Science and Mathematics Education Commons^™

Harmonic Scale Transformations, John H. Chalmers

The Transdisciplinary STEAM+ Journal

My artwork derives from a project to delineate the transformations certain types of harmonic musical scales undergo as the sizes of their generating intervals vary over the space of the octave.

From Stem To Steam: Students’ Beliefs About The Use Of Their Creativity, Ayse Tugba Oner, Sandra Bonorden Nite, Robert M. Capraro, Mary Margaret Capraro

The Transdisciplinary STEAM+ Journal

To be successful in a STEM career, not only STEM knowledge and skills but also creativity is required. Therefore, the arts have been integrated into STEM disciplines and subsequently designated as STEAM education (Sousa & Pilecki, 2013). One example of informal learning environments that STEAM education provided is a summer camp. In this study, middle and highs school students’ use of their creativity in the Project-based Learning (PBL) courses was examined to determine students’ belief about the use of the arts in STEM activities. The results showed that students believed that they used their creativity in eight of the nine …

Maker Education: The Steam Playground, Amanda Opperman

The Transdisciplinary STEAM+ Journal

Educators who are committed to teaching STEAM in their classes and programs will be inspired and encouraged by the capabilities for multidisciplinary instruction and project based learning offered by an emerging pedagogy known as Maker Education. While making was previously thought of as STEM-focused, it can easily be integrated across all subjects. Maker Ed's Resource Library has a section on Projects and Learning Approaches, which includes many cross-curricular project ideas that expand this model of education from STEM to STEAM and beyond.

Race, Space, And The Conflict Inside Us, Francis Su

All HMC Faculty Publications and Research

Talking about race is hard. Our nation is wrestling with some open wounds about race. These sores have been around a while, but they have been brought to light recently by technology, politics, and an increasingly diverse population. And regardless of the outcome of the U.S. presidential election, we will all need to work at healing these sores, not just in our personal lives, but in our classrooms and in our profession.

Freedom Through Inquiry, Francis Su

All HMC Faculty Publications and Research

I delivered this speech at the Inquiry‐Based Learning Forum & 19th Annual Legacy of R.L. Moore Conference on August 4, 2016. It is partly an homage to an influential teacher, partly an excuse to articulate what makes some styles of teaching so effective, and partly an excuse to talk about difficult issues facing our nation and our classrooms today.

Calculus Problems, Joshua N. Cooper

Journal of Humanistic Mathematics

No abstract provided.

A Truly Beautiful Theorem: Demonstrating The Magnificence Of The Fundamental Theorem Of Calculus, Dan Mcquillan, Darlene M. Olsen

Journal of Humanistic Mathematics

In standard treatments of calculus, the Fundamental Theorem of Calculus is often presented as a computational method to evaluate definite integrals, with such powerful utility that one is tempted to overlook its beauty. To improve students' appreciation for the first part of the Fundamental Theorem of Calculus, we suggest a few classroom examples focusing on the accumulation function, to be introduced early and often throughout an introductory calculus course. These examples are small enough that they would not necessarily result in changes to a typical course schedule; yet we believe their contribution to student understanding can be significant. Furthermore, such …

Stop Ruining Math! Reasons And Remedies For The Maladies Of Mathematics Education, Rachel M. Steinig

Journal of Humanistic Mathematics

Did you love math as a kid? Or was it ruined for you? Sadly, many people have had math ruined for them for various reasons. Some might say that it was because of not understanding what was going on, being bored in class, parental or societal pressure to achieve in math, not seeing a point in learning math, wrong amount of homework, grades, curriculum, physical concerns, mean teachers, or any number of things. This article delves into the many common reasons why math is ruined for so many kids, and offers solutions so that math can be enjoyable for everyone. …

What Has An Impact On Grades? Instructor-Made Videos, Communication, And Timing In An Online Statistics Course, Regina Aragon, Indika P. Wickramasinghe

Journal of Humanistic Mathematics

This study investigates student success in an online introductory statistics class. We examine the impact of several variables: amount of time that a student watches instructor-made videos (IMV), the nature of communication between the student and the instructor, and the amount of time spent on completing the online assignments and exams on student grades in an introductory level online statistics course. Findings suggest that IMVs of short dur ation, the subject- related communication between the student and the instructor, and homework completion time have significant association with student performance. Though the average time spent on online exams does not show …

Bringing Students Back To Mathematics: Classroom Knowledge And Motivation, Giang-Nguyen T. Nguyen, Joel B. Goodin

Journal of Humanistic Mathematics

This paper reports part of a larger research study that investigated how teachers motivate students to learn mathematics at the college level. Findings from the study indicated that teachers have the power to influence and reinvigorate students who had given up learning mathematics. In the framework of Self-Determination Theory (SDT), the researchers analyzed five students’ motivational levels based on intrinsic and extrinsic motivation to see how each student was motivated by their teacher. Findings from the study could provide some directions for future research on students’ motivation to learn mathematics.

Using Ibl In A History Of Mathematics Course: A Skeptic’S Success, Michael E. Matthews, Angela M. Hodge

Journal of Humanistic Mathematics

A college professor, who is highly skeptical of change, but sensing a need for teaching in a more inspiring and engaging way, implements an inquiry-based learning (IBL) approach to teaching the history of mathematics. The first author (Matthews) worked with an experienced IBL colleague mentor (Hodge) on the course. Some student data was collected to document the effects of the class on the students. The approach taken for the course is described in detail including how the students of the course learned about and used IBL in key peer-to-peer teaching about historical mathematics (with a primary focus on the mathemat- …

Humanizing Mathematics Through Ethnomodelling, Milton Rosa, Daniel Clark Orey

Journal of Humanistic Mathematics

Ethnomathematical techniques and modelling tools allow us to examine systems taken from the real world and offer us insight into forms of mathematics performed in holistic contexts [3]. A pedagogical approach that connects a diversity of cultural forms of mathematics can be implemented by the use of ethnomodelling, a process of translation and elaboration of problems and questions taken from non-academic systems. Here, we offer examples of studies conducted in Brazil and in the United States that explore this pedagogical approach. Our goal is to broaden the discussion of possibilities for ethnomathematics and associated ethnomodelling perspectives that respect the …

Math Education: A Messy Problem, Gizem Karaali

Pomona Faculty Publications and Research

The current state of math education in America is certainly not ideal, writes Gizem Karaali, but mathematicians, researchers, policy makers and others are working on it -- and it is definitely a problem worth working on.

Jay Leno And Abstract Algebra, Adam Glesser, Martin Bonsangue

Journal of Humanistic Mathematics

The Jay Leno skit Jaywalking, showing ordinary people struggling to answer basic questions, is both entertaining and applicable to teaching. This article describes how an instructor can strengthen students' conceptual understanding by creating an element of confusion, or "cognitive dissonance," in the students' minds using Jaywalking-style interactions in the classroom.

Dramathizing Functions: Building Connections Between Mathematics And Arts, Gunhan Caglayan

Journal of Humanistic Mathematics

This article focuses on connections between mathematics and performance arts (drama). More specifically we offer an exposition of a segment of college algebra mathematics (an introduction to functions), with an approach primarily emphasizing the aesthetic aspects of mathematical learning, teaching, and performing.

What If?: Mathematics, Creative Writing, And Play, Emily Clader

Journal of Humanistic Mathematics

Mathematics can inform creative writing by suggesting structures for it to follow, as well as by providing the imaginative impetus for common rules to be broken. In a workshop co-taught by the author, a class of sixth-grade students explored this interplay as they produced fractal-inspired poetry and geometry-inspired fiction. This article describes the form and results of the workshop in the context of a broader discussion of the influence of mathematics upon literature.

The Importance Of Surprise In Mathematical Beauty, V. Rani Satyam

Journal of Humanistic Mathematics

Mathematicians, mathematics education researchers, and philosophers have written about mathematical beauty and many of the qualities commonly associated with it, such as simplicity, brevity, enlightenment, etc. One key theme that underlies many of these qualities is surprise or the unexpected. In this article, I discuss the integral role surprise plays in mathematical beauty. Through examples, I argue that simplicity alone is oftentimes not enough for a piece of mathematics to be considered beautiful, but rather it is unexpected simplicity that we seek. I propose, moreover, that surprise is necessary for enlightenment. The paper also reports results from an activity designed …

The Role Of Sequence In The Experience Of Mathematical Beauty, Leslie Dietiker

Journal of Humanistic Mathematics

In this article, I analyze the aesthetic dimensions of a sequence of mathematical events found in an unusual first grade lesson in order to demonstrate how sequencing may affect an individual’s experience of mathematical beauty. By approaching aesthetic as a sense or felt quality of an experience in context (Sinclair, 2001, 2011), this analysis explains how sequence can affect the way mathematical objects or actions are experienced by an individual. Thus, rather than questioning whether or in what ways a set of mathematical objects are beautiful or not, this paper addresses under what conditions is the mathematics in play beautiful. …

Surprise And The Aesthetic Experience Of University Students: A Design Experiment, Ofer Marmur, Boris Koichu

Journal of Humanistic Mathematics

Little is known about instructional means by which the aesthetic experience of mathematics can be enhanced for undergraduate learners. This paper presents and discusses an iterative lesson design process towards creating an opportunity for students to appreciate the beauty of an unexpected solution to a challenging calculus problem. The lesson design draws on insights from both mathematics education research on aesthetics and research on aesthetic appreciation in music. The data were collected over the course of five lessons with different groups of calculus students in which the intended problem was presented in two different ways. In addition, stimulated-recall interviews were …

From Chilly Climate To Warm Reception: Experiences And Good Practices For Supporting Lgbtq Students In Stem, Carolyn S. Brinkworth

CGU Theses & Dissertations

Lesbian, gay, bisexual, transgender, and queer/questioning students (LGBTQ) face unique challenges during their university or college careers, and while society has generally become more accepting of sexual and gender minorities (SGM) over the past decade, students still often face chilly or outright hostile campus climates, as well as institutional and departmental policies and practices that create barriers to their learning and feeling of belonging in their classrooms and on their campuses. Research suggests that these issues are particularly pervasive in the disciplines of Science, Technology, Engineering and Mathematics (STEM), and there is some evidence to suggest that LGBTQ individuals are …

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.

Encouraging Teachers To W.A.I.T Before Engaging Students In Next Generation Science Standards Steam Activities., Mason Kuhn

The Transdisciplinary STEAM+ Journal

Effective art integration in K-12 curricula has clear benefits for classroom teachers (i.e. student achievement on standardized tests, student engagement, improving critical thinking). This paper proposes a framework based off of Claudia Cornett's levels of art integration. Teaching With About and In Through (WAIT) the arts can serve as a model for teachers who want to transform their science lesson to include art integration.

Ecoscience + Art Initiative: Designing A New Paradigm For College Education, Scholarship, And Service, Changwoo Ahn

The Transdisciplinary STEAM+ Journal

The paper presents a new initiative, EcoScience + Art, which blooms at George Mason University. The creator explains the background, history, and recent activities of the initiative, and also introduces an on-going special project called “The Rain Project”, a student participatory project to design, construct, and monitor a green infrastructure (i.e., floating wetland) for sustainable stormwater management on campus. The special project is geared to design and present a new paradigm to integrate college education, scholarship, and service. The relevance of the initiative and the special project to STEAM education is discussed.

Putting The Team In Steam: The Art Of Robot Making, Teresa Walker, David Thompson

The Transdisciplinary STEAM+ Journal

What began as a life partnership has evolved into an early learning STEAM team. Artist, David Thompson, uses science, technology, engineering and math, on a daily basis, to create robots and much more. Teresa Day Walker is an assistant professor of early childhood education. Through necessity they discovered their combined talents could be used to promote STEAM in early childhood. David and Teri teamed up to provide a nearly impromptu robot making demonstration for 100 kindergarten students. After reading their co-authored book, Robot Hide and Seek, both, clay based and 3-D modeled images were used to generate interest and …

From Stem To Steam: Reframing What It Means To Learn, Nicole M. Radziwill, Morgan C. Benton, Cassidy Moellers

The Transdisciplinary STEAM+ Journal

Although involvement in art and design have been shown to play an essential role in catalyzing STEM research, true integration is still an area of active research. The realization of STEM education via STEAM lends itself to interactive and participatory dialogic art; this juncture provides a nonjudgmental space to cultivate the question-making aspect of inquiry, the ability to comfortably hold uncertainty, and a sensitivity to the process of discovery. Even though STEM education can (and often is) inquiry-based, assessments still tend to focus on whether knowledge or skills have been obtained, and this is no different than the current general …

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 …

Reflections On Math Students’ Circles: Two Personal Stories From Colorado, Diana White, Lori Ziegelmeier

Journal of Humanistic Mathematics

Math Students’ Circles provide an opportunity for mathematicians to work in their communities to engage young students in mathematics as a human, aesthetic, and social endeavor. Sometimes referred to simply as Math Circles, these venues give mathematicians experience in introducing children to topics not typically seen in school curricula in an exciting, hands-on format. This article explores two Math Students’ Circles (MSCs) in the state of Colorado from the point of view of two pre-tenure faculty members. One participated in MSCs for four years while working on her Ph.D. in mathematics, the other started an MSC as an offshoot of …

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 …

Attitudes And Experiences In Liberal Arts Mathematics, Jennifer Clinkenbeard

Journal of Humanistic Mathematics

For many university students, the last formal experience in a mathematics classroom is a single semester “general education” mathematics class. Traditionally, students in this type of class often hold negative attitudes towards mathematics. Here I study a sample of students from this population (49 students at a large, urban, comprehensive public university enrolled in a “math for liberal arts majors” course) to research whether a positive experience in a freshman-level general education mathematics course correlates with a positive change in the students’ attitude towards mathematics in general. I also explore which specific aspects of such a course contribute most to …