Mathematics Commons^™

Qualitative Analysis Of Corequisite Instruction In A Quantitative Reasoning Course, Zachary Beamer

Inquiry: The Journal of the Virginia Community Colleges

In corequisite models of instruction, marginally prepared students are placed directly into college-level coursework, taught with a paired support course. Initial research suggests that such models yield significant improvements in the number of students passing credit-level mathematics when compared to previous models of prerequisite remediation. The present study employs qualitative methods to investigate methods of instruction at one community colleges to understand how instructors identify and respond to student needs. It concludes with recommendations for practice and highlights advantages of small format corequisite classes taught by the same instructor.

Shall We Ignore All Intermediate Grades?, Christian Servin, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In most European universities, the overall student's grade for a course is determined exclusively by this student's performance on the final exam. All intermediate grades -- on homework, quizzes, and previous texts -- are, in effect, ignored. This arrangement helps gauge the student's performance by the knowledge that the student shows at the end of the course. The main drawback of this approach is that some students do not start studying until later, thinking that they can catch up and even get an excellent grade -- and this hurts their performance. To motivate students to study hard throughout the semester, …

How To Teach Advanced Highly Motivated Students: Teaching Strategy Of Iosif Yakovlevich Verebeichik, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

The paper describes and explains the teaching strategy of Iosif Yakovlevich Verebeichik, a successful mathematics teacher at special mathematical high schools -- schools for students interested in and skilled in mathematics. The resulting strategy seems counterintuitive and contrary to all the pedagogical advice. Our explanation is not complete: it worked well for this teacher, but others who tried to follow seemingly the same strategy did not succeed. How he made it work, how can others make it work -- this is still not clear. In the words of Verebeichik himself, while mathematics itself is a science, teaching mathematics is an …

Secondary Teachers’ Noticing Of Students’ Mathematical Thinking As They Participate In A Professional Development Program Centered On Task-Based Student Interviews, Gurkan Kose

Theses, Dissertations and Culminating Projects

Teacher’s noticing of students’ mathematical thinking has been an important focus of research in the past two decades (e.g., Jacobs et al., 2010; Sherin et al., 2011). Noticing matters, but it is not an end in itself (Schoenfeld, 2011). It is operationalized within the context of teachers’ dispositions and knowledge which shape decisions teachers make while responding to student thinking and planning the next instructional steps. In order for teachers to adapt productive beliefs about how children learn and shift to student-centered instruction, they need to acknowledge the importance of understanding students' existing conceptions of mathematical ideas (Carpenter & Lehrer, …

Factors That Influence Teachers' Utilization Of Siop Learning Strategies When Teaching English Language Learners, Courtney R. Stuart

Theses and Dissertations

Despite standardized certification tests and popular English Language Learner trainings, the strategies and methods used in two educators’ classes would not be identical. In this case-study we look to see what variables cause teachers to utilize certain strategies and how these variables affect the number of strategies used consistently when teaching ELLs. We study the effect of teachers’ language experiences, certifications, participation in SIOP trainings, education levels, perceived preparedness, and years spent in the classroom.

Using quantitative and qualitative data we conclude that dual-language fluency and professional advancements can lead to teachers using more ELL learning strategies in their classrooms, …

Coordinating Stem Core Courses For Student Success, Cristina Villalobos, Hyung Won Kim, Timothy J. Huber, Roger Knobel, Shaghayegh Setayesh, Lekshmi Sasidharan, Anahit Galstyan, Andras Balogh

School of Mathematical & Statistical Sciences Faculty Publications

Research indicates multi-section coordination improves the academic performance of students in STEM education. This paper describes the process of coordination in Precalculus, Calculus 1, and Calculus 2 courses undertaken by a large department that grew from the merger of two institutions through a pilot program, and a project grant. Components introduced in the project courses are documented, including collaborative problem-solving sessions, student learning assistants, Q&A sessions, and additional technology resources. Preliminary data is provided on the impacts of the initiative on student success. The study findings provide a template for coordination, faculty buy-in, and increased student engagement at similar institutions …

Developing Better Instruction, Better Instructors, And New Investigators, Clay Vander Kolk, Abigail Pyle

Celebration of Scholarship 2021

This research discusses how HAMTE and future educators collaborated to use the Principles to Action Professional Learning Toolkit in their classes and the tools they used to measure and gather conclusions about the development in the future teachers.

Ready To Engage? Urban Middle School Teachers’ Responsiveness To Targeted Engagement Interventions On Their Virtual Instructional Practices: An Action Research Study, Svetlana Nikic

Dissertations

Teachers’ effectiveness is associated with their instructional practices and is ultimately linked to students’ learning outcomes. In order to impact teachers’ effectiveness, schools focus substantial effort and resources on professional development led by an assumption that teachers’ classroom practices can be improved through targeted interventions. Even if this premise is correct, little information is available about how much a teacher’s practice may change through interventions, or which aspects of instructional practice are more receptive to improving teacher effectiveness (Garret et al., 2019).

This study took place at an urban middle school and examined teachers’ responsiveness to targeted engagement intervention in …

Stitching Dedekind Cuts To Construct The Real Numbers, Michael P. Saclolo

Analysis

No abstract provided.

Talking The Talk:” Mathematical Language, Linguistic Bias, And The Delusion Of Meritocracy In The Study And Practice Of Mathematics, Gene T. Witkowski , '21

Senior Theses, Projects, and Awards

Challenging the dominant narrative of meritocracy, objectivity and moral/ideological neutrality embraced by many mathematicians, this thesis critically interrogates the form and function of mathematical language within academic and professional mathematical spaces. Grounded in my own experience as a s tudent within the discipline and the frameworks of various scholars within the subdiscipline of literacy education, I offer an understanding of the language of these spaces as a veritable form of literacy implicated in a flexible sociocultural context and dependent on one’s access to forms of capital. I submit that this language serves various functions including, but not limited to: the …

An Astronomer’S Journey Into Quantitative Reasoning, Jeffrey Bennett

Numeracy

The University of Colorado Boulder campus introduced what may have been the world’s first quantitative reasoning (QR) requirement in 1984 and started offering a QR course in 1988. Although I am an astronomer by training, I had the privilege of creating and teaching that course, which led to my co-authorship of the first textbook directed specifically at QR courses. In this “Roots and Seeds” piece, I will discuss how this course and textbook came to be, how I as an astronomer ended up involved in it, and how this work has connected with other aspects of my career.

Modeling The Ecological Dynamics Of A Three-Species Fish Population In The Chesapeake Bay, Iordanka N. Panayotova, Maila B. Hallare

CODEE Journal

We present an inquiry-based project that is designed for a mathematical modeling class of undergraduate junior or senior students. It discusses a three-species mathematical model that simulates the biological interactions among three important fish species in the Chesapeake Bay: the prey Atlantic menhaden and its two competing predators, the striped bass and the non-native blue catfish. The model also considers the following ecological issues related to these three species: the overfishing of menhaden, the invasiveness of the blue catfish, and the harvesting of blue catfish as a method to control the population. A series of modeling scenarios are considered based …

Engaging Students Early By Internationalizing The Undergraduate Calculus Course, Chinenye Ofodile

CODEE Journal

Today's world is global. However, despite increasing numbers and diversity of participants in Study Abroad programs, only 10% of U. S. college students get that experience. There is an ever-growing need for students to become aware of and experience other cultures, to understand why others think and act differently. Internationalization is the conscious effort, begun nearly 40 years ago, to integrate an international, intercultural, and global dimension into the purpose, functions, and delivery of post-secondary education.

Albany State University began a Global Program Initiative in the 1990s. In 2016, we extended into mathematics the curriculum innovations of this program. The …

Qualitative Analysis Of A Resource Management Model And Its Application To The Past And Future Of Endangered Whale Populations, Glenn Ledder

CODEE Journal

Observed whale dynamics show drastic historical population declines, some of which have not been reversed in spite of restrictions on harvesting. This phenomenon is not explained by traditional predator prey models, but we can do better by using models that incorporate more sophisticated assumptions about consumer-resource interaction. To that end, we derive the Holling type 3 consumption rate model and use it in a one-variable differential equation obtained by treating the predator population in a predator-prey model as a parameter rather than a dynamic variable. The resulting model produces dynamics in which low and high consumption levels lead to single …

Epidemiology And The Sir Model: Historical Context To Modern Applications, Francesca Bernardi, Manuchehr Aminian

CODEE Journal

We suggest the use of historical documents and primary sources, as well as data and articles from recent events, to teach students about mathematical epidemiology. We propose a project suitable -- in different versions -- as part of a class syllabus, as an undergraduate research project, and as an extra credit assignment. Throughout this project, students explore mathematical, historical, and sociological aspects of the SIR model and approach data analysis and interpretation. Based on their work, students form opinions on public health decisions and related consequences. Feedback from students has been encouraging.

We begin our project by having students read …

Facing The Pandemic Together: Forming A Collaborative Research Group, Michael C. Barg

CODEE Journal

This is an account of how a reading and writing project in an introductory differential equations course was transitioned to a professor-student research group collaborative project, in response to the global COVID-19 pandemic. Adapting on the fly to the ever-evolving pandemic, we collected data, estimated parameters in our models, and computed numerical solutions to SIR-based systems of differential equations. This is a description of what we did and how we found comfort in the project in this time of great uncertainty. The collaboration yielded successes and more questions than we had answers for, but the situation provided an opportunity of …

Engaging Learners: Differential Equations In Today's World

CODEE Journal

Engaging Learners: Differential Equations in Today's World

CODEE Journal, Volume 14, Issue 1

Math Escape Rooms: A Novel Approach For Engaging Learners In Math Circles, Janice F. Rech, Paula Jakopovic, Hannah Seidl, Greg Lawson, Rachel Pugh

Journal of Math Circles

Engaging middle and high school students in Math Circles requires time, planning and creativity. Finding novel approaches to maintain the interest of a variety of learners can be challenging. This paper outlines a model for developing and implementing math escape rooms as a unique structure for facilitating collaborative problem solving in a Math Circle. These escape rooms were designed and hosted by undergraduate secondary mathematics education majors. We provide possible structures for hosting escape rooms that could translate to a range of settings, as well as reflections and lessons learned through our experiences that could inform practitioners in other settings.

Effects Of Creative Play Activities On Early Mathematics Performance Among Preschoolers, Chong Chai Fung

Student Works (2020-2029)

The purpose of this study was to examine the effects of creative play activities on early mathematics performance among preschool children’s number operations in addition and subtraction skills. The sample consisted of 60 six years old children from two different Sekolah Kebangsaan preschools who were selected to participate in this study. 30 children from Preschool A were placed in the Experimental group and 30 children from Preschool B were placed in the Control group. The research instruments consisted pre-test and post-test addition and subtraction questions, 10 lessons of creative play activities on early mathematics in addition and subtraction games for …

“You Will Remain Unwavering In Your Determination To Succeed No Matter How Long It Takes”: A Mathematico-Emotional Analysis Of A Guide To Higher Learning, Kathleen M. Clark, Oksana M. Rubis

Journal of Humanistic Mathematics

In this article we present an analysis of the multi-fold artist’s book, A Guide to Higher Learning (Chen, 2009). In our analysis, we propose different perspectives from which to view the mathematical and philosophical aspects found within the book. We explore aspects of “higher learning” by analyzing the complex mathematical equations and textual elements that readers meet in the book. Chen challenges the reader with: “This is a test. You will not be given any assistance or instructions on how to proceed. You will not be told when to begin or when to stop” (Chen, 2009). Thus, in our exploration …

How I First Heard About Calculus, Bradley J. Lucier

Journal of Humanistic Mathematics

An attempt to motivate a class of engineering students leads to insights both personal and pedagogical.

Computational Thinking In Mathematics And Computer Science: What Programming Does To Your Head, Al Cuoco, E. Paul Goldenberg

Journal of Humanistic Mathematics

How you think about a phenomenon certainly influences how you create a program to model it. The main point of this essay is that the influence goes both ways: creating programs influences how you think. The programs we are talking about are not just the ones we write for a computer. Programs can be implemented on a computer or with physical devices or in your mind. The implementation can bring your ideas to life. Often, though, the implementation and the ideas develop in tandem, each acting as a mirror on the other. We describe an example of how programming and …

Using Mathematical Equations To Communicate And Think About Karma, Kien H. Lim, Christopher Yakes

Journal of Humanistic Mathematics

Two equations are presented in this article to communicate a particular understanding of karma. The first equation relates future experiences to past and present actions. Although the equation uses variables and mathematical symbols such as the integral sign and summation symbol, it reads more like a literal translation of an English sentence. Based on the key idea in the first equation, a second equation is then created to highlight the viability of using math to communicate concepts that are not readily quantifiable. Analyzing such equations can stimulate thinking, enhance understanding of spiritual concepts, raise issues, and uncover tensions between our …

Real-World Modelling To Increase Mathematical Creativity, Robert Weinhandl, Zsolt Lavicza

Journal of Humanistic Mathematics

Modelling could be characterised as one of the core activities in mathematics education. However, when learning and teaching mathematics, mathematical modelling is mostly used to apply and deepen mathematical knowledge and competencies. Our educational study aims to explore how mathematical modelling, using real objects and high-quality mathematical technologies, could be utilised to acquire mathematical knowledge and competencies, and how learners could creatively use their existing knowledge. To discover the potential of mathematical modelling using real objects and high-quality mathematical technologies to acquire mathematical knowledge and competencies, and to stimulate learners' creativity, first, we combined cognitive and creative spirals and mathematical …

A Holistic Mathematics Curriculum Revision: An Adelphi University Case Study, Salvatore J. Petrilli

Journal of Humanistic Mathematics

Join me as I take you on a journey with the faculty of the Department of Mathematics and Computer Science at Adelphi University during our two-year re-envisioning and implementation of our mathematics curriculum. From the beginning this involved a data-driven initiative that naturally led to the revisions. Here I describe in detail the process that our department followed. In closing I end with some recommendations for interesting research directions in the field of mathematics education.

Peer Motivation: Getting Through Math Together, Jessica Mean, Wes Maciejewski

Journal of Humanistic Mathematics

Students have a complex relationship with mathematics. Some love it, but more often than not, the feelings are less favorable. These feelings can lead to decreased motivation which makes it difficult for students to engage with the subject as the semester progresses. Instructors also have difficulty addressing this waning motivation. In this paper, we claim peers are better able to connect with the students and this can be leveraged to better motivate students. We present an approach to having peers motivate their students. These peer interactions integrated with a mandatory mathematics course might improve students’ motivation.

Raise The (Proportion) Bar!, Michael Waters

Journal of Humanistic Mathematics

This article, drawing mainly on references to teacher preparation textbooks, proposes proportion bars as a somewhat novel graphical approach to solving simple (direct) proportion problems and to illustrate the advantages of such an approach, which include accessibility with materials at early grade levels, allowance of students to better develop number sense and estimation, facilitation of setting up proportions, allowance for conceptual understanding and motivation of the procedure for solving direct proportions, assistance with part-to-part and part-to whole comparisons, and drawing of connections among mathematical topics. The emphasis is on teaching with understanding, rather than procedural knowledge.

Mathematical Zendo: A Game Of Patterns And Logic, Philip Deorsey, Corey Pooler, Michael Ferrara

Journal of Math Circles

Mathematical Zendo is a logic game that actively engages participants in pattern recognition, problem solving, and critical thinking while providing a fun opportunity to explore all manner of mathematical objects. Based upon the popular game of Zendo, created by Looney Labs, Mathematical Zendo centers on a secret rule, chosen by the leader, that must be guessed by teams of players. In each round of the game, teams provide examples of the mathematical object of interest (e.g. functions, numbers, sets) and receive information about whether their guesses do or do not satisfy the secret rule. In this paper, we introduce Mathematical …

Math Department 2020-2021 Newsletter, Mathematics Department

Mathematics Newsletter

This was an unusual year for our department as the coronavirus pandemic continued. However, we made the best of the situation and did as many activities as we could -- In the Fall, we inaugurated our new math major with three tracks: the traditional track, actuarial science track, and data science track -- Faculty changes -- Graduating seniors -- Pi Mu Epsilon Induction Ceremony and Awards Night -- Alumni Page -- Faculty spotlight -- Noyce grant -- Alumni night -- Coming attractions.

Development Of A Gamified Number Line App For Teaching Estimation And Number Sense In Grades 1 To 7, Debbie Marie Verzosa, Ma. Louise Antonette N. De Las Peñas, Maria Alva Q. Aberin, Agnes Garciano, Jumela F. Sarmiento, Mark Anthony C. Tolentino

Mathematics Faculty Publications

Fraction knowledge is known to be a gatekeeper to more advanced mathematical learning. On the basis of the literature on early number learning, a number line mobile application called Catch the Carrot was designed to develop students’ knowledge of whole number and fraction magnitude. This paper aims to describe the design of the Catch the Carrot app and discusses the rationale for using number lines as representational scaffolds for developing children’s understanding of numbers, particularly their estimation and number sense skills. The gamification features of the app, as well as strategies for integration in a classroom are also presented. This …