James Pietsch
At an education conference ten years ago, I recall the presenter recommending that education should be focused on that which is ‘ungoogleable’. I don’t think that is actually a word, but the sentiment was evident to all in attendance. In the age of Google, where you could search for literally anything and receive an answer in a nanosecond, what value do we place on knowledge, facts and figures? Does anyone really need to remember quotes, or dates, or formulae anymore when all of these, and so much more, are accessible online?
How far we have come in ten years. With the rise of large language model AI tools, not only can we find facts and figures, but we can also generate essays, sermons, speeches for specific occasions, lesson plans, cooking recipes, analyses of literature, reflections on popular culture—in fact, almost anything that one might have written in the past can now be generated in an instant by a machine. Does anyone need to learn to write anymore?
Looking further back, I can recall when I was in Year 8 and my mathematics teacher was reluctantly introducing calculators into the classroom and we were asking similar questions. Does anyone need to know their times tables anymore?
The answer to all these questions, of course, is yes. Machines can do incredible things, but they do so without the reasoning capabilities of a human being. They do so without contextual knowledge that often directs our reasoning and leads us down different paths towards the solutions to contextually bound problems. It is why a computer can, at times, provide answers that are clearly nonsensical, but have no awareness that this is so. The iPhone in my car is an incredibly complex machine. And yet, whenever it plays the song ‘Hey Jude’ it states, for some reason that I cannot fathom, that ‘Hey Jude’ is performed by ‘Artist Unknown’. For a smart phone, it can, at times, be incredibly dumb.
And yet, we find ourselves at a point in history that some might describe as inflexional, revolutionary or transformative. The degree to which computers can interact with us is almost indistinguishable from the way that humans do—the Turing Test is passed over and over again when we find chatbots online that we cannot distinguish from human interlocutors. But AI—genuine artificial intelligence—is, and always will be, a chimera. There will always be a fundamental category distinction that separates the human mind from the programmed workings of a computer. While some may be attracted to Dennett’s functionalist accounts of mental activity which propose that our brains are syntactical and semantic machines in a way that is functionally parallel to the operations of a computer, there remains a fundamental distinction between the way that human beings comprehend and understand the world, and the way that computers do.
Francis Su’s recent book The Mathematics of Human Flourishing (Yale University Press, 2021) outlines the very human nature of mathematical activity and how engaging in mathematical thinking contributes to human flourishing. Mathematics gives us opportunities to imagine new possibilities, and to engage with, and appreciate more fully, the transcendent beauty that we find within the cosmos, as well as the beauty that we find within an elegant proof or mathematical relation. Mathematics helps us to make meaning, to find order within apparent chaos, to appreciate the transcendent unity of all that can be said to exist. When doing mathematics, we can be playful with ideas, exploring new ways of understanding both the material and the non-material. In each of these ways, and in so many more, we are engaged in activities that are uniquely human—activities that cannot be performed by a calculator or any other machine, no matter how powerful it is, or how cleverly programmed it may be.
Francis spoke at Inaburra School recently, suggesting that in our current climate of both wonder and fear regarding the role of AI in our culture (and in our schools), we need to lean in to our humanity, building our capacity, and the capacity of our students, to be human. To ask questions about the world around us; to have empathy for those who suffer; to engage with the good, the beautiful and the true; to live at the intersection of the transcendent and the immanent whereby our hopes, dreams and aspirations emerge from our experience of the material interacting with the immaterial. And finally, to be intellectually curious, always seeking to understand our world in all its beauty and complexity.
What we learn in the mathematics classroom is so much more than the application of formulae or techniques to solve problems. We learn how to be human. We learn what it is like to be playful with ideas, to imagine new possibilities, to seek out truth and experience struggle. We learn how to persevere in the face of challenges, how to seek justice, how to learn and teach others. Francis Su argues that the calculations which can be performed by a calculator are not what mathematics is all about. In the context of mathematical activity, we learn how to learn, and we learn how to grow. In the same way, education is not about learning the information which we can glean from Google. It, too, is about learning how to learn and learning how to grow.
In mathematics, as in every other subject area within the curriculum, we also find ourselves drawn into a world of truth and beauty, of abstraction, patterns and relations. This capacity for abstraction—for asking questions that go beyond the data, that go beyond the given—is uniquely human. Our engagement with the material leads us to reflect on the immaterial and ask questions about the deeper nature of reality that we are learning about in a way that computers never will. Simone Weil, a Christian mystic and philosopher of the twentieth century, described how the study of mathematics reveals the transcendent to us. As a teacher, it would be fair to say that she had some unusual pedagogical practices. Geometry, for Weil, was a key area of study in mathematics, in which she encouraged students to wait for the underlying structures to reveal themselves in the classroom. In an attitude of prayer or meditation, Weil would ask her students to sit in silence and contemplate the geometrical as the first step towards experiencing the transcendental. But Weil’s emphasis on assisting students to see the unseen remains a key focus for educators who are focused on students becoming more fully human through their engagement in educational activities. Today, we face the same challenge of how we can be actively engaged with our students in seeing the unseen, in peeling back the veneer of the material to reveal the underlying immaterial reality within which we find truth and beauty and the nature of God, in whom all transcendent qualities have their origin and terminus.
Education is one aspect of our personal journey towards becoming fully human, as God intended. We are more than calculators and more than computers. We are creatures with the unique capacity to be in relationship with the creator, living in the intersectional space between this world and the next world, between the immanent and the transcendent, the finite and the infinite, the world that is passing away and the eternal world that is to come. No other creature, indeed no other creation, created either by human hands or by God’s, resides within this space. As Christian educators, our goal may be understood as providing an ongoing invitation to our students to locate themselves within this same space in which humanity and the divine come together in such a way as to make God known to all of creation.
Dr James Pietsch is the Principal of Inaburra School, Sydney. After studying psychology and mathematics, James undertook a PhD in education at Sydney University, focusing on sociocultural theories of mathematics education. He is married to Margie.
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