Digital Commons Network^™

Critical Issues In Middle And Secondary Mathematics Placement: A Case Study, Morgan E. Summers

Undergraduate Honors Capstone Projects

This qualitative research project focuses on the issues facing middle and secondary mathematics placement through an extensive literature review as well as a case study of a local school district. As students move from elementary school to middle and secondary schools, they are placed into classes that appear to be based on ability. One of the driving questions of this project is how is this ability level determined? Through an in-­‐depth look at one school district, it is found that a primary source of information is both norm-­‐referenced and criterion-­‐referenced assessments given to students in fifth and eighth grades. In …

Group Colorability And Hamiltonian Properties Of Graphs, Hao Li

Graduate Theses, Dissertations, and Problem Reports (ETD)

The research of my dissertation was motivated by the conjecture of Thomassen that every 4-connected line graph is hamiltonian and by the conjecture of Matthews and Sumner that every 4-connected claw-free graph is hamiltonian. Towards the hamiltonian line graph problem, we proved that every 3-edge-connected, essentially 4-edge-connected graph G has a spanning eulerian subgraph, if for every pair of adjacent vertices u and v, dG(u) + dG(v) ≥ 9. A straight forward corollary is that every 4-connected, essentially 6-connected line graph with minimum degree at least 7 is hamiltonian.;We also investigate graphs G such that the line graph L(G) is …

2011 Sonia Kovalevsky Math For Girls Day Flyer, Association For Women In Mathematics, Lincoln University Of Missouri, Donna L. Stallings

Math for Girls Day Documents

6th Annual Lincoln University Sonia Kovalevsky Math for Girls Day program flyer on April 29, 2011.

2011 Sonia Kovalevsky Math For Girls Day Evaluation Forms, Association For Women In Mathematics, Lincoln University Of Missouri, Donna L. Stallings

Math for Girls Day Documents

Presenter, student and teacher evaluation forms for the 6th Annual Lincoln University Sonia Kovalevsky Math for Girls Day program flyer on April 29, 2011.

A Census Of Vertices By Generations In Regular Tessellations Of The Plane, Alice Paul '12, Nicholas Pippenger

All HMC Faculty Publications and Research

We consider regular tessellations of the plane as infinite graphs in which q edges and q faces meet at each vertex, and in which p edges and p vertices surround each face. For 1/p + 1/q = 1/2, these are tilings of the Euclidean plane; for 1/p + 1/q < 1/2, they are tilings of the hyperbolic plane. We choose a vertex as the origin, and classify vertices into generations according to their distance (as measured by the number of edges in a shortest path) from the origin. For all p ≥ 3 and q ≥ 3 with 1/p + 1/q ≤ 1/2, we give simple combinatorial derivations of the rational generating functions for the number of vertices in each generation.

Fractional Weak Discrepancy And Split Semiorders, Alan Shuchat, Randy Shull, Ann N. Trenk

Faculty Research and Scholarship

The fractional weak discrepancy wd_F(P) of a poset P=(V,≺) was introduced in Shuchat et al. (2007) [6] as the minimum nonnegative k for which there exists a function f:V→R satisfying (i) if a≺b then f(a)+1≤f(b) and (ii) if a∥b then |f(a)−f(b)|≤k. In this paper we generalize results in Shuchat et al. (2006, 2009) [5] and [7] on the range of wd_F for semiorders to the larger class of split semiorders. In particular, we prove that for such posets the range is the set of rationals that can be represented as r/s for which 0≤s−1≤r<2s.

Stock Exchanges In The Middle East: Risky Business Or Smart Investing?, Jed A. Haddad

Honors Projects in Finance

The goal of any investor is to obtain the highest possible return for his or her money. However for years, the debate has continued; stocks, bonds, mutual funds; which of these financial instruments will produce the greatest gain to give the investor the highest profit? Historically, stocks have been known to provide investors with high returns. With the world becoming increasingly globalized, international markets have proven to offer investors more options to help diversify their portfolios. The Middle East has been known as a region of recent economic growth and stability. Three prominent examples of such are Kuwait, Israel, and …

Mathematics Discipline Assessment Report 2010/2011, Mathematics Discipline

Assessment of Student Learning Reports

No abstract provided.

On Russell's Logicism, Sebastian Lange

Macalester Journal of Philosophy

No abstract provided.

The Total Weak Discrepancy Of A Partially Ordered Set, Alan Shuchat, Randy Shull, Ann N. Trenk

Faculty Research and Scholarship

We define the total weak discrepancy of a poset P as the minimum nonnegative integer k for which there exists a function f : V → Z satisfying (i) if a \prec b then f(a) + 1 ≤ f(b) and (ii) Σ|f(a) − f(b)| ≤ k, where the sum is taken over all unordered pairs {a, b} of incomparable elements. If we allow k and f to take real values, we call the minimum k the fractional total weak discrepancy of P. …

An Analysis Of Mathematics Interventions: Increased Time-On-Task Compared With Computer-Assisted Mathematics Instruction, James M. Calhoun Jr.

Electronic Theses and Dissertations

Student achievement is not progressing on mathematics as measured by state, national, and international assessments. Much of the research points to mathematics curriculum and instruction as the root cause of student failure to achieve at levels comparable to other nations. Since mathematics is regarded as a gate keeper to many educational opportunities as well as, eventually, potential job prospects, critics are asking schools to fix the problem.

This research project is a comparison of two different interventions used to improve student performance as tested on the Colorado State Assessment Program (CSAP). The first intervention, increased time-on-task, was used at Freedom …

The Socioeconomic Achievement Gap In Mathematics, Adam Meador

Dissertations

Currently in the United States a gap exists in the education of high and low socio-economic students. There is an education available for the socioeconomically challenged and a different system of education for those who live in a higher socioeconomic status. The purpose of this study was to explore the achievement gap in mathematics for elementary students. Specifically, the gap between the students’ scores who attended a school with a free and reduced price meal percentage below 25% and students’ scores who attended a school with a free and reduced price meal percentage above 75% was explored. Additionally, the focus …

Year-Round Calendars At The High School Level, Matthew Nohner

Mathematics Graduate Theses

The purpose of this paper is to explore the effects of a year round calendar on math scores at the high school level. Students forget facts, especially math facts, over long extended breaks. Year round calendars aim to address this dilemma by minimizing long breaks from learning. The results of year round calendars have been mixed. Some schools have reported both academic and monetary gains after switching from a traditional calendar, while other schools have seen modest gains in student learning. All studies cited in this paper report that at-risk and low socioeconomic students benefit academically from a year round …

Quantum Stochastic Flows: Trotter Product Formula, Dilations And Quantum Brownian Motion., Biswarup Das Dr.

Doctoral Theses

Motivated by the major role played by probabilistic models in many areas of science, several quantum (i.e. non-commutative) generalizations of classical probability have been attempted by a number of mathematicians. The pioneering works of K.R. Parthasarathy, L. Accardi, R.L. Hudson, P.A. Meyer and others led to the development of one such non-commutative model called ‘quantum probability’ which has a very rich theory of quantum stochastic calculus a la Hudson and Parthasarathy. Within the framework of quantum stochastic calculus, the ‘grand design’ that engages us is the canonical construction and study of ∗-homomorphic flows (jt)t≥0 on a given C ∗ or …

Curriculum Committee Course Proposals 02/16/11, Curriculum Committee

Curriculum Committee Reports

No abstract provided.

King, John (Sc 594), Manuscripts & Folklife Archives

Manuscript Collection Finding Aids

Finding aid and full-text (click on "Additional Files" below) for Manuscripts Small Collection 594. Ciphering book of John King including mathematical exercises, numeration of money, simple and compound reduction, weights and measures, and word problems.

Curd, Spencer, 1788-1832 (Sc 966), Manuscripts & Folklife Archives

Manuscript Collection Finding Aids

Finding aid and full text (click on "Additional Files" below) for Manuscripts Small Collection 966. Ciphering book (94 p.), focusing chiefly on surveying and navigating rules for solving problems as well as giving specific problems, of Spencer Curd, Logan County, Kentucky, with accompanying genealogical data.

Using Technology To Increase Interest In The Learning Of Mathematics, Teresa May Anderson

All Graduate Projects

The purpose of this project was to develop unit openers in the form of PowerPoint presentations to introduce students to upcoming topics. Within the PowerPoint presentations, relevant visual images are used to pique the interest of the students. Also, within the presentations are opportunities for students to use a hand-held Student Response System to respond to questions. The questions the students answer are related to the upcoming material. After responses are entered, a visual display will show the responses and discussion will follow between the students and the teacher. The project will be used in geometry mathematics classrooms at the …

The Impact Of Bilingual Treatment On The Math Skills Of Hispanic High School Algebra Students, Robert Kirk

Education Dissertations and Projects

This dissertation was designed to measure the impact of instructional techniques in the Foundations of Algebra classroom to bridge linguistic barriers between Hispanic students and the language of teaching. Two consecutive years of failing to meet anticipated yearly growth among Hispanic students in Algebra I, as determined by the North Carolina End of Course exams, indicated a cognitive gap among these students when it comes to learning mathematics.

The writer developed an experiment to be delivered among 9 sections of Algebra in a North Carolina high school. The control group used Microsoft PowerPoint slides created for every lesson plan determined …

Making It Add Up : An Examination Of The Preparation Of Undergraduates To Teach Mathematics At Csumb, Erin Barnes

Capstone Projects and Master's Theses

Elementary teachers’ lack of conceptual knowledge negatively affects their confidence, beliefs and teaching ability. The implementation of earlier exposure to teaching mathematics in the undergraduate career can benefit the pre-service teacher’s future career by giving them the opportunity to examine their beliefs and attitudes towards math and gain confidence in their teaching. Interviews were conducted with teachers at California State University Monterey Bay who instruct Math 308 and Math 309 as well as a professor at the credential program. These interviews gave insight into the goals of the classes, the effectiveness of the classes and the teachers’ thoughts and opinions …

Approximate Transversals Of Latin Squares, Jon Kyle Pula

Electronic Theses and Dissertations

A latin square of order n is an n by n array whose entries are drawn from an n-set of symbols such that each symbol appears precisely once in each row and column. A transversal of a latin square is a subset of cells that meets each row, column, and symbol precisely once.

There are many open and difficult questions about the existence and prevalence of transversals. We undertake a systematic study of collections of cells that exhibit regularity properties similar to those of transversals and prove numerous theorems about their existence and structure. We hope that our results …

Common Features Of Professional Development Activities For Mathematics And Science Teachers, Patricia S. Moyer-Packenham, J. J. Bolyard, J. Oh, N. I. Cerar

Teacher Education and Leadership Faculty Publications

This study examines professional development activities provided for mathematics and science teachers in the National Science Foundation’s Math and Science Partnership Program by analyzing a cross-sectional sample of over 2000 professional development (PD) activities in the program. Data were gathered from secondary source documents and surveys to examine core and structural features of professional development offerings (i.e. form, collective participation, content, duration and outcomes). The results from this sample of PD activities for mathematics and science teachers were mixed. There was evidence of researchbased practices, including the collective participation by teachers at the same grade levels, a focus on content-specific …

Improving Core Mathematical Skills In Engineering Undergraduates, Michael Carr

Teaching Fellowships

A large number of engineering undergraduates being their third level education with significant deficiencies in their core mathematical skills. Every year, in the Technological University Dublin (DIT) , a diagnostic test is given to incoming first year students, consistently revealing problems in basic mathematics. It is difficult to motivate many students to seek help in the Maths Learning Centre to address these problems. As a result, they struggle through several years of engineering, carrying a serious handicap of poor core mathematical skills, as confirmed by exploratory testing of final year students

In order to improve these skills in engineering students …

Both Ways Strong: Using Digital Games To Engage Aboriginal Learners, Robyn Jorgensen, Tom Lowrie

Aboriginal Policy Research Consortium International (APRCi)

Engaging Aboriginal learners in the school curriculum can be quite a challenge given issues of cultural and linguistic differences. Even more so, these differences can be expanded when the students are in their adolescence. Creating learning environments that engage learners, while providing deep learning opportunities, is one of the biggest challenges for teachers in remote communities. This paper reports on a reform initiative that centred on the use of a digital game, Guitar Heroes, in a remote Aboriginal school. It was found that the digital media provided teachers with opportunities for new learning spaces and resulted in additional unintended learning …

Problem Solving As A Pedagogical Practice: Useful Conceptions Of Professional Learning, Michelle Lang, Immaculate Kizito Namukasa

Education Publications

Problem solving as a pedagogical practice is a recent focus of mathematics education research and of professional learning. This study employs the phenomenographic framework for studying teachers’ conceptions of ongoing professional learning opportunities focused on the teaching of mathematics through problem solving. Eleven grade 7 to 8 school teachers who participated in ongoing professional learning over the course of one to five years were purposively selected. Survey method was employed. Findings from the study reveal that most teachers view professional learning mainly as a source for ideas and resources, whereas others hold more complex views ranging from viewing professional learning …

Finding Relationships Between Multiple-Choice Math Tests And Their Stem-Equivalent Constructed Responses, Nayla Aad Chaoui

CGU Theses & Dissertations

The study takes a close look at relationships between scores on a Mathematics standardized test in two different testing formats - Multiple-Choice (MC) and Constructed Response (CR). Many studies have been dedicated to finding correlations between item format characteristics with regards to race and gender. Few studies, however, have attempted to explore differences in the performance of English Learners in a low performing, predominantly Latino high school. The study also determined relationships between math scores and gender and math scores and language proficiency, as well as relationships between CAHSEE and CST scores.

Statistical analyses were performed using correlations, descriptive statistics, …

Reflections On The Tenth Anniversary Of Mathematics And Democracy, Lynn Arthur Steen, Bernard L. Madison

Numeracy

Two independent reflections by early proponents of quantitative literacy connect today's numeracy initiative with its origin in concern about school tests, its impact on students today, and the challenges of democracy. Even as interest in QL grows in many places, evidence of need also grows. Moreover, well-meaning programs with other goals—especially at the K-12 level—often channel education in directions that fail to advance numeracy. Examples show that both students and teachers are enthusiastic when offered QL opportunities, but that individual beliefs and public decisions often belie the goals of QL.

Calculus, Biology And Medicine: A Case Study In Quantitative Literacy For Science Students, Kim Rheinlander, Dorothy Wallace

Numeracy

This paper describes a course designed to enhance the numeracy of biology and pre-medical students. The course introduces students with the background of one semester of calculus to systems of nonlinear ordinary differential equations as they appear in the mathematical biology literature. Evaluation of the course showed increased enjoyment and confidence in doing mathematics, and an increased appreciation of the utility of mathematics to science. Students who complete this course are better able to read the research literature in mathematical biology and carry out research problems of their own.

Postcard, Proof At Studio@620, St. Petersburg, Florida, Studio At 620

Postcard Collection

A promotional postcard for the play Proof by David Auburn, presented by students from Pinellas County Center for the Arts at The Studio@620. The play, which won the 2001 Tony Award for Best Play and the Pulitzer Prize for Drama, follows Catherine, the daughter of a recently deceased mathematical genius, as she grapples with her father's legacy and her own mathematical talents.

Models And Methods For Computationally Efficient Analysis Of Large Spatial And Spatio-Temporal Data, Chengwei Yuan

Doctoral Dissertations

With the development of technology, massive amounts of data are often observed at a large number of spatial locations (n). However, statistical analysis is usually not feasible or not computationally efficient for such large dataset. This is the so-called "big n problem".

The goal of this dissertation is to contribute solutions to the "big n problem". The dissertation is devoted to computationally efficient methods and models for large spatial and spatio-temporal data. Several approximation methods to "the big n problem" are reviewed, and an extended autoregressive model, called the EAR model, is proposed as a parsimonious model that accounts for …