Mathematics Commons^™

A New Class Of Generalized Power Lindley Distribution With Applications To Lifetime Data, Broderick O. Oluyede, Tiantian Yang, Boikanyo Makubate

Mathematical Sciences: Faculty Publications

In this paper, a new class of generalized distribution called the Kumaraswamy Power Lindley (KPL) distribution is proposed and studied. This class of distributions contains the Kumaraswamy Lindley (KL), exponentiated power Lindley (EPL), power Lindley (PL), generalized or exponentiated Lindley (GL), and Lindley (L) distributions as special cases. Series expansion of the density is obtained. Statistical properties of this class of distributions, including hazard function, reverse hazard function, monotonicity property, shapes, moments, reliability, quantile function, mean deviations, Bonferroni and Lorenz curves, entropy and Fisher information are derived. Method of maximum likelihood is used to estimate the parameters of this new …

Characterizing Mathematics Graduate Student Teaching Assistants’ Opportunities To Learn From Teaching, Yvonne Lai, Wendy Smith, Nathan Wakefield, Erica R. Miller, Julia St. Goar, Corbin M. Groothuis, Kelsey M. Wells

Department of Mathematics: Faculty Publications

Exemplary models to inform novice instruction and the development of graduate teaching assistants (TAs) exist. What is missing from the literature is the process of how graduate students in model professional development programs make sense of and enact the experiences offered. A first step to understanding TAs’ learning to teach is to characterize how and whether they link observations of student work to hypotheses about student thinking and then connect those hypotheses to future teaching actions. A reason to be interested in these connections is that their strength and coherence determine how well TAs can learn from experiences. We found …

Teachers' Perceptions Of Manipulatives During Middle School Math Instruction, Angela L. Vizzi

Walden Dissertations and Doctoral Studies

In a Colorado school district, school personnel and parents were concerned that middle school math proficiency levels were low for 2011-2014 and math teachers were not using manipulatives in their classes to increase math performance. The district's math coordinator did not foresee providing specific professional development (PD) for math manipulative use to address these concerns. Without this PD, math teachers may be ill-quipped to teach math concepts when using manipulatives, which, in turn, could lead to further poor math performance. The purpose of this qualitative bounded collective case study was to explore middle school teachers' perceptions of PD and perceived …

Understanding The Relationships Among Students' Goal Orientations, Self-Efficacy, Anxiety, And Accelerated Academic Success In The Redesign Of Developmental Mathematics, Kelly Ann Hogan

Walden Dissertations and Doctoral Studies

The low success rates of increasing numbers of underprepared students taking developmental mathematics classes 'often minority and economically disadvantaged' are challenging community colleges across the United States. These students, who must start in the lowest levels of precollege mathematics courses, are unlikely to pass the first course and earn a credential. Using a mastery goal orientation theoretical framework, a quantitative, survey research design was used to ascertain any correlations between students' goal orientations, self-efficacy, test anxiety, and success in a new model of learning. Survey data were used to answer 3 research questions: (a) the relationship between success and students' …

A Quantitative Quasi-Experimental Study Of An Online High School Mathematics Remediation Program, Terry Meehan

Walden Dissertations and Doctoral Studies

The local problem that drove this study is that a high school in an upper middle class suburban city in Pennsylvania wants to improve its student scores on its end-of-course Algebra 1 Keystone Exam. The purpose of this study was to conduct a quantitative, quasi-experimental assessment of an online high school mathematics remediation program to determine if the remediation program was successful in its endeavor to remediate students. This research study, informed by the self-efficacy and the behaviorist learning theories, attempted to determine whether students who (a) scored below proficient on the May algebra exam and were placed in the …

Junior High School Teachers' Perceptions Of Math Instruction For African American Students, Sandra Denise Richardson

Walden Dissertations and Doctoral Studies

A mathematics achievement gap exists between 8th grade African American students and other ethnic groups. Guided by the conceptual framework of constructivism, the purpose of this case study was to examine 8, Grade 8 math teachers' perceptions of factors contributing to mathematical performance gap in their African American students and what instructional strategies can be used to help reduce the achievement gap in southwest Georgia. Data were obtained through interviews and classroom observations and were coded and analyzed using typological analysis, followed by inductive analysis. The results of the data revealed teachers perceived recruiting and retaining African American teachers and …

Secondary Mathematics Teachers' Disposition Toward Challenge And Its Impact On Teaching Practice, Yirah Mariana Valverde

Open Access Theses & Dissertations

This two phase, sequential exploratory study focused on mathematics teachers' disposition toward challenge and its impact in their teaching practice and students' performance. This heavily qualitative study employed a mixed methodology to answer the following guiding research question: how do teachersâ?? disposition towards challenge affect teaching practice and what is the nature of that relationship?

During the initial phase (quantitative), two teachers who were enrolled in a graduate mathematics at a University in the southwestern U.S. were selected for the study (N=5). The goal of the class was to increase the participants' mathematical knowledge for teaching. The purposive selection was …

The Prominence Of Affect In Creativity: Expanding The Conception Of Creativity In Mathematical Problem Solving, Eric L. Mann, Scott A. Chamberlin, Amy K. Graefe

Faculty Publications

Constructs such as fluency, flexibility, originality, and elaboration have been accepted as integral components of creativity. In this chapter, the authors discuss affect (Leder GC, Pehkonen E, Törner G (eds), Beliefs: a hidden variable in mathematics education? Kluwer Academic Publishers, Dordrecht, 2002; McLeod DB, J Res Math Educ 25:637–647, 1994; McLeod DB, Adams VM, Affect and mathematical problem solving: a new perspective. Springer, New York, 1989) as it relates to the production of creative outcomes in mathematical problem solving episodes. The saliency of affect in creativity cannot be underestimated, as problem solvers require an appropriate state of mind in order …

On The Stability Of A Pexiderized Functional Equation In Intuitionistic Fuzzy Banach Spaces, Nabin C. Kayal, Pratap Mondal, T. K. Samanta

Applications and Applied Mathematics: An International Journal (AAM)

During the last few decades several researchers have been devoted to establishing stability of different kinds of functional equations, differential equations, functional differential equations, fractional differential equations, etc. under different sufficient conditions in different spaces like Banach spaces, Banach modules, fuzzy Banach spaces etc. In this paper, we remain confined in the discussion of stability of functional equations in intuitionistic fuzzy Banach spaces. Ulam was the first person who introduced an open question concerning the stability of a group homomorphism in an international conference. Thereafter several researchers have replied and are still replying to this open question in different contexts. …

Black Male Students And The Algebra Project: Mathematics Identity As Participation, Melva R. Grant, Helen Crompton, Deanna J. Ford

STEMPS Faculty Publications

In this article, the authors examine the mathematics identity development of six Black male students over the course of a 4-year The Algebra Project Cohort Model (APCM) initiative. Mathematics identity here is defined as participation through interactions and positioning of self and others. Data collection included nearly 450 minutes of video recordings of small-group, mathematics problem solving in which student actions, coded as acts of participation, were tallied. These tallied actions were conceptualized descriptively in terms of mathematics identity using the lenses of agency, accountability, and work practices. The analyses suggest that the APCM students’ confidence in self and peers …

The Effects Of Prompted Tutoring On An Emporium Model Math Course, Juliette Michelle Young

Honors Theses

My research goal is to investigate how specific prompting of students would affect their involvement and progress in an emporium developmental math course. With the aim of increasing the students’ involvement and progress I tested a method that was in tended to increase students’ perceived connectedness with the classroom and promote the use of the available tutors and teachers. I monitored consenting students’ progress in the Spring 2015 courses and sent emails to students who met any one of three different criterion: (1) If the students time investment was below a threshold. (2) If the student’s mastery pace was less …

Extended Lindley Poisson Distribution, Mavis Pararai, Gayan Warahena-Liyanage, Broderick O. Oluyede

Mathematical Sciences: Faculty Publications

The Extended Lindley Poisson (ELP) distribution which is an extension of the extended Lindley distribution [2] is introduced and its properties are explored. This new distribution represents a more flexible model for the lifetime data. Some statistical properties of the proposed distribution including the shapes of the density, hazard rate functions, moments, Bonferroni and Lorenz curves are explored. Entropy measures and the distribution of the order statistics are given. The maximum likelihood estimation technique is used to estimate the model parameters and a simulation study is conducted to investigate the performance of the maximum likelihood estimates. Finally, we present applications …

Critical Thinking And High-Level Discourse In A 1:1 Environment, Ryan G. Zonnefeld, Valorie L. Zonnefeld

Faculty Work Comprehensive List

Learn about our experiences co-teaching a K–8 methods course using 1:1 tablets in a high-tech lab. This innovative course included a move away from a textbook to a dynamic research-based curriculum supported by NCTM resources and CCSSM as well as integral utilization of apps, web 2.0 tools, and professional learning networks.

Tight Super-Edge-Graceful Labelings Of Trees And Their Applications, Alex Collins, Colton Magnant, Hua Wang

Mathematical Sciences: Faculty Publications

The concept of graceful labeling of graphs has been extensively studied. In 1994, Mitchem and Simoson introduced a stronger concept called super-edge-graceful labeling for some classes of graphs. Among many other interesting pioneering results, Mitchem and Simoson provided a simple but powerful recursive way of constructing super-edge-graceful trees of odd order. In this note, we present a stronger concept of “tight” super-edge-graceful labeling. Such a super-edge graceful labeling has an additional constraint on the edge and vertices with the largest and smallest labels. This concept enables us to recursively construct tight super-edge-graceful trees of any order. As applications, we provide …

On The Stability Of Cycles By Delayed Feedback Control, Dmitriy Dmitrishin, Paul Hagelstein, Anna Khamitova, Alexander M. Stokolos

Mathematical Sciences: Faculty Publications

We present a delayed feedback control (DFC) mechanism for stabilizing cycles of one dimensional discrete time systems. In particular, we consider a delayed feedback control for stabilizingT-cycles of a differentiable functionf:R→Rof the form

x(k+1)=f(x(k))+u(k)

where

u(k)=(a₁−1)f(x(k))+a₂f(x(k−T))+...+a_Nf(x(k−(N−1)T)),

with a₁+...+a_N=1. Following an approach of Morgül, we construct a map F:R^T+1→R^T+1 whose fixed points correspond to T-cycles of f. We then analyze the local stability of the above DFC mechanism by evaluating the stability of the corresponding equilibrum points of F. We associate to each periodic orbit of f an …

Supporting Teachers’ Learning About Mathematical Modeling, June L. Gastón, Barbara A. Lawrence

Publications and Research

In the United States, one of the Standards for Mathematical Practice of the Common Core Curriculum (Common Core State Standards Initiative, 2010) is Model with mathematics. This standard requires that students be taught in a manner that will enable them to ―apply the mathematics they know to solve problems arising in everyday life, society, and the workplace‖ (p. 7). However many prospective and practicing teachers acquire a pedagogical style that does not support this standard. To promote higher levels of student thinking associated with mathematical modeling, teachers must thus be taught not only what mathematical modeling is, but how it …

Gorenstein Flat Preenvelopes, Alina Iacob

Mathematical Sciences: Faculty Publications

We consider a two sided noetherian ring R such that the character modules of Gorenstein injective left R-modules are Gorenstein flat right R-modules. We then prove that the class of Gorenstein flat right R-modules is preenveloping. We also show that the class of Gorenstein flat complexes of right R-modules is preenevloping in Ch(R).

In the second part of the paper we give examples of rings with the property that the character modules of Gorenstein injective modules are Gorenstein flat. We prove that any two sided noetherian ring R with i.d.Rop R < 1 has the desired property. We also prove that if R is a two sided noetherian ring with a dualizing bimodule R VR and such that R is left n-perfect for some positive integer n, then the character modules of Gorenstein injective modules are Gorenstein flat.

A New Class Of Generalized Modified Weibull Distribution With Applications, Broderick O. Oluyede, Shujiao Huang, Tiantian Yang

Mathematical Sciences: Faculty Publications

A new five parameter gamma-generalized modified Weibull (GGMW) distribution which includes exponential, Rayleigh, modified Weibull, Weibull, gamma-modified Weibull, gamma-modified Rayleigh, gamma-modified exponential, gamma-Weibull, gamma-Rayleigh, and gamma-exponential distributions as special cases is proposed and studied. Some mathematical properties of the new class of distributions including moments, distribution of the order statistics, and Renyi entropy are presented. Maximum likelihood estimation technique is used to estimate the model parameters and applications to a real datasets to illustrates the usefulness of the proposed class of models are presented.

Art, Math, And Physics; All About For, Chris Brownell, Steve Pauls

The Transdisciplinary STEAM+ Journal

Anish Kapoor’s public sculpture “Cloud Gate” and Frame of Reference.

Ambiguity In Speaking Chemistry And Other Stem Content: Educational Implications, Mick D. Isaacson, Michelle Michaels

Journal of Science Education for Students with Disabilities

Ambiguity in speech is a possible barrier to the acquisition of knowledge for students who have print disabilities (such as blindness, visual impairments, and some specific learning disabilities) and rely on auditory input for learning. Chemistry appears to have considerable potential for being spoken ambiguously and may be a barrier to accessing knowledge and to learning. Educators in chemistry may be unaware of, or have limited awareness of, potential ambiguity in speaking chemistry and may speak chemistry ambiguously to their students. One purpose of this paper is to increase awareness of potential ambiguity in speaking chemistry and other STEM fields …

Contracting Endomorphisms And Dualizing Complexes, Saeed Nasseh, Sean Sather-Wagstaff

Mathematical Sciences: Faculty Publications

We investigate how one can detect the dualizing property for a chain complex over a commutative local Noetherian ring R. Our focus is on homological properties of contracting endomorphisms of R, e.g., the Frobenius endomorphism when R contains a field of positive characteristic. For instance, in this case, when R is F-finite and C is a semidualizing R-complex, we prove that the following conditions are equivalent: (i) C is a dualizing R-complex; (ii) C ∼RHomR(nR,C) for some n > 0; (iii) GC-dimnR < ∞ and C is derived …

Analytical Review Of Maritime Education And Training Model For Chinese Seafarers, Jiaojiao Yang

Maritime Safety & Environment Management Dissertations (Dalian)

No abstract provided.

The Design And Validation Of A Group Theory Concept Inventory, Kathleen Mary Melhuish

Dissertations and Theses

Within undergraduate mathematics education, there are few validated instruments designed for large-scale usage. The Group Concept Inventory (GCI) was created as an instrument to evaluate student conceptions related to introductory group theory topics. The inventory was created in three phases: domain analysis, question creation, and field-testing. The domain analysis phase included using an expert consensus protocol to arrive at the topics to be assessed, analyzing curriculum, and reviewing literature. From this analysis, items were created, evaluated, and field-tested. First, 383 students answered open-ended versions of the question set. The questions were converted to multiple-choice format from these responses and disseminated …

A Survey Of Mathematical Models Of Dengue Fever, James P. Braselton, Iurii Bakach

Mathematical Sciences: Faculty Publications

In this paper, we compare and contrast five models of dengue fever, a serious illness that affects tropical and subtropical areas around the world. We evaluate each model using different scenarios and identify the strengths and weakness of each of the models. The goal of our analysis is to indicate the strengths and weaknesses of current mathematical models of dengue fever that should assist future researchers in forming models that accurately measure the variables they are studying that affect the spread and progression of the disease.

Homology Over Trivial Extensions Of Commutative Dg Algebras, Luchezar L. Avramov, Srikanth B. Iyengar, Saeed Nasseh, Sean Sather-Wagstaff

Mathematical Sciences: Faculty Publications

Conditions on the Koszul complex of a noetherian local ring R guarantee that TorRi(M,N) is non-zero for infinitely many i, when M and N are finitely generated R-modules of infinite projective dimension. These conditions are obtained from results concerning Tor of differential graded modules over certain trivial extensions of commutative differential graded algebras.

The Integration Of Kinesthetic Learning Through The Math & Movement Program: Pilot Study 2015, Benjamin Ferder

Master's Theses

Purpose: The primary purpose of this pilot study was to verify that the use of kinesthetic learning (Math & Movement Program) in the classroom increases retention of multiplication facts at a greater rate than traditional drill and practice. The Math & Movement Program uses a kinesthetic learning-based approach for practicing, learning, and memorizing mathematics through the incorporation of bodily movement(s). Participants: The directors of the research project for the participating school district selected the sample of convenience. The population size of this study included 213 third and fourth grade students during the second half of the 2011-2012 school years. Data …

Guidelines For Good Mathematical Writing, Francis Su

All HMC Faculty Publications and Research

Communicating mathematics well is an important part of doing mathematics. Many of us know from writing papers or giving talks that communicating effectively not only serves our audience but also clarifies and structures our own thinking. There is an art and elegance to good writing that every writer should strive for. And writing, as a work of art, can bring a person great personal satisfaction.

Within the MAA, we value exposition and mathematical communication. In this column, I’m sharing the advice I give my students to help them write well. There are more extensive treatments (e.g., see Paul Halmos’s How …

Extended Book Review: Really Big Numbers, By Richard Evan Schwartz; The Boy Who Loved Math: The Improbable Life Of Paul Erdös, By Deborah Heiligman; The Short Seller, By Elissa Brent Weissman, Gizem Karaali

Pomona Faculty Publications and Research

The genre of math lit for children is not huge, but it is growing. My kid loves the early reader books by my friend and colleague Julie Glass (A Dollar for Penny (1998), The Fly On the Ceiling (2000)). I found Izolda Fotiyeva’s Math with Mom (2003) too late for my daughter but will definitely read it with my son. For a neat twist on the traditional alphabet book, I recommend The Technical Alphabet (2014) by the engineer sisters Lavanya and Melissa Jawaharlal. More recently a colleague introduced me to Laura Overdeck’s Bedtime Math series; these will soon join …

Meander Graphs And Frobenius Seaweed Lie Algebras Ii, Vincent Coll, Matthew Hyatt, Colton Magnant, Hua Wang

Mathematical Sciences: Faculty Publications

We provide a recursive classification of meander graphs, showing that each meander is identified by a unique sequence of fundamental graph theoretic moves. This sequence is called the meander’s signature and can be used to construct arbitrarily large sets of meanders, Frobenius or otherwise, of any size and configuration. In certain special cases, the signature is used to produce an explicit formula for the index of seaweed Lie subalgebra of sl(n) in terms of elementary functions.

On Similarities And Differences Between Proving And Problem Solving, Milos Savic

Journal of Humanistic Mathematics

A link between proving and problem solving has been established in the literature [5, 21]. In this paper, I discuss similarities and differences between proving and problem solving using the Multidimensional Problem-Solving Framework created by Carlson and Bloom [2] with Livescribepen data from a previous study [13]. I focus on two participants’ proving processes: Dr. G, a topologist, and L, a mathematics graduate student. Many similarities between the framework and the proving processes of Dr. G and L were revealed, but there were also some differences. In addition, there were some distinct differences between the proving actions of the …