Physical Sciences and Mathematics Commons^™

The Automathography: A Humanistic Autobiographical Writing Assignment For Mathematics Courses, Colton Sawyer, Ron Buckmire

Journal of Humanistic Mathematics

In this article, we discuss an autobiographical writing assignment that we call an “automathography” which can be used in different types of mathematics and mathematics education courses, and by extension, in other disciplines as well. This assignment can enhance student-instructor interactions, develop student communication skills, and provide outlets for student creativity by leveraging the lived experiences of students. We have deployed the assignment in different kinds of classes (general education [service] courses and major-only seminars) at different kinds of institutions (a private, open-admission, large university on the East Coast and a private, highly selective, small liberal arts college on the …

Using Bloom's Taxonomy For Math Outreach Within And Outside The Classroom, Manmohan Kaur

Journal of Humanistic Mathematics

Not everyone is a great artist, but we don’t often hear, “I dislike art.” Most people are able to appreciate visual arts, music and sports, without necessarily excelling in it themselves. On the other hand, the phrase “I dislike math” is widely prevalent. This is especially ironic in our current society, where mathematics affects our day-to-day activities in essential ways such as e-commerce and e-mail. This paper describes the opportunity to popularize mathematics by focusing on its fun and creative aspects, and illustrates this opportunity through a brief discussion of interdisciplinary topics that expose the beauty, elegance and value of …

Making Art In Math Class During The Pandemic, Larson Fairbairn, Kameelah Jackson, Ksenija Simic-Muller

Journal of Humanistic Mathematics

For many of us, the pandemic has changed how we teach and how we support students. This manuscript highlights creativity as a way to support for student mathematical and emotional well-being. It describes the positive impact that creative assignments in a mathematics content course for preservice K-8 teachers had on students during the early days of the pandemic. The story is told by the instructor and two former students in the course.

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 …

Mental Logic: Two Poems, Ashley Delvento

Journal of Humanistic Mathematics

My submission is comprised of two poems that aim to intertwine mathematical themes with that of creative struggle, a working title for this pairing being “Mental Logic”. The first poem, ‘-ematics’ is a literary work created in the midst of mathematical problem solving. Being an avid writer and a mathematics enthusiast, the theme of this poem struck me while completing the University of Rochester Mathematics Olympiad. There seems to be a belief that literary creativity and mathematics cannot compliment one another, but throughout solving a probability problem on this Olympiad proved to be the ultimate moment of inspiration. This poem …

Using Departmental Publications To Foster Student Creativity In Mathematics, Zohreh Shahbazi, Parker Glynn-Adey

Journal of Humanistic Mathematics

This paper discusses the design and implementation of mathematical departmental publications. We argue that these publications foster students’ creativity and written communication skills.

Going Beyond Promoting: Preparing Students To Creatively Solve Future Problems, Kristin M. Arney, Kayla K. Blyman, Jennifer D. Cepeda, Scott A. Lynch, Michael J. Prokos, Scott Warnke

Journal of Humanistic Mathematics

While we cannot know what problems the future will bring, we can be almost certain that solving them will require creativity. In this article we describe how our course, a first-year undergraduate mathematics course, supports creative problem solving. Creative problem solving cannot be learned through a single experience, so we provide our students with a blend of experiences. We discuss how the course structure enables creative problem solving through class instruction, during class activities, during out of class assessments, and during in class assessments. We believe this course structure increases student comfort with solving open-ended and ill-defined problems similar to …

Fostering Student Discovery And Conjecture In Multivariable Calculus, Aaron Wangberg

Journal of Humanistic Mathematics

Who owns the mathematical ideas in the undergraduate classroom? A traditional mathematics classroom and curriculum imposes several barriers that prevent students from discovering and engaging with mathematical concepts. Definitions, notations, and theorems require mastery before students can work meaningfully with the underlying mathematical concepts. Raising Calculus to the Surface utilizes a different approach by providing students multiple entry points to engage meaningfully with mathematics ideas and allows students to promote meaningful ideas and conjectures into the classroom discourse to formalize their explorations. In this paper, we describe several characteristics built into the project materials, including a rubric designed to encourage …

Innovative Induction And Mathematical Code Switching, Benjamin Dickman, Erik Nauman

Journal of Humanistic Mathematics

In the first part of this paper, we provide an example of a project designed to foster mathematical creativity among students at an independent, all-girls school in the Northeast United States. The mathematical motivator for the project is a polyomino proof by induction first formulated by Solomon Golomb. We explain how the project has been implemented over the past two years at the school’s Innovation Lab in collaborative work between a mathematics instructor and an educational technologist, provide instructions and background information to facilitate the implementation of this project at other learning sites, and show examples of student work along …

The Surname Impossibility Theorem, Adam Graham-Squire

Journal of Humanistic Mathematics

The Surname Impossibility Theorem offers solace to anyone who has struggled in the quagmire of choosing a surname for a child. I posit that it is impossible to find a method for giving a child a surname that satisfies the important criteria of being traditional, aesthetically pleasing, ancestor-respecting, non-sexist, gender-neutral and non-heterosexist. My mathematical approach defines what those criteria would mean and analyzes different naming systems to conclude that no method could satisfy all criteria. In the same way that Arrow's Impossibility Theorem proved that no voting method can satisfy all criteria for a fair election, I prove the impossibility …

The Emergence Of Creativity: Insights From Carnatic Raaga Improvisation And Mathematical Proof Generation, Srividhya Balaji, Sean Chorney

Journal of Humanistic Mathematics

Creativity is a broad phenomenon that scholars have interpreted in a multitude of ways. We notice that a majority of the views describe creativity as something innate. This paper aims to verge from this perspective and explore creativity in terms of the constant mutual interaction of a person and their environment. Using the theoretical framework, enactivism, and the notion of emergence, we investigate the creative processes involved in musical improvisations of south Indian classical or Carnatic music and mathematical proof generation. Interview excerpts from professional Carnatic musicians and research mathematicians on their respective creative processes during musical improvisation and proof …

Does Your Course Effectively Promote Creativity? Introducing The Mathematical Problem Solving Creativity Rubric, Kayla K. Blyman, Kristin M. Arney, Bryan Adams, Tara A. Hudson

Journal of Humanistic Mathematics

As believers in the power of blending the creative with the quantitative, we design our courses with an eye towards developing creative problem solvers. However, when it comes time to evaluate our course's success in developing creative problem solvers we come away with a plethora of qualitative evidence and yet we are left hungry for the quantitative evidence we desire as mathematicians.

In this article we describe the development of the Mathematical Problem Solving Creativity Rubric and its pilot use in a freshman-level Mathematical Modeling and Introduction to Calculus course at the United States Military Academy. We not only come …

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 …

The Graduate Student Blues, Marion D. Cohen

Journal of Humanistic Mathematics

This is a memoir about my rather unconventional path to a mathematics Ph.D. There were difficulties, due partly to university politics, partly to my youth and immaturity, and partly to the thesis material itself – it was, in the words of some of my fellow students, “not what’s being done now”. I had written the thesis entirely on my own, without help from my Master’s thesis advisor or any other professor at my school. This is not the usual procedure of course. Nobody in my department could understand the thesis or was willing to vouch for it. There followed three …

On Mathematicians' Eccentricity, Robert Haas

Journal of Humanistic Mathematics

Eccentricity, though not inevitable, happens. Lightheartedly classifying examples, the author traces it back to factors, like creativity and absorption, essential to mathematical success, and recommends an attitude of amused tolerance towards others as well as to ourselves.