*This post originally appeared on my old blog site in October 2012. I am reposting it because someone recently suggested to me that they found it useful. I have avoided the urge to edit it.*

I was thinking recently about John Searle’s “Chinese Room,” concept and whether it has anything to offer the educator. To understand the Chinese Room you first have to be familiar with the “Turing Test”. This was posited in the 1950s in a series of papers by the English mathematician and scientist, Alan Turing, as a test for whether a computer can truly gain artificial intelligence. Interestingly, Turing was fed up with thinking about whether machines can be intelligent from a definitional perspective; what is a machine? what is intelligence? etc. Instead, he proposed a material test to see whether a computer can use it’s intelligence to do what a human can do. There are several forms of the test but it boils down to a person sending typed questions to the machine and receiving typed responses. If the person sending the questions is convinced that the responses are coming from a real human being, then the machine passes the test.

Any computer that passes the Turing test must be running a computer programme, and a computer program is simply an algorithm; a set of, “If… then…” statements. Such a programme would, in reality, be extremely complex and the difficulty of simulating the “common sense” of a real human respondent would be vast – read, “Everything is Obvious,” by Duncan J Watts for a fascinating account of the issues. However, in principal, the computer programme could be written out in a book.

Now, imagine that we have written down the computer programme for passing a Chinese language Turing test in a book. In other words, this programme would convince Chinese native speakers (and writers) that they are conversing with a real Chinese person. Imagine further that the programme is written out in English. We give the book to John Searle and place him in a closed room. This is after the argument of John Searle’s 1980 paper.

Native Chinese speakers then write down their questions and place them in a slot in the wall of the room; something like a letterbox. Searle takes the questions, follows the instructions in the book and writes a response. He then places this back in the slot for his questioners to read. His questioners think that they are conversing with a real Chinese person, yet Searle cannot speak or write a word of Chinese; he is only following a set of instructions.

Searle makes the point that he does not understand Chinese; he is simply appearing to. In other words, he is simulating intelligence without being conscious of what he is actually doing. The argument can be extended to suggest that computers running complex programmes that pass the Turing test are merely doing the same; they are mindlessly executing a series of instructions without actually achieving anything akin to consciousness.

There are many objections to Searle’s argument. The one that I am most fond of is the idea that, although Searle may not understand Chinese, the Searle-book-room system does understand Chinese. Peculiar.

Let’s now extend this. Many students learning mathematics are trying to understand, and be conscious of, operating different sets of rules and algorithms. It is possible to answer mathematical questions by simply following a set of rules. You may also answer them by having an insight about how the problem relates to other problems and facts that you know. This latter description would be more like what a mathematics teacher would describe as truly understanding the problem although, as many have pointed out, there continue to be many maths students and teachers who see memorisation of the relevant algorithm as understanding.

It is as if the learner is in a Chinese room. Unlike Searle’s Chinese room, we are unlikely to get perfect answers to our questions; our respondent is, after all, still learning. But how, as educators, are we to tell if there really is a consciousness in there, understanding our instructions and perceiving the problem or, instead, a person who doesn’t understand Chinese but is simply following the rules? This is a key question.

Let me put it another way: Let’s Assume that there really is a level of conscious, relational understanding which it is desirable for mathematics students to achieve. Assuming that we want to, then how may we measure this? Perhaps we should require students to articulate their understanding. However, any such assessment will be measuring communication skills as much as mathematical insight and can we rule out the possibility of students simply learning what to say? Some have suggested that they key to demonstrating understanding is the concept of “transfer”; the ability to apply your learning in new and different contexts. However, what if you understand the maths but not the context? Many contexts are surprisingly culturally specific and the description of the context itself can pose a literacy challenge. What if the number of potential contexts is limited or have the same form? Could students simply learn the contexts? Does a student not simply need a more complex algorithm in order to get by?

As mentioned in my previous post, Daniel Willingham makes the point that something that we might consider as understanding may be present, but a student is not yet able to transfer this to new contexts; their understanding is locked to the context in which it was learnt, but it is still understanding. Willingham describes this as inflexible knowledge and distinguishes it from rote knowledge which is knowledge in the absence of meaning; in the absence of understanding.

Ultimately, perhaps, we will be able to peer inside the Chinese room. Brain imaging studies currently verge on the pseudo-scientific, but there is evidence about what different forms of cognition might look like. However, I suspect that it will be some time yet before we are routinely scanning our students’ brains in order to figure out whether they just “got” how to solve simultaneous equations.

So what should we do? I suspect that high stakes maths tests and exams will, by and large, continue to assess the products of understanding – the ability to solve certain problems – rather than the understanding itself. They are assessing a latent characteristic by looking for a likely proxy and, in many ways, why shouldn’t they? It is, after all, the ability to do maths that is useful so should our tests not be agnostic on the Chinese room argument?

Mathematics teachers should continue to seek understanding. However, this will continue to be ill defined. Unlike writing or painting, where the product effectively is the desired learning, mathematical understanding will remain an elusive concept. That box in the curriculum documentation that asks for a description of the understanding will either need to be left blank, filled with a proxy in the form of the type of question that this particular understanding will allow a student to be able to answer, or simply fudged.

And the best maths teachers? They will be talking to their students, gaining feedback, triangulating this feedback and using what are, effectively, quite sophisticated versions of the Turing test to try to peer inside their students’ brains. And largely, they will be successful.

Reblogged this on The Echo Chamber.

Greg,

I don’t understand the issue here. Mathematics is a subject that always offers another more complex question to apply to as a test of understanding. Whatever problems a student has memorized there is another one available. Also these can all be culturally context free. For example you don’t have to go far from basic integer arithmetic into number theory to generate all sorts of interesting questions that will test the understanding of multiplication, addition and division of integers and rational numbers. The people creating math competitions go out of their way to create these sorts of problems. Sure the subjects under test will apply memorized techniques but the problems are such that only by understanding them can someone decide which technique to apply and do well when time constrained.

Sure there is still the Chinese room aspect but in a test of a Turing test you want multiple testers to agree and I suspect if you gave students enough competition math problems and examined their responses there would be good agreement by the people who created the problems on which answers were by students who understand the mathematics.

Stan

I personally try not to get at all hung up about teaching understanding with Mathematics. Very few people need to understand Mathematics at all well in order to do their jobs or solve problems. What they need is basic skills that can be relied on, so that later learning can be built on that.

I feel once a student has learned how to do a skill sufficiently automatically that understanding will follow from that, not

vice versa.I learned to drive a manual car. I didn’t “understand” what I was doing. After learning my understanding of how it works came naturally.

To me the Chinese room problem asks the wrong question. It’s not “is the room thinking?” but “how do I write the book?”.