Digital Commons Network^™

Proof And Reasoning In An Inquiry-Oriented Class: The Impact Of Classroom Discourse, Susan D. Generazzo

Doctoral Dissertations

Over the past decade, mathematics educators and researchers have become increasingly aware of the impact of social interactions on students' learning (NCTM, 2000; Bowers & Nickerson, 2001; Forman, 2003). Current research indicates that the classroom environment, including the activities and discussions that take place, can have a significant effect on the ways students make sense of mathematical concepts (Yackel, 2001). Understanding mathematics involves knowing how to make sense of key concepts through the processes of reasoning and justification. Educators and researchers agree on the importance of providing students with opportunities in class to explore, conjecture, and prove in order to …

Homotopy Mapping Spaces, Jeremy Brazas

Doctoral Dissertations

In algebraic topology, one studies the group structure of sets of homotopy classes of maps (such as the homotopy groups pin( X)) to obtain information about the spaces in question. It is also possible to place natural topologies on these groups that remember local properties ignored by the algebraic structure. Upon choosing a topology, one is left to wonder how well the added topological structure interacts with the group structure and which results in homotopy theory admit topological analogues. A natural place to begin is to view the n-th homotopy group pi n(X) as the quotient space of the iterated …

On Decompositions And Connes's Embedding Problem Of Finite Von Neumann Algebras, Jinsong Wu

Doctoral Dissertations

A longstanding open question of Connes asks whether every finite von Neumann algebra embeds into an ultraproduct of finite-dimensional matrix algebras. As of yet, algebras verified to satisfy Connes's embedding property belong to just a few special classes (e.g. amenable algebras and free group factors). In this dissertation we establish Connes's embedding property for von Neumann algebras satisfying Popa's co-amenability condition. Some decomposition properties of finite von Neumann algebras are also investigated.

Chapter 1 reviews von Neumann algebras, completely bounded mappings, conditional expectations, tensor products, crossed products, direct integrals, and Jones basic construction.

Chapter 2 introduces new decompositions of finite …

Parts Of The Whole : Cognition, Schemas, And Quantitative Reasoning, Dorothy Wallace

Numeracy

Based loosely on ideas of Jean Piaget and Richard Skemp, this Parts of the Whole column considers the construction of knowledge in mathematics and quantitative reasoning. Examples are chosen that illustrate an important cognitive difference between quantitative numeracy and classical mathematics, and which illuminate the particular choices instructors must make in order to teach either or both of these.

Learning Mathematics With Technology: The Influence Of Virtual Manipulatives On Different Achievement Groups, Patricia S. Moyer-Packenham, J. M. Suh

Teacher Education and Leadership Faculty Publications

This study examined the influence of virtual manipulatives on different achievement groups during a teaching experiment in four fifth-grade classrooms. During a two-week unit focusing on two rational number concepts (fraction equivalence and fraction addition with unlike denominators) one low achieving, two average achieving, and one high achieving group participated in two instructional treatments (three groups used virtual manipulatives and one group used physical manipulatives). Data sources included pre- and post-tests of students’ mathematical content knowledge and videotapes of classroom sessions. Results of paired samples t-tests examining the three groups using virtual manipulatives indicated a statistically significant overall gain following …

I Have A Solution To Share: Learning Through Equitable Participation In A Mathematics Classroom, Mary Q. Foote, Rachel Lambert

Education Faculty Articles and Research

Student participation is an issue of equity. Without participation there can be no learning. This study focuses on the participation (and therefore learning) of struggling students (those with individual education plans [IEPs]) during the implementation of a relational thinking routine in a third-grade inclusion classroom. Students with IEPs often initially used direct modeling with linking cubes as a resource for presenting their thinking. In this way, they were able to demonstrate their ability to think relationally. As the year progressed, these students, who had earlier been reluctant to share and had done so only by using several of the resources …

Four Popular Books On Consumer Debt: A Context For Quantitative Literacy, Andrew J. Miller

Numeracy

The topics of credit cards, mortgages, subprime lending, and fringe banking are rich sources of problems and discussions for classes focused on quantitative literacy. In this theme book review, we look at four recent books on the consumer debt industry: Credit Card Nation, by Robert Manning; Maxed Out, by James Scurlock; Collateral Damaged, by Charles Geisst; and Broke, USA, by Gary Rivlin. Credit Card Nation takes a scholarly look at the history of credit in America with a focus on the genesis and growth of the credit card industry up to the turn of the 20th century. Maxed Out also …

Anxiety And Visual Discriminations In Undergraduates, Katherine Bowers

The Journal of Undergraduate Research

Mathematics tests were used to create anxiety in undergraduates. Heart rates were recorded as a measure of anxiety. Following each mathematics test, participants completed a different visual discrimination tasks, Stroop Colored Word Tests, Where’s Waldo Puzzles, and IQ Matching Tests. Reaction times and accuracy were measured for each task. The hypothesis was that those with more difficult mathematics tests would have longer reaction times and be less accurate. The results of the study suggest that mathematics anxiety did not have a significant effect on reaction times for any task, and was only significant for the accuracy of the IQ matching …

Mathematics In The Age Of Technology: There Is A Place For Technology In The Mathematics Classroom, Helen Crompton

Teaching & Learning Faculty Publications

In today’s world of ubiquitous computing there are a number of technologies available to K-12 educators for teaching and learning mathematics. However, Koehler and Mishra (2008) have described how teaching and learning with such technologies presents a “wicked problem,” as it can involve a number of variables, independent of each other and contextually bound, that need to be brought together. This article highlights the advantages technology offers for mathematics education and looks at some of the reasons behind the poor uptake, such as teacher beliefs and lack of training. A number of solutions are offered to address these issues, including …

Strategies To Improve Math Fact Fluency In Elementary School Students, Jennifer Whealy

All Graduate Projects

The purpose of this project is to develop a guide that contains strategies to improve math fact fluency in elementary school students. The guide is developed to be used by elementary school teachers in Washington State to show them how to incorporate strategies for math fact fluency into their math curriculum. The math fact fluency strategies ca:n be used to help teachers support students in their understanding of their basic addition, subtraction, multiplication, and division facts. This guide will contain research based strategies to improve math fact fluency for kindergarten through fifth grade students. The guide will include research based …

The Effects Of Learning Groups On Student Achievement And Attitude In A Sixth Grade Mathematics Class, Jay Randall Mcguffin

All Graduate Projects

A handbook for implementing "Student Team Learning" as an alternative teaching strategy for middle level math teachers was developed after conducting extensive action research project within a sixth grade math classroom. A literature review on barriers to learning mathematics in middle schools and Student Team Learning as a teaching strategy was conducted. An action research project was conducted and from the pre to post-test data and best practices implementation regarding student team learning methods the handbook project was constructed. The handbook includes an introduction to Student Team Learning; guidelines for implementation; a student attitude survey; lesson practice questions, review sheets, …

Fifth Grade Children's Use Of Reciprocal Teaching To Solve Word Problems In Mathematics, Mary Helen Collen

Legacy Theses & Dissertations (2009 - 2024)

Reciprocal teaching, a social constructivist instruction method, was explored in this study on the mathematical word problem solving skills of fifth grade students in two elementary schools within a suburban school district in upstate New York. Eighty-five students in four intact classes participated in this mixed methods study.

The Relationship Between Special Education Teachers' Mathematical Knowledge, Instructional Choices, And Beliefs About Teaching And Learning Mathematics, Virginia Rich Lee

Legacy Theses & Dissertations (2009 - 2024)

Thirty-four certified special education teachers completed four instruments in addition to viewing video recordings of students engaging in mathematical tasks. The mathematical beliefs of special education teachers were investigated through the use of the Mathematics Beliefs Scales (Capraro, 2005). Special education teachers' mathematical knowledge was measured using the Fraction Knowledge Assessment, which included a range of fraction tasks drawn from state and national elementary level mathematics standards. The proposed instruction of the special education teachers was examined through participants' written responses to video recordings of students solving fraction problems. Demographic information was obtained through the use of a questionnaire. Results …

Open-Ended (Extended/Constructed) Response Questions As Predictors Of Success On Subsequent State Mathematics Examination : The Influence Of Mathematical Awareness And Conceptual Knowledge, Kathy Ann Gullie

Legacy Theses & Dissertations (2009 - 2024)

This study investigated the predictive ability of students' responses to open-ended, constructed/extended questions in third and fourth grade mathematics content sub-categories on subsequent fifth grade mathematics achievement proficiency levels. Open-ended, extended/constructed response questions reflected content as outlined by the National Council of Teachers of Mathematics (2007) in statistics and probability, number sense, numeration and operations, geometry, algebra, and measurement. Archival data from over 300 third, fourth and fifth grade students in one public school in New York State during the 2003- 2009 academic school years were utilized. Third grade predictor variables included statistics and probability, number sense, numeration and operations, …

An Examination Of Secondary Mathematics Teachers' Tpack Development Through Participation In A Technology-Based Lesson Study, Julie Whitten Riales

Electronic Theses and Dissertations

This qualitative research study used a layered case study (Patton, 2002) to examine the technological, pedagogical, and content knowledge (TPACK) of a group of inservice secondary mathematics teachers as they participated in a technology-based lesson study. Using the TPACK Development Model (Niess, 2009) as a lens, this dissertation examines interactions of the group members during lesson study meetings as well as individual case studies of four of the six participants. Data were gathered from initial surveys, initial and post-interviews, initial and post-classroom observations, writing prompts, and transcriptions of lesson study group meetings. Data were analyzed to determine the TPACK development …

Problems With And Without … Problems!, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This book is addressed to College honor students, researchers, and professors. It contains 136 original problems published by the author in various scientific journals around the world. The problems could be used to preparing for courses, exams, and Olympiads in mathematics. Many of these have a generalized form. For each problem we provide a detailed solution.

I was a professeur coopérant between 1982-1984, teaching mathematics in French language at Lycée Sidi EL Hassan Lyoussi in Sefrou, Province de Fès, Morocco. I used many of these problems for selecting and training, together with other Moroccan professors, in Rabat city, of the …

Women In Mathematics: An Historical Account Of Women's Experiences And Achievement, Kendra D. Huff

CMC Senior Theses

For a long time, women have struggled to gain complete acceptance in the mathematics field. The purpose of this paper is to explore the history of women in the field of mathematics, the impact and experiences of current female mathematicians, and the common trends for women in the mathematics field, through literature review and personal interviews. This paper looks at the lives of four famous female mathematicians, as well as female mathematicians in the Claremont Colleges who were interviewed for this paper. Specifically this paper examines the discrimination they faced and how they overcame this discrimination, as well as the …

Personal And Professional Numeracy: A Unit For Pre-Service Teachers At The University Of Tasmania, Jane M. Watson

Numeracy

This paper addresses issues associated with the development of a unit preparing pre-service teachers to be quantitatively literate in three respects. These issues surround (i) the need to be aware of numeracy demands across the curriculum, (ii) the need to model numerate behavior in all interactions of teachers, and (iii) the need to be able to interpret and use system data provided from local and national testing programs. The context for the unit described is Australia, where a national testing program for literacy and numeracy requires teachers to analyze extensive data on their students, a national curriculum requires teachers of …

Go Figure: Calculus Students' Use Of Figures And Graphs In Technical Report Writing, Thomas J. Pfaff, Michael Rogers, Ali Erkan, Jason G. Hamilton

Numeracy

Understanding how to read and use graphs to communicate scientific and mathematical information is critical for STEM majors, as well as an important part of quantitative literacy. Our study suggests that first-semester calculus students do not know how to use graphs in a technical report without explicit instruction. Although not a surprising result, it leaves us wondering about when such skills are developed, and if calculus I is a place to start. Our work is now exploring the potential benefit on students' use of graphs by having them formally evaluate other students' reports.

Review Of Sex, Drugs And Body Counts: The Politics Of Numbers In Global Crime And Conflict, Edited By Peter Andreas And Kelly M. Greenhill, Aaron G. Montgomery

Numeracy

Andreas, Peter, and Greenhill, Kelly M. (Eds.). Sex, Drugs, and Body Counts: The Politics of Numbers in Global Crime and Conflict, (Ithaca, NY: Cornell University Press, 2010). 287 pp. ISBN 978-0-8014-4861-4 (cloth); ISBN 978-0-8014-7618-1 (pbk).

The ten scholarly papers in Sex, Drugs and Body Counts explore the generation and propagation of numbers that drive policy decisions in the U.S. government regarding human trafficking, drug trade, and armed conflict (including the war on terror). Each of these papers, written by different authors, provides an illuminating insight into how some of the numbers we hear or read in the news are derived. …

Ganas And The Swan: American Materialism In Mathematics Education, Taylor Berliant

CMC Senior Theses

Math is a unique subject. It is a different type of thinking for many people. Even though topics in math are separate, math is seen as a whole unlike many other subjects. Science, literature, history, art, languages, and physical education, the subjects, in addition to math, that make up the typical high school curriculum, are hardly ever referred to without additional labeling. Many of the subjects even contain topics with nearly incomparable material. The idea of math as a whole, at least in high school, is not completely untrue. A lot of the topics rely on the knowledge of previous …

Negotiating The "Relevant" In Culturally Relevant Mathematics, N. Enyedy, J. Danish, Deborah A. Fields

Instructional Technology and Learning Sciences Faculty Publications

One approach to promoting successful engagement of underrepresented groups in mathematics classrooms is Culturally Relevant Pedagogy (CRP). However, it has been argued that CRP risks essentializing students or watering down academic content. We report our analysis of a case study of a group of three 6th grade students who took part in a 6-week mathematics curriculum. This curriculum used Geographical Information System (GIS) maps to engage students in designing personally meaningful research projects while learning about measures of central tendency (i.e., learning statistics). The case study was chosen as representative of how students in this urban classroom (47 total) successfully …

Effects Of Instructional Technology On The Mathematics Achievement Of Eighth Grade Students, Paul Burkhart

OTS Master's Level Projects & Papers

The problem of this study was to determine how Norfolk Middle School Mathematics teachers’ use of instructional technology in their classroom affected student’s success on the 8th grade Standards of Learning (SOL) test.

Enrollment In Technology Education Based Upon Scores In Mathematics And Science, Robert D'Souza

OTS Master's Level Projects & Papers

The problem of this study was to determine if a relationship exists between 7th and 8th grade students choosing to enroll in technology education as an elective based on their success in mathematics and science subjects.

The Teaching Of Mathematics And Science In English : A Discourse Analysis Of Editorials In A Chinese Daily / Ma Jing., Jing Ma

Student Works (2010-2019)

No abstract provided.

Engineering Mathematics And Virtual Learning Environments: A Case Study Of Student Perceptions, Annette Louise Taylor

School of Engineering, Computing and Mathematics Theses

The study involved BTec National (level 3) engineering students studying at a large Further Education College in the South West region. The disciplines of Electrical/Electronic, Mechanical, Operations and Maintenance, Manufacturing, Telecommunications and Fabrication where all included in the study. Several students were sent by their employers on day release programmes and apprenticeships, and these formed the majority of the part time students. There were also other employed students who attended full time for terms 1 and 3 as part of a block release programme. The remaining students were full time, and mainly 16-18 years old. The study focused upon the …

Springer Representations On The Khovanov Springer Varieties, Heather M. Russell, Julianna Tymoczko

Department of Math & Statistics Faculty Publications

Springer varieties are studied because their cohomology carries a natural action of the symmetric group S_n and their top-dimensional cohomology is irreducible. In his work on tangle invariants, Khovanov constructed a family of Springer varieties X_n as subvarieties of the product of spheres (S²)ⁿ. We show that if X_n is embedded antipodally in (S²)ⁿ then the natural S_n-action on (S²)ⁿ induces an Sn-representation on the image of H_*(X_n). This representation is the Springer representation. Our construction admits an elementary (and geometrically …

African American Community College Student Perceptions Of Mathematics Instructor Immediacy Behaviors And Perceived Cognitive Learning, Georgia Lynne Toland

Master's Theses

The purpose of this research is to examine what instructor immediacy behaviors are perceived to most positively affect the perceived cognitive learning of African American community college mathematics students. Data were provided via voluntary student surveys collected in various mathematics classrooms at two community colleges. The survey instrument was modeled from the works of Gorham (1988) and Sanders and Wiseman (1990) and included an experimental survey method of direct questioning. The perceptions of African American community college students regarding the behaviors of their mathematics instructors, along with their stated preferred instructor behaviors, produced a subset of effective strategies similar to …

Construction And Simplicity Of The Large Mathieu Groups, Robert Peter Hansen

Master's Theses

In this thesis, we describe the construction of the Mathieu group M₂₄ given by Ernst Witt in 1938, a construction whose geometry was examined by Jacques Tits in 1964. This construction is achieved by extending the projective semilinear group PΓL₃(F₄) and its action on the projective plane P²(F₄). P²(F₄) is the projective plane over the field of 4 elements, with 21 points and 21 lines, and PΓL₃(F₄) is the largest group sending lines to lines in P²(F₄).This plane has 168 6-point subsets, hexads, with the …

The Four Color Theorem, Jordan Stein

Undergraduate Theses and Senior Projects

No abstract provided.