Mathematics Commons^™

Subdivision Rules, 3-Manifolds, And Circle Packings, Brian Craig Rushton

Theses and Dissertations

We study the relationship between subdivision rules, 3-dimensional manifolds, and circle packings. We find explicit subdivision rules for closed right-angled hyperbolic manifolds, a large family of hyperbolic manifolds with boundary, and all 3-manifolds of the E^3,H^2 x R, S^2 x R, SL_2(R), and S^3 geometries (up to finite covers). We define subdivision rules in all dimensions and find explicit subdivision rules for the n-dimensional torus as an example in each dimension. We define a graph and space at infinity for all subdivision rules, and use that to show that all subdivision rules for non-hyperbolic manifolds have mesh not going to …

Professional Learning Community Impacts On Student Achievement In Middle School Mathematics, Jessica Stuewe

Mathematics Graduate Theses

The development of professional learning communities in middle level education is a relatively new and trendy concept sweeping the nation. School professional development committees are training large numbers of teachers through conferences, book studies and online webinars on how to collaborate to improve student learning. This research will explore the impact of the first year of implementation of a departmental professional learning community (PLC) on student achievement at the middle school level in the content area of mathematics. Student standardized test scores from 2010 and 2011 will be compared as a measure of success of the PLC. Teacher surveys are …

Prove It!, Kenny W. Moran

Journal of Humanistic Mathematics

A dialogue between a mathematics professor, Frank, and his daughter, Sarah, a mathematical savant with a powerful mathematical intuition. Sarah's intuition allows her to stumble into some famous theorems from number theory, but her lack of academic mathematical background makes it difficult for her to understand Frank's insistence on the value of proof and formality.

Connected Inverse Limits With A Set-Valued Function, Van C. Nall

Department of Math & Statistics Faculty Publications

In this paper we provide techniques to build set-valued functions whose resulting inverse limits will be connected.

Σary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

The Impact Of Manipulatives On Learning In The Elementary And Middle School Mathematics Classroom, Laura Dahl

Mathematics Graduate Theses

This paper is a review of research pertaining to the use of manipulatives in the elementary and middle school mathematics classrooms. It embodies the logic behind using manipulative materials in the classroom setting and the impact their use will have on student understanding and enjoyment for learning mathematical concepts. This research paper will identify the struggles and concerns of manipulative use along with the need of increased professional development and training for teachers to be better prepared for the daunting, yet rewarding challenges of successfully teaching mathematics.

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 …

Twisted Virtual Biracks, Jessica Ceniceros

CMC Senior Theses

This thesis will take a look at a branch of topology called knot theory. We will first look at what started the study of this field, classical knot theory. Knot invariants such as the Bracket polynomial and the Jones polynomial will be introduced and studied. We will then explore racks and biracks along with the axioms obtained from the Reidemeister moves. We will then move on to generalize classical knot theory to what is now known as virtual knot theory which was first introduced by Louis Kauffman. Finally, we take a look at a newer aspect of knot theory, twisted …

Inverse Limits With Set Valued Functions, Van C. Nall

Department of Math & Statistics Faculty Publications

We begin to answer the question of which continua can be homeomorphic to an inverse limit with a single upper semi-continuous bonding map from [O, 1) to 2^(O,l). Several continua including (0, 1) x (0, 1) and all compact manifolds with dimension greater than one cannot be homeomorphic to such an inverse limit. It is also shown that if the upper semi-continuous bonding maps have only zero dimensional point values, then the dimension of the inverse limit does not exceed the dimension of the factor spaces.

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 …

Manipulatives In The Secondary Mathematics Classroom Using A Traditional Algebra Text, Christina Mutnansky

Mathematics Graduate Theses

This paper is a review of the research available on manipulative use in the mathematics classroom. Mathematical manipulatives, objects that are used to aid a student in learning a mathematical concept, provide a way for students to learn abstract mathematical concepts in a non lecture situation through hands-on learning and discovery. It specifically focuses on the use of manipulatives in the secondary Algebra classroom and how they can be integrated into a traditional curriculum. It discusses the different types of manipulatives that are available as well as reasons why instructors do not use manipulatives. Guidelines are given for their proper …

Σary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

Symmetry From Nature To The Classroom, Rochelle Lueders

Honors Capstones

Capstone submitted as a graduation requirement for the BSU Honors Program.

Problem Solving Based Instruction In The High School Mathematics Classroom, Lawrence Vettleson, Jr.

Mathematics Graduate Theses

This paper is a review of research pertaining to the use of problem solving in classroom instruction. It covers the stages of problems solving as listed by George Polya and how they can be used to enhance mathematics instruction. This research paper will identify that problem solving is a need based on Minnesota state mathematics standards and National mathematics standards. Covered in this paper is the research on the effects of mathematics instruction using problem solving. The research covers some of the benefits to student education if students learn mathematics using a problem solving based approach to classroom instruction.

The Norm Of A Truncated Toeplitz Operator, William T. Ross, Stephan Ramon Garcia

Department of Math & Statistics Faculty Publications

We prove several lower bounds for the norm of a truncated Toeplitz operator and obtain a curious relationship between the H² and H^∞ norms of functions in model spaces.

Manipulatives In Mathematics Instruction, Jessica Strom

Mathematics Graduate Theses

This paper is a review of research pertaining to the use of manipulatives in middle and secondary school mathematics instruction. It covers the research on the rationale for using manipulatives, the psychology behind learning with manipulatives, the common mistakes when teaching with manipulatives, and the suggested process to follow when using manipulatives in the classroom. There is a large amount of research and information on manipulatives in the classroom. One of the most prevalent topics addresses that the concrete characteristics of manipulatives allow students to progress through a natural learning process on their way to an abstract understanding of mathematical …

Grades 7-8 Mean, Median, And Mode, Rich Miller Iii

Math

This lesson is a math lesson for seventh and eighth grade students on mean, medium, and mode. Through this lesson students will be able to understand the measures of central tendency and their definitions, how to calculate them and what steps are involved, and how the theories can be applied on real life. In this lesson, students are tiered by ability and are able to pick a project based off of their interest and the math concept they are working on. Each activity has a tiered task card to guide the students.

Engaging Math-Avoidant College Students, M. Paul Latiolais, Wendi Laurence

Numeracy

This paper is an informal, personal account of how we, as two college teachers, became interested in math anxiety, decided to explore it amongst students at our institution in order to inform our teaching, and became convinced that the massive problem is math avoidance. We tried discussion groups, but few students attended, although those that did made useful suggestions. Thus informed, we designed an innovative course, Confronting College Mathematics as a Humanities course with the possibility of credit toward the math requirement, but it was undersubscribed in its first offering and had to be canceled. How can we get college …

Σary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

The Effects Of Block Scheduling On Ap Calculus Ab Student Achievement, Larry A. Lightner

Mathematics Graduate Theses

Student achievement on the AP Calculus AB Exam is always a concern for teachers and school districts that offer the exam. A factor of concern that also arises is a school’s schedule. A school’s schedule may have an affect on achievement. This study examines the comparison in achievement of students who take the AP Calculus AB Exam under a block schedule and a traditional schedule system. Block Scheduling is defined as a class period of 80-90 minutes with 4 periods each day, allowing a full year’s curriculum to be offered in one semester. Traditional scheduling is defined as a class …

Cooperative Learning In The Mathematics Classroom, Janine Regnier

Mathematics Graduate Theses

Student interactions are important which provokes the idea that cooperative learning should be incorporated into classrooms. Research states many benefits for incorporating cooperative learning and are included in the literature review. Cooperative groups were introduced and studied by the author, who ultimately concluded that cooperative learning does have a place in Mathematics classrooms and should be used when the lesson lends itself to a cooperative environment. The study results can be found in this paper following the literature review.

Σary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.

Differential Equations: A Universal Language, Bethany Caron

Senior Honors Projects

“Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country.” – David Hilbert Differential equations are equations of one or more variables that involve both functions and their derivatives. These equations have many applications to the everyday “non-math” world, including modeling in engineering, physics, biology, chemistry, and economics. Differential equations are used when a situation arises where one needs to study a continuously changing quantity (expressed as a function) and its rate of change (expressed through its derivatives). The solutions to differential equations are functions that make the original equation hold true, and they can …

Examining The Validity Of The Spring 2007 Math 1050 Common Final, Angela K. Brock

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

I began this study wanting to know more about the Math 1050 Common Final. I've heard so many negative things about the class from students, I wondered if the common final, which has so much influence on students' grades, is actually valid. A measurement is valid to the degree that it is both reliable and relevant, so I needed to address both relevance and reliability. To do this, I began by finding a reliability coefficient for the multiple choice section. I then analyzed each item with respect to difficulty, discrimination and efficiency. To determine content and learning level relevance, I …

The Philosophy Of Mathematics, Erin Wilding-Martin

Sabbaticals

The philosophy of mathematics considers what is behind the math that we do. What is mathematics? Is it some cosmic truth we discover, or is it created by humans? Do mathematical objects such as numbers and functions really exist, or are they just symbols we have invented? Two of the great debates in the history of mathematical philosophy center around ontology and epistemology. Where did mathematics come from? How do we know that it is true?

Where did mathematics come from? Is it discovered or created? Ontological questions are concerned with the nature and status of mathematical objects. Some people …

Truncated Toeplitz Operators On Finite Dimensional Spaces, William T. Ross, Joseph A. Cima, Warren R. Wogen

Department of Math & Statistics Faculty Publications

In this paper, we study the matrix representations of compressions of Toeplitz operators to the finite dimensional model spaces H²ƟBH², where B is a finite Blaschke product. In particular, we determine necessary and sufficient conditions - in terms of the matrix representation - of when a linear transformation on H²ƟBH² is the compression of a Toeplitz operator. This result complements a related result of Sarason [6].

Indestructible Blaschke Products, William T. Ross

Department of Math & Statistics Faculty Publications

No abstract provided.

Mathematically Modeling Pcr: An Asymptotic Approximation With Potential For Optimization, Martha J. Garlick

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

A mathematical model for PCR (Polymerase Chain Reaction) is developed using the law of mass action. Differential equations are written from the chemical equations, preserving the detail of the complementary DNA single strand being extended one bas e pair at a time. The equations for the annealing stage are solved analytically. The method of multiple scales is used to approximate solutions for the extension stage. A map is then developed from the solutions to simulate PCR. The advantage of this model is the ability to use the map to optimize the process. Our results suggest that dynamically optimizing the extension …

Gender Disparity In Mathematical Performance Revisited: Can Training In Problem Solving Bring Difference Between Boys And Girls?, M.A. Adeleke

Essays in Education

This study examined the problem solving performance of male and female students’ mathematical problem-solving performances using Conceptual Learning Strategy (CLS) and Procedural Learning Strategy PLS). A sample of 124 science students assigned into CLS, PLS and Conventional Method (CM) groups were involved in the study making use of pretest, post test control group design. The sample was drawn from three intact Senior Secondary School Two (SSII) classes from three local government Areas of Osun State in Nigeria and were taught for a period of eight weeks. Findings of the study showed a non significant difference in the performance of boys …

Σary, Minnesota State University Moorhead, Mathematics Department

Math Department Newsletters

No abstract provided.