Symposium Scientific Program - Computational Participation in MathComputational Participation in Math

Keynotes

Title: Five Powerful Ideas about Technology and Education

Abstract:

I will present “five powerful ideas” concerning the very best ways to enhance education via computers. These ideas have stood the test of time in that they have guided decades of my own work, and they have been reinforced and adjusted as we have had experience with them. Some of them even originated directly in surprising experiences we had working with students and teachers.

These ideas are subtle, deep, and unfamiliar to many. A “once in several centuries innovation,” information technology, impinges on profound epistemological and cultural issues. None of them is “easy to implement,” and there are also cultural dissonances with popular ways of understanding how to use computers in education. Each idea stands on its own. But they also relate synergistically to the umbrella idea of “computational literacies,” which I will also motivate and introduce.*

My talk will seek to bring these ideas to life in examples and will include commentary on avenues of progress and also on blocks and limitations impeding quicker progress.

*For further information about computational literacies, or as a preparation for the talk, the organizers of this conference recommend a previous, recorded talk by Prof. diSessa: https://www.youtube.com/watch?v=3pnc_ry5Y1c

A written exposition is: diSessa, A. A. (2018). Computational literacy and “The Big Picture” concerning computers in mathematics education. Mathematical Thinking and Learning, 20(1), 3-31.

Reactor: Dr. Brent Davis (Werklund School of Education, University of Calgary, Canada)

Andrea diSessa

Andrea diSessa holds a PhD in physics (MIT) and is Corey Professor Emeritus at University of California, Berkeley. He is a member of the National Academy of Education and Fellow of the American Educational Research Association. His research centers on the role of intuitive knowledge in learning science, and the development of computational literacies. He is the prime designer of Boxer, a medium to support computational literacy. diSessa wrote the books Turtle Geometry: The Computer as a Medium for Exploring Mathematics, with H. Abelson (1981), and Changing Minds: Computers, Learning and Literacy (2000). He has authored over 100 journal articles and book chapters, including “Local Sciences: Viewing the Design of Human-Computer Systems as Cognitive Science” (1991), “Toward an Epistemology of Physics” (1993), “What Do ‘Just Plain Folk’ Know about Physics” (1996), “Conceptual Change in a Microcosm” (2017), and “Computational literacy and ‘The Big Picture’ concerning computers in mathematics education” (2018).

Title: Coded Bias: Decoding Racism in AI Technologies

Abstract:

With advancement in technology, tools built on artificial intelligence (AI) technology have made their way into the justice system. AI tools are now being used in recidivism risk assessment to predict the likelihood of reoffending by individuals in the criminal justice system. Also, AI facial recognition technology is being used in identifying subjects and suspects in the criminal justice system. While these tools might have been designed with the best intent, their use in the justice system has raised serious concerns about their potential to perpetuate racism and racial bias. This is especially the case where the tools are designed using historical data from era of biased policing, biased bail and sentencing regimes characterised by systemic discrimination against particular sections of the society. Algorithmic racism has been coined to describe this problem. This presentation will discuss racial biases encoded in various AI technologies used in the justice system and their potentially adverse impacts on Blacks and other racial minorities.

Reactor: Dr. Ron Eglash (School of Information, University of Michigan)

Gideon Christian

Dr. Gideon Christian is an Assistant Professor of AI and Law at the Faculty of Law, University of Calgary. Prior to joining the University of Calgary in Summer 2019, he was e-discovery counsel with the National Litigation Sector at the federal Department of Justice where he conducted electronic discovery in high profile litigation involving the Government of Canada. His research interests are in artificial intelligence and law, legal impacts of new and emerging technologies among other areas. In 2019, he was featured as an AI subject matter expert in the Udocs original documentary film “The A.I. Taxman”. His current research seeks to develop the concept of algorithmic racism which is defined as race-based bias arising from the use of AI-powered tools in the analysis of data in decision making resulting in unfair outcomes to individuals from a particular segment of the society distinguished by race. Dr. Christian obtained his masters in law (with specialization in law and technology) and PhD from the University of Ottawa.

Working Groups

The symposium will employ a working group model like the Canadian Mathematics Education Study Group (CMESG). Working groups have leaders who plan discussions and activities to frame the work of their group. Symposium participants are invited to choose one working group to attend, in which they work closely with their group members for an extended period of time over the entire duration of the symposium (2 hours on Day 1, two 90-minute sessions on Day 2, and 2 hours on Day 3). Showing up and sharing your ideas are key to the success of this model. After the symposium, working group leaders and participants produce a report synthesizing their work and its outcomes, which serves as a pertinent contribution to the field.

Working Group A: Coding and computational modeling in elementary and early years mathematics education (EEYME)

Abstract:

Coding and computational modeling are increasingly becoming curricular requirements across all age-ranges (Floyd, 2022). This working group will explore this phenomenon by focusing on elementary and early years education with an emphasis on mathematics while acknowledging and respecting the interdisciplinary nature of the work of teachers during this dynamic and diverse period of child development. The working group’s focus may include,

discussion of affordances and limitations of different metaphorical frames and descriptions for coding used in EEYME such as ‘literacy’ (diSessa, 2017), recipe, puzzle, playground (Bers, 2020), creative expression, and architecture (low floor, high ceilings, wide walls).
developing and evaluating instructional materials and approaches for teaching coding and computational thinking in elementary and early years math classrooms (earlymath.ca)
examining the impact of coding and computational thinking on students’ math skills and attitudes
exploring the use of technology and software tools to support coding and computational thinking in EEYME.
investigating the ways in which coding and computational thinking can be used to enhance problem-solving and critical thinking skills in EEYME.
sharing research findings, learning trajectories, and emerging best practices for teaching coding and computational thinking in EEYME.
critical discussion about under-articulated or less explicit goals such as computational participation (Kafai & Burke, 2017), productive computational disposition (Pérez, 2018) as well as opportunities for considerations of ethics, equity, and the development of empathy (Bers, 2022).

The WG is dedicated to examining how and why opportunities to code across the early years through elementary provokes mathematics learning with a combination of hands-on activities and critical discussions. Participants will have the opportunity to try out some unplugged and plugged tasks that have been tested in the mathematics classroom and explore the affordances of the Micro:bit (microbit.org) as a potentially equitable tangible coding platform.

References

Iain Brodie

Iain Brodie is a former 28-year elementary teacher who spent his career teaching all the grades from 1 – 8, especially in combined grades. He learned to code alongside his students in 2014 and since has integrated computational thinking into his teaching practice as a further way of learning mathematics and another effective way for students to express their learning. Since retiring in 2018, Iain has been helping teacher candidates to integrate computational thinking into their teaching practice and teachable subjects as well as teaching STEM, mathematics, and more at Ontario Tech University and in Western’s online masters program. An advocate for reforming assessment practices, Iain has been using ungrading and delayed grading practices with his students in order to foster greater critical thinking and creativity in their learning and future teaching practices.

Steven Khan

Dr. Steven Khan is an Assistant Professor of Mathematics Education originally from Trinidad. He works primarily in pre-service teacher education. He enjoys well designed video-games, puzzles, and multi-player board games and other spaces where ideas related to coding, computational thinking and mathematics may be curated.

Alexandra (Sandy) Youmans

Dr. Alexandra (Sandy) Youmans is an adjunct assistant professor at the Faculty of Education, Queen’s University. She is a former elementary teacher, who is passionate about equipping educational professionals with the skills, knowledge, attitudes, and resources needed to support learner success. She is the co-lead of the Critical Transitions in Early Math Community of Practice, a part of the Math Knowledge Network). Dr. Youmans has taught elementary curriculum courses (i.e., Mathematics, Science, Literacy) in the Bachelor of Education program and courses on innovative curriculum planning, program evaluation, and collaborative inquiry in the Professional Master of Education program. She is co-editor of the book, Beyond 1, 2, 3: Early Mathematics Education in Canada (in press, Canadian Scholars). Dr. Youmans co-created the Coalition Model for Professional Development, published in the international journal of Teachers and Teaching. Her areas of research interest include elementary mathematics education, collaborative inquiry, adult education, and program evaluation.

Working Group B: Coding and computational modeling in secondary and university mathematics education

Abstract:

Mathematics is used when coding and designing algorithms (Modeste, 2016), and coding is often used to expand the class of mathematical problems that can be solved or the set of concepts that can be explored (Buteau et al, 2020; Lovric, 2018). Mathematics and coding can also be used jointly with principles from other disciplines to model real-world situations (Giabbanelli & Mago, 2016; Caron, 2019).

In this working group, we examine coding and computational modeling in secondary and university mathematics by working with and developing hands-on activities for students and educators.

We explore ready-made programs related to secondary and university mathematical concepts, along with tasks that have been or could be built from these programs, and then consider the characteristics of effective program-task combinations.

Important concepts, practices and ideas associated with computational thinking, computational modeling, mathematics, or computer science will be identified in the effective activities. As we develop our ideas in discussing activities and teaching, we will connect them to (or contrast them with) existing research and associated frameworks (Weintrop et al., 2016; Grover & Pea, 2017; diSessa, 2018; Modeste, 2018; Bråting & Kilhamn, 2021; Dohn, 2020). Key elements could be made part of a foundation to create new activities, and envision improved integration of mathematics, coding, and computational modeling instruction.

We invite participants to bring, if they wish, their own samples of coding or programming tasks.

References

France Caron

France Caron has been a professor of mathematics education at Université de Montréal since 2001, after more than ten years in the telecom industry. She holds a B.Sc. in mathematics and computer science, an M.Sc.A. in applied mathematics and a Ph.D. in education. Her research interests include integration of mathematical modelling, interdisciplinarity and technology in mathematics education. She collaborates in research and development with partners from secondary schools and postsecondary institutions. She has led several working groups at the Canadian Mathematics Education Study Group (CMESG/GCEDM), at the Canadian Mathematics Education Forum, and at the international Espace mathématique francophone (EMF). She is an active contributor to the International Study Group for Mathematical Modelling and Applications (ICTMA). She was president of the Association mathématique du Québec (AMQ) from 2009 to 2013. She is one of the founding editors of Accromath.

Steven Floyd

Steven Floyd completed his PhD at Western University with a focus on Curriculum Studies. Since 2003, Steven has been a high school computer science teacher, resource developer, e-learning course writer, B.Ed. instructor, and educational consultant. He has worked with school boards in Canada and the US in supporting computer science education in the K-12 grades, and was awarded the 2017 Computer Science Teachers Association Award for Teaching Excellence in Computer Science and the 2019 Canadian Research Centre on Inclusive Education Research Award. Steven’s research focuses on technology and computer science in K-12 education.

Miroslav Lovric

Miroslav Lovric is a professor of mathematics at McMaster University. His research interests include Riemannian geometry, mathematics and medicine and mathematics education. Miroslav has taught mathematics to a wide variety of students from almost every program at his university. He created a much-needed numeracy course and has been collaborating on creating learning modules for improving health numeracy among health care professionals. Miroslav’s major educational project involves working on a natural integration of computational thinking and coding into teaching mathematics. He has co-created Python labs for life sciences students, and his students code to solve challenging problems in his level 3 advanced problem-solving course. Presently, he is collaborating on a project that will create teaching modules for mathematical modelling of social justice problems. Miroslav is an active member of the community of university math and stats instructors. Besides mathematics, his greatest passion is travelling.

Working Group C: Equity, diversity, and inclusivity in coding and computational modeling in mathematics education

Abstract:

Coding and computational thinking (CT) is being integrated into K-12 mathematics education around the world. Researchers have identified numerous potential benefits for integrating CT with mathematics including “make[s] abstract mathematical concepts concrete” (Wilensky, 1995, p.257), dynamic modelling to develop mathematical concepts and relationships (Gadanidis, 2015), support transfer of learning from the classroom to real-world settings (Lunce, 2006). Other researchers suggested: motivation to experiment; the development of mathematical intuitions; critical reflection; and working with abstraction and different representations (Howson & Kahane, 1986; King et al., 2001; Marshall & Buteau, 2014).

However, this rapid integration of CT & mathematics raises many potential equity issues, including equitable access to technology for coding, equitable access to quality instruction and instruction that makes coding attractive to a diverse range of students.

Equity, diversity, and inclusivity

This workshop addresses the issue of quality equitable pedagogy as the benefits of coding for mathematics learning are based on instruction that promotes problem-solving, computational thinking and connections to mathematical thinking for ALL students. Incorporating this equitable pedagogy is difficulty for most teachers who have 1) little to no prior experience learning coding as problem-solving, 2) little access to quality teaching materials (Wu et al., 2020; Yadav et al., 2016) nor 3) no vision of integrating & connecting between CT / CM and mathematics teaching (Gleasman & Kim, 2018).

This workshop explores equity issues around quality pedagogy for coding and mathematics, developing strategies and vision to make coding more inclusive. Participants will then examine existing coding and mathematics activities through an equity lens before modifying the activities to develop mathematical reasoning for all students. In this way the workshop hopes to develop equitable math and coding activities, and develop a vision for future adaptations. In creating more equitable coding and mathematics activities, and a framework for modifying other activities, this workshop hopes to harness “the power to change pedagogies and students’ experience of mathematics learning” (Ford, 2018, p. 27).

References

Annie Savard

Annie Savard is an Associate Professor in the Department of Integrated Education Studies in the Faculty of Education at McGill University. She holds a master’s degree in Science Education and a Ph.D. in Mathematics Education. She is a fellow of the CIRANO-Interuniversity Center for Research in Analysis of Organizations. In 2019, she received the title Professor Honoris Causa from the Universitatea Ovidius din Constanta, Romania. Her research interests concern the teaching and learning of mathematics in elementary and secondary school from an ethnomathematical point of view and in connection with the development of citizenship competencies, such as decision-making and critical thinking. She is a pioneer in conceptualizing the field of Financial Education in elementary and secondary schools. She is particularly interested by different reasoning such as statistical reasoning, early algebraic thinking, and computational thinking. She studies the professional development of teachers in initial training and through professional learning communities.

Ricardo Scucuglia

Ricardo Scucuglia is an associate professor of the Institute of Biosciences, Languages, and Exact Sciences at Sao Paulo State University (UNESP), Campus of Sao Jose do Rio Preto, SP, in Brazil. He is a professor of mathematics education in two graduate programs at UNESP: (a) mathematics education and (b) teaching and formative processes (position as the assistant dean as well). He completed his PhD at Western University. Since 2000, he has been a member of the Research Group on Informatics, Media and Mathematics Education. Dr. Scucuglia has been developing research on the following topics in mathematics education: use of digital technology (including computational thinking), arts and aesthetics, music and audiovisual production, teaching and learning, teacher education, and history and philosophy of mathematics.

Diane Tepylo

Diane Tepylo taught secondary programming and mathematics classes for over 15 years before completing a PhD in mathematics education. Diane is currently an Associate Teaching professor at Ontario Tech University, and integrally involved in the development and teaching of mathematics and coding courses for preservice teachers. Diane also developed and taught the continuous learning course Coding for Teachers and works with teachers learning to code from around the province. Diane recently completed a SSHRC Insight project with Ami Mamolo and Robyn Ruttenberg-Rozen entitled “Using mathematical models to disrupt probabilistic misconceptions about social issues.”

Panels

Research Panel*: How do computational thinking and mathematical thinking interact (in terms of knowledge, ways of thinking, and competencies)?

Abstract:

Over the past decade, there has been an upsurge of interest in the research on computational thinking. Many countries are in the process of introducing computational thinking into their school curricula, either as a new dedicated subject, a cross-curricular theme, or integrated within an existing subject, such as computing or mathematics. The relationship between computational thinking and mathematical thinking has been of particular interest and there is variation in how computational thinking is perceived by different stakeholders in the mathematics education discipline, including researchers, teacher practitioners, and teacher educators. In this interactive research panel, we will discuss characterizations of computational thinking and how it relates to mathematical thinking in terms of knowledge, ways of thinking,and competency. We will consider a historical overview, relevant literature, and state-of-the-art research, hoping to bring forward arguments for the importance and value of computational thinking in mathematics education in the 21st century. In doing so, we seek to highlight relevant questions and issues related to computational thinking that are relevant for the mathematics education research community. We will invite the audience to engage in active participation and will discuss with the audience their views and perceptions regarding all the issues raised.

Nathalie Sinclair, Panel Chair

Nathalie Sinclair is a distinguished University Professor at Simon Fraser University. She is the founding and current editor of Digital Experiences in Mathematics Education. She has co-published several books, including Mathematics and the Body: Material Entanglements in the Classroom. She has also the co-developed tools TouchCounts and TouchTimes for engaging children in gestural arithmetic. Her research interests include the history and philosopher of mathematics, the embodied nature of mathematics thinking and learning, and the role of digital technology in school mathematics. Her first and formative exposure to computational thinking was as a research assistant in the Centre for Experimental and Constructive Mathematics.

Paul Drijvers, Panelist

Paul Drijvers is scientific director and full professor in mathematics education at the Freudenthal Institute of Utrecht University’s Science Faculty. His research interests include the role of ICT in mathematics education, mathematical and computational thinking, and embodiment in mathematics education. He was PI in an NWO-funded project on computational and mathematical thinking in upper-secondary mathematics education. Paul chairs the IPC of the CERME13 conference. For more information please visit Paul’s website

Eirini Geraniou, Panelist

Eirini Geraniou is an associate professor of mathematics education at the UCL Institute of Education, University College London, UK. Her research interests involve the use of digital technologies for the learning and teaching of mathematics, the design and implementation of bridging resources for mathematical learning with digital technologies, students’ mathematical and computational thinking, and students’ and teachers’ mathematical digital competencies. Eirini has been an active member of the European Society for Research in Mathematics Education (ERME), co-chairing the Thematic Working Group on ‘Learning Mathematics with Technology and Other Resources’ at CERME10 and CERME11; being the IPC co-chair for CERME12 and in 2021 becoming an elected member of the ERME board. Eirini is involved in a 4-year research project (2020-2023), that investigates programming, computational thinking and mathematical digital competencies in the teaching of mathematics in Denmark, Sweden and the UK. For more information please visit her UCL IRIS profile.

Elise Lockwood, Panelist

Elise Lockwood is Associate Professor in the Department of Mathematics at Oregon State University, and she is currently serving as a rotating program officer in the Division of Undergraduate Education at the National Science Foundation in the US. Her research focuses on undergraduate students’ reasoning about combinatorics and discrete mathematics, and recently she has been investigating the role of computing in supporting students’ mathematical thinking and activity. She is currently serving as a Co-Editor-in-Chief for the International Journal of Research in Undergraduate Mathematics Education. Elise was a 2019 Fulbright Scholar to Oslo, Norway, where she collaborated with researchers at the Center for Computing in Science Education at the University of Oslo.

*Some panelists may be presenting virtually.

Practice Panel*: Mathematics Education incorporating Coding: Practical Challenges and Opportunities
In-person and livestreamed in collaboration with the Fields MathEd Forum April 2023 meeting.

Abstract:

Coding or programming is ubiquitous across the world. But what coding means, how it is learned and developed and how it is exploited as a tool to explore topics in different subject areas varies enormously across jurisdictions: for example, coding can be introduced and developed as part of a school computing curriculum, as part of the school mathematics curriculum or more informally within out-of-school clubs. These different structural organisations inevitably serve to define what happens in practice in schools, shapes how students develop coding skills and learn key coding concepts, informs how teaching might be enhanced through coding, and ultimately how coding might be exploited outside of computing as a tool to think with and explore mathematics.

This panel will touch on some these issues with a particular focus on the interactions between mathematics and coding in practice. The discussion will aim to tease out the challenges, risks and opportunities of integrating coding into mathematics classrooms while addressing questions such as: Why should coding be incorporated mathematics classrooms? What is the specificity of coding in mathematics and the links between coding and mathematics? What can coding bring to mathematics in terms of new content or new ways to support mathematics teaching and improve learning? Which mathematical topics are most aligned to the incorporation of coding and why? What are the links between coding and algorithmics, applied mathematics and reasoning?

The panel will comprise a chair and four invited panelists from four different countries with different curricular structures. It will conclude by a reaction, titled ‘Past, Present, and Future: 1980s – 2020s – 2050s’.

Celia Hoyles, Panel Chair

Professor Dame Celia Hoyles, D.B.E, O.B.E, PhD, M.Ed, BSc. (Hons), CMath,
Professor of Mathematics Education
UCL Institute of Education, University College London, U.K
I aim to use digital technology to open access to mathematics and have researched ways to do this in different contexts.
I was first recipient of the International Commission of Mathematics Instruction (ICMI) Hans Freudenthal medal in 2004, the Royal Society Kavli Education Medal in 2011 and the Suffrage Science award for Communications in 2016.
I was the UK Government’s Chief Adviser for mathematics (2004- 07), and the Director of the National Centre for Excellence in the Teaching of Mathematics (2007-13). I have given many keynotes with notable examples: to the 16th International Group for the Psychology of Mathematics Education (PME 16) in 1992, and to the International Congress on Mathematical Education, (ICME, 11), Monterrey, Mexico in 2008.
I was President of the Learned Society, Institute of Mathematics and its Applications (IMA) (2014-15). I was made an Officer of the Order of the British Empire in 2004 and a Dame Commander in 2014.

George Gadanidis, Panelist

George Gadanidis (Western University) works in mathematics education with interest in mathematical wonder and storytelling (a.k.a., inspiring answers to “What did you do in math today?”) and computational modelling of mathematical concepts and relationships. More on his work at imaginethis.ca

Oh Nam Kwon, Panelist

Oh Nam Kwon is Professor of Mathematics Education at Seoul National University. Her earlier professional appointments include Assistant Professor and Associate Professor of Department of Mathematics Education at Ewha Womans. She has been involved in more than 30 grants as Principal Investigator and Collaborator. She is in Editorial Board for book series “Advances in Mathematics Education” by Springer. She has served as committee member for numerous international (including International Programme Committee of ICME-12) and Korean organizations of mathematics education. She has served as National Committee of Korean Institute of Curriculum and Evaluation. She is a member of OECD/PISA MEG (Mathematics Expert Group) She received the Best Teaching Awards, Seoul National University in 2009. She has served the jury for Mathematics Planet Earth 2013 Virtual Modules Competition and the committee member for Leelavati Prize 2014. She received the 2021 Svend Pedersen Lecture Award Awards, Stockholm University. Her research interests include curriculum development, teaching and learning of collegiate mathematics, and inquiry-oriented teaching.

Simon Modeste, Panelist

Simon Modeste is assistant professor at the University of Montpellier, in the laboratory IMAG, in the team DEMa – Didactics and Epistemology of Mathematics. He got his PhD in 2012 from the University of Grenoble, dealing with the teaching and learning of algorithmics in mathematics in the French High School. His research interests are principally in didactics and epistemology of mathematics, of computer science and of their interactions. He also works in the training of secondary school teachers of mathematics and computer science.

Elena Prieto-Rodriguez, Panelist

Dr Elena Prieto-Rodriguez is an Associate Professor in Mathematics Education at the University of Newcastle, Australia. She holds a Bachelor degree in Mathematics and a PhD in Theoretical Computer Science. From 2005, she has worked extensively in STEM education, including several large-scale research projects amounting to over $15M in funding. She is currently engaged in research focused on the use of technology for the learning of mathematics and teacher training and professional development. From 2017 to 2021 she conducted several projects focusing on the effect of ScratchMaths in teachers and students, and found both deep engagement from students and strong commitment to the integration of programming into mathematics by teachers. She also identified the need for explicit connections to coding within the Australian mathematics curriculum and her future research will focus on this topic.

Richard Noss, Reactor

*Some panelists may be presenting virtually.

Poster Session: Research and Innovative Practices

The organizers of the Symposium invite submissions of poster presentation proposals contributing insights into Coding, Computational Modelling, and Equity in Mathematics Education. Poster proposals may focus on research or innovative practices. In the research category posters may present completed or preliminary research and must include a clear statement of the context, goals, research questions, and findings of research. In the practice category posters may highlight innovative practices or projects and must include a description of the project or innovation including the goals, activity/tasks, teaching/learning experiences and outcomes if applicable. The posters will be displayed and presented at the Symposium poster session that will take place on Day 2 from 1pm to 3pm (in two one-hour sub-sessions). Materials (poster boards, tables, etc.) to assist in setting up posters and displays will be available.

Those interested in presenting a poster must submit a poster proposal indicating the poster category and including a) title, and (b) 500 word abstract (references are not included in the word count).

Submission: Please fill out this form

Submission deadline: Feb 10

Decision and notification: Feb 28

For any questions, please contact:

Dr. Joyce Mgombelo (jmgombelo[at]brocku.ca)
Dr. Marisol Santacruz-Rodiguez (marisol.santacruz[at]correounivalle.edu.co)