Mathematics Commons^™

Technology Integration In Secondary Mathematics Classrooms: Effect On Students’ Understanding, Megan Sheehan, Leah Nillas

Scholarly Publications

Technology use in secondary mathematics courses has the potential to bring about broad changes in learning environment and teaching pedagogy, allowing students to communicate and collaborate in new ways and to conjecture, justify, and generalize findings. However, this potential is only realized when teachers use technology in ways encouraging these outcomes (Galbraith, 2006). The purpose of this study is to examine the integration of technology in secondary mathematics classrooms and to evaluate the effectiveness of its use in relation to students’ learning outcomes. This self study research was conducted in honors geometry and AP calculus classes. Data sources included transcripts …

Note On Gradient Estimates Of Heat Kernel For Schrödinger Operators, Shijun Zheng

Mathematical Sciences: Faculty Publications

Let H = -Δ+V be a Schrödinger operator on Rⁿ. We show that gradient estimates for the heat kernel of H with upper Gaussian bounds imply polynomial decay for the kernels of certain smooth dyadic spectral operators. The latter decay property has been known to play an important role in the Littlewood-Paley theory for L^p and Sobolev spaces. We are able to establish the result by modifying Hebisch and the author’s recent proofs. We give a counterexample in one dimension to show that there exists V in the Schwartz class such that the long time gradient heat …

An Attempt To Get And Keep Women Involved In Physics, Jim Crumley, Kristen Nairn, Lynn Ziegler

MapCores Faculty Publications

In this talk I will briefly review some of the obstacles to the full participation of women in the STEM disciplines. In order to increase the number of women in physics, computer science, and mathematics we have started a cohort-based program with curricular and scholarship components for women in these majors. I will present the results of our program so far and offer some advice based on our experiences.

Impact Of Interdisciplinary Undergraduate Research In Mathematics And Biology On The Development Of A New Course Integrating Five Stem Disciplines, Lester Caudill, April L. Hill, Kathy Hoke, Ovidiu Z. Lipan

Department of Math & Statistics Faculty Publications

Funded by innovative programs at the National Science Foundation and the Howard Hughes Medical Institute, University of Richmond faculty in biology, chemistry, mathematics, physics, and computer science teamed up to offer first- and second-year students the opportunity to contribute to vibrant, interdisciplinary research projects. The result was not only good science but also good science that motivated and informed course development. Here, we describe four recent undergraduate research projects involving students and faculty in biology, physics, mathematics, and computer science and how each contributed in significant ways to the conception and implementation of our new Integrated Quantitative Science course, a …

Impact Of Interdisciplinary Undergraduate Research In Mathematics And Biology On The Development Of A New Course Integrating Five Stem Disciplines, Lester Caudill, April L. Hill, Kathy Hoke, Ovidiu Z. Lipan

Biology Faculty Publications

Funded by innovative programs at the National Science Foundation and the Howard Hughes Medical Institute, University of Richmond faculty in biology, chemistry, mathematics, physics, and computer science teamed up to offer first- and second-year students the opportunity to contribute to vibrant, interdisciplinary research projects. The result was not only good science but also good science that motivated and informed course development. Here, we describe four recent undergraduate research projects involving students and faculty in biology, physics, mathematics, and computer science and how each contributed in significant ways to the conception and implementation of our new Integrated Quantitative Science course, a …

"Beyond Bio2010: Celebration And Opportunities" At The Intersection Of Mathematics And Biology, John R. Jungck, Holly D. Gaff, Adam P. Fagen, Jay B. Labov

Biological Sciences Faculty Publications

With this special edition of CBE-LSE, which focuses on connections between and integration of the biological and mathematical sciences, it is especially fitting that we report on an important symposium, Beyond BIO2010: Celebration and Opportunities,1 which was held at the National Acad- emy of Sciences (NAS) in Washington, D.C. on May 21–22, 2010. This symposium was organized to assess what progress has been made in addressing the challenges and recommendations in the National Research Council’s (NRC) report: BIO2010: Transforming Undergraduate Education for Future Research Biologists (NRC, 2003a). Most of the presen- tations and posters at this event emphasized the increasing …

Mathematical Manipulative Models: In Defense Of "Beanbag Biology", John R. Jungck, Holly Gaff, Anton E. Weisstein

Biological Sciences Faculty Publications

Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process-1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets-we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational …

Teaching Calculus With Wolfram Alpha, Andrew Lang

College of Science and Engineering Faculty Research and Scholarship

This article describes the benefits and drawbacks of using Wolfram|Alpha as the platform for teaching calculus concepts in the lab setting. It is a result of our experiences designing and creating an entirely new set of labs using Wolfram|Alpha. We present the reasoning behind our transition from using a standard computer algebra system (CAS) to Wolfram|Alpha in our differential and integral calculus labs, together with the positive results from our experience. We also discuss the current limitations of Wolfram|Alpha, including a discussion on why we still use a CAS for our multivariate calculus labs.

Virtual Manipulatives In The Classroom And Resulting Articles And Lesson Plans, Cheryl Juliana

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

Upon coming across mathematical manipulatives generated and produced by Utah State University, as a math teacher, I conducted a classroom teaching experiment in three pre-algebra classes with students of various achievement levels. After teaching the entire year using no manipulatives in the classroom, I tested my students with a general, end-of-year, core criterion, or cumulative test. Their scores were noted. The students in the study group were then given opportunities to try several manipulatives offered on the "National Library of Virtual Manipulatives," both as a class, and alone, and then retested. The following paper gives the parameters of the study, …

Anxiety In The Math Classroom, Jean Benner

Mathematics Graduate Theses

Math anxiety is a learned response that inhibits cognitive performance in the math classroom. It is widespread among students from elementary age through college. Students suffering from math anxiety have difficulty performing calculations and maintaining a positive outlook on mathematics. Math anxiety is the result of a cycle of math avoidance that begins with negative experiences regarding mathematics. Facts pertaining to math anxiety are discussed and strategies are suggested to assist teachers in helping students to overcome math anxiety or avoid the phenomenon altogether.

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 …

Applications Of Linear Programming To Coding Theory, Nathan Axvig

Department of Mathematics: Dissertations, Theses, and Student Research

Maximum-likelihood decoding is often the optimal decoding rule one can use, but it is very costly to implement in a general setting. Much effort has therefore been dedicated to find efficient decoding algorithms that either achieve or approximate the error-correcting performance of the maximum-likelihood decoder. This dissertation examines two approaches to this problem.

In 2003 Feldman and his collaborators defined the linear programming decoder, which operates by solving a linear programming relaxation of the maximum-likelihood decoding problem. As with many modern decoding algorithms, is possible for the linear programming decoder to output vectors that do not correspond to codewords; such …

Vanishing Of Ext And Tor Over Complete Intersections, Olgur Celikbas

Department of Mathematics: Dissertations, Theses, and Student Research

Let (R,m) be a local complete intersection, that is, a local ring whose m-adic completion is the quotient of a complete regular local ring by a regular sequence. Let M and N be finitely generated R-modules. This dissertation concerns the vanishing of Tor(M, N) and Ext(M, N). In this context, M satisfies Serre's condition (S_{n}) if and only if M is an nth syzygy. The complexity of M is the least nonnegative integer r such that the nth Betti number of M is bounded by a polynomial of degree r-1 for all sufficiently large n. We use this notion of …

Creating A Masters In Numeracy Program, Eric Gaze

Numeracy

The Master of Science in Numeracy program at Alfred University received full approval from the New York State Education Department (NYSED) in May of 2007. This first-of-its-kind program seeks to provide teachers at all levels, from across the curriculum, the skills, and more importantly the confidence, to introduce relevant quantitative concepts in their own disciplines. Created to be a complement of the MS Ed. in Literacy, the 30-hour MS in Numeracy program consists of four required core courses (Teaching Numeracy, Teaching with Data, Assessment and Learning Theories in Numeracy, and Doing Science and Numeracy), five electives from a list of …

Parts Of The Whole: Thinking About Variance: Standards, Targets, Tracking, And Other Thoughts, Dorothy Wallace

Numeracy

Variation is a natural result of any process, including education. Understanding how variation propagates and increases is necessary for designing educational interventions that work for the intended population. We show how common strategies such as setting standards and tracking can accidentally produce unintended and undesirable results due to the way variation moves through a system.

Spreadsheets Across The Curriculum, 1: The Idea And The Resource, H L Vacher, Emily Lardner

Numeracy

This paper introduces Spreadsheets Across the Curriculum, a workshop-based educational materials development project to build a resource to facilitate connecting mathematics and context in undergraduate college courses where mathematical problem solving is relevant. The central idea is “spreadsheet modules,” which, in essence, are elaborate word problems in the form of short PowerPoint presentations with embedded Excel spreadsheets. Students work through the presentations on their own, making and/or completing the spreadsheets displayed on the slides in order to perform calculations or draw graphs that address the issue (context) posed in the word problem. The end result of the project is the …

Reorganizing School Mathematics For Quantitative Literacy, Rick Gillman

Numeracy

This paper offers an alternative curriculum for high school mathematics. It proposes replacing the Algebra-Geometry-Algebra rush to calculus model with one which focuses on improving student problem-solving skills and general quantitative literacy skills while reinforcing basic manipulative skills. Most of these goals are gained by expanding the current single-year algebra-one course into two years. The model proposes moving “learning to write proofs” from the traditional geometry course into a separate discrete mathematics course. It requires statistics for every student, and requires a senior-level modeling course for every college-going student. In addition, the proposed model creates opportunities for students to move …

Quantitative Reasoning In The Contemporary World, 2: Focus Questions For The Numeracy Community, Bernard L. Madison, Shannon W. Dingman

Numeracy

Numerous questions about student learning of quantitative reasoning arose as we developed, taught and assessed the Quantitative Reasoning in the Contemporary World course described in the companion paper in this issue of Numeracy. In this paper, we present some of those questions and describe the context in which they arose. They fall into eight general problem areas: learning that is context-bound and does not easily transfer (i.e., situated learning); the need for a productive disposition regarding mathematics; the connection between QL and mathematical proficiency; the persistence of students, despite our efforts, for using the wrong base for percents; the inconsistent …

Quantitative Reasoning In The Contemporary World, 1: The Course And Its Challenges:, Shannon W. Dingman, Bernard L. Madison

Numeracy

The authors describe successes and challenges in developing a QL-friendly course at the University of Arkansas. This work is part of a three-year NSF project Quantitative Reasoning in the Contemporary World (QRCW) that supported the expansion of the course. The course, MATH 2183, began experimentally in Fall 2004 as a section of finite mathematics known informally as “News Math” for 26 students from arts and humanities disciplines. Over the past six years, the course has evolved and now MATH 2183 is approved to satisfy the College of Arts and Sciences mathematics requirement for the Bachelor of Arts degree. In 2009-2010, …

Quantitative Literacy: Does It Work? Evaluation Of Student Outcomes At Colby-Sawyer College, Benjamin Steele, Semra Kilic-Bahi

Numeracy

Colby-Sawyer College has adopted a mission for quantitative literacy (QL) to give students the “necessary skills to understand and use quantitative information in their personal and professional lives.” We have implemented an across-the-curriculum approach to develop these skills. As part of this QL program, we administer two assessment tests, one in basic mathematical skills and one that applies those skills, plus an attitude survey to both freshmen and seniors. Three years of data show that seniors score about 10 percentage points higher than freshmen on these tests. However, seniors still scored below 55 percent on both tests, and many cannot …

Advancing Assessment Of Quantitative And Scientific Reasoning, Donna L. Sundre, Amy D. Thelk

Numeracy

Advancing Assessment of Quantitative and Scientific Reasoning is a four-year NSF Project (DUE-0618599) in part designed to evaluate the generalizability of quantitative (QR) and scientific reasoning (SR) assessment instruments created at James Madison University to four other four-year institutions with very distinct missions and student demographics. This article describes the methods, results, and findings we obtained in our studies. More specifically, we describe how to conduct content-alignment exercises in which faculty members map each item from a prospective test to the student learning objectives taught at the institution. Our results indicated that 92-100% of the QR and SR items were …

Science Literacy: Hand In Glove With Numeracy, Gerry G. Meisels

Numeracy

Science Literacy requires numeracy as part of its foundation, and much of Numeracy draws on examples and applications from the sciences. They share the goal of creating a society that is mathematics numerate and science literate, and are interrelated. National priorities to strengthen both among all our students are driven by practical considerations of economic competitiveness that increasingly depend on technological innovation. It is also critical to each individual for long-term job opportunities and for informed citizenship. With up to 80% of 21st century jobs requiring mathematics and science skills, a large majority of the 2,900,000 students who graduate from …

On The Characteristic Polynomial Of Regular Linear Matrix Pencil, Yan Wu, Phillip Lorren

Mathematical Sciences: Faculty Publications

Linear matrix pencil, denoted by (A,B), plays an important role in control systems and numerical linear algebra. The problem of finding the eigenvalues of (A,B) is often solved numerically by using the well-known QZ method. Another approach for exploring the eigenvalues of (A,B) is by way of its characteristic polynomial, P(λ)=A − λB. There are other applications of working directly with the characteristic polynomial, for instance, using Routh-Hurwitz analysis to count the stable roots of P(λ) and transfer function representation of control systems governed by differential-algebraic equations. In this paper, we …

Assessing The Impact Of A Computer-Based College Algebra Course, Ningjun Ye

Dissertations

USM piloted the Math Zone in Spring 2007, a computer-based program in teaching MAT 101and MAT 099 in order to improve student performance. This research determined the effect of the re-design of MAT 101 on student achievements in comparison to a traditional approach to the same course. Meanwhile, the study investigated possible effects of the Math Zone program on students’ attitude toward studying mathematics.

This study shows that there was no statistically significant difference on MAT101 final exam scores between the Math Zone students and the Classroom students in Fall 2007, Spring 2008 and Fall 2008. At the same time, …

The Effect Of Explicit Timing On Math Performance Using Interspersal Assignments With Students With Mild/Moderate Disabilities, Fangjuan Hou

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Explicit timing and interspersal assignments have been validated as effective methods to facilitate students' math practice. However, no researchers have explored the combinative effect of these two methods. In Study 1, we extended the literature by comparing the effect of explicit timing with interspersal assignments, and interspersal assignments without timing. Generally, participants' rate of digits correct on easy and hard addition problems was higher during the explicit timing condition than during the untimed condition. However, the participants' rate of digits correct decreased after initial implementation of the explicit timing condition.

Motivation plays a crucial role in maintaining performance levels and …

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.

Software Internationalization: A Framework Validated Against Industry Requirements For Computer Science And Software Engineering Programs, John Huân Vũ

Master's Theses

View John Huân Vũ's thesis presentation at http://youtu.be/y3bzNmkTr-c.

In 2001, the ACM and IEEE Computing Curriculum stated that it was necessary to address "the need to develop implementation models that are international in scope and could be practiced in universities around the world." With increasing connectivity through the internet, the move towards a global economy and growing use of technology places software internationalization as a more important concern for developers. However, there has been a "clear shortage in terms of numbers of trained persons applying for entry-level positions" in this area. Eric Brechner, Director of Microsoft Development Training, suggested …

A Unified Theory Of Function Spaces And Hyperspaces: Local Properties, Szymon Dolecki, Frédéric D. Mynard

Mathematical Sciences: Faculty Publications

Many classically used function space structures (including the topology of pointwise convergence, the compact-open topology, the Isbell topology and the continuous convergence) are induced by a hyperspace structure counterpart. This scheme is used to study local properties of function space structures on C(X,R), such as character, tighntess, fan-tightness, strong fan-tightness, the Fr{\'e}chet property and some of its variants. Under mild conditions, local properties of C(X,R) at the zero function correspond to the same property of the associated hyperspace structure at X. The latter is often easy to characterize in terms of covering properties …

Cryptography: A History In Mathematics, An Application In The Classroom, Brian Olmanson

Honors Capstones

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