Science and Mathematics Education Commons^™

Table Of Contents

Early College Folio

(2023) "Table of Contents," Early College Folio: Vol. 3: Iss. 1, Article 1. Available at: https://digitalcommons.bard.edu/earlycollegefolio/vol3/iss1/1

Polygon Quadrature And Dodecagonal Tessellation With Pattern Blocks, Gunhan Caglayan, Ben Kamau

Journal of Humanistic Mathematics

The age-old challenge of polygon quadrature involves converting a polygon into a square of equal area. In this educational resource, we utilize pattern blocks, commonly employed instructional aids in K-12 education across the United States, to visually demonstrate the transformation of different equilateral and regular pattern block polygons into squares. This is achieved through the application of the area conservation principle and geometric congruence/similarity reasoning.

Seating Groups And 'What A Coincidence!': Mathematics In The Making And How It Gets Presented, Peter J. Rowlett

Journal of Humanistic Mathematics

Mathematics is often presented as a neatly polished finished product, yet its development is messy and often full of mis-steps that could have been avoided with hindsight. An experience with a puzzle illustrates this conflict. The puzzle asks for the probability that a group of four and a group of two are seated adjacently within a hundred seats, and is solved using combinatorics techniques.

Sharing Four Biscuits Between Three People: An Illustrative Example Of How Mathematics Is Intertwined With Human Values, Lovisa Sumpter, David Sumpter

Journal of Humanistic Mathematics

Despite convincing arguments by mathematicians, philosophers, sociologists and machine learning practitioners to the contrary, there remains a widespread notion amongst many members of the general public (and some practitioners) that mathematics is neutral, that it is free from human values. One reason why this notion persists is that we lack clear-cut examples that demonstrate how mathematics and values are intertwined. In this paper, we offer one such example. In particular, we show that when sharing four biscuits between three people, several possible mathematical and ethical frameworks can be used. We demonstrate that different solutions—hiding one biscuit, arbitrarily sharing the extra …

Gödel's Theorem In The Continuing Education Of Mathematics Teachers, Ana J. Lemes

Journal of Humanistic Mathematics

The notion of dépaysement épistémologique (epistemological disorientation) aims to capture the sense of disorientation when a learner is led to question their prior assumptions and understandings, generating uncertainty in a context in which they thought they had certain knowledge. This article describes an activity used with a group of practicing mathematics teachers in Uruguay that integrates elements of the history of mathematics related to Gödel’s incompleteness theorem, with the aim of provoking in the participants the experience of dépaysement épistémologique. Results show that several of the teachers participating in the activity felt dépaysement épistémologique, and this feeling triggered …

Finding Your Mathematical Roots: Inclusion And Identity Development In Mathematics, Linda Mcguire

Journal of Humanistic Mathematics

This paper details a semester-long course project that has been successfully adapted for use in mathematics courses ranging from introductory level, general-education classes to advanced courses in the mathematics major. Through creating aspirational mathematical family trees and writing mathematical autobiographies, this assignment is designed to help battle belonging uncertainty, to challenge students to self-situate in relation to the history of mathematical and scientific knowledge, and to make visible a student’s developing identity in mathematics and, more broadly, in STEM.

The construction and scaffolding of the project, assignments, examples of student work, foundational readings, assessment and outcomes, and adaptation strategies for …

Faith And Stem Education: A Path To Mutual Elevation In Catholic Schools, Michael Szopiak, Matthew Kloser

Journal of Catholic Education

Amidst increasing religious disaffiliation, often due to a perceived tension between faith and the STEM disciplines, Catholic schools provide critical opportunities for young people to recognize how these domains can be mutually elevating. The field, however, lacks guidance as to how this integration should occur in practice. This conceptual paper first provides an overarching framework for how aspects of the Catholic tradition, like Scripture and the Catholic social tradition, can shape traditional educational domains of STEM teaching and learning. Secondly, we provide a heuristic of three criteria for deeply engaging students at the interface of the Catholic faith and the …

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

Creating Mandalas For World Peace While Incorporating Mathematics, Art, Literature, Writing, And Technology, Joseph M. Furner

Transformations

Across the USA there are more and more students whose parents are from around the world. It is important teachers can effectively teach mathematics to reach all students, particularly those with limited English proficiency, while establishing interdisciplinary and cultural connections and even working toward world peace. The purpose of this paper is to share how a class of students from an elementary school in South Florida with their teacher created mandalas to teach mathematics, art, writing, and even world peace to their students. Math teachers should strive to bridge the cultural gap among all students by incorporating innovative ideas as …

Synesthesia: 3.1415... Orange.Whiteperiwinklewhiteblue..., Shelly Sheats Harkness, Bethany A. Noblitt, Nicole Giesbers

Journal of Humanistic Mathematics

In this paper we address the questions: What is synesthesia? What support(s) can teachers provide for their students who have synesthesia? Nicole, a future mathematics teacher who possesses this synesthesia “superpower”, describes how it impacted her learning. We collected data for this case study through an audio-recorded and transcribed interview, as well as from subsequent email correspondence between the three authors. We asked Nicole three kinds of questions: questions she is frequently asked, questions she would like to be asked, and questions teachers (like Shelly and Beth) might ask. Results indicate that synesthesia may have helped Nicole learn English as …

Review: Teaching Stem To First Generation College Students: A Guidebook For Faculty And Future Faculty By Gail Horowitz, Jessica S. Robbins

Early College Folio

Book Review: Gail Horowitz’s Teaching STEM to First Generation College Students: A Guidebook for Faculty and Future Faculty (Information Age Publishing, 2019). Horowitz taught chemistry at Bard High School Early College Newark.

Artist Into An Educator—Educator Inside An Artist, Raheela Qabool Abro Ms

Early College Folio

This study is a self-investigation of the author's identity by exploring her two professions: an artist as well as an art educator. Her insights as an educator provided a background for her as an artist through the production of this series of miniature artworks created with cell phone SIM cards. A SIM card, which stands for “Subscriber Identification Module,” contains information tied to the identity of the individual using it. For this reason, the author chose it as a medium for creating an art series to represent identity. In the dialogue of artist and educator, Abro confronts changes to the …

Teaching Food Studies In Early College: Experiments In Collaboration, Cynthia Brown, Maryann Tebben

Early College Folio

This article outlines the process of designing and teaching a collaborative course on sustainable food and agriculture on multiple campuses at once, including two early college institutions. The authors offer insights on the specific elements of the course they designed as well as methods for designing the course, what worked in practice, and what they would change. This article will be useful for faculty who would like to work with other early college colleagues to plan a collaborative course in general or a specific course on sustainable food and farms.

Commitment To Access: A Conversation About The Unconventional And College-In-Prison, Elías Beltrán, Megan Callaghan

Early College Folio

The Bard Prison Initiative (BPI) currently operates full-tuition scholarship Bard College degree programs across seven New York State prisons, three Microcollege campuses created in partnership with community-based institutions, and on the Annandale campus of Bard College, where adult students are completing degrees through the BardBac. Since 2005 when the first degrees were granted to BPI students, the program has issued over 5,000 credits and more than 700 degrees.

This conversation between BPI alumnus Elías Beltrán, who earned his Bard College bachelor’s degree in 2017 while incarcerated, and Megan Callaghan, the program’s Dean, touches upon Elías’s upcoming transition to BPI faculty, …

Rolling A Boulder Up A Mountain: The Path To Higher Education In Displacement Concepts, Rebecca Granato

Early College Folio

Students in contexts affected by displacement and forced migration are at a disadvantage when it comes to accessing and successfully completing higher education, as well as translating their learning into post-graduation opportunities. Universities with clear social missions and networks of institutions have the power and the obligation to support the creation of “opportunities pipelines” for these populations.

Solving Higher Education In Burma, The Global South, And Beyond, Myat Su San

Early College Folio

By introducing readers to a migrant student from Burma, the author unpacks the longstanding and increasingly complicated barriers to higher education, which many students face across the Global South. Readers are then introduced to one institution seeking to dismantle those barriers through innovation and expansive access, Parami University.

Move, May Honey Maung

Early College Folio

“Move” is a call to action that urges leaders to work together to create a world where education is accessible and inclusive to everyone regardless of their socioeconomic status or background. Drawing inspiration from the author’s own educational experiences as both a student and employee of Phaung Daw Oo, this poem is a reminder that education is not a privilege but a fundamental human right; we all have a responsibility to ensure that it is available to all learners. The author—whose country is currently facing violence and economic and educational instability due to a February 2021 coup d’état—relays the hopeful …

Case Study: Phaung Daw Oo International University, Yee Wai Than Ma

Early College Folio

The case study discusses an unconventional path to education in Myanmar, one that serves as an alternative to government-controlled institutions. The article highlights the challenges faced by students and educators in the country and presents Phaung Daw Oo Monastic School (PDO) and its mission to contribute to society through excellence in education and lifelong learning. The school provides necessary schooling for children who did not receive adequate education at the traditional age, students who are up to five years off from what is considered aligned with the expectations of state-sponsored education. The article also discusses the establishment of Phaung Daw …

Editor's Note, Kyaw Moe Tun

Early College Folio

Editor's Note, Early College Folio, Volume 2, Issue 2 (Spring 2023).

Contributors

Early College Folio

Contributors, Early College Folio, Volume 2, Issue 2 (Spring 2023).

Table Of Contents

Early College Folio

Table of Contents, Early College Folio, Volume 2, Issue 2 (Spring 2023).

Du Undergraduate Showcase: Research, Scholarship, And Creative Works, Caitlyn Aldersea, Justin Bravo, Sam Allen, Anna Block, Connor Block, Emma Buechler, Maria De Los Angeles Bustillos, Arianna Carlson, William Christensen, Olivia Kachulis, Noah Craver, Kate Dillon, Muskan Fatima, Angel Fernandes, Emma Finch, Colleen Cassidy, Amy Fishman, Andrea Francis, Stacia Fritz, Simran Gill, Emma Gries, Rylie Hansen, Shannon Powers, Jacqueline Martinez, Zachary Harker, Ashley Hasty, Mykaela Tanino-Springsteen, Kathleen Hopps, Adelaide Kerenick, Colin Kleckner, Ci Koehring, Elijah Kruger, Braden Krumholz, Maddie Leake, Lyneé Alves, Seraphina Loukas, Yatzari Lozano Vazquez, Haley Maki, Emily Martinez, Sierra Mckinney, Mykaela Tanino-Springsteen, Audrey Mitchell, Kipling Newman, Audrey Ng, Megan Lucyshyn, Andrew Nguyen, Stevie Ostman, Casandra Pearson, Alexandra Penney, Julia Gielczynski, Tyler Ball, Anna Rini, Christina Rorres, Simon Ruland, Helayna Schafer, Emma Sellers, Sarah Schuller, Claire Shaver, Kevin Summers, Isabella Shaw, Madison Sinar, Claudia Pena, Apshara Siwakoti, Carter Sorensen, Madi Sousa, Anna Sparling, Alexandra Revier, Brandon Thierry, Dylan Tyree, Maggie Williams, Lauren Wols

DU Undergraduate Research Journal Archive

DU Undergraduate Showcase: Research, Scholarship, and Creative Works

Lessons From Human Experience: Teaching A Humanities Course Made Me A Better Math Teacher, Erin Griesenauer

Journal of Humanistic Mathematics

As a professor at a Liberal Arts college, I recently taught a General Education course called Human Experience. Far from my normal experiences in the mathematics classroom, in Human Experience I was tasked with teaching topics from the humanities, including art, philosophy, history, and political science. Teaching this course was challenging, but it was also transformative. Teaching a course so far from my background gave me the opportunity to experiment with different pedagogical techniques and to reflect on how I set up my math classes. I learned many lessons that I have brought back to my math classes—lessons that have …

Becoming A Stem-Focused Catholic School: Insights Into Adopting A Curricular Specialization, Julie W. Dallavis

Journal of Catholic Education

School choice policies seek to increase access to educational opportunities and stimulate innovations in schooling. This study examines the early stages of one such innovation—school-wide curricular specialization—in three Catholic elementary schools adopting a STEM focus and uses interviews to consider how and why different levels of support exist for the shift and under what conditions private and religious schools are prepared to make significant changes in instructional practice. Findings suggest that school resources—material, human, and social along with professional development—play an important role in shaping engagement in the adoption of a school-wide curricular focus.

Streaming With Butterflies: A Whole School Stream Project, Carey L. Averill, Janet M. Herrelko

Journal of Catholic Education

This study explores the commitment of a school faculty to use the pedagogical practices needed to employ a project-based unit of Science, Technology, Religion, Engineering, Arts, and Mathematics (STREAM). The unit of study concentrated on environmental sustainability of butterflies through project-based learning (PBL). Teacher interviews were analyzed to reveal the similarities and differences, strengths and weaknesses in the teachers’ reactions to implementing a cross-curricula content unit designed for a pre-kindergarten (PK) to eighth grade school. Analysis of teacher data and classroom artifacts provided evidence of: content mastery at the student levels; implementation of scaffolding for developmental levels; and the need …

The House Of Seminar Needs Overhaul: The General Education Seminar In Theory And Practice, Matthew J. Park

Early College Folio

Matthew Park's intellectual and institutional history of the General Education Seminars at Bard College at Simon’s Rock. This historical analysis, which the author revolves around a discussion of the genealogy and philosophy of Seminar more broadly, serves as a multidisciplinary lens through which teachers and students of Seminar across the Bard Early Colleges may center current and future discussions of the course(s).

Mathematics Education As Dystopia: A Future Beyond, Peter Appelbaum, Charoula Stathopoulou, Constantinos Xenofontos

Journal of Humanistic Mathematics

We argue that scholars and practitioners of mathematics education need to find new directions through recognition of its dystopic characteristics, and embrace these characteristics as both the source of challenges and method of response. This contrasts with the generally utopic approach of most scholarship in the field. We offer critical ethnomathematics education as a model, since it has its own origins in lingering dystopic legacies. A perpetual hopelessness and disempowerment is one implicit curriculum of contemporary mathematics education, where the mathematics one learns might help to describe things, yet hardly assists in transforming the reification of power and agency in …

Higher Meanings: A Speaker Series Connecting Mathematics And Religion, Lawrence M. Lesser, Patricia S. Barrientos, Ben Zeidman

Journal of Humanistic Mathematics

An innovative grant-funded general adult audiences international speaker series on connections between mathematics and religion yielded six 2021 (now archived) presentations. We share reflections and lessons learned, informed by two sets of surveys.

Benny, Barbara, And The Ethics Of Edtech, Geillan Aly

Journal of Humanistic Mathematics

Erlwanger (1973) shook the mathematics education world when he introduced Benny, a student who successfully worked through a behavioristic curriculum. Erlwanger showed how far removed Benny’s understanding of mathematics was from expectations. Erlwanger’s legacy is the basis for this comparative case study which explores students’ actions in the modern, in-class computer-centered emporium classroom. Many striking similarities are found between Pearson’s MyMathLabs (MML) and Benny’s Individually Prescribed Instruction curriculum. In this case study we meet Barbara, a student who succeeds in MML but shows little understanding of mathematical concepts and demonstrates that the legacy of Benny is his continued appearance in …

Contributors

Early College Folio

Contributors, Early College Folio, Volume 1, Issue 2 (May 2022)