The SESAME Colloquium

Embedding the Canonical Mathematics Curriculum Within an Unconventional Education Context

Davide Ravaioli

University of Bologna, Italy; Mathematics

Abstract

This presentation explores the integration of the traditional Italian high school mathematics curriculum into an unconventional educational setting, drawing from a two- year engagement as a student and team intern at the Paideia Campus in Pollica, Italy. The institute’s initiatives encompass a wide range of topics, including environmental and food sustainability, digital literacy, and the history of the Mediterranean Sea.

The presentation will unveil the fundamental principles underlying Paideia's philosophy, including Prosperity Thinking, Integral Ecology, and Transdisciplinarity. In this regard, the outcome of recent studies will be presented, having investigated the connections between mathematics with the humanities, arts, and STEM subjects through inspirations captured in the natural and cultural context of Pollica. The activities in which I was involved include:

• Metaphysics and Motion - investigating the philosophical theories of Parmenides and Zeno starting from a visit to the Archeological Park in Velia, while tracing the evolution of our perception of motion from Magna Graecia to Heisenberg.

• Blue Economy - examining the impact of commercial competition on marine biodiversity, with the objective of designing a Marine Protected Area for the enhancement of sustainable small-scale and traditional fishing.

This study was conducted in an attempt to shape the fundamentals of an educational method that provides cross-curricular skills by relating school content, students' dispositions, and socially relevant issues. With this purpose, we intend to reduce vertical specialization (and professionalization) in the high school cohort by following an approach that enables students to engage in multidimensional thinking, as the ability to consider and analyze complex problems and concepts from multiple perspectives, taking into account various dimensions such as cultural, ethical, and systemic factors.

This colloquium seeks to underscore the transformative potential of bridging the traditional high school mathematics curriculum with multidimensional thinking. In the Italian scenario, the implications of this integration extend beyond the boundaries of the classroom, urging educators and policymakers to reconsider educational paradigms. By embracing a cross-disciplinary approach that intertwines core subjects with broader societal and ecological themes, education could cultivate adaptable individuals with a profound sense of responsibility towards the world around them, fostering a generation capable of addressing multifaceted challenges with creativity and insight.

About the speaker

Dr. Davide Ravaioli is a Mathematics student at the University of Bologna. In 2019, he co-founded eRelief, a 3D modeling start-up in the field of cultural heritage accessibility for people with visual impairments. Since 2021, he is working as team intern at the Paideia Campus in Pollica (Italy), contributing to the design of extracurricular mathematics activities for the local community.

Achieving Epistemic Aims of Online Learning

Hsin-Yi Chang

Abstract

Educational researchers and practitioners around the world have gained diverse experiences and shown significant interest in reflecting on online learning since the COVID-19 pandemic. In this talk, Dr. Chang will share her recent work and perspectives on online and science learning. Specifically, she has focused on two crucial factors related to online learning: the epistemic and metacognitive aspects.

In a qualitative study, she observed and analyzed how metacognition and personal epistemology play roles in fostering successful scientific modeling. In another quantitative study, she and her colleagues identified various patterns and profiles of university students' online learning and related them to the metacognitive and epistemic factors. During the talk, she will introduce these two studies and also showcase an example of designing online learning activities and scaffolds to address the epistemic aims of education. The research results will hopefully stimulate discussions about the future of online and science learning.

About the speaker

Dr. Hsin-Yi Chang is a Distinguished Professor in the Program of Learning Sciences at National Taiwan Normal University. She earned her Ph.D. in Science Education from the University of Michigan in 2007 and conducted her postdoctoral research with Prof. Marcia Linn at University of California, Berkeley in 2008.

She currently serves as an Associate Editor of the International Journal of Science and Mathematics Education (SSCI) and as Co-Vice Executive Editor of the International Journal on Digital Learning Technology (TSSCI). Her research interests encompass online inquiry learning environments and assessments, computer simulations and visualizations to support science learning, and design-based research.

Bimanual Coordination Meets Mathematics Education

Franz Mechsner

Independent Researcher, Berlin, Germany, Movement Science

Abstract

I will present and demonstrate in situ experiments on elementary bimanual coordination phenomena. These experiments suggest that even very simple human movements are organized and executed directly as perceptual-cognitive (and possibly emotional) events rather than by way of learned neuro-muscular motor programs. This result implies that movements are genuinely mindful and meaningful. If so, the human cognitive system can be used to perform movements that are flexibly adapted to the purpose and situation.

To my astonishment, I learned that Dor Abrahamson and his group at Berkeley School of Education conducted pedagogical experiments and developed ideas that share strong similarities with my own studies. Dor’s experiments also suggest that even very simple human movements are organized and executed as perceptual-cognitive events. In Dor’s experiments however, bimanual movements result from cognitive problem solving, and come to form students’ grounding meaning of the mathematical concepts they are studying.

In my talk, I will discuss Dor’s and my own experiments and ideas in close parallel. Four fundamental hypotheses can be derived:

• Hypothesis 1: Movements are directly mentally organized and executed, with the underlying neuro-muscular patterns spontaneously and flexibly tuned in.
• Hypothesis 2: Very difficult movements may become easy as part of a well perceptible whole.
• Hypothesis 3: Mental movement structure (= strategy) integrates body and environment in a unified processual “Gestalt.”
• Hypothesis 4: Physical tasks in movement execution are mentally mastered.

With a focus on mathematical problem solving and mathematics education, I will expand the perspective to the question of how more abstract mathematical operations might be interpreted under these guiding ideas.

About the speaker

Franz Mechsner is a neurobiologist by education, with a dissertation on a theoretical model of the cerebellum. Subsequently, he investigated human movement under the guiding idea that movements are organized directly on a psychological level, namely as intended perceptions. Franz Mechsner has worked at Max Planck Institute of Psychological Research (Munich, Germany), Hanse Institute for Advanced Study (Delmenhorst/Bremen, Germany), and Northumbria University (Newcastle upon Tyne, UK). He also has worked as a science journalist for quality German magazines and newspapers.

Inquiry Workshop on Educating to Counter Oppression in Required Math Courses

Katrin Wehrheim

University of California, Berkeley, Department of Mathematics

Abstract

In collective inquiry — guided by the example of UC Berkeley's Linear Algebra and Differential Equations course — we will explore what "Educating to Counter Oppression" can look like in the reality of a Math Course that >99% of students take "just" to satisfy a major requirement:

How might we teach "with social justice" in a dehumanizing institutional context (starting with immense grade pressure) ?

How might we teach "about social justice" in a course with extreme privilege variations and dense syllabus ?

How might we teach "for social justice" — that is, towards emancipating our students and ourselves from a deeply unjust, unfair world ?

What transformative student experiences might be possible when a single instructor "goes for broke"?

What challenges do we expect in scaling such approaches ?

About the speaker

Katrin Wehrheim (they/them) is an anti-fascist by calling and a global analyst by training. Applying this training to questions in low-dimensional topology and symplectic geometry — while appeasing the power structure with women-in-math outreach activities – led them to hold positions at ETH Zurich, Princeton University, IAS Princeton, and MIT. After losing the battle for proofs in symplectic geometry, they moved to UC Berkeley Math in 2013 — then as the first woman to be hired with tenure.

Their civic engagement has been on matters of genocide accountability, reparations, and justice at large. The intersecting crises of 2020 led them to combine their identities with the goal of embodying a "mathematics educator to counter oppression.” Guided by principles of antiracism pedagogy and the BPP Oakland Community School, they redesigned the mandatory 1st year Math-GSI pedagogy course into an oppression-informed 'Building Thinking Classrooms' approach, transformed MATH54 (Linear Algebra & Differential Equations) into an inquiry-based course with alternative grading, and are now working on a book to empower other educators to follow their north star.

MOVES-Number Line: Digital Solutions for Coordinating Enactive and Symbolic Perspectives—The Case of Basic Arithmetic With Positive and Negative Integers

Giulia Cosentino¹ and Jacqueline Anton²

1. Norwegian University of Science and Technology, Department of Computer Science, Trondheim, Norway

2. University of California, Berkeley, and San Francisco State University, Joint Doctoral Program in Special Education

Abstract

We present an innovative educational design for basic arithmetic that responds to students’ documented difficulties with adding and subtracting positive and negative numbers. The design utilizes MOVES, a technological architecture that combines floor- and screen-projected interactive interfaces. Students enact arithmetic operations, such as, “3 - (-2)”, by walking along a projected body-scale number line, and their actions are captured and analyzed to provide in-the-moment feedback. Next, a screen-based avatar is introduced who mimics their whole-body movements. Finally, analogous problems are presented on a tablet, where students walk an avatar action figure along a standard-sized number line.

Our research focuses on promoting conceptual understanding through coordinating full-body egocentric experiences on a body-scale number line with the allocentric experience  of “puppeting” the avatar along the desk-scale number line. Based on pilot trials, we speculate on the nature and type of supports students require to coordinate these perspectives, and discuss implications for future iterations of the design.

About the speakers

Giulia Cosentino: Giulia Cosentino is pursuing a Ph.D. degree in interaction design and learning technologies at the Department of Computer Science, Norwegian University of Science and Technology, Trondheim, Norway. She works at the Learner–Computer Interaction Lab, and her research interests include learning analytics to investigate various interaction modalities in light of educational contexts, as well as innovative multisensory settings and technologies that increase students' chances of learning success.

Jacqueline Anton: Jacqueline Anton is a student in the Joint Doctoral Program in Special Education at the University of California, Berkeley, and San Francisco State University. Her research addresses embodied mathematics interventions for students with moderate/extensive support needs. She is also interested in inclusive mathematics pedagogy and teacher education. Her work is inspired by her previous experience as both a general and special education Math teacher.

This talk has been cancelled due to illness.

Conceptual change and education: A multi-level approach comparing knowledge-in-pieces, ontological theory, framework theory, and developmental teaching

Thomas Gennen

Université Libre de Bruxelles, Faculty of Psychology and Educational Sciences, Brussels, Belgium

Abstract

Conceptual change (CC) research studies the types of knowledge that are difficult to learn because they require significant changes (i.e., 'conceptual changes') in learners’ prior knowledge. For example, it is difficult to learn the Newtonian concept of force (i.e., the force of an object is precisely its mass multiplied by its acceleration) because it diverges from students’ common assumption that thrown objects acquire or contain an internal force. CC research is fractured into different positions. Three main theories of CC and related sets of educational recommendations to foster CC are knowledge-in-pieces, ontological theory, and framework theory.

First, I show that there is another set of promising CC approaches that has been ignored in the CC literature. These are developmental teaching (DT) approaches, also known as (Neo-)Vygotskian approaches, including El’konin-Davydov’s developmental education and Gal’perin’s method of stage-by-stage formation of mental actions and concepts.

Second, I delineate the convergences and divergences between DT approaches and the three CC trends aforementioned. I do this by delineating the epistemological assumptions of all these approaches about what CC is and how the difficulties of CC are interpreted. Then, I show the relations of implication between theses assumptions and the related educational recommendations to foster CC, in particular the main educational principles and methods favored. I demonstrate that this multi-level approach (epistemological assumptions, educational principles, methods) is particularly suited to (a) delineating the specificities, convergences, and divergences between CC approaches; (b) envisioning productive articulations between them in the fractured field of CC research; and (c) engaging in critical dialogues.

This presentation is based on the following article and the public debate that followed with diSessa, the main proponent of knowledge-in-pieces:

Gennen, T. (2023). Conceptual change and education: The neglected potential of developmental teaching approaches. Human Development, 67(2), 88–107. DOI: https://doi.org/10.1159/000530247

diSessa, A. (2023). Conceptual change and developmental teaching: Comment on Gennen. Human Development, 67(2), 108–113. DOI: https://doi.org/10.1159/000530505

Gennen, T. (2023). Developmental teaching and knowledge-in-pieces: A reply to diSessa. Human Development. DOI: https://doi.org/10.1159/000534803

About the speaker

Thomas Gennen majored in the philosophy of education and the anthropology of learning. He is completing a Ph.D. in educational psychology. His research analyzes how distinct epistemological assumptions inform various existing educational approaches. His analytical approach encompasses multiple levels, from fundamental epistemological assumptions to educational principles, methods, and practices. This method serves both analytical and critical purposes and is applied to address key debates and fields within education, including the constructivist–instructivist debate, conceptual change research, the impact of assumptions about concepts on education, and the correlation between teachers' epistemological beliefs and their instructional practices.

Facilitating teachers' professional learning with and about digital technologies by fostering professional learning communities

Catalina Lomos

Luxembourg Institute of Socio-Economic Research (LISER), Esch-sur-Alzette, Luxembourg

Abstract

Teachers' professional development and learning have long been receptive to the advances in information and communications technologies (ICT) and digital technologies. Digital resources, digital learning platforms, games, or artificial intelligence, are just a few of the recent transformations that influence teacher practice and learning. Teachers interact with digital technologies in the classroom, in their work with students, and in their ongoing professional learning.

New designs for professional development and learning with and about digital technologies could build on effective theories and practices of teacher professional learning. Teacher collaboration in professional learning communities is one such practice that could support and empower teachers in their professional learning with and about ICT.

This presentation will focus on a professional development and learning program we designed (https://mathematic.lu/plc) and implemented in 10 primary schools and involving 62 teachers. The primary goal of the program was to support and guide teachers in using a digital learning platform for mathematics in their classroom practice. The secondary goal was to facilitate the emergence of professional learning communities within the schools, so that teachers could support each other in the long term while using the digital learning platform in their classroom practice. The format of the program was hybrid, in that it was delivered online, but each session required teachers to meet and work together at their school.

In discussing the findings of this study, I will touch on the benefits and barriers that teachers perceived as part of this professional development and learning program and the perceived processes of developing professional learning communities. Building on known theories and practices of teacher learning can facilitate the emergence of new professional learning models that could support teachers in exploring and using digital technologies in practice.

About the speaker

Catalina Lomos is a researcher at the Luxembourg Institute of Socio-Economic Research (LISER). She holds a Ph.D. in Education from the University of Groningen in the Netherlands.

Her recent work has examined teachers' use of ICT in classroom practice, using large-scale data and data from digital learning platforms in education. She has worked closely with the Ministry of Education in Luxembourg on many educational projects.

Catalina is a Fulbright Visiting Scholar at the Embodied Design Research Laboratory (EDRL) at UC Berkeley for the academic year 2023-2024.