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Generative AI as Mathland and Constructionist Frontier

Colorado Convention Center, 108/10/12

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Constructing Modern Knowledge
Constructing Modern Knowledge founder Gary Stager is co-author of “Invent To Learn – Making, Tinkering, and Engineering in the Classroom” and author of “Twenty Things to Do with a Computer + 50.” In addition to being a popular keynote speaker at some of the world’s most prestigious education conferences, Gary Stager is recognized for his pioneering leadership and outspoken edtech advocacy, especially for programming, physical computing, and learning-by-doing. Dr. Stager led professional development in the world’s first laptop schools and played a major role in the early days of online education. This will be his 35th ISTE/NECC as a presenter.

Session description

Amidst the fearmongering and hype surrounding Generative AI, its inevitability causes educators to either scream their objections into the abyss or resign themselves to passive consumption. Constructionists suggest a third option; children developing sufficient computational fluency to gain agency over the technology and face the future with personal empowerment.


Wolfram's concept of Computational Notebooks
Number theory
Probabilistic behavior

A draft of the full paper may be found at

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This work is based on decades of collaboration with pioneers in the field of educational computing, including the father of educational computing and originator of constructionism, MIT Professor Seymour Papert.

My own personal experience experimenting with popular generative AI models led me to explore ways in which children might come to understand the affordances and constraints of such environments through personal hands-on computational experiences, including computer programming.

Some of these activities are timeless projects rooted in a half-century of Logo research, others were invented or adapted for modern computing environments, while others still were developed in collaboration with notable scientist and mathematician Dr. Stephen Wolfram.

Each of the experiences described have been tested and refined in classrooms and with educators in a variety of settings across the United States, Australia, and online.

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This series of activities rushed into a couple hours of contact time with students could and should be extended to allow for students to take ownership of the project, test hypotheses, “break each other’s programs,” and share results. Even the tiny microworld of dollar words demonstrates the competence of children, the importance of computational thinking, and the need for rich programming experiences if students are to be prepared to navigate an uncertain future.

The Gossip, Plural, and Dollar Words project prompts are not old. They are timeless. While generative AI and environments like ChatGPT are embryonic, hot, and novel, they are not automatically superior to timeless tools, techniques, and processes. Imagine if a group of students could turn the gossip program into one that generated poetry and then drew illustrations or created animations based on that random poetry. The sky is the limit.

In the context of this study, Logo was an excellent environment for students to explore powerful ideas from a variety of ancient and emergent domains in their own style to grasp the potential of generative artificial intelligence. Logo has always prided itself on featuring a low threshold and high ceiling. In this case, the latest technological craze was no match for the mind of an elementary school student who armed with computational programming tools can construct knowledge in exciting and myriad ways. A comprehensive amplification of the Logo community’s legacy, contributions, and insights through the lens of 2023-24 is imperative.

Length constraints force the author to ignore the contributions of Papert and other constructionists in the development of artificial intelligence. Logo was born from seminal AI research (Papert, 1980) and its creators offered prescient insights decades about the misguided direction of the research that produced ChatGPT. Logo was based on LISP, the primary language of artificial intelligence since 1959. LISP stands for list processing, the very computing concepts developed by children in this study. While there are lessons for educators about learning to be gained from the AI community, there is much that educators can teach the AI community as well.

The convergence of list processing, linguistic tinkering, artificial intelligence fact-checking, probabilistic behavior, and symbolic programming creates a Mathland (Papert, 1980) (Evenson, 1997) that would excite Seymour Papert. Sophisticated computational tools allow children and one of the world’s leading mathematicians to “mess about” with the same math problem as naturally as they might engage in conversation, joyously and with great intensity. There are undoubtedly countless such learning adventures that could become part of the intellectual and creative diet of children.

Once again, this work reminds observers of the confidence, creativity, competence, and untapped computational power of children and their teachers.

A draft of the full paper may be found at

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Constructionists should assert their roots in AI, Piaget, and progressive education to guide practice and shape discussions of artificial intelligence in education.

Modern versions of Logo, with low threshold and high ceilings need to be developed for learners of all ages.

The constructionism community can make important contributions to educational progress by building Logo- like environments on top of the large language models and computational stacks in Wolfram Language. The Logo community can make important contributions to making such computational power more accessible with simpler syntax.

Full paper, video, ancillary materials, and sample code will be available to interested educators.

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Burns, M., & Weston, M. (1991). The $1.00 Word Riddle Book. Math Solutions.
Evenson, L. (1997). SUNDAY INTERVIEW -- Seymour Papert / Computers In the Lives of Our Children / An MIT mathematician and philosopher is
exploring how technology can educate the next generation -- and their parents. San Francisco Chronicle.
Goldenberg, E. P., & Feurzeig, W. (1987). Exploring language with Logo. Mit Press.
Papert, S. (1980). Mindstorms: children, computers, and powerful ideas. Basic Books.
Papert, S. (1991). Perestroika and Epistemological Politics. In I. Harel & S. Papert (Eds.), Constructionism (pp. 13-28). Ablex Publishing Corporation. Papert, S. (2000). Papert talks about middle school mathematics education.
Papert, S. (2006). Seymour Papert Keynote Lecture at ICMI 17 Conference in Hanoi, Viet Nam.
Resnick, M. (1993). Logo Overnight.
Wolfram, S. (2016a). How to Teach Computational Thinking.
Wolfram, S. (2016b). How to teach computational thinking. Stephen Wolfram Blog.
Wolfram, S. (2017). What Is a Computational Essay?
Wolfram, S. (2023a). ChatGPT Gets Its “Wolfram Superpowers”!
Wolfram, S. (2023b). Instant Plugins for ChatGPT: Introducing the Wolfram ChatGPT Plugin Kit.

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Session specifications

Artificial Intelligence
Grade level:
Curriculum/district specialists, Teachers, Technology coordinators/facilitators
Attendee devices:
Devices useful
Attendee device specification:
Laptop: Chromebook, Mac, PC
Participant accounts, software and other materials:
Web access
Subject area:
Computer science, STEM/STEAM
ISTE Standards:
For Educators:
  • Set professional learning goals to explore and apply pedagogical approaches made possible by technology and reflect on their effectiveness.
  • Explore and apply instructional design principles to create innovative digital learning environments that engage and support learning.
For Students:
Computational Thinker
  • Students formulate problem definitions suited for technology-assisted methods such as data analysis, abstract models and algorithmic thinking in exploring and finding solutions.