics more deeply, and some will not. In the process of expecting more from students, the frustration level of both the students and the teacher increased. As …

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“Let’S Review.” A Look At The Effects Of Re-Teaching Basic Mathematic Skills, Thomas J. Harrington Jul 2007

“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 …

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Generating Interest In Mathematics Using Discussion In The Middle School Classroom, Jessica Fricke Jul 2007

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 …

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Cooperative Learning As An Effective Way To Interact, Gary Eisenhauer Jul 2007

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 …

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Ua64/2 The Challenge: Magazine Of The Center For Gifted Studies (No. 19, Summer 2007), Center For Gifted Studies, Tracy Inman Editor Jul 2007

Ua64/2 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.

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