Words are funny things. They purport to clarity, to providing us with a better sense of understanding. They allow us to formulate complicated thoughts, feelings, ideas, and transfer those to another person. Of all the things that make humans a distinct group in the animal world – the creation and use of tools, the control of fire, strategic planning on extended time scales – the ability to use words to communicate complex and nuanced thoughts is probably the most essential.
And yet words fail us all the time. This is in part because they are in no way perfect. Words are variable and shaded with all kinds of meanings. Communication requires both the speaker and the audience to have an overlapping understanding of what is being said. At a simple level this requires them to speak the same language. Because I don’t know Mandarin, words spoken in that language communicate nothing to me and are not distinctly different than the various chirps and pops of dolphins. But even within the same language and the same dialect, the meanings of the words we use and the thoughts they are supposed to transfer from one to another are never as clear as we generally assume. Maybe the intonation doesn’t match or maybe one person doesn’t understand the full implications of what another is saying. Sometimes it’s just a matter of a difference in the images that are brought to people’s minds. Communication is never a perfect transfer of thought from one brain to another. Something always gets altered in translation.
It’s quite possible you saw the Cheryl-Albert-Bernard logic problem on the internet this past week. Ava printed it out and brought it home for me to try. The basic premise of the challenge is that Albert and Bernard don’t know Cheryl’s birthday, and instead of telling them she has them guess from among ten possible dates. Then she tells Albert the month and Bernard the day. After a couple of comments from each the two boys figure out the answer and you are supposed to be able to determine what it is by using their comments and making logical deductions.
This problem came from a standardized test used in Singapore, and I think it went viral because while it is a fun game there is also something fundamentally unclear about it. The absence of clarity is subtle and I think people shared it with one another because they weren’t sure whether it was them or a fundamental problem with the challenge itself.
The solution to the problem hinges on Albert’s first comment which is “I don’t know the answer and I know that Bernard doesn’t either.” This is supposed to tell you that Albert knows that he doesn’t have enough information to answer the problem and that he knows that Bernard doesn’t have enough either. Recognizing this sets the logical deductions in motion. However, when I read the problem, I imagined the three people having a conversation. In this conversation, Albert learns that Bernard doesn’t know the answer either, however one cannot make the same logical deductions from that situation that you can if you understand the statement to mean that Albert knows without talking to Bernard that Bernard doesn’t know the answer either. It is a subtle difference and not on the face of things particularly problematic. But, my inability to correctly comprehend the question led me to not having any chance of answering it correctly. It wasn’t that I couldn’t do the logical steps, it was that I couldn’t see the problem in the way it was intended to be seen. In my case, there was a disjuncture in communication. The speaker and the audience were not hearing the same thing.
Pip encountered a similar conceptual difficulty this week with some of his homework. The teacher gave him a simple measurement sheet where he was directed to use the ruler on the page to indicate the length of different lines to the nearest ¼ of an inch. Now Pip’s smart and studious. He listens in class and he takes care when he does his work. And he got five out of the eight measures wrong.
I know this because Pip’s teacher sends home all student work on Fridays and permits them to correct any errors and resubmit the work on Monday. Pip usually comes in and plows through this in a matter of five minutes, but with this sheet he was having lots of trouble. He just couldn’t figure out why he had gotten so many of these problems wrong. He called me for help and when I came over to look at things I could see what was wrong, but I couldn’t figure out why he had answered the questions the way he did. For example, for one line that was clearly 2 ½ inches long, he had written 2 ¼. On another that was 5 inches long, he’d written 4 ¾. At first I thought he was reading the ruler wrong and so I just told him to look at them again. When he came back just as confused as before, I went through every problem to see if I could determine how he was approaching them. It turns out that the only two he got right were lines that measured 1 ¾ and 3 ¼. It also turned out that all of his answers contained either ¼ or ¾. Pip had taken the instructions to mean find the measurement to the nearest ruler mark that contained a 4 in the denominator (i.e. ¼ or ¾), so he had rounded down all the measurements to reach one of those two choices.
After I realized this it took a surprisingly long time to explain to him that the nearest quarter of an inch means every quarter inch increment including whole number marks and ½ inch marks. It was something that had not clicked intuitively in his mind and thus was something that he had a tricky time fitting together. For him ½ inch was ½ inch, and he had to work to see it as being 2/4 inch (Interestingly, my word processor has the same problem. It automatically shifts ¼ and ¾ to fraction forms but leaves 2/4 unchanged).
The point of this is that while Pip could very easily perform the skill, the language of the problem didn’t fit with what he knew. Now whether that’s his responsibility to learn or the test maker’s responsibility to clarify is always going to be a negotiable thing, but it is a reminder to me of one of the constants of parenting – and human interaction in general – words are not neutral. Words are not standard. They have meaning because we have each learned them in certain ways and those ways are all unique in subtle and unknowable ways.
It also reminds me that when you think the problem is with someone else’s understanding, the problem probably also has something to do with you.