Mathematics Commons^™

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 …

Using Mobile Technology To Promote Higher-Order Thinking Skills In Elementary Mathematics, Debbie Marie Versoza, Ma. Louise Antonette N. De Las Peñas, Jumela F. Sarmiento, Maria Alva Q. Aberin, Mark Anthony C. Tolentino, Mark L. Loyola

Mathematics Faculty Publications

The problem of rote-based learning in mathematics is well documented. Mobile technology can provide a potential solution; especially when application (app) design is based on sound pedagogical principles and gamification elements. However; an inventory of available mobile apps for mathematics reveals that many of the available apps are guided by a behaviorist perspective that favors repetition over meaningful learning. This paper reports on the design of mobile mathematics apps that harness gamification techniques to promote higher-order thinking skills (HOTS) even in basic elementary school concepts such as number comparison; and addition and subtraction. The integration of these apps in the …

Designing Performance Tasks In Mathematics Using Technological Tools, Ma. Louise Antonette N. De Las Peñas, Debbie Marie Versoza, Maria Alva Q. Aberin, Agnes Garciano, Jumela F. Sarmiento, Mark Anthony C. Tolentino

Mathematics Faculty Publications

In the Philippines, the performance task is one of the major summative assessments in the K to 12 curriculum. This paper discusses how performance tasks may utilize mathematical apps within the context of blended learning. Guidelines on designing performance tasks; as well as the GRASPS framework; are discussed. Performance tasks that cut across various grade levels and strands of mathematics are presented. These involve divisibility (Numbers); integer and polynomial operations (Algebra); triangle centers (Geometry); and statistics (Statistics). The performance tasks described in this paper can provide an initial idea for the design of other summative assessments and contribute to the …

Interdisciplinary Thinking: Financial Literacy Crosses Disciplinary Boundaries, Marla A. Sole

Publications and Research

Financial literacy is ideally suited to be integrated into mathematics courses and taught in an interdisciplinary manner. Students learn best and are motivated when tackling real-world meaningful questions. This article shares how elementary mathematics was applied to better understand the debate about raising the minimum wage and the United States National Debt. To serve as a guide for other teachers who wish to incorporate financial literacy into their mathematics courses and take an interdisciplinary approach, this article suggests readings, data sets, and pedagogical practices. Students were engaged and enthusiastic to work on problems that challenged their thinking about financial issues.

Interdisciplinary Thinking: Financial Literacy Crosses Disciplinary Boundaries, Marla A. Sole

Publications and Research

Financial literacy is ideally suited to be integrated into mathematics courses and taught in an interdisciplinary manner. Students learn best and are motivated when tackling real-world meaningful questions. This article shares how elementary mathematics was applied to better understand the debate about raising the minimum wage and the United States National Debt. To serve as a guide for other teachers who wish to incorporate financial literacy into their mathematics courses and take an interdisciplinary approach, this article suggests readings, data sets, and pedagogical practices. Students were engaged and enthusiastic to work on problems that challenged their thinking about financial issues.

Non-Academic Support Math Faculty Members Provide In Developmental Accelerated And Corequisite Support Courses In California Community Colleges, David Vakil '92

Doctoral Dissertations

To guide practitioners of rapidly evolving developmental math reform in community colleges, this study surveyed California community college math faculty who taught accelerated developmental courses or corequisite support courses. The survey was conducted during the early implementation phase of both course types, during spring and fall 2018 terms. This study measured faculty’s self-reported provision of forms of non-academic support, frequency of implementation, and reasons faculty believed the support would help students succeed. The literature review guided grouping non-academic support into five forms: nurturing, helping students’ motivation, providing a growth mindset theory of intelligence, helping provide social integration, and helping to …

Floor Plan Assignment In Elementary Mathematics Education, Tunde Jakab

Open Educational Resources

In this upper elementary mathematics education assignment, the prospective teachers gain hands-on experience in measuring distances in feet and inches, calculating areas, and converting distance and area measurements. Moreover, they solve a real-life situation by choosing the most economical tiles for their kitchen. This last part (3) of the assignment develops critical thinking and expressing one's thought processes. Part 3 can be used as an in-class discussion, which further promotes reasoning skills.

Proctoring And Apps In College Algebra, Cynthia M. Shelton

Theses and Dissertations--Education Sciences

The pandemic forced more instructors and students to move to online learning. For the first time, many experienced a loosening of the reigns and were forced to allow students to submit non-proctored work. Many may have questioned what students really learned in the year 2020. Many college math course competencies emphasize procedures. Now that apps can do that for students, where does that leave math instructors? Additionally, online instruction has exploded over the last decade and has challenged the teaching of college mathematics. While online instruction opens the door to access, it does beg the question of whether students complete …

Analyzing Applied Calculus Student Understanding Of Definite Integrals In Real-Life Applications, Cody Hood

Graduate Theses, Dissertations, and Problem Reports (ETD)

An individual’s knowledge of definite integrals can range from rote memorization to a strong foundational connection harkening back to its Riemann sum limit definition. In my research, I conducted seven task-based face-to-face interviews with Applied Calculus students. Through the use of real-life examples and guided reinvention, I analyzed ways in which these students, who all initially demonstrated rote memorization, could exhibit a Riemann sum based level of comprehension. This research was conducted in the confines of a student population with definite integral experience, but no formal instruction on limits. My results show that the lack of computational emphasis in class …

Using Mobile Technology To Promote Higher-Order Thinking Skills In Elementary Mathematics, Debbie Marie Versoza, Ma. Louise Antonette N. De Las Peñas, Jumela F. Sarmiento, Maria Alva Q. Aberin, Mark Anthony C. Tolentino, Mark L. Loyola

Mathematics Faculty Publications

The problem of rote-based learning in mathematics is well documented. Mobile technology can provide a potential solution, especially when application (app) design is based on sound pedagogical principles and gamification elements. However, an inventory of available mobile apps for mathematics reveals that many of the available apps are guided by a behaviorist perspective that favors repetition over meaningful learning. This paper reports on the design of mobile mathematics apps that harness gamification techniques to promote higher-order thinking skills (HOTS) even in basic elementary school concepts such as number comparison, and addition and subtraction. The integration of these apps in the …

Teacher Understanding Of Instructional Strategies In Elementary Mathematics, Erica Boatwright Glover

Walden Dissertations and Doctoral Studies

Synergizing Elementary School (pseudonym) consistently experiences low state-required mathematics test scores in grades 3 and 4 below district and state proficiency rates in mathematics. The purpose of this qualitative case study was to investigate what instructional practices used by Grade 3 and Grade 4 teachers are, aligned or not aligned, with research-based planning, standards-based instruction, attention to conditions of learning, and professional responsibilities of teachers to support students’ achievement in mathematics. This study's conceptual framework was grounded in Robert Marzano's model of teaching effectiveness called the focus teacher evaluation model. Data for this case study were gathered from semi-structured interviews …

Factors Impacting Students’ Perceptions Of Mathematics, Amber Souza

Honors Program Theses and Projects

I want to be able to present math in a positive light to all of my future students, regardless of race, gender, and math background. However, for teachers as a whole to be able to take this important step, they must first develop a deeper understanding of why math is a sore spot for many students.

Extending Power Series Methods For The Hodgkin-Huxley Equations, Including Sensitive Dependence, James S. Sochacki

CODEE Journal

A neural cell or neuron is the basic building block of the brain and transmits information to other neurons. This paper demonstrates the complicated dynamics of the neuron through a numerical study of the Hodgkin-Huxley differential equations that model the ionic mechanisms of the neuron: slight changes in parameter values and inputted electrical impulses can lead to very different (unexpected) results. The methods and ideas developed for the ordinary differential equations are extended to partial differential equations for Hodgkin-Huxley networks of neurons in one, two and three dimensions.

Development Of A Mobile Ten Frames App For Philippine K-12 Schools, Debbie Marie Versoza, Ma. Louise Antonette N. De Las Peñas, Jumela F. Sarmiento, Mark Anthony C. Tolentino, Mark L. Loyola

Mathematics Faculty Publications

This paper reports on the Quick Images app, whose design framework is informed by research on ten-structured thinking and gamification principles. Inclusivity was also a major consideration, especially in the context of a developing country. Thus, the app was made freely available and required only moderate system requirements. Pilot studies revealed that the app has the potential to promote children’s ability to see two-digit numbers in relation to tens and ones, which is a major goal of elementary school mathematics. Collaborations with the Philippine Department of Education to ensure the app’s sustained use are also discussed.

Ethnomathematics: Art, Culture, And Social Justice, John R. Jungck

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Impact Of Concept-Based Mathematics Instructional Strategies On Seventh Grade Student Achievement, Katherine Annette Lawley Ellsworth

Doctoral Dissertations and Projects

In a nation with declining enrollment in college math courses, it is important to examine how mathematics is being taught in the K-12 education system and to identify best practices. The purpose of this study was to examine the impact concept-based instructional strategies has on middle school student achievement in mathematics when integrated into the traditional mathematics curriculum. Participants included 424 seventh grade students from two middle schools. Students Measures of Academic Progress (MAP) Fall-to-Winter data 2018 prior to implementation was used a covariate and Fall-to-Winter data 2019 data during the implementation of concept-based instructional strategies integrated into the traditional …

Specifications-Based Grading Reduces Anxiety For Students Of Ordinary Differential Equations, Mel Henriksen, Jakob Kotas, Mami Wentworth

CODEE Journal

Specifications-based grading (SBG) is an assessment scheme in which student grades are based on demonstrated understanding of known specifications which are tied to course learning outcomes. Typically with SBG, students are given multiple opportunities to demonstrate such understanding. In undergraduate-level introductory ordinary differential equations courses at two institutions, SBG has been found to markedly decrease students’ self-reported anxiety related to the course as compared to traditionally graded courses.

Effectiveness Of Virtual Manipulative Teaching Method In Enhancing Year Four Pupils’ Understanding Of Fractions, Kavitha Karbal Singh

Student Works (2020-2029)

Fractions are common numerical representations in mathematics. However, they seem to be a complicated mathematical concept to master, particularly among school pupils. Pupils have a hard time studying fraction due to insufficient understanding of the concept. An effective teaching method is therefore essential for the teaching and learning of this particular component. The purpose of this study is to determine the effectiveness of the virtual manipulative teaching method in improving the understanding of fraction among Primary Year Four pupils. Essentially a quasi-experimental research, the method used was a non-equivalent, control group pretest-posttest approach. A total of 80 pupils from a …

Faktor Yang Mempengaruhi Kebolehan Perwakilan Ikonik Dan Simbolik Murid Tahun Empat Dalam Nombor Pecahan Di Sekolah Jenis Kebangsaan Cina, Wee Pu Lim

Student Works (2020-2029)

Perwakilan matematik telah mula diberi perhatian lalu menjadi salah satu proses utama yang perlu dikuasai oleh murid. Hal ini kerana perwakilan merupakan satu elemen baharu dalam Kurikulum Standard Sekolah Rendah (KSSR). Kajian ini bertujuan untuk menentukan sama ada faktor jantina murid dan tahap pencapaian matematik murid mempengaruhi kebolehan murid tahun empat dalam perwakilan ikonik dan simbolik tentang nombor pecahan serta interaksi antara kedua-dua faktor tersebut. Untuk menjawab tiga soalan kajian ini, reka bentuk kajian perbandingan punca dan kajian faktorial telah digunakan. 596 orang murid tahun 4 (293 lelaki, 303 perempuan) daripada 5 buah sekolah dengan menggunakan pensampelan kluster dua tahap …

Social Justice Mathematical Modeling For Teacher Preparation, Patrick L. Seegmiller

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Today's math teachers face significant social and political challenges for which they receive little preparation. Mathematics content courses can potentially provide additional preparation in this regard by providing future teachers with experiences to mathematically explore social justice issues. This provides them with opportunities to increase their awareness and sensitivity to social justice issues, develop greater empathy for their future students, and serve as examples for high quality instruction that they can emulate in their future careers. This dissertation recounts the development and revision of three social justice mathematical modeling projects, and shares evidence from student work samples of the ways …

The International Conference On Creative Mathematical Sciences Communication: Online Event (Cmsc'20) And Cmsc'21, Frances Rosamond

Journal of Humanistic Mathematics

You are warmly invited to register now for the 5th International Conference on Creative Mathematical Sciences Communication (CMSC’21) which will be held at Adam Mickiewicz University in Poznań, Poland, 2–6 July, 2021.

The International Conference on Creative Mathematical Sciences Communication (CMSC) is a unique gathering of computer scientists and mathematicians, teachers, musicians, dancers, dramatists, game designers, educators and communicators of all sorts.

Due to the pandemic, the in-person event scheduled for 2020 has been post- poned and a short CMSC Online Event was organized as a “teaser” or trailer in order to feel the spirit of the full 5th CMSC …

The Human Face Of Mathematics: Reuben Hersh (1927-2020) In Memoriam, Elena Anne Corie Marchisotto

Journal of Humanistic Mathematics

Reuben Hersh (1927-2020) celebrated mathematics as a human endeavor, historically evolved and intelligible only in a social context. It is therefore appropriate to remember him in the Journal of Humanistic Mathematics. There have been many tributes to Reuben, which commemorate his life and impressive mathematical and philosophical achievements. This memoriam to Reuben instead focuses on showing how his humanistic philosophy was so indicative of the person he was.

Creative Assignments In Upper Level Undergraduate Courses Inspired By Mentoring Undergraduate Research Projects, Malgorzata A. Marciniak

Journal of Humanistic Mathematics

This article describes methods and approaches for incorporating creative projects in undergraduate mathematics courses for students of engineering and computer science in an urban community college. The topics and the grading rubrics of the projects go way beyond standard homework questions and contain elements of finding own project, incorporating historical background, inventing own questions and exercises, or demonstrating experiments to illustrate some aspects of the project. After analyzing challenges and outcomes of these projects, I identified several skills which help students be successful, including the skills of creativity. These skills are writing, oral presentation, math skills, and collaboration skills. I …

What Would The Nautilus Say? Unleashing Creativity In Mathematics!, Megan E. Selbach-Allen, Cathy A. Williams, Jo Boaler

Journal of Humanistic Mathematics

While the nautilus shell is often represented in popular culture as an example of a golden spiral, according to many mathematicians it is not. In this paper we examine multiple arguments for and against considering the nautilus as a “golden” spiral and offer a semi-structured task that is accessible to middle school students and beyond to begin their own investigation. Our hope is that asking, what would the nautilus say, can serve as a starting point for children and adults alike to push against the walls we so often draw around mathematical questions and begin to see where their creativity …

A Study Of Problem Posing As A Means To Help Mathematics Teachers Foster Creativity, Deborah Moore-Russo, Amanda A. Simmons, Michael J.D. Tulino

Journal of Humanistic Mathematics

Research suggests that mathematical creativity often results from extended periods of mathematical activity and reflection based on the use of deep and flexible content knowledge [14, 15]. This implies that instruction can influence creativity. However, for teaching to foster creativity in mathematics, there should be purposefully designed instructional tasks. It is doubtful that routine, mechanical exercises would foster creativity. Moreover, mathematical creativity may neither be explicitly promoted, nor fully appreciated, by students when a learning space involves only problem solving, even if the problems are challenging and engaging. For students to get an authentic sense of mathematics and to develop …

Guided Reinvention As A Context For Investigating Students' Thinking About Mathematical Language And For Supporting Students In Gaining Fluency, Kristen Vroom

Dissertations and Theses

Fluency with mathematical language is important for students' engagement in many disciplinary practices such as defining, conjecturing, and proving; yet, there is growing evidence that mathematical language is challenging for undergraduate students. This dissertation study draws on two design experiments with pairs of students who were supported to encode their mathematical meanings with more formal language. I aimed to investigate the teaching and learning of mathematical language, and particularly the language in statements with multiple quantifiers, by engaging students in this type of activity. In the first paper, I investigated the complex ways in which the students in my study …

Cross-Cultural Comparisons: The Art Of Computing The Greatest Common Divisor, Mary K. Flagg

Number Theory

No abstract provided.

Combining Transformation Of Graphs With Solutions To Absolute Value Inequalities, Ryan D. Fox

Colorado Mathematics Teacher

I present how transformations can be applied to support students’ solving linear inequalities involving absolute value. In particular, the horizontal dilations/compressions and translations of graphical representations of distances from zero along a number line are important tools to emphasize a visual representation of the solutions to absolute value inequalities.