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Solving A System Of Linear Equations Using Ancient Chinese Methods, Mary Flagg 2017 University of St Thomas

Solving A System Of Linear Equations Using Ancient Chinese Methods, Mary Flagg

Linear Algebra

No abstract provided.


Pascal's Triangle And Mathematical Induction, Jerry Lodder 2017 New Mexico State University

Pascal's Triangle And Mathematical Induction, Jerry Lodder

Number Theory

No abstract provided.


Primes, Divisibility, And Factoring, Dominic Klyve 2017 Central Washington University

Primes, Divisibility, And Factoring, Dominic Klyve

Number Theory

No abstract provided.


Babylonian Numeration, Dominic Klyve 2017 Central Washington University

Babylonian Numeration, Dominic Klyve

Number Theory

No abstract provided.


Gaussian Integers And Dedekind's Creation Of An Ideal: A Number Theory Project, Janet Heine Barnett 2017 Colorado State University-Pueblo

Gaussian Integers And Dedekind's Creation Of An Ideal: A Number Theory Project, Janet Heine Barnett

Number Theory

No abstract provided.


Construction Of The Figurate Numbers, Jerry Lodder 2017 New Mexico State University

Construction Of The Figurate Numbers, Jerry Lodder

Number Theory

No abstract provided.


Rigorous Debates Over Debatable Rigor: Monster Functions In Introductory Analysis, Janet Heine Barnett 2017 Colorado State University-Pueblo

Rigorous Debates Over Debatable Rigor: Monster Functions In Introductory Analysis, Janet Heine Barnett

Analysis

No abstract provided.


The Definite Integrals Of Cauchy And Riemann, Dave Ruch 2017 Ursinus College

The Definite Integrals Of Cauchy And Riemann, Dave Ruch

Analysis

Rigorous attempts to define the definite integral began in earnest in the early 1800's. One of the pioneers in this development was A. L. Cauchy (1789-1857). In this project, students will read from his 1823 study of the definite integral for continuous functions . Then students will read from Bernard Riemann's 1854 paper, in which he developed a more general concept of the definite integral that could be applied to functions with infinite discontinuities.


The Derivatives Of The Sine And Cosine Functions, Dominic Klyve 2017 Central Washington University

The Derivatives Of The Sine And Cosine Functions, Dominic Klyve

Calculus

No abstract provided.


The Closure Operation As The Foundation Of Topology, Nicholas A. Scoville 2017 Ursinus College

The Closure Operation As The Foundation Of Topology, Nicholas A. Scoville

Topology

No abstract provided.


A Compact Introduction To A Generalized Extreme Value Theorem, Nicholas A. Scoville 2017 Ursinus College

A Compact Introduction To A Generalized Extreme Value Theorem, Nicholas A. Scoville

Topology

In a short paper published just one year prior to his thesis, Maurice Frechet gives a simple generalization one what we might today call the Extreme value theorem. This generalization is a simple matter of coming up with ``the right" definitions in order to make this work. In this mini PSP, we work through Frechet's entire 1.5 page paper to give an extreme value theorem in more general topological spaces, ones which, to use Frechet's newly coined term, are compact.


Beyond Problem-Solving: Elementary Students’ Mathematical Dispositions When Faced With The Challenge Of Unsolved Problems, Jenna R. O'Dell 2017 Illinois State University

Beyond Problem-Solving: Elementary Students’ Mathematical Dispositions When Faced With The Challenge Of Unsolved Problems, Jenna R. O'Dell

Theses and Dissertations

The goal of this study was to document the characteristics of students’ dispositions towards mathematics when they engaged in the exploration of parts of unsolved problems: Graceful Tree Conjecture and Collatz Conjecture. Ten students, Grades 4 and 5, from an after-school program in the Midwest participated in the study. I focused on the cognitive, affective, and conative aspects of their mathematical dispositions as they participated in 7 problem-solving sessions and two interviews.

With regard to cognitive aspects of the students’ dispositions, I focused on the students attempts to identify and justify patterns for labeling graphs. Overall, the unsolved problems were ...


Curriculum Alignment And Science And Engineering Practices In The Classroom, Victoria L. Davis 2017 University of Wyoming

Curriculum Alignment And Science And Engineering Practices In The Classroom, Victoria L. Davis

SMTC Plan B Papers

The release of the Next Generation Science Standards (NGSS) in 2013 introduced educators to the three dimensions of science literacy, which are the (a) Disciplinary Core Ideas (DCIs), (b) Cross-Cutting Concepts (CCCs), and the (c) Science and Engineering Practices (SEPs). For educators to address all three dimensions, they must analyze not only the expected content, but also how that content is presented and connected. Curriculum mapping is a tool developed in 1980 that can be used to analyze curricular alignment. This project focused on the creation of rubrics to analyze and evaluate the use of SEPs in conjunction with curriculum ...


The Impact Of Teacher Beliefs On Integrated Unit Design, Amanda J. Lopez 2017 University of Wyoming

The Impact Of Teacher Beliefs On Integrated Unit Design, Amanda J. Lopez

SMTC Plan B Papers

Teacher beliefs are personal constructs that develop over a lifetime and are influenced by a teacher’s personal experiences, experience with schooling and instruction, and experience with formal knowledge. A teacher’s belief system has a greater impact on their practice than their subject matter knowledge, which translates into the design of classroom materials. This study was conducted to explore the impact of my teacher beliefs and understanding of threedimensional learning on the development of a theme-based, integrated, standards aligned unit. Teacher beliefs can be changed through the implementation of authentic professional learning communities (PLCs). PLCs are defined as the ...


Ngss And Science Museums: How Learning Progressions Can Inform Field Trip Lesson Planning For Informal Science Centers, Dorothy Jablonski 2017 University of Wyoming

Ngss And Science Museums: How Learning Progressions Can Inform Field Trip Lesson Planning For Informal Science Centers, Dorothy Jablonski

SMTC Plan B Papers

Many states, including Wyoming, have adopted the Next Generation Science Standards (NGSS) or a very similar version of science standards. Research shows that in order to remain competitive in the field trip market, science museums need to align their curriculum to the same standards (Anderson, Kisiel, & Storksdieck, 2006). The major challenge for museums engaged in this process is the gaps in content introduced to various grade levels across performance expectations. I proposed that these gaps may be filled by creating a learning progression to inform the alignment process. Literature on cognitive development, informal learning, and previous learning progressions is used ...


Know Thyself: Using Student Self-Assessment To Increase Student Learning Outcomes, Winsor Demore 2017 University of Wyoming

Know Thyself: Using Student Self-Assessment To Increase Student Learning Outcomes, Winsor Demore

SMTC Plan B Papers

Student assessment in the classroom is necessary to support student growth and increase students’ content knowledge. Formative assessment, or assessment that helps guide instruction and learning, can take many forms. One widely-used form is student self-assessment, in which students assess their own learning and set goals to increase their understanding of a topic. While experts agree that the process of self-assessment is valuable, this value is dependent on the teaching methods, practice and support provided by teachers for students in the classroom throughout the school year. A number of research-based best practices were incorporated into a middle-school science self-assessment, which ...


Contextualizing Developmental Math Content Into Introduction To Sociology In Community Colleges, Stuart Parker, Amy E. Traver, Jonathan Cornick 2017 CUNY Kingsborough Community College

Contextualizing Developmental Math Content Into Introduction To Sociology In Community Colleges, Stuart Parker, Amy E. Traver, Jonathan Cornick

Publications and Research

Across community colleges in the United States, most students place into a developmental math course that they never pass. This can leave them without the math skills necessary to make informed decisions in major areas of social life and the college credential required for participation in growing sectors of our economy. One strategy for improving community college students’ pass rate in developmental math courses is the contextualization of developmental math content into the fabric of other courses. This article reviews an effort to contextualize developmental math content (i.e., elementary algebra) into Introduction to Sociology at Kingsborough Community College and ...


Finland: An Exemplary Stem Educational System, Hui Fang Huang "Angie" Su, Nancy Ledbetter, Jocelyn Ferguson, La'Trina Timmons 2017 Nova Southeastern University

Finland: An Exemplary Stem Educational System, Hui Fang Huang "Angie" Su, Nancy Ledbetter, Jocelyn Ferguson, La'trina Timmons

Transformations

There is a need for an increase in the number of students entering fields of science, technology, engineering, and mathematics (STEM) and the only way for that to happen is for educational reforms to be put into place (PCAST, 2012). Improvement and focus on STEM education are a concern of all nations whether they have an emerging economy or one that is long established. The world of the 21st century is such that in order to compete globally countries must invest in STEM education (Kennedy & Odell, 2014). The United States scores on the Program for International Student Assessment (PISA) were ...


Developing Mathematical Content Knowledge For Teaching Elementary School Mathematics, Eva Thanheiser, Christine A. Browning, Meg Moss, Tad Watanabe, Gina Garza-Kling 2017 Portland State University

Developing Mathematical Content Knowledge For Teaching Elementary School Mathematics, Eva Thanheiser, Christine A. Browning, Meg Moss, Tad Watanabe, Gina Garza-Kling

Eva Thanheiser

In this paper the authors present three design principles they use to develop preservice teachers' mathematical content knowledge for teaching in their mathematics content and/or methods courses: (1) building on currently held conceptions, (2) modeling teaching for understanding, (3) focusing on connections between content knowledge and other types of knowledge. The authors share results of individual research projects and teaching approaches focusing on helping preservice elementary teachers develop such knowledge. Specific examples from different content areas (whole number, fractions, angle, and area) are discussed.


Prevalence Of Typical Images In High School Geometry Textbooks, Megan N. Cannon 2017 University of South Florida

Prevalence Of Typical Images In High School Geometry Textbooks, Megan N. Cannon

Graduate Theses and Dissertations

Visualization in mathematics can be discussed in many ways; it is a broad term that references physical visualization objects as well as the process in which we picture images and manipulate them in our minds. Research suggests that visualization can be a powerful tool in mathematics for intuitive understanding, providing and/or supporting proof and reasoning, and assisting in comprehension. The literature also reveals some difficulties related to the use of visualization, particularly how illustrations can mislead students if they are not comfortable seeing concepts represented in varied ways. However, despite the extensive research on the benefits and challenges of ...


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