This is a *perfect* parable for the way math has been taught for decades:That's a really interesting use of the Chinese Room example (it is well known as such to philosophers). http://plato.stanford.edu/entries/chinese-room/
"A person lives inside a room that has baskets of tokens of Chinese characters. The person does not know Chinese. However, the person does have a book of rules for transforming strings of Chinese characters into other strings of Chinese characters. People on the outside write sentences in Chinese on paper and pass them into the room. The person inside the room consults the book of rules and sends back strings of characters that are different from the ones that were passed in. The people on the outside know Chinese. When they write a string to pass into the room, they understand it as a question. When the person inside sends back another string, the people on the outside understand it as an answer, and because the rules are cleverly written, the answers are usually correct. By following the rules, the person in the room produces expressions that other people can interpret as the answers to questions that they wrote and passed into the room. But the person in the room does not understand the meanings of either the questions or the answer." (From Searle (1980) via Greeno (1997) via dy/dan today - http://blog.mrmeyer.com/).
It's encouraging to see recent trends in math instruction trying to move beyond the "Old Way" - that hallowed, relentless focus on the process of performing calculations without ever helping students see what the calculations *mean*. In addition to being able to calculate, people need to actually *understand* math. If they don't understand it, the only times in their lives that math will ever be useful to them is when they're confronted by a textbook.
It's a total crime when you think about: 10 or so *years* studying the subject, and all that many people have to show for it are the most utterly banal applications of addition and multiplication. Maybe some subtraction. (Division is way too complicated.) Certainly nothing taught after elementary school.
I continue to be completely amazed - absolutely stunned - at how vehemently many in Utah and around the country are fighting against educators' efforts to help students learn math in a way that teaches them both to calculate *and* to understand. Why don't they want them to understand? Why do they want to sentence their child to life in the Chinese Room?
I have to add, too, that I'm increasingly confused by the popular fetish with the algebra, trigonometry, and calculus pathway. When's the last time you read a news story involving polynomials? Or heard a piece on the radio involving the law of cosines? Never. But when was the last time you were manipulated by a media conglomerate, or a government agency, or a news outlet, or a campaign ad because you don't understand statistics? Sadly, it was probably earlier today. Normal people have infinitely more opportunities to use the concepts taught in statistics in their lives than they do the concepts taught in the traditional math sequence. How about some love for statistics?
The example was originally intended as a response to the 'Turing Test' model for evaluating artificial intelligence. http://plato.stanford.edu/entries/turing-test/ The idea of the Turning Test is that a machine could be considered intelligent if its responses are sufficient to fool a human interlocutor.
One response to the example suggests that a machine could not actually succeed in responding without actually understanding. It would need to form models and comprehend principles in order to anticipate the variety of comments and questions thrown at it.
Another, related, response is that the example appears to an intuition that has not itself been validated. If we did not believe a priori that the combination of person and machine did not understand, would the example convince us that they don't? (This is sometimes called the 'systems' response.)
My own take is that the example, if it succeeds, succeeds because of oversimplification. Our interactions are not in fact composed entirely of conversations in words. If the understanding of the Chinese Room is inadequate, it is because cognition thought of as interaction via text is inadequate.
The same sort of responses could be offered with respect to testing. First, the student could not really succeed in the test without actually understanding (call that the 'Brainbench' example. Second, the capacity to respond to thee tests is itself a form of understanding (call that the cognitivist response). Third, appropriate testing would go well beyond text-based questions and answers (call that the recognition response).
I would also add that despite the weaknesses of the algebra, trigonometry, and calculus pathway, the suggestion that people learn statistics instead is not a viable alternative, for the primary reason that it is not an actual alternative.
Once you get into the study of anything beyond simply statistics, you are going to be involved in the study of algebra, trigonometry, and calculus. Statistics is the study of change, and change can come in pretty much any mathematical form. http://www.downes.ca/post/53662