Science and Mathematics Education Commons^™

The Czechoslovak Way Of Competing For Better Mathematics In 1950s, Petra Antošová

Journal of Humanistic Mathematics

In the period after World War II, many significant changes took place in Czechoslovakia. This paper focuses on the changes that were taking place in the field of mathematical education. Education, in general, acquired a new structure as a response to the school reform of 1948 and subsequent reforms. Great emphasis began to be placed on polytechnic education, of which mathematics was a key part. Teachers sought out ways to find mathematical talents and to excite students about mathematics in various ways.This paper focuses on mathematical circles (whether tutoring or inspirational) and other motivational methods such as mathematics competitions that …

Numbers, Patterns, And Memories: Early Experiences Of Mathematicians And Mathematics Education Researchers, Constantinos Xenofontos

Journal of Humanistic Mathematics

This paper offers a reflective analysis of early mathematical experiences shared by fifty-six mathematicians and mathematics education researchers, including my own, as part of Cambridge Mathematics’ “Seven Questions with . . . ” interview series. Drawing on thematic analysis, I identify five key patterns across participants’ recollections: the context of early mathematical engagement, the influence of significant others, emotional responses, shifts in mathematical thinking, and mathematics as a social or competitive experience. Many accounts emphasise informal, everyday encounters with mathematics—often preceding formal education—as central to developing interest and confidence in the subject. The findings challenge the notion of innate mathematical …

Impact Of Covid-19 Pandemic On Mathematics Achievement And Problem-Solving Ability: Insights From Secondary Schools In India, Laishram Nirtish Singh, Anand Jyoti Sanasam, Jocyline Thokchom, Ningombam Cha Cogent, Laisom Sharmeswar Singh

Journal of Humanistic Mathematics

The COVID-19 pandemic disrupted students’ engagement with mathematics. This study aims to contribute to our understanding of the extent of this disrupting by examining differences in mathematics achievement and problem-solving ability between adjacent cohorts who learned Class 8 under different schooling conditions in India: Group A (pandemic-exposed Class 8 cohort) and Group B (post-reopening Class 8 cohort). Using a descriptive design in a natural setting, we selected a stratified sample of 1,200 students from Class 9 and Class 10 across 21 secondary schools in Manipur, India. The sample was stratified by gender, family type, school type, and locality to ensure …

The Math Teaching Atlas: Trails, Anchors, And Compass In Action, Ivan Z. Feng

Journal of Humanistic Mathematics

This paper advocates a shift grounded in mathematical reasoning: teach and write math through explicit routeways rather than narratives, anchor new ideas to familiar concepts on a roadmap, and use motivation and concrete examples as a compass and simulation for discovery.

Creating Art With The Generalized Pythagorean Theorem, Ángel Colín

Journal of Humanistic Mathematics

The Pythagorean Theorem and its generalizations have been widely studied. In this article we focus on one particular generalization that asserts that the area of a polygon with one side the hypotenuse of a right triangle is the sum of the areas of similar polygons whose corresponding sides are the other two sides [4]. Using this theorem together with interactive software or simply pencil and paper, we create some visually enticing artwork. This activity, we believe, can contribute positively to geometry teaching at all academic levels.

Let's Play Uno! Training Mathematical Thinking With An Inclusive Card Game, Thierry Meyrath, Clara-Ioana Mincu, Antonella Perucca

Journal of Humanistic Mathematics

We explore probability exercises based on the game UNO. Excluding the Wild cards, the deck contains precisely 100 cards, which makes it convenient to express probabilities as percentages. We discuss the mathematical relation between cards that can be played after other cards. We also propose an algebraic exercise that relates several quantities, such as the number of cards left in the losing player’s hand. Finally, we argue that UNO is a very inclusive game: it is logistically easy to play, allows for players of different skill levels, and can be adapted to meet special needs. Beyond being playful exercises, our …

Invitations To Stem: Activities For Building Community And Enthusiasm From A First-Year Seminar, Dusty Grundmeier, Shanelle Davis

Journal of Humanistic Mathematics

We reflect on and analyze a first-year seminar designed as an invitation to Science, Technology, Engineering, and Mathematics (STEM) fields. We present sample activities designed to develop mathematical and scientific problem-solving skills while also building community and enthusiasm. Through solving mathematical puzzles, project-based learning, and reflective activities, students develop a supportive and welcoming STEM-focused community and identity. Along with sample activities, we share our goals, challenges, and student feedback. Finally, we suggest some guiding principles for designing and choosing problems for similar STEM enrichment activities and seminars.

How Did Cauchy Prove His Integral Theorem? A Historical Reconstruction For Education Research, José Gerardo Piña-Aguirre, Rosa María Farfán Márquez

Journal of Humanistic Mathematics

In his article “Mémoire sur les Intégrales Définies, prises entre des limites imaginaires” of 1825, Cauchy proves that the integral of a complex function f defined on complex numbers is independent of the path of integration if the function f remains finite and continuous along the chosen path. In contemporary literature that analyzes the mathematics of Cauchy, the specific mathematical process that allowed Cauchy to prove this result is not explicitly presented. The purpose of this manuscript is to communicate a symbolic-algebraic derivation that justifies the narrative argument used by Cauchy to support his proof, thus hopefully filling this gap. …

Emergent Collective Argumentation Types In A Socio-Critical Mathematical Modeling Activity, Ayse Ozturk, Ozgul Kartal

Journal of Humanistic Mathematics

Socio-critical mathematical modeling encourages students to employ mathematics as a tool for social inquiry and action, promoting critical thinking and social awareness. While research on collective argumentation in mathematical modeling exists, its connection to socio-critical modeling remains underexplored. This study addresses this gap by examining the types of collective argumentation that emerge during small-group and whole-group discussions as students navigate different phases of the modeling process. Using an adapted version of Toulmin’s argumentation model and a framework for socio-critical modeling phases, this study analyzes classroom discussions in which high school students engage in a modeling task focused on fair raise …

Let’S Teach More Accurate And Inclusive History! The Case Of Islamic Contributions To Mathematics And Science, Nuh Aydin

Journal of Humanistic Mathematics

Schools commonly teach a history of mathematics and science that is Eurocentric. This selective version of the history of science, called Classical Narrative by some, is rooted in colonial times and mindset, and has reinforced certain negative opinions about other cultures. It ignores or downplays contributions to mathematics and sciences from non-western civilizations, and falsely attributes many scientific discoveries to European scholars. Medieval Islamic Civilization, which had strong connections to Renaissance Europe, serves as a clear example of how this narrative is distorted. Based on research on primary sources since the middle of the 20th century, we now know that …

From Shudu [Sudoku 數獨] To Dushu [Learning Of Mathematics 讀數]?, Man Keung Siu

Journal of Humanistic Mathematics

The puzzle game Sudoku has been popular for over two decades, and even at one time became a craze for the public. This paper will briefly describe what the game is, a little bit of its history, and how to play it, but will leave the details to the many published books about the game. Some interesting and difficult mathematical problems relevant to the game will be highlighted, again leaving the detailed discussion to specific books published on this issue. The main point the paper tries to focus on is a discussion on the cognitive and the psychological aspects of …

Math Anxiety And Shame Exemplified On The Reality Show Survivor, James Drimalla, Dru Horne

Journal of Humanistic Mathematics

In an episode of season 45 of the reality show Survivor, three contestants competed in a challenge involving mathematics. In their reflections and responses to the challenge, the contestants discussed feelings of anxiety, fear, and shame. In this article, we describe (a) the challenge, (b) the three contestants’ attempts to complete the challenge and their responses to the challenge, (c) responses to the challenge in the media, and (d) relevant details of our personal experiences and related backgrounds. We then discuss themes of math anxiety, shame, and virtues, and encourage leaders in mathematical spaces to place a higher value on …

Introducing The Linear Poem, Cristian Ramirez Rodriguez

Journal of Humanistic Mathematics

In this article I introduce the linear poem, a poetic form I developed in fall 2023 as a pedagogical tool for high-school students. The linear poem is a poem which represents an integer valued linear function, treating the line numbers as inputs and the linguistic units in a line as outputs. Two examples of linear poems are given as well as the steps taken to produce them. By interpreting poetic forms as integer-valued functions as is done in this article, interdisciplinary pedagogy can be achieved, allowing educators and students to express mathematical ideas such as slope-intercept form in a creative …

Exploring Commutativity In A Hindi Language Classroom, Kumar Gandharv Mishra

Journal of Humanistic Mathematics

Commutativity is an important concept in mathematics. However, not much emphasis is given to it in the elementary or secondary school curriculum, as there is a lack of interesting noncommutative examples at this level. Since most examples of binary operations provided deal with numbers, commutativity appears trivial. In this article we offer an interesting example of noncommutativity that is familiar to Indian school children from a different context. Students in India study a chapter based on the joining of vowels in Hindi grammar. This process is analogous to producing commutative as well as noncommutative operations. When we bring in mathematical …

Near-Peer Student-Run Virtual Stem Summer Camp: Lessons Learned, Andrew Lee, Jeremy Reynolds, Margaret Reynolds, Freda Li, Lubjana Beshaj

Journal of Humanistic Mathematics

The United States Military Academy is uniquely positioned to contribute to our nation’s Science, Technology, Engineering, and Math (STEM) outreach initiatives. As one of the country’s most highly regarded undergraduate engineering schools, the institution receives a steady influx of Cadet near-peer mentors who volunteer to lead STEM modules. When the COVID-19 pandemic shut down in-person STEM workshops for the better part of 2020-2021, the Center for Leadership and Diversity in STEM adeptly transitioned to a virtual platform. Informed by research on STEM education and delivery, the Center successfully executed its signature summer camp event in a virtual format for two …

Engaging Mathematicians One Step At A Time: Math Trails, Mary L. Dalton, Jennifer Yantz

Journal of Humanistic Mathematics

Mathematics is present in everything we see and do. Sometimes we look past it, looking for some mathematical mystery when the beauty of mathematics is evident in the most obvious ways. One way to engage students to notice connections to mathematics in these everyday objects and events is to direct them in a guided math trail. A math trail is an activity where participants follow a map or guide to various locations while they are encouraged to take notice of connections to mathematical patterns and concepts in the objects around them. An important benefit is that going on a math …

An Unlikely Duo: Injecting Art Projects In The Lower-Division Mathematics Classroom, Douglas T. Pfeffer, Christina Durón

Journal of Humanistic Mathematics

Too often society has sterilized mathematics to the point that many view it as drab and deplete of aesthetic intrigue---in higher education, this is particularly true of students in the lower-division classroom. In this paper, we propose the use of art projects as a novel way to alter this perspective. Art projects function as a hands-on, active way to invite students to both identify connections between math and various non-mathematical disciplines as well as view math as overall more intriguing, inviting, and interesting. This paper details our implementation and discusses anonymously solicited survey data that highlights our successes.

7th International Conference On Creative Mathematical Sciences Communication (Cmsc`24), Frances A. Rosamond

Journal of Humanistic Mathematics

The 7th International Creative Mathematical Sciences Communication (CMSC) conference is scheduled for October 2024 in Trier, Germany. Initiated in Darwin, Australia in 2013, CMSC aims to explore novel methods of imparting computational thinking to diverse audiences including non-specialists, modern citizens, and children. Participants from around the world and from various and interdisciplinary disciplines such as science, education, dance, drama, and visual arts convene to exchange ideas, present experimental approaches, and collaborate on engaging children in the exploration of ongoing, unresolved research challenges.

The Value Of Adding Nothing: A Call For Reform-Oriented Polynomial Division, Jonathan Clark, Jeneva Clark

Journal of Humanistic Mathematics

The call to implement reform practices in schools reflects the historical turn away from the behaviorist theory of learning in education. Yet the praxis of this turn remains a significant challenge, particularly within mathematics classrooms where procedural memorization is emphasized. In this article, we show one means of how to advance our pursuit of meaningful mathematics into polynomial division. Building on the literature for reform-based division methods, an alternative to the long division algorithm will be explored that relies solely on adding zero and fundamental algebraic principles.

Sociomathematical Norms And Automated Proof Checking In Mathematical Education: Reflections And Experiences, Merlin Carl

Journal of Humanistic Mathematics

According to a widely held view, mathematical proofs are essentially (indications of) formal derivations, and thus in principle mechanically checkable (this view is defended, for example, by Azzouni [3]). This should in particular hold for the kind of simple proof exercises typically given to students of mathematics learning to write proofs. If that is so, then automated proof checking should be an attractive option for math education at the undergraduate level. An opposing view would be that mathematical proofs are social objects and that what constitutes a mathematical proof can thus not be separated from the social context in which …

Mathematical Anxiety In The Turkish Context: Mathematical Experiences Of High School Students, Vahap Yorgun, Serdal Mert

Journal of Humanistic Mathematics

Although a handful of studies have investigated the prevalence of math anx- iety among Turkish school children and its relationship with several variables like attitudes toward math, gender, self-efficacy, parental style, there is as of now no study focusing on development psychological interventions to cope with math anxiety. Most of the extant studies use quantitative approaches, but in order to develop intervention programs, researchers need to know how math anxiety develops, what kinds of personal variables or factors take place in this process, and what kind of emotional and cognitive reactions hold by students about math. Thus in our research, …

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.

Undergraduate Mathematics Students Question And Critique Society Through Mathematical Modeling, Will Tidwell, Amy Bennett

Journal of Humanistic Mathematics

Mathematics can be used as a tool to question and critique society and, in doing so, give us more information about the world around us and how it operates. This however, is not a common perspective that is conveyed to students during their undergraduate mathematics coursework. This paper contributes to the understanding of how undergraduate mathematics students question and critique society via mathematical modeling tasks. In two courses at two universities, 27 mathematics majors and secondary preservice teachers engaged in the modeling process situated in authentic contexts to learn specific concepts and make mathematical connections across domains and disciplines. Both …

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 …

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 …

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 …

More Than Free Textbooks: Labor And Pedagogy In Implementing Open Resources In A Trigonometry Course, Caleb Holloway

Journal of Humanistic Mathematics

This paper reports the implementation of open educational resources (OER) in a university trigonometry class, with an emphasis on the pedagogical considerations and academic labor involved. To date these two matters have been underreported in the literature on OER. I provide an account of the work involved both in choosing an open textbook and in creating hundreds of accompanying homework exercises for an online learning platform. I also present the pedagogical lens that informed this implementation, discuss how it informed my adoption of an open textbook, and provide specific examples of how it guided the creation of these exercises. Based …

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 …

“I Got You”: Centering Identities And Humanness In Collaborations Between Mathematics Educators And Mathematicians, Anne M. Marshall, Sarah Sword, Mollie Applegate, Steven Greenstein, Terrance Pendleton, Kamuela E. Yong, Michael Young, Jennifer A. Wolfe, Theodore Chao, Pamela E. Harris

Journal of Humanistic Mathematics

Existing literature widely reports on the value of collaborations between mathematicians and mathematics educators, and also how complex those collaborations can be. In this paper, we report on four collaborations that sought to address what mathematics is and who gets to do it. Drawing on the literature and from the careful and intentional work of the collaborators, we offer a framework to capture the richness of those collaborations – one that acknowledges the importance of acknowledging and welcoming the extensive personal and professional experience of each person involved in the collaboration – and a look at how collaborations built with …