Science and Mathematics Education Commons^™

Practice Through Play Using Mobile Technology, Agnes D. Garciano, Debbie Marie B. Verzosa, Ma Louise Antonette N. De Las Peñas, Maria Alva Q. Aberin, Juan Carlo F. Mallari, Jumela F. Sarmiento, Mark Anthony C. Tolentino

Mathematics Faculty Publications

This paper discusses the Just Keep Solving apps that are designed based on deliberate practice model for developing mathematical skills. Features of deliberate practice include well-defined goals involving areas of weakness as determined by a knowledgeable other such as a teacher. The integration of game design features provides a positive environment wherein the learning goals critical in a deliberate practice model are emphasized. Possible strategies for integrating the apps in a classroom are also discussed using Hughes, Thomas and Scharber’s RAT (Replacement, Amplification, Transformation) framework. The games can replace traditional pen-and-paper classroom activities, amplify learning by personalizing a student’s experience …

How Elementary Teachers Implement The Eureka Mathematics Curriculum To Improve Mathematics Outcomes, Shannell A. Swan-Clarke

Walden Dissertations and Doctoral Studies

Many states use research-based mathematics curricula as an instructional tool to improve mathematics performance outcomes on state assessment scores. The problem was that despite the implementation of a research-based curriculum, students at XYZ Elementary School (pseudonym) had underperformed on the Partnership for Assessment of Readiness for College and Careers standardized mathematics tests since 2018. The purpose of this basic qualitative study was to discover the implementation practices of teachers using the Eureka Mathematics Curriculum to improve student outcomes at XYZ Elementary School. Dewey’s experiential learning theory was used to support and explore ideas involving the influences of curriculum implementation on …

How Elementary Teachers Implement The Eureka Mathematics Curriculum To Improve Mathematics Outcomes, Shannell A. Swan-Clarke

Walden Dissertations and Doctoral Studies

Many states use research-based mathematics curricula as an instructional tool to improve mathematics performance outcomes on state assessment scores. The problem was that despite the implementation of a research-based curriculum, students at XYZ Elementary School (pseudonym) had underperformed on the Partnership for Assessment of Readiness for College and Careers standardized mathematics tests since 2018. The purpose of this basic qualitative study was to discover the implementation practices of teachers using the Eureka Mathematics Curriculum to improve student outcomes at XYZ Elementary School. Dewey’s experiential learning theory was used to support and explore ideas involving the influences of curriculum implementation on …

Interactive White Boards In A Secondary Mathematics Classroom, Leann Bolhuis

Mathematics Graduate Theses

"A Formal Portfolio Submitted to the Faculty of the DEPARTMENT OF MATHEMATICS & COMPUTER SCIENCE In Partial Fulfillment of the Requirements For the Degree of MASTER OF SCIENCE IN MATHEMATICS".

A View Into Secondary Education Mathematics, Thomas Krieger Jr.

Honors Theses

Teaching methods, and the effects they can have on students, are important to consider for a classroom because when teaching you should allow for every student to have an opportunity. Every student should feel encouraged in the classroom, however not every method may allow for that. An important task for a teacher is to find out how to reach their students in their classroom; be it adapting methods or choosing when to implement one item over another. This task differs with every student that enters the classroom as no student is the same. Every students’ differences stem from their academic …

A Generalized Method Of Undetermined Coefficients, James S. Cook, William J. Cook

CODEE Journal

The method of undetermined coefficients is used to solve constant coefficient nonhomogeneous differential equations whose forcing function is itself the solution of a homogeneous constant coefficient differential equation. In this paper, we show that the classical methods for tackling constant coefficient equations, including the method of undetermined coefficients, generalize to much wider class linear differential equations which, for example, include Cauchy-Euler type equations. This general method includes an explicit construction of the fundamental solution sets of such equations. We also briefly consider where this method can be applied by producing the most general second and third order differential equations that …

“Math Talks Are Like An Alarm Clock Waking You Up”: Language’S Crucial Role In Mathematics, Gabriella M. Wasser

Journal of Practitioner Research

Whole group math talks, or number talks, are a common practice to get students talking about their own understanding of mathematical concepts. The purpose of this study was to implement math talks in small group settings to see what would happen, specifically to students’ conceptual understanding as well their general perceptions of math talks. This study took place in a fourth-grade math classroom, and math talks were implemented with the whole class for a week and then moved to small groups for the remaining three weeks of the study. During the study, a pre-and post-assessment was given, field notes were …

Teaching Euclidean Geometry Using Proof And Dynamic Geometry Software, Cheryl Stoddard

Mathematics Graduate Theses

This paper examines incorporating proofs and dynamic geometry software when teaching Euclidean geometry to produce deeper understanding of geometric relationships for middle and secondary level students. The utilization of technology through classroom investigations and activities has shown to have an impact on the achievement scores on posttests and in the development of mathematical proof.

Investigating Elementary School Students’ Reasoning About Dynamic Angles, Erell Germia

Theses, Dissertations and Culminating Projects

Angle measurement is a significant topic in almost all areas of mathematics learning and also in many disciplines outside mathematics education, such as engineering and architecture. According to the literature, there are three common conceptions of angles – as union of rays, rotations, and wedges. Researchers argued that students must consider these three angle concepts together to construct a meaningful understanding of angles. However, the curriculum standards for mathematics often present these angle conceptions separately to students, probably resulting in a fragmented understanding of the angle concept. In addition to this problem, the research literature documents multiple alternative conceptions that …

Mathematics Education As Dystopia: A Future Beyond, Peter Appelbaum, Charoula Stathopoulou, Constantinos Xenofontos

Journal of Humanistic Mathematics

We argue that scholars and practitioners of mathematics education need to find new directions through recognition of its dystopic characteristics, and embrace these characteristics as both the source of challenges and method of response. This contrasts with the generally utopic approach of most scholarship in the field. We offer critical ethnomathematics education as a model, since it has its own origins in lingering dystopic legacies. A perpetual hopelessness and disempowerment is one implicit curriculum of contemporary mathematics education, where the mathematics one learns might help to describe things, yet hardly assists in transforming the reification of power and agency in …

Higher Meanings: A Speaker Series Connecting Mathematics And Religion, Lawrence M. Lesser, Patricia S. Barrientos, Ben Zeidman

Journal of Humanistic Mathematics

An innovative grant-funded general adult audiences international speaker series on connections between mathematics and religion yielded six 2021 (now archived) presentations. We share reflections and lessons learned, informed by two sets of surveys.

Benny, Barbara, And The Ethics Of Edtech, Geillan Aly

Journal of Humanistic Mathematics

Erlwanger (1973) shook the mathematics education world when he introduced Benny, a student who successfully worked through a behavioristic curriculum. Erlwanger showed how far removed Benny’s understanding of mathematics was from expectations. Erlwanger’s legacy is the basis for this comparative case study which explores students’ actions in the modern, in-class computer-centered emporium classroom. Many striking similarities are found between Pearson’s MyMathLabs (MML) and Benny’s Individually Prescribed Instruction curriculum. In this case study we meet Barbara, a student who succeeds in MML but shows little understanding of mathematical concepts and demonstrates that the legacy of Benny is his continued appearance in …

Bbt Acoustic Alternative Top Bracing Cadd Data Set-Norev-2022jun28, Bill Hemphill

STEM Guitar Project’s BBT Acoustic Kit

This electronic document file set consists of an overview presentation (PDF-formatted) file and companion video (MP4) and CADD files (DWG & DXF) for laser cutting the ETSU-developed alternate top bracing designs and marking templates for the STEM Guitar Project’s BBT (OM-sized) standard acoustic guitar kit. The three (3) alternative BBT top bracing designs in this release are
(a) a one-piece base for the standard kit's (Martin-style) bracing,
(b) 277 Ladder-style bracing, and
(c) an X-braced fan-style bracing similar to traditional European or so-called 'classical' acoustic guitars.

The CADD data set for each of the three (3) top bracing designs includes …

Understanding Compactness Through Primary Sources: Early Work Uniform Continuity To The Heine-Borel Theorem, Naveen Somasunderam

Analysis

No abstract provided.

Bbt Side Mold Assy, Bill Hemphill

STEM Guitar Project’s BBT Acoustic Kit

This electronic document file set covers the design and fabrication information of the ETSU Guitar Building Project’s BBT (OM-sized) Side Mold Assy for use with the STEM Guitar Project’s standard acoustic guitar kit. The extended 'as built' data set contains an overview file and companion video, the 'parent' CADD drawing, CADD data for laser etching and cutting a drill &/or layout template, CADD drawings in AutoCAD .DWG and .DXF R12 formats of the centerline tool paths for creating the mold assembly pieces on an AXYZ CNC router, and support documentation for CAM applications including router bit specifications, feeds, speed, multi-pass …

How To Guard An Art Gallery: A Simple Mathematical Problem, Natalie Petruzelli

The Review: A Journal of Undergraduate Student Research

The art gallery problem is a geometry question that seeks to find the minimum number of guards necessary to guard an art gallery based on the qualities of the museum’s shape, specifically the number of walls. Solved by Václav Chvátal in 1975, the resulting Art Gallery Theorem dictates that ⌊n/3⌋ guards are always sufficient and sometimes necessary to guard an art gallery with n walls. This theorem, along with the argument that proves it, are accessible and interesting results even to one with little to no mathematical knowledge, introducing readers to common concepts in both geometry and graph …

Remotely Close: An Investigation Of The Student Experience In First-Year Mathematics Courses During The Covid-19 Pandemic, Sawyer Smith

Honors Program: Senior Projects (Public)

The realm of education was shaken by the onset of the COVID-19 pandemic in 2020. It had drastic effects on the way that courses were delivered to students, and the way that students were getting their education at the collegiate level. At the University of Nebraska – Lincoln, the pandemic dramatically changed the way that first-year mathematics courses looked for students. By Spring 2021, students had the opportunity to take their first-year math courses either in-person or virtually. This project sought to identify differences between the two methods of course delivery during the Spring 2021 semester, regarding interaction with peers …

Learning Mathematics From The Master: A Collection Of Euler-Based Primary Source Projects For Today’S Students, Part I, Janet Heine Barnett, Dominic Klyve, Kenneth M. Monks, Adam E. Parker

Euleriana

This article and its sequel will together highlight a set of nine classroom ready projects that draw on the remarkable writing of Leonhard Euler (1707–1783) as a means to help students develop an understanding of standard topics from today’s undergraduate mathematics curriculum. Part of a larger collection of primary source projects intended for use in a wide range of undergraduate mathematics courses, these projects are freely available to students and their instructors. We provide a general description of the pedagogical design underlying these projects, more detailed descriptions of the individual projects themselves, and instructions for obtaining downloadable copies for classroom …

Analysis Of A Mathematical Model Of Real-Time Competitive Binding On A Microarray, Frank H. Lynch

CODEE Journal

A mathematical model of competitive binding on a microarray in real-time yields a planar system of nonlinear ordinary differential equations. This model can be used to explore dimensionless formulation, linear approximation, and reduction. Real-time competitive binding is proposed as an uncommon approach to advance the study of planar systems of differential equations.

An Urgent Plea For More Graduate Programs In Statistics Education, David Eli Drew, Sam Behseta, Cherie L. Ichinose

Journal of Humanistic Mathematics

Lately, much has been written about the importance of amplifying statistics-related content in the K-12 curricula. This can be viewed in parallel or as an addendum to the existing mathematics curricula in the United States. Nevertheless, a key component of this debate is the lack of robust and cutting-edge academic programs in statistics education. In this piece, we emphasize the urgent need for investing in creating strong statistics education programs, which would significantly contribute to nurturing quantitative literacy as well as preparing a more informed citizenry in the 21^st century.

In Search Of Star Clusters: An Introduction To The K-Means Algorithm, Marcio Nascimento

Journal of Humanistic Mathematics

This article is a gentle introduction to K-means, a mathematical technique of processing data for further classification. We begin with a brief historical introduction, where we find connections with Plato’s Timæus, von Linné’s binomial classification, and the star clustering concept of Mary Sommerville and collaborators. Artificial intelligence algorithms use K-means as a classification methodology to learn about data in a very accurate way, because it is a quantitative procedure based on similarities.

Middle School Students Generating Mathematical Problems From A Real-Life Situation, David Coffland, Ying Xie

Journal of Humanistic Mathematics

In this study, we examined the effect of different presentation formats of a realistic situation on students’ mathematical problem-posing behavior. We divided thirty-six middle school students into two groups, gave them a pretest, and then showed them a realistic, problem-posing situation in Artifact or Video format. We used Silver’s core dimensions of creativity, namely fluency, flexibility, and originality, to measure participants’ problem-posing activity. The results for the fluency measures showed that the Artifact group wrote more questions than the Video group but the same number of mathematics problems. The Video group posed problems in more mathematical domains than the Artifact …

Plane Figurate Number Proofs Without Words Explained With Pattern Blocks, Gunhan Caglayan

Journal of Humanistic Mathematics

This article focuses on an artistic interpretation of pattern block designs with primary focus on the connection between pattern blocks and plane figurate numbers. Through this interpretation, it tells the story behind a handful of proofs without words (PWWs) that are inspired by such pattern block designs.

Exploring The Complex Relationship Between Engineering Students Math Experiences And Identity Formation, Jill Davishahl, Joseph Brobst, Elizabeth Litzler, Andrew Klein, Sura Alqudah

Division of Research and Economic Development Faculty & Staff Publications

This paper shares the experiences of a group of S-STEM scholarship students as they progressed through their first year of undergraduate mathematics education including a math placement exam, a math focused bridge program, and calculus course(s). In addition, connections between student experiences and their math identity development were investigated with the goal of better understanding math identity formation. The authors used a mixed-methods approach to explore the math-related experiences of 12 students over the first year of participation in an NSF-funded S-STEM program. Data includes answers to select survey questions and transcripts of student focus groups. First, each student case …

The Efficacy Of The South Dakota State University Summer Jacks Leap Program, Tessa M. Sundermann

Electronic Theses and Dissertations

Today, several studies detail the continuing struggle many students have with college mathematics courses at universities across the United States. The South Dakota State University Summer Jacks LeaP program is a summer bridge mathematics program aimed at improving incoming students’ mathematics success. This analysis used a mixed methods research design to examine the efficacy of the Summer Jacks LeaP program. First, we analyzed the LeaP students’ homework averages, exam 1 scores, final exam scores, and overall grade scores to determine if they were finding success in their fall semester mathematics courses. We also used hypothesis testing to compare LeaP participants …

Math Department 2021-2022 Newsletter, Mathematics Department

Mathematics Newsletter

Welcome to our annual Mathematics Department Newsletter. As we are slowly coming out of the pandemic, we were able to resume many of our normal events.

Deployment Of Mathematical Resources To A Philippine High School Through A Community Lte Network, Ma. Louise Antonette N. De Las Peñas, Maria Alva Q. Aberin, Agnes Garciano, Juan Carlo F. Mallari, Jumela F. Sarmiento, Mark Anthony C. Tolentino, Debbie Marie Verzosa

Mathematics Faculty Publications

In the Philippines, one challenge that continues to be faced by the Department of Education in bringing educational content in a blended learning modality is the lack of internet access of the learners. This paper discusses the distribution, through a community LTE network, of mathematical resources for Grades 7 to 10 to teachers and students of a particular high school in the Philippines. It also gives details on particular technological tools (mathematical applications) that were created to help the mathematical learning of students in a remote setting.

Development Of An App And Videos To Support The Fraction Learning Trajectory From Grades 1-7, Debbie Marie Verzosa, Ma. Louise Antonette N. De Las Peñas, Maria Alva Q. Aberin, Agnes Garciano, Jumela F. Sarmiento, Juan Carlo F. Mallari, Mark Anthony C. Tolentino

Mathematics Faculty Publications

Lack of procedural fluency in fractions impedes access to advanced mathematical courses and limits opportunities for entry into STEM-related fields. This paper describes the design and pedagogical basis of the Moving Fractions app and supplementary fraction videos for promoting fraction learning. Moving Fractions utilizes game-design factors to draw students through a trajectory of fraction learning from part-whole comparisons to a more robust understanding of the measurement concept of fractions. The supplementary video immerses students in a broad range of fraction representations. The app and video are intended to form a fraction learning package for distribution in Philippine schools. Future work …

Participatory Action Research: Undergraduate Researchers Engaging Secondary Students In Social Justice Mathematics, Isabelle Miller, Alexis Grimes, Camryn Adkison

The Journal of Purdue Undergraduate Research

No abstract provided.

Tech & Toys To Teach Linear Algebra, Kelly W. Remijan

Publications & Research

6th - 12 Grade Math teachers will Discover activities involving tech and/or toys:

1. CNC Machines- graphing points & line segments
2. Desmos/GeoGebra & flags- graphing linear equations/inequalities w/ domain/range
3. CBR & movement- graphing/analyzing lines
4. Push toys- systems of equations
5. Water growing toys- growth rate
6. Ziplines, Balloons, Barbie, & Lego People - slope & linear equations