You are in a closed room. A passer by slips a sheet under the door containing a list of questions written in Chinese. The bad news is that you do not understand a word of Chinese (only you know this). The good news: in the room, there is an instructional manual written in English that guides you, step by step, to convert the given characters to a set of new ones that correspond to the answers. The passer by receives your answers and is convinced you understand Chinese.
This is a slight embellishment of John Searle’s aptly named ‘Chinese Room’ thought experiment. Searle was probing the nature of machine intelligence. His experiment illustrates that intelligence is not achieved simply through formal computation on symbols (what machines are built for). Thus the famed Turing test for computers is flawed because it reduces intelligence to a purely syntactic form.
You were able to manipulate Chinese, to the extent of answering questions in the same language, but you could not assign meaning or context to those pesky symbols. At no moment did you possess even an iota of understanding of Chinese. The mere appearance of intelligence is inadequate.
Searle did not need a thought experiment to make his point. The ‘Chinese room’ scenario is the reality of maths classrooms across the world.
Most fifth graders can perform long division. It is mandated by curriculum standards, drilled by teachers and lathered across textbook pages. Long division is presented as a fixed sequence of computations. It is irrefutable; something to be learned but not understood, memorised in the name of fluency. Students play the role of symbol pushers as they employ ‘bus stop methods’ and other such tricks to rattle off singularly focused long division problems. Yet they can make no meaningful sense of why their methods work.
Students’ understanding of mathematical concepts sags under the hefty weight of mindless procedure.
I have taken aim at long division, but you can substitute it for virtually any curriculum topic, as well as other domains. Searle’s experiment will dredge up memories for those who, like me, learned to read, write and recite Arabic with minimal comprehension. This bizarre state of knowledge is a result of the drill-based pedagogy that governs many well-intended madrassas in the western world. I can play with Arabic, yet I do not understand it.
Back in the realm of mathematics, algorithms and procedures are not the culprits of symbol pushing (if you have an affinity to these objects you may even consider them victims). That dubious accolade belongs to the folks who deem it fit to force-feed concepts without understanding.
Knowledge of mathematical procedures must be nurtured alongside conceptual understanding, not least because they reinforce one another.
Mathematical knowledge of any kind is a misnomer if understanding is absent. It places students back in the Chinese room, blindly manipulating syntax and successfully answering questions with the aid of prescriptive instructional materials. Pushing symbols gives the appearance of intelligence; it makes students feel smart. They graduate from school armed with the tools prescribed by maths education. They can do mathematics but they do not truly know it. And they will soon arrive at the tragic realisation that to be educated is not to exhibit intelligence.
Searle’s thought experiment is not without irony. He modeled human behaviours to shine a light on the nature of intelligence which, according to his conclusions, is elusive to computers. I wonder if Searle reflected on the state of maths education. He might then see that we are educating humans away from the mindful elements of intelligence and towards the syntactic leanings of computers.
The Turing test may be meaningful after all, but only because we have cheapened human intelligence to a computational form.
The modern day whizz is he who can calculate with terrifying speed and accuracy. She who can imitate the computing power of machines. And therein is another twist of ironical fate. The term ‘computer’ has its origins in the nineteenth century, when it referred to humans whose job was to, well, compute. That was our calling card. But the silicon computers of today render those jobs moot.
The procedural focus of mathematics education regresses us back to the core competences that differentiated humans in the nineteenth century. This view of intelligence is woefully unfit for the machine age. Only by reconceiving our distinctly human capabilities will we give students the mathematics education they need and deserve in today’s silicon-powered world.
We need to escape the fallacies of the Chinese room.
I am a research mathematician turned educator working at the nexus of mathematics, education and innovation.
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