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On Gödel’S Incompleteness Theorem, David Pierce

Journal of Humanistic Mathematics

Gödel’s Incompleteness Theorem is about the logic of mathematics. It is that a certain mathematical structure is so rich that its theory cannot be completely axiomatized. This means there will always be true statements about the structure that cannot be proved as theorems from previously given axioms. To give meaning to this conclusion, we review some examples of mathematical theorems, and their proofs, in geometry, algebra, and logic; we also give an example of a structure that is so simple (while still being interesting) that its theory can indeed be completely axiomatized. First we look at a couple of popular …

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 …

Revisiting A 19th Century Vector Algebra Book, Olcay Coskun, Alp Eden, Ersin Karabudak

Journal of Humanistic Mathematics

Hidden gems of mathematics can be recovered when one digs into what might seem an obscure text. In 1882, military officer Vidinli Hüseyin Tevfik Pasha published a book on vector algebra titled Linear Algebra. In this article we revisit the second edition of this book, emphasizing the special multiplication that we call the ’v-product’. This product has both geometric and algebraic characteristics. We attempt to clarify its relationship with complex and quaternion multiplication both geometrically and algebraically. The resulting algebra is called the Vidinli algebra. This algebra admits a Lie algebra structure that gives rise to Heisenberg algebra. We introduce …

Should College Students Be Inventors? A Case Study Of A Mathematics Professor In India, Praveen Chhikara, Rochelle Gutiérrez

Journal of Humanistic Mathematics

This qualitative case study attempts to understand instructional roles and goals that a mathematics professor in India sets and envisions for engaging students around abstract mathematical concepts. We generated the data with the professor while he participated in professional development program sessions we provided on the active role of students in learning mathematics. Guided by two theoretical lenses of Realistic Mathematics Education and Rehumanizing Mathematics, our data analysis identified three main themes through the teaching practices that he employs or conceives: (1) Supporting students to avoid faulty foundations by developing proofs, (2) Offering opportunities for exploration by giving appropriate guidance, …

Memes As An Effective Approach To Increase Public Engagement With Mathematical Concepts, Juan M. Romero, Carlos Trenado

Journal of Humanistic Mathematics

A meme is a graphical concept or cultural item that is disseminated via the Internet, often through social media platforms. Memes serve as a mechanism for replicating cultural traits by incorporating aspects of cultural mutation and evolution. The potential of memes in learning and education has been emphasized in several recent studies. The present article examines the impact of memes in increasing public engagement with mathematics and mathematical concepts. By focusing on memes that exhibit specific attributes—such as emotional facial expressions of recognizable human characters and dialogues emphasizing the usefulness or beauty of a mathematical concept—we observe a significant increase …

Evaluating Methods Used To Quantify Racial Segregation, Sarah Cannon, Zarina Dhillon

Journal of Humanistic Mathematics

Racial segregation has long been a problem in communities across the United States. One approach to help understand such an important issue is to attempt to describe it quantitatively. Many metrics have been developed, all with various strengths and weaknesses, but none fully capture the nuances of this complicated issue. This work provides an overview of four of the mathematical approaches that have been developed to study segregation, explains how they function using small examples, and compares and contrasts their effectiveness in various situations. We then focus on segregation in Los Angeles (LA) County, including a detailed exploration of the …

Graphical Timetables As A Real-Life Example Of Different Representations Of Functions, Olav G. Imenes

Journal of Humanistic Mathematics

This paper examines 203 pre-service teachers' reactions and learning when they were introduced to a real-life situation in which it is natural to publish officially both graphs and tables of a given function: the situation of operating a railway. I found that almost all the pre-service teachers managed the easiest tasks, like calculating speeds, distances, and time for train represented by graphs. However, the more complicated tasks, which required interpretations of the graphs and tables, such as planning for a delayed train, finding which trains were locals, freight trains etc., were more difficult for them to grasp. There were few …

A Practical Rule Of Divisibility By 7 In Uqlīdisī’S Kitāb Al-Fuṣūl Fī Al-Ḥisāb Al-Hindī, Müjdat Takıcak, Mertkan Şimşek

Journal of Humanistic Mathematics

There are many known examples of divisibility rules in modern mathematics. However, some of these rules are far from being practical, such as the current divisibility rule by 7. A far more useful method can be found in the work of the tenth-century Islamic mathematician Abū al-Ḥasan al-Uqlīdisī (d. 980), who proposed a divisibility rule for 7 in his treatise Kitāb al-Fuṣūl fī al-Ḥisāb al-Hindī. Compared to modern techniques, Uqlīdisī’s rule is both simpler and more practical. This article (re)introduces this rule, and provides an exposition of the mathematical reasoning that underpins it.

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

What Can Mathematics Do For Us?, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

Strahlungen, Ernest Jünger

Hannah Arendt Marginalia - All

Tübingen, Heliopolis-Verlag [1949]

Call #: PT2619 .U43 S8

Arendt copy contains marginalia

PDF Information: 134 pages – 9.1MB

The Complete Jefferson, Thomas Jefferson

Hannah Arendt Marginalia - All

New York, Distributed by Duell, Sloan & Pearce, Inc. [1943]

Call #: E302 .J4564

Contains marginalia, underlining, marginal lining and endpaper notes

PDF Information: 43 pages – 3 MB

The Life And Selected Writings Of Thomas Jefferson, Thomas Jefferson

Hannah Arendt Marginalia - All

New York: The Modern library, 1944

Contains light underlining and marginalia.

Call #: E332 .J47

PDF Information: 35 pages – 13.7mb

An Editorial Moment Of Silence In Honor Of H. Len Vacher, Nathan D. Grawe

Numeracy

H. Len Vacher, co-founding editor of Numeracy and giant in our field, passed away April 21, 2025. A brief testament to his contributions to numeracy can be found in an editorial in the previous issue of this journal. Here, we take a moment of editorial silence in Len's honor.

Considering What Counts: The Limits Of Proxy Measures, Keith R. Johnson, Joel Best

Numeracy

People working with data adopt proxy measures when they find it difficult to measure something directly. In the U.S., infanticide (fairly easy to count) is used as a proxy for physical child abuse. However, infanticide is harder to count cross-nationally, leading researchers to use sex ratios as a proxy for infanticides

Bayes In The Brain: A Review Of Everything Is Predictable: How Bayesian Statistics Explain Our World, (2024) By Tom Chivers., Michael T. Catalano

Numeracy

Tom Chivers’ Everything is Predictable: How Bayesian Statistics Explain Our World, is an interesting and wide-ranging narrative on Bayesian thinking, its history, and its applicability to both our everyday lives and the pursuit of scientific truth. Although appropriate for the non-expert, afficionados and teachers of quantitative literacy should find the plethora of examples, links to psychology as it applies to how people reason about probabilities, and even Chivers’ philosophical musings informative and thought-provoking.

Zeitschrift FüR Sozialforschung, Instituts Fur Sozialforschung, Max Horkheimer

Hannah Arendt Marginalia - All

Paris : Librairie Felix Alcan, 1935

Call #: HM1.Z4 H6 1939

Contains underlining & marginal lining

PDF information: 5 pages – 453 KB

Das Naturbild Der Heutigen Physik, Werner Heisenberg

Hannah Arendt Marginalia - All

Hamburg : Rowohlt, 1956, c1955

Call #: QC6 .H45 1956

Contains underlining and marginal lining

PDF Information: 29 pages – 2 MB

Schellings Abhandlung ÜBer Das Wesen Der Menschlichen Freiheit (1809), Martin Heidegger

Hannah Arendt Marginalia - All

Tübingen, M. Niemeyer, 1971

Call #: BJ1463 .H4

Contains underlining and marginal lining.

PDF Information: 220 pages – 98 mb

Training To Teach: Creating Inclusive Learning Environments, Rebecca Anne Rose

Plymouth Interdisciplinary Education Open Journal

Inclusion is often discussed as a policy imperative, but its true impact is realised only through daily classroom practice. As student teachers, we argue that inclusion should move beyond compliance to become a mindset and a lived commitment. Our experiences reveal that policy and practice are not always as intertwined as we hope. As future educators, we aspire for inclusion to require ongoing self-reflection, courage, and compassion, ensuring every student is seen, valued, and empowered to succeed. We believe policy must genuinely support and reflect this commitment, making inclusion not just a requirement, but a fundamental part of educational culture …

Reflection On The ‘Power Of Us’ Conference: How Mainstream Schools In England Offer Provision To Children With Special Educational Needs (Sen), Grace H A Cooper

Plymouth Interdisciplinary Education Open Journal

The majority of children in England with Special Educational Needs or Disabilities (SEND) are educated within mainstream schools. Due to the broad range of needs of children, it is essential that mainstream schools are provided with adequate funding, preparation and training to ensure that the inclusion of every child is achievable and expected. Furthermore, sometimes schools feel that they cannot offer ample provision to give every child an equitable access to learning and therefore they are directed to SEND schooling – can a mainstream school be considered inclusive if they cannot support all children? This article will consider these arguments …

Making Our Voices Heard: Viewpoints Of Staff And Students At Chilton Bridge School, Emma Etherington

Plymouth Interdisciplinary Education Open Journal

Shared at the Power of Us Conference, this reflection explores my work as a Horticulture Practitioner at Chilton Bridge School, where I support SEN students through hands-on, nature-based learning. From planting trees to gaining qualifications in conservation, students are encouraged to learn in ways that suit them — practical, flexible, and rooted in the real world. This approach builds their confidence, self-esteem and sense of achievement. By listening to students and adapting to their individual needs, we create an environment where they feel included, valued, and capable, and where their voices are heard.

The Power Of Us: Reflections On Leadership, Inclusion And Change In Education, Meaghan Ryder-Green

Plymouth Interdisciplinary Education Open Journal

This paper, originating from the ‘Power of Us!’ conference held in June 2025, reflects on different sessions exploring Exploring Leadership, Wellbeing, and Inclusion in Education. With a particular focus on the experiences of neurodivergent children and those with special educational needs and disabilities (SEND), the session highlighted the urgent need for systemic change. This paper offers an insight into the session, sharing reflections from the discussions and research findings—including the application of Seligman’s PERMA model of positive psychology and the importance of adult social-emotional learning—and calls for action to create a truly inclusive educational system that values all voices and …

‘They Actually Made Me Feel Like They Wanted Me In The Classroom’: Reflections Of Inclusion, Katherine Gulliver, George Osborne

Plymouth Interdisciplinary Education Open Journal

This article highlights the value of listening to individuals with lived experience in creating inclusive environments. Drawing on Gulliver’s (2023, 2024) research and the personal reflections of George Osborne, a disability advocate with Williams Syndrome, the article recognises the importance of early intervention, tailored support, and educator awareness in supporting children with rare disabilities. Through an awareness-raising exhibition and personal narratives, the article illustrates how inclusion can be meaningfully achieved when schools adapt to the needs of the child - rather than requiring the child to adapt to the school. George’s story demonstrates how empathetic, informed practice can help contribute …

Vive La Revolution, Hamish Kemp-Harington

Plymouth Interdisciplinary Education Open Journal

This article was written in response to the ‘Power of Us!’ conference which was held in May 2025 at the University of Plymouth. The conference focused on how we can make our schools and education systems more inclusive for the purpose of giving all students the opportunity to flourish and thrive in education. My account speaks of the preparation for the event and my own experiences in school as both a student and as an educator.

One Story, Jo Hawkes

Plymouth Interdisciplinary Education Open Journal

This paper, originating from the ‘Power of Us!’ conference held in June 2025, reflects on the session titled One Story, which considered how stories can help us to learn about others. The paper offers an insight into the session, sharing reflections from the discussions and calling for a renewed attention to how we teach with literature and how we help children find a love of reading.

Power Of Us: Listening To Families, Tara J. Vassallo

Plymouth Interdisciplinary Education Open Journal

This article, originating from the ‘Power of Us!’ conference held in June 2025, reflects on the session titled ‘Listening to families’ which offered an experienced parent panel, providing a forum for discussion. The session had a particular focus on the experiences of families and their children with neurodivergent and other individual educational needs and the families’ pursuit of genuine co-production with their children’s school. The article offers an insight into the session, sharing reflections from the discussions, and calls for action aimed at creating a truly inclusive educational system.

Creativity, Inclusion And Participation, Heather Knight

Plymouth Interdisciplinary Education Open Journal

This paper, originating from the ‘Power of Us!’ conference held in June 2025, reflects on the session titled ‘Creativity, Inclusion and Participation’, which drew upon different theories to explore what is creativity and question why many people believe they are not creative. This raises questions about what happens to creativity and what is the role that education plays in developing or hindering creativity. The paper offers an insight into the session, sharing reflections from the discussions, and exploring the idea that creativity can be seen as a democratic and social process. It argues that everyone can be creative in the …

A Preston Bridge School (Pbs) Approach To Inclusive Multisport Practices Within Sen, Jack Smith

Plymouth Interdisciplinary Education Open Journal

This paper, originating from the ‘Power of Us!’ conference held in June 2025, reflects on the session titled A Preston Bridge School Approach To Inclusive Multisport Practices Within SEN, which captured the current physical provision offer at Preston Bridge, with a particular focus on how the implementation of inclusive practices enable young people with SEN to meet and achieve their EHCP targets through physical education. The paper offers an insight into the session delivered, sharing best practice, staff and student reflections, and calls for action to promote the inclusion of young people with SEN within the context of physical education.

Positive Psychology And Positive Education: A Strengths-Based Approach To Sen, Michelle Y. Tytherleigh

Plymouth Interdisciplinary Education Open Journal

This paper, originating from the ‘Power of Us!’ conference held in June 2025, reflects on the session titled: Positive psychology and positive education: a strengths-based approach to SEN, which looked at how positive psychology and positive education can be applied to better support students, and with a particular focus on those with SENs.The paper offers an insight into the session, sharing reflections from the discussions and research findings, and calls for action to create a truly inclusive educational system.