George Gadanidis’s research while affiliated with The University of Western Ontario and other places

Educational jurisdictions worldwide are integrating AI education in their curricula, across grades K-12, and across subject areas, with a focus on AI applications, societal implications, and AI ethics. Jurisdictions also focusing on how AI works and how AI is developed are realizing that AI relies heavily on mathematical algorithms. The jurisdictions that are advancing K-12 AI mathematics curricula to prepare students to understand and apply the mathematics concepts used by AI systems are focused on grades 11-12 courses. This paper investigates how AI mathematics curricula may be designed for younger grades. First, we take a close look at the nature of a neural network and identify the mathematics typically used. Second, we review K-12 AI curricula in Canada and internationally and note that they lack a focus on AI mathematics. Third, we offer examples of how we may engage students across grades with mathematics used in the neural networks. Last, we look at future directions of AI mathematics education and research. Neural networks are not the only approach to AI, and there is more to AI than neural networks. However, neural networks have led to impressive progress in the field of AI, such as the development of large language models like ChatGPT. For our paper, focusing on neural networks gives us a sufficient starting point for addressing the questions we raise. This paper contributes to conversations about the intersection of AI education and mathematics education, and the development and research of AI mathematics curricula and teaching and learning resources across K-12.

The authors of Integrated Education and Learning were asked how they would see the future of their field 30 years later. This chapter presents the authors’ views on cognitive semiotics as an integrated field of science in 2050, along with thinking skills (computational thinking, scientific thinking, and critical thinking); early childhood education and its importance in developing a new intelligence and social and emotional learning; the role of arts in education and preparing learners for systems thinking and thinking sustainability; future forms of education and learning (e-learning, inquiry-based learning, self-directed learning, developmental education, evidence-based education, education of information age, entrepreneurial STEM education, education for super-smart society), and the role of integrated science in education (education for equality and for controlling social and ethical issues).

We have been working for several years in classrooms in Canada and in Brazil, collaborating with teachers in developing aesthetic mathematics experiences for students, using a design model that addresses teachers’ need to cover the curriculum while also wrapping their mandated content in richer contexts that offer low floor, high ceiling access to mathematical surprise and insight. In this paper, we discuss our forays beyond project classrooms, to share what we learn with a larger education audience. We also discuss the potential of coding (computer programming) as a vehicle (1) to enable teachers and students to travel to new mathematics experiences and (2) to transport such experiences to a wider education audience. We share examples of this potential in relation to the new Ontario Grades 1–8 mathematics curriculum, which is especially interesting as it has a focus on the beauty and aesthetics of mathematics while also incorporating the use of coding in the study of algebra across Grades 1–8.KeywordsMathematics educationAesthetic experiencesCoding

Computer programming has permeated many fields as a tool to model phenomena and processes and to make new discoveries. Curricula in many jurisdictions have been revised to use computer languages across K-12, and in some cases in mathematics education. The literature suggests that while digital media in mathematics education can be used as tools that serve our purposes, they also serve to reorganize knowledge. This paper investigates the interactions among computer programming and mathematics teaching and learning. Our data sources are a) Ontario curriculum documents, b) resources developed by our team in Ontario and in Brazil, and c) our research in Ontario and Brazil. diSessa’s idea of computational literacy serves as a theoretical framework and as an analytical lens for conceptualizing how the integration of computer programming may alter the structure and experience of school mathematics.

A experimentação possibilita a exploração empírica da Matemática, valorizando diferentes formas de raciocínio e representação. Neste artigo, apresenta-se características da experimentação realizada por estudantes do nono ano do Ensino Fundamental ao se engajarem na resolução de problemas matemáticos e computacionais. O estudo se apoia nas ideias de Alan Schoenfeld, sobre a tomada de decisão em atividades orientadas por objetivos, e no construto seres-humanos-com-mídias, sobre o papel das mídias no pensamento e na produção do conhecimento. Os dados foram produzidos com duas duplas de estudantes que participaram de Sessões de Investigação, nas quais eles interagiram com simulações de construção de padrões para realizar diferentes atividades. Os registros produzidos foram gravações e diário de campo, também houve coleta da produção escrita dos estudantes. A análise ocorreu por meio de procedimentos qualitativos. Como resultados, aponta-se que a experimentação ocorreu por meio de teste e depuração de ideias, evidenciando a dinamicidade e o potencial de visualização da simulação. Houve a experimentação com elementos numéricos, que possuíam sentidos diversos, e com outros parâmetros. O processo também revelou conhecimentos dos estudantes. Em conclusão, pontua-se que a experimentação possibilitou a exploração de conceitos matemáticos empiricamente, e a mobilização de diversos recursos, evidenciando o pensamento com a simulação.

In this chapter, we follow up on the call by Borba et al. (2014) for historical research to understand technology trends in education. We conduct a historical scan of the origin of Computing in Education. We start with the Logo movement led by Papert and present an overview of the implementation of Computing in Education, including a survey of the main technological resources used and talk about robotics in educational contexts. We continue by recognizing the growth of research on Computational Thinking worldwide and present a brief history of this type of thinking, as well as its characteristics. We also describe some current research that deals with this theme in Basic Education, from Early Childhood Education to High School. With this, we seek to indicate possible trends for research on Computational Thinking in Education and Mathematical Education, enabling a reflection on the future. Therefore, in the conclusion in section 5, we provide a synthesis of what may be learned from the past and the present, so that we can look to the future of Mathematics Education with regard to the use of Computing in Basic Education.