True Story 10.16
Getting the correct answer but not knowing how
The setting for this story
For two years, John Gay and Michael Cole worked among the Kpelle people of Liberia, carrying out research aimed at improving the teaching of mathematics in Africa. To better grasp the patterns of Kpelle thinking, they presented a mental challenge to unschooled Kpelle adults.
A story of misaligned minds20
John and Michael hoped to gain insight into the Kpelles’ ability to recognize a repeating pattern, use it to mentally construct a generalization or rule, then apply that rule to interpret future events.*
Two pieces of colored cloth were placed before an adult; one piece comprised red and green cloth, the other comprised red and yellow cloth. The adult was asked to select one of the two pieces, then told that his choice was correct or incorrect. This process kept on being repeated, with one difference: One of the two pieces was always red and green; the other was red and any other color but green. As the process was repeated, the Kpelle adult gradually came to realize that the “correct” piece was red and green.
The process of placing cloth pieces before an adult ten times in a row was a “trial.” Trials continued until, within the same trial, the adult correctly chose the red and green option all ten times. On average, adults began their run of ten correct choices after the fourteenth trial.
Then the adult was asked to describe what had enabled him to repeatedly choose correctly. Rarely did an answer cite a general rule. Some simply described the correct pair. Others replied, “God told me,” “I know it by my sense,” and “I can see it.” Chiefs and elders found the question insulting.
John and Michael’s question
What change in these adults’ minds finally enabled them to realize what the “correct” choice is?
Critique of story 10.16
This research occurred during the 1960s, when the daily lives of unschooled Kpelle adults rarely included any event or task that required them to think using abstract categories (e.g., color) or generalized rules (e.g., only A and B is correct). Their day-to-day experience presented them with complete, undivided wholes – persons, places, things – within familiar backgrounds and contexts.
Performing well on this experiment required the subject to become aware of, and to mentally distinguish, an abstract quality (color) from the complete, undivided wholes (pieces of cloth) that were being placed before them. In other words, to perform well, each subject needed to be able to “decontextualize” colors, an abstract quality, from a succession of tangible, real-life, objects. It is unlikely that unschooled Kpelle adults had previously encountered a need for such mental gymnastics.
And that wasn’t all they needed to become aware of. They also had to recognize that a certain combination of colors (red and green) was always being specified “correct.” Finally, they needed to construct – consciously or subconsciously – a general rule (“only red-and-green is correct”) and apply it to every future choice.
Kpelle children who had been attending the local school – an import from the industrialized West – figured out the general rule after just a few trials. Schooling had introduced them to a key foundation of scientific thought: the mental ability to separate from complete wholes (e.g., cloth), and to manipulate as abstract concepts, qualities like size, shape, texture and, in this case, color.
John and Michael set out to discover what change – what “ah-ha” – in the adults’ minds enabled them “to realize that” the correct choice was red and green. They did not find a good answer. All we can say with moderate confidence is that it is not because the adults consciously recognized and usefully applied a general rule (an abstraction). Subconsciously? Your guess is as good as anyone else’s.
I wonder whether there’s a similarity between how these Kpelle adults learned the correct answer and how, in story 10.04, the 50-year-old native of Somalia, Abdiya, was able to learn German to fluency. What do you think?
For thought
After two years of fieldwork, John Gay and Michael Cole definitely did form several conclusions about the patterns of Kpelle thinking. Here’s my paraphrase of a few passages from their book.21
For the Kpelle, knowledge is the ability to demonstrate one’s mastery of Kpelle ways. Truth is the conformity of one’s behavior to Kpelle ways. All values are rooted in the past, maintained by the elders’ authority. New information holds no interest; what is unknown will never be known. What is known is good for our lives. Other people’s way of life is good for them. We’re OK; they’re OK.
Children are fashioned in the mold of their ancestors. But children who attend school and acquire new values and ideas are regarded as emigrants. They have joined a new tribe. They have nothing useful to tell their parents. Educated children are OK; their parents are OK.
Related stories
Story 10.03 concerns the challenges of teaching what “1” means to youngsters who haven’t learned to think analytically. Story 10.13 is also based on Gay and Cole’s Kpelle research.
* Consider the four-group sequence 1.2.3.4, 2.2.3.4, 3.2.3.4, 4.2.3.4. The generalization or rule is that, with each repetition of the group, the first digit increases by one. How would that rule apply to four groups starting with 6.7.8.9? This is an example of abstracting, which is discussed in the note at the bottom of Story 10.13.
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Endnotes:
20 Gay & Cole, 81–82, 84.
21 Gay & Cole, 89–90.
Full citations are available at misalignedminds.info/References.