News & Events

Course D5-1: Argumentation, Proof, and Proving

Instructors: Dr. Knipping & Dr. Papadaki,

University of Bremen

Course Period: 07/11/2025 – 06/02/2026

Start Date: 7th November 2025 8:00-10:00 CET

Zoom ID for all meetings: 616 4799 4734

Course Information:
Mathematical proof is often equated with formal proof, where statements are considered true when they are deductively derived and formally represented within a mathematical theory. Proofs in this formal sense are widely recognized as difficult and challenging to understand. However, such proofs are rarely found in school mathematics, as the school curriculum is not structured as an axiomatic system. This creates a divide between different realms of mathematics: academic mathematics at the university level, where formal proof is central, versus school mathematics and applied mathematics, where proof struggles to find a meaningful place. This phenomenon reflects
what Felix Klein (1932) described as a discontinuity in mathematics education—the conceptual and structural gap between school and university mathematics, which makes the transition between these levels challenging both for learners and teachers.

From the perspective of learning and understanding mathematics, this discontinuity highlights the limitations of a solely formal view of mathematical proof, rendering it problematic. Mathematical knowledge is more than an accumulation of facts and procedures; it is an active understanding of properties and concepts that humans create and use. To bridge the gap that Klein identified, we
need to provide students with opportunities to experience this kind of knowledge and familiarize themselves with a conception of proof that emphasizes the practice of proving and reasoning –
that is, the processes of developing mathematical arguments and proofs. Such an approach highlights the social dimension of proof, which includes the negotiation and acceptance of proofs
within a community, both in the classroom and in the broader mathematical community. Argumentation, understood as providing reasons for mathematical statements, plays a crucial role in this perspective.

In this course, significant publications and scholarly work in the area of argumentation, proving, and reasoning in mathematics education are studied and discussed. The concept of mathematical proof is examined from an educational perspective, broadening its traditional meaning. A more process-oriented and socially situated understanding of proof is emphasized, one that considers diverse social and cultural contexts of education – from primary to high school, and from academic programs to engineering programs at the tertiary level. Furthermore, different theoretical frameworks and approaches are explored to capture a nuanced and complex picture of what mathematical proof actually is and can be.

Active and extensive reading is expected in this course. A discussion format taking place every two weeks will support the study of a broad range of publications. For students who require credit points for their Master’s or PhD program, the design of a learning environment is required. This environment should foster proof and proving in a specific educational context and be grounded in the studied literature.

For colleagues who are interested in discussing matters of proof and proving in teaching and education more generally, this course serves as an open forum to interact with Master’s and PhD students, as well as interested scholars and colleagues.

Reference
Klein, F. (1932). Elementary mathematics from a higher standpoint: Arithmetic, algebra, analysis (E. R. Hedrick & C. A. Noble, Trans.). Dover Publications. (Original work published
1908)

Course Schedule:

Recording on YouTube: https://youtu.be/UC8dKFBGsOk

What aspects of student language use do not comport with mathematical logic?

Speaker: Paul Christian Dawkins,
Professor of Mathematics,
Texas State University

Date: August 11, 2025

Time: 0800 hours (Dallas) 
1000 (Brasilia) 1500 (Paris)
1830 (Bangalore) 2100 (Beijing)

Abstract:

Based on over a decade of experiments working to support students in reflecting on their use of mathematical language to help them reinvent some basic logical structures, I have gained some insights about university students’ untrained interpretations of mathematical language.

Combining these empirical findings with insights from psychology, pragmatics, and linguistics, I have come to appreciate the coherence and rationality of students’ language use even when it proves incompatible with logical structure.

In this talk, I will share some stories of student thinking that have given me some helpful insight into how their language use differed in important ways from mathematical language use. Hopefully, these contrasts will help instructors and researchers understand the challenges that logic instruction must overcome to support students in formalizing and systematizing their reasoning about mathematical language.

BRITISH COLLOQUIUM FOR THEORETICAL COMPUTER SCIENCE (BCTCS) 2025 Education Track

Conference, University of Strathclyde

Date: April 14-16, 2025

Website: https://msp.cis.strath.ac.uk/bctcs2025/

CONTRIBUTED TALKS
This year BCTCS will host a focused Theoretical Computer Science Education Track on Wednesday the 16th of April.
To propose a talk, please fill in the submission form.

We invite 20 or 30 minutes talk proposals on teaching experiences, highlighting specific challenges and/or innovations related to particular theoretical computer science topics or courses. This track is designed to facilitate reflection on both the breadth and depth of TCS topics offered across institutions, from introductory courses to advanced topics such as computational complexity theory, quantum computing, algorithmic game theory, model checking, programming language theory and semantics, to name a few. A central theme of this event will be exploring how TCS can continue to serve as a foundational element of computer science education, with challenges lying in keeping students engaged and demonstrating relevance considering emerging technologies like generative AI.

We put no restrictions on the originality or publication status of submissions. There will be no formal proceedings, but the collection of the contributed abstracts will appear in the Bulletin of the EATCS.

REGISTRATION
We hope to open registrations in March 2025. The registration fees will be as follows:

– Early registration (until 24 March): £45

* Late registration (until 7 April): £60

TCS Education Track Chairs:
– Oana Andrei, University of Glasgow. https://www.gla.ac.uk/schools/computing/staff/oanaandrei/
– Alasdair Lambert, University of Strathclyde. https://www.strath.ac.uk/staff/lambertalasdairmr/,

Further details are available at https://msp.cis.strath.ac.uk/bctcs2025/ or contact directly the education track chairs.
This event is sponsored by SICSA, the Scottish Informatics and Computer Science Alliance

Webinar on logic education: Tools for Teaching Logic

Speaker(s): Professor María Manzano

Date: April 8, 2025

Time: 10:00 New York, 14:00 GMT, 16:00 Amsterdam, 19:30 Bangalore, 22:00 Beijing

Abstract:

I will tell you about the European ALFA project on Tools for Teaching Logic that we had last century and about the International TTL Congresses that we held in 2000, 2006, 2011, 2015, and 2023.

The first goal of the ALFA project was to share our experience as teachers among Aracne members. We proposed: (1) the preparation of a metabook (with hypertext version), (2) the design of an on-line dictionary of logic terms, (3) the investigation of the existing software for the teaching of logic, (4) the translation of both elementary and interdisciplinary texts and software, (5) to help potential authors to write lecture notes, (6) the dissemination of our project both within our academic community and outside it (high school), thus bolstering a good image of Logic and (7) to support women’s participation in higher education.

The network we created was interdisciplinary and included professors and researchers from philosophy, mathematics, computer science, and linguistics. Some of the results of the project can be consulted on the Aracne website (aracne.usal.es) and others in the Summa Logicae digital library (logicae.usal.es)

Speaker Bio: 

María Gracia Manzano Arjona is a Spanish philosopher specializing in mathematical logic and model theory. Manzano earned her Ph.D. in 1977 from the University of Barcelona. Her dissertation, Sistemas generales de la lógica de segundo orden [General systems of second-order logic], was supervised by Jesús Mosterín. She is a professor of logic and the philosophy of science at the University of Salamanca. She is the author of several books on logic and model theory.

https://en.wikipedia.org/wiki/Mar%C3%ADa_Manzano 

Panel discussion on logic teaching

Panellist(s): Johan van Benthem, Mihir Chakraborty, and Sujata Ghosh

    Moderator: R. Ramanujam

Date: February 7, 2025

Time: 14:30-15:30

This panel discussion will take place during AWPL (Asian Workshop on Philosophical Logic), Feb 6-8, 2025,
Jadavpur University, Kolkata, India

Panel discussion on careers and education in logic

Speaker(s): Janos Makowsky, Anil Nerode, R Ramanujam, Shashi Srivastava, R Venkatesh

Date: February 5, 2025

Time: 16-17:30

This panel discussion will take place during ICLA (Indian Conference on Logic and Applications), Feb 3-5, 2025,
Indian statistical institute, Kolkata, India

International group discussion on logic and computing education

Speakers: Viviane Durand-Guerrier, Kyeyong Hah-Roh, R Ramanujam and Sebastian Sequoia-Grayson

Date: July 10 and 13, 2024

Group discussion took place during ICME-15 (the 15th International Congress on Mathematics Education), July 7-14, 2024, Sydney, Australia