Science and Mathematics Education Commons^™

E-Brock Bugs©: An Epistemic Mathematics Computer Game, Laura Broley, Chantal Buteau, Eric Muller

Journal of Humanistic Mathematics

Devlin in [7] argues that video games are an ideal medium for the teaching and learning of mathematics, though he points out that very few ’good’ mathematics video games exist. Building on a probabilistic board game developed in the 1980s, we created a mathematics computer game, E-Brock Bugs. The design of the game carefully follows Devlin’s principles of a good mathematics video game, including a well-developed storyline, the selection of an in-game avatar, and an environment where mathematics arises in a natural and meaningful way. As a result, we argue that E-Brock Bugs is an epistemic computer game [1]; …

To The Mathematical Beach, Francis Su

All HMC Faculty Publications and Research

What context am I missing that hinders my connection with my students? How often do I take the time to get to know their backgrounds? What are the primary experiences that shaped them, and do those present obstacles or opportunities for learning? And in what ways does the mathematical beach say “open to all” but still feel restricted?

These questions appear unrelated to mathematics, but if we ignore their effects, some of our students will not flourish.

On Mathematics And Culture: Insights From An International School, M. Sencer Corlu, Burcu Alapala

Journal of Humanistic Mathematics

We explore the factors that influence the relationship between mathematics and culture in the international school context. First, we share some thoughts about international schools in general and the international mathematics curriculum implemented at the middle grades level at our school in particular. Second, we present some interesting snapshots from our culturally-diverse mathematics classrooms.

How Can Mathematics Students Learn To Play?, Christopher K. Storm, Holly Zullo

Journal of Humanistic Mathematics

When we teach mathematics, we strive to teach students to think like mathematicians. In this paper we discuss one particular mathematical habit of mind that students do not naturally display. More specifically our study of voting patterns in data collected from classroom voting questions indicates that the undergraduate students who were in the classes using these questions did not understand the significance of counterexamples to statements, or lacked the ability to construct them, or both. Searching for counterexamples to disprove statements is a natural habit of mind for professional mathematicians. In this paper we give examples, and make some recommendations. …

Recreational Mathematics – Only For Fun?, Lovisa Sumpter

Journal of Humanistic Mathematics

In this paper, I explore recreational mathematics from two perspectives. I first study how the concept appears in educational policy documents such as standards, syllabi, and curricula from a selection of countries to see if and in what way recreational mathematics can play a part in school mathematics. I find that recreational mathematics can be a central part, as in the case of India, but also completely invisible, as in the standards from USA. In the second part of the report, I take an educational historical approach. I observe that throughout history, recreational mathematics has been an important tool for …

Improving Project Success In An Online Mathematics Course, David Shoenthal

Journal of Humanistic Mathematics

With more mathematics courses migrating to online environments, it is important to know whether these courses are comparable to their face-to-face counterparts. To that end, in two different years, I taught an online and a face-to-face section of the same finite mathematics course. After analyzing the data regarding differences in the two sections for the first year, I incorporated changes intended to improve the consistency of project success between the two sections as well as the overall success of the class projects in the online section. My main tool was mimicking the interaction of group members and providing immediate instructor …

On The Persistence And Attrition Of Women In Mathematics, Katrina Piatek-Jimenez

Journal of Humanistic Mathematics

The purpose of this study was to investigate what motivates women to choose mathematics as an undergraduate major and to further explore what shapes their future career goals, paying particular attention to their undergraduate experiences and their perceptions of the role of gender in these decisions. A series of semi-structured, individual interviews were conducted with twelve undergraduate women mathematics majors who were attending either a large public university or a small liberal arts college. This study found that strong mathematical identities and enjoyment of mathematics heavily influenced their decisions to major in mathematics. At the career selection stage, these women …

The Discipline Of History And The “Modern Consensus In The Historiography Of Mathematics”, Michael N. Fried

Journal of Humanistic Mathematics

Teachers and students of mathematics often view history of mathematics as just mathematics as they know it, but in another form. This view is based on a misunderstanding of the nature of history of mathematics and the kind of knowledge it attempts to acquire. Unfortunately, it can also lead to a deep sense of disappointment with the history of mathematics itself, and, ultimately, a misunderstanding of the historical nature of mathematics. This kind of misunderstanding and the disappointment following from it--both raised to the level of resentment--run through the paper "A Critique of the Modern Consensus in the Historiography of …

Two Bit Circus, Elise Lemle

The Transdisciplinary STEAM+ Journal

Two Bit Circus collaborated with the Girl Scouts of the Greater Los Angeles Area to explore the exciting world of wearable electronics. Over the course of the program, the students explored concepts of introductory electronics while designing and creating their own illuminated fashion piece. The program was held in Montrose, CA in Fall 2013. The students were approximately 10 girls ages seven to 14. The program was held over seven sessions with each session lasting 80 minutes.

Full Steam Ahead: Creativity In Excellent Stem Teaching Practices, Danah Henriksen

The Transdisciplinary STEAM+ Journal

This article emphasizes the value of creativity and arts-based learning in the sciences (STEAM education), using one example from a recent research study of creative and effective classroom teachers. The future of innovative thinking in STEM disciplines relies on breaking down the distinction between disciplines traditionally seen as “creative” like the arts or music, and STEM disciplines traditionally seen as more rigid or logical-mathematical (Catterall, 2002). The most exceptional thinkers in fields like science or math are also highly creative individuals who are deeply influenced by an interest in, and knowledge of, music, the arts and similar areas (Caper, 1996; …

What Is So Negative About Negative Exponents?, Geoffrey D. Dietz

Journal of Humanistic Mathematics

While teaching college-level mathematics (from College Algebra to Calculus to Abstract Algebra), I have observed that students are often uncomfortable using negative exponents in calculations. I believe the fault partially lies in the manner in which negative exponents are taught in Algebra 1 or Algebra 2 courses, especially in rigid instructions always to write answers using only positive exponents. After reviewing a sample of algebra texts used in the United States over the last two centuries, it appears that while attitudes toward negative exponents have varied from author to author over time, the current trend is to declare explicitly that …

Benjamin Banneker's Original Handwritten Document: Observations And Study Of The Cicada, Janet E. Barber, Asamoah Nkwanta

Journal of Humanistic Mathematics

Benjamin Banneker, farmer, mathematician, astronomer, and scientist, is known for his mathematical puzzles, ephemeris calculations, almanacs, his wooden clock, land surveying work, and famous letter on human rights. However, as a naturalist, his scientific and systematic observations of the cicadas are less known. In this paper we publicize Banneker’s naturalistic study of the seventeen-year periodic cycle of the cicada and make available the original handwritten document of his observations. We also introduce the audience of this journal to an intriguing natural problem involving prime numbers.

An Investigation Of Teachers’ Noticing, Cognitive Demand, And Mathematical Knowledge For Teaching: Video Reflections In An Elementary Mathematics Context, Lorelei R. Coddington

CGU Theses & Dissertations

In the past decade, mathematics performance by all students, especially minority students in low socioeconomic schools, has shown limited improvement nationwide (NCES, 2011). Traditionally in the United States, mathematics has consisted of arithmetic and computational fluency; however, mathematics researchers widely believe that this method of instruction does not enhance the development of mathematical reasoning and ignores the research on students’ mathematical development (Blanton & Kaput, 2005; Stigler & Hiebert, 1999). Recommendations by the mathematics community are to broaden and strengthen teacher content knowledge in mathematics and to provide the pedagogical tools needed by teachers to extend their students’ thinking and …

Extended Book Review: Mathematics In Popular Culture: Essays On Appearances In Film, Fiction, Games, Television And Other Media, Edited By Jessica K. Sklar And Elizabeth S. Sklar; Loving+Hating Mathematics: Challenging The Myths Of Mathematical Life, By Reuben Hersh And Vera John-Steiner; Mathematicians: An Outer View Of The Inner World, By Mariana Cook, Gizem Karaali

Pomona Faculty Publications and Research

I was delighted to have the opportunity to review three books on a topic near and dear to my heart. In recent years it has become a passion of mine to think of and speak about the place of mathematics in the real world, in the world of those who are not doing mathematics for a living. I care about the applications and the implications of mathematics, but more than that, I care about the feelings and the impressions attached to it. Often math anxiety or skepticism comes up; the latter may be due to how frequently others (mis)use statistics, …

My Mathematics, Karen Morgan Ivy

Journal of Humanistic Mathematics

This poem reflects a personal kaleidoscopic perspective into a world of actively engaging others in teaching and learning mathematics.

Selling Mathematics: Service & Quality, Jon Jacobsen

Journal of Humanistic Mathematics

Is there a difference between teaching mathematics and selling mathematics? The author presents his personal experience on the topic and reflects on how this perspective can be used to improve public perception of and engagement with mathematics.

Math Stories: Learning And Doing Mathematics Through Fiction Writing, Frederick Chen, Janna Raley

Journal of Humanistic Mathematics

In this paper, we advocate the writing of mathematical fiction (i) as an aid for students in learning mathematics, and (ii) to engage students in doing mathematics.

Cultural Immersion And Mathematics Teacher Education: Explorations In Morocco And South Africa, Kori L.H. Maxwell, Iman C. Chahine

Journal of Humanistic Mathematics

This article examines the first author's personal experiences as a mathematics educator studying ethnomathematics and indigenous knowledge systems (IKS) through immersion in indigenous cultures. In describing these encounters, we highlight the importance and impact of cultural immersion experiences on educators' perspectives regarding the nature of mathematical knowledge. We argue that cultural immersion not only builds a well-rounded individual, but also provides educators with the necessary tools to maintain relevance in the diverse and constantly evolving landscape that is the classroom. Insights gained from this study have direct implications in our teaching practices as they remind us to be mindful of …

Mathematical Knowledge For Teaching And Visualizing Differential Geometry, Nathan Pinsky

HMC Senior Theses

In recent decades, education researchers have recognized the need for teachers to have a nuanced content knowledge in addition to pedagogical knowledge, but very little research was conducted into what this knowledge would entail. Beginning in 2008, math education researchers began to develop a theoretical framework for the mathematical knowledge needed for teaching, but their work focused primarily on elementary schools. I will present an analysis of the mathematical knowledge needed for teaching about the regular curves and surfaces, two important concepts in differential geometry which generalize to the advanced notion of a manifold, both in a college classroom and …

Landscapes To Learnscapes: Exploring Schoolyard-Based Education, Emily I. Palena, Caroline T. Spurgin

Pitzer Senior Theses

This thesis explores schoolyard-based education as a viable and necessary method for rectifying the shortcomings within the American public school system and the Nature-deficit Disorder epidemic. We argue that schoolyard-based education should be fully integrated into the school system, not in the sole form of popularized school gardens, but as a standard teaching method. We show this using extensive research and a case study of three elementary schools in Claremont, California.

School Gardens: Reconnecting Children With Nature And Food, Alyssa M. Boyle

Scripps Senior Theses

This thesis discusses the importance of school gardens. First, two current environmental and societal problems are highlighted: the industrialized food system and what Richard Louv has termed, "Nature Deficit Disorder," in children. School gardens are then presented as an effective tool that can address and remedy such issues. Lastly, a how-to manual for implementing such projects in schools is provided as well as a few sample lesson plans to be used in conjunction with the garden in each subject across the curriculum.

Full Steam Ahead – A Collaborative Colloquium, Hilary Dito

The Transdisciplinary STEAM+ Journal

On February 2, 2012, Contra Costa County Office of Education organized its 2^nd Annual STEAM Colloquium: Full STEAM Ahead. This forum brought together over 150 educators, business leaders and community members to discuss and share best practices in Science, Technology, Engineering, Arts and Mathematics (STEAM) education

Steam With A Capital A: Learning Frenzy, David Rufo

The Transdisciplinary STEAM+ Journal

A student dipped a brush into a bowl of viscous tempera paint and in a few quick strokes formed thick magenta letters on a large display board. Nearby a handful of students were working together to attach string to paper cups and balloons. Across the room a small group of girls were lying on the floor carefully adding multi-colored text to a poster. Two others created characters out of Popsicle sticks for a puppet show...This is how the integration of Science, Technology, Engineering, Arts, & Math (S.T.E.A.M.) happened with the fourth and fifth graders during the first few weeks of …

Keeping Abreast With Liberal Arts And Science Through Steam, Tanya Rivas, Gregory Knotts

The Transdisciplinary STEAM+ Journal

The integrated unit on breast cancer described here includes biological science and visual art standards and was targeted at high school juniors and seniors. The goal was to make a potentially controversial and taboo subject relatable through an art-science approach

Reflections ~ How Stem Becomes Steam, Ruth Catchen

The Transdisciplinary STEAM+ Journal

Reflections from designing a STEAM class for high-risk students.

Merging Science And Art: The Bigger Picture, Natasha Hall

The Transdisciplinary STEAM+ Journal

It has been stated that artists comprehend and chronicle the completeness of the visible world (Wallach & Bret, 1987), defining Art as the creative expression of knowledge about the visual world. But to what extent does that awareness extend into a scientific appreciation of the world? The acronym STEAM is an abbreviation of Science, Technology, Electronics, Arts and Mathematics. Weaving interactions between Science and Art, have been shown by Clarke and Button (Clarke & Button, 2011), to intensify interconnections between nature, with Landscape, and ultimately with sustainability.

Getting Real About The E In Steam, James Catterall

The Transdisciplinary STEAM+ Journal

STEM and STEAM are in the news. Researchers and educators in my field (cognition, art, and creativity) argue reasons for adding the A to STEM. While I visit this below, my focus is elsewhere. In this brief essay, I want to explore the meaning and importance of the E appearing in both STEM and STEAM. What’s engineering doing in this mix? And what are some reasons for affirming the arts when the role of engineering is clarified?

At The Gate Of Discovery, Jan Nordgreen

Journal of Humanistic Mathematics

This is the story of how a mathematical problem was discovered. Although it was never solved, it gave great joy to the discoverer.

Developing A Healthy Scepticism About Technology In Mathematics Teaching, Peter J. Rowlett

Journal of Humanistic Mathematics

A reflective account is presented of experiences which took place alongside a research project and caused a change in approach to be more sceptical about implementation of learning technology. A critical evaluation is given of a previous e-assessment research project, undertaken from a position of naive enthusiasm for learning technology. Experiences of teaching classes and designing assessment tasks lead to doubts regarding the extent to which the previous project encouraged deep learning and contributed to graduate skills development. Investigations of the benefits of another technology – in-class response systems – lead to revelations about learning technology: its enthusiastic introduction in …

Incorporating Pólya’S Problem Solving Method In Remedial Math, Shenglan Yuan

Journal of Humanistic Mathematics

György Pólya’s problem solving method has influenced generations of mathematicians and non-mathematicians alike. Though almost all math teachers have come across Pólya’s problem solving method, his ideas are not regularly implemented in the classroom. Few studies have examined the effectiveness of his approach in teaching remedial math. In this article we revisit this once well-known teaching method and show how it can be used in basic skills math classes to ease student fears of math, and potentially change their common misconceptions of the subject.