Mathematics Commons^™

Can Addressing Language Skills For Fifth Grade Ells In A Multiplication Curriculum Help Address The Achievement Gap In Math? A Multiplication Workbook For Big Kids, Michelle Douglas

Master's Projects and Capstones

Currently, the state of California has 1,332,405 students from grades k-12 who speak a language other than English at home (Caledfacts, 2016). When I started my first year teaching fifth grade with 95% of my students being English language learners (ELLs), I was surprised to see an achievement gap of two to three years in my student’s reading and math skills. I found that my student’s developmental language and math skills contributed to a lack of engagement during math time. Upon further research, I found that these three factors play a role in the wide achievement gaps between ELLs and …

Hodge Theory On Transversely Symplectic Foliations, Yi Lin

Department of Mathematical Sciences Faculty Publications

In this paper, we develop symplectic Hodge theory on transversely symplectic foliations. In particular, we establish the symplectic dδ-lemma for any such foliations with the (transverse) s-Lefschetz property. As transversely symplectic foliations include many geometric structures, such as contact manifolds, co-symplectic manifolds, symplectic orbifolds, and symplectic quasi-folds as special examples, our work provides a unifying treatment of symplectic Hodge theory in these geometries.

As an application, we show that on compact K-contact manifolds, the s-Lefschetz property implies a general result on the vanishing of cup products, and that the cup length of a 2n+1 dimensional compact K-contact manifold with the …

Improving The Problem With Problem Solving, Cole Thibert

Essential Studies UNDergraduate Showcase

As a prospective math educator who will be teaching in the near future, I was concerned with the idea of preparing my future students for college math courses. I decided to research the effects of teaching students how to appropriately use problem solving strategies in math. My research led me towards looking at the benefits of students becoming better problem solvers and how teachers can implement problem solving into their daily lessons.

When this implementation is successful, students can become more independent with their learning, they are able to work and persevere through challenging problems, and they have a greater …

Farlie-Gumbel-Morgenstern Family: Equivalence Of Uncorrelation And Independence, G. Barmalzan, F. Vali

Applications and Applied Mathematics: An International Journal (AAM)

Considering the characteristics of the bivariate normal distribution, in which uncorrelation of two random variables is equivalent to their independence, it is interesting to verify this problem in other distributions. In other words, whether the multivariate normal distribution is the only distribution in which uncorrelation is equivalent to independence. In this paper, we answer to this question and establish generalized Farlie-Gumbel-Morgenstern (FGM) family is another family of distributions under which uncorrelation is equivalent to independence.

The Calculus War: The Ultimate Clash Of Genius, Walker Briles Bussey-Spencer

Chancellor’s Honors Program Projects

No abstract provided.

The Wright Message, 2017-2018, University Of Northern Iowa. Department Of Mathematics.

The Wright Message

Inside this issue:

-- New Faculty
--Faculty Spotlight
--Around Wright Hall
--Interview
--Alumni Spotlight
--Hari Shankar Lecture
--Wright Hall Centenary
--News from the CTLM
--Student Spotlights
--Mathematical Ideas Conference
--Donor Spotlight
--Retiring Faculty
--Classrooms Named in Honor of Faculty
--Contributions to an Account – Recognition
--Department Funds

Apathy And Concern Over The Future Habitability Of Earth: An Introductory College Assignment Of Forecasting Co2 In The Earth’S Atmosphere, Benjamin J. Burger

Journal on Empowering Teaching Excellence

Non-science, first year regional undergraduate students from rural Utah communities participated in an online introductory geology course and were asked to forecast the rise of CO₂ in the Earth’s atmosphere. The majority of students predicted catastrophic rise to 5,000-ppm sometime over the next 3,100 years, resulting in an atmosphere nearly uninhabitable to human life. However, the level of concern the students exhibited in their answers was not directly proportional with their timing in their forecasted rise of CO₂. This study showcases the importance of presenting students with actual data and using data to develop student forecasted models. …

The Roots Of Early Group Theory In The Works Of Lagrange, Janet Heine Barnett

Abstract Algebra

No abstract provided.

The Pell Equation In India, Toke Knudsen, Keith Jones

Number Theory

No abstract provided.

Generating Pythagorean Triples: A Gnomonic Exploration, Janet Heine Barnett

Number Theory

No abstract provided.

The Effects Of Gender And Ethnicity On Students' Perceptions Of Small-Group Learning In Collegiate Mathematics Courses, Layla Potts

Master's Theses and Doctoral Dissertations

Qualitative studies of students' perceptions on small-group work are limited, and few offer insights on the perceptions of women and minority students, for whom quantitative research suggests that small-group work is most beneficial. The aim of this research project is to conduct a qualitative analysis on the perceptions of women and minority students on their small-group learning experiences in collegiate mathematics courses. We conducted a Likert-scale survey of 114 Eastern Michigan University undergraduate students who were enrolled in a cross section of mathematics courses. The data were analyzed using statistical measures such as the frequency and modes of each response, …

Characterizing The "Realistic-Ness" Of Word Problems In Secondary Mathematics Textbooks, Mary L. Dalton

Theses, Dissertations and Culminating Projects

Word problems are an integral part of any secondary mathematics curriculum and one purpose has been to prepare students for the real-world – for everyday events as well as workplace problem-solving. Prior literature suggests that word problems have not met this objective, in part, because the textbook problems do not mirror the kinds of problems commonly found in real life situations.

In this dissertation, I investigate a sample of word problems from two contemporary non-traditional textbooks to uncover the aspects that may influence if and how the problems might be used in the classroom. I utilize a qualitative content analysis …

Cahost Facilitating The Johnson-Neyman Technique For Two-Way Interactions In Multiple Regression, Stephen W. Carden, Nicholas Holtzman, Michael Strube

Department of Mathematical Sciences Faculty Publications

When using multiple regression, researchers frequently wish to explore how the relationship between two variables is moderated by another variable; this is termed an interaction. Historically, two approaches have been used to probe interactions: the pick-a-point approach and the Johnson-Neyman (JN) technique. The pick-a-point approach has limitations that can be avoided using the JN technique. Currently, the software available for implementing the JN technique and creating corresponding figures lacks several desirable features–most notably, ease of use and figure quality. To fill this gap in the literature, we offer a free Microsoft Excel 2013 workbook, CAHOST (a concatenation of the first …

Voices: Conference On Teaching Stem With Music, September 27-28, 2017, Gregory J. Crowther

Journal of Humanistic Mathematics

This first-of-its-kind, online-only conference will explore the use of music to teach STEM (science, technology, engineering, and mathematics) at the college level (including AP courses). Presentations will be live-streamed from the conference website, https://www.causeweb.org/voices. Online registrations (for only $10 apiece!) will be accepted at the conference website until the conclusion of the conference on September 28, 2017.

Special Issue Call For Papers: Mathematics And Motherhood, Pamela E. Harris, Becky Hall, Carrie Diaz Eaton, Emille Davie Lawrence

Journal of Humanistic Mathematics

The Journal of Humanistic Mathematics is pleased to announce a call for papers for a special issue on Mathematics and Motherhood. Please send your abstract submissions via email to the guest editors by October 1, 2017. Initial submission of complete manuscripts is due January 1, 2018. The issue is currently scheduled to appear in July 2018.

A Mathematician’S Journey From Mentee To Mentor: Reflections On The Edge Program, Sarah Bryant, Alejandra Alvarado

Journal of Humanistic Mathematics

The programs supporting diversity in mathematics are as important as ever. So why are they losing funding? And what hope do they have of thriving in the current political climate? In this collaborative interview, two past participants of EDGE (Enhancing Diversity in Graduate Education) explore these questions; Sarah probes and narrates as Alejandra thinks out loud about the ways that the program has shaped her life and how she hopes to see the program continue.

I Love You Fifty, Nat Banting

Journal of Humanistic Mathematics

This article chronicles the merging of my roles of teacher and learner of mathematics with that of a relatively new pursuit: parenthood. Amidst my attempts to dutifully provide opportunities for my son to interact with various mathematical ideas and artifacts, it was an unanticipated moment of epiphany that allowed me to enter into his emerging world of mathematical significance and rediscover what first drew me to the teaching and learning of mathematics. My son’s innocent, yet potent, understanding of number provides an image of the power of mathematics to organize experience, structure significance, and communicate meaning.

Inquiry Based Learning From The Learner’S Point Of View: A Teacher Candidate’S Success Story, Caroline Johnson Caswell, Derek J. Labrie

Journal of Humanistic Mathematics

The goal of this paper is to review current research on Inquiry Based Learning (IBL) and shed some light, from a student's perspective, on the challenges and rewards of this pedagogy. The first part of the article provides an extensive review of the literature on IBL. The second part focuses on one student's experiences in an IBL classroom.

In particular, a graduate secondary mathematics student reflects upon his experiences in a college mathematics class where the instructor implemented an Inquiry Based Learning model. His experience is validated by current research on IBL educational methodology which structures the classroom environment for …

Figures And First Years: An Analysis Of Calculus Students' Use Of Figures In Technical Reports, Nathan J. Antonacci, Michael Rogers, Thomas J. Pfaff, Jason G. Hamilton

Numeracy

This three-year study focused on first-year Calculus I students and their abilities to incorporate figures in technical reports. In each year, these calculus students wrote a technical report as part of the Polar Bear Module, an educational unit developed for use in partner courses in biology, computer science, mathematics, and physics as part of the Multidisciplinary Sustainability Education (MSE) project at Ithaca College. In the first year of the project, students received basic technical report guidelines. In year two, the report guidelines changed to include explicit language on how to incorporate figures. In year three, a grading rubric was added …

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.

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

Analysis

No abstract provided.

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.

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

Topology

No abstract provided.

Construction Of The Figurate Numbers, Jerry Lodder

Number Theory

No abstract provided.

Generating Pythagorean Triples: The Methods Of Pythagoras And Of Plato Via Gnomons, Janet Heine Barnett

Number Theory

No abstract provided.

Pascal's Triangle And Mathematical Induction, Jerry Lodder

Number Theory

No abstract provided.

Babylonian Numeration, Dominic Klyve

Number Theory

No abstract provided.

Primes, Divisibility, And Factoring, Dominic Klyve

Number Theory

No abstract provided.

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

Number Theory

No abstract provided.

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

Linear Algebra

No abstract provided.