Picture a boy in Recife, in the northeast of Brazil, in the early 1980s. He is twelve years old and in the third grade, and after school he sells coconuts in the street. A customer asks the price of one. Thirty-five, the boy says. The customer says he would like ten.
The boy pauses. Three coconuts come to 105, he says. Three more, 210. Four are still owed, so he adds three, which makes 315, and then one more, which makes 350. The answer is right. What matters is how he reached it. He did not multiply 35 by ten. He built the total out of a price he already knew, 105 for three, and added his way up to it.
The customer was a researcher. A week later, the same children were given the same kinds of problems as written sums, and most of them got the problems wrong.
I start with that boy because this season keeps asking who teaches whom, in whose language, and who decided. This week adds one more question. When a child already knows something, who sees it?
What the street showed
The study is one of the clearest pieces of research I know on the cultural context of learning, so it deserves a careful telling.
Three researchers at the Federal University of Pernambuco went looking for children who worked in the markets and on the street corners of Recife. They found five, four boys and a girl, between nine and fifteen years old, with anywhere from one to eight years of schooling. The children sold coconuts, popcorn, roasted peanuts, lemons, and watermelon by the kilo.
The researchers posed as customers. They bought things, asked for change, asked what three of something would cost, and wrote down how each child worked it out. Within the week they returned with a formal test built from the same problems and the same numbers, now presented the way teachers present them, as bare sums or as word problems from a textbook.
In the street, the children solved 98 percent of the problems correctly. Out of 63, they missed one. As word problems, they scored about 74 percent. As bare sums with no context, 37 percent.
Same children. Same numbers. Same week. The only thing that changed was whether the work happened inside a sale or on a sheet of paper.
The children were not failing mathematics. They were struggling with one particular way of writing it down. In the market they broke a quantity into pieces whose prices they knew and put the pieces back together, and the method worked almost every time. On paper they set that method aside and reached for the procedure they had been taught, lining up digits, carrying, borrowing. They could not run that procedure as reliably as the one they used every afternoon.
The obvious objection deserves a fair hearing. Five children is a small group, and street problems might simply be easier than school problems. The second point is answered by the design, because the numbers were the same. Size is answered by what came after. The Brazilian mathematician Ubiratan D’Ambrosio argued the same year that every culture builds its own mathematics for its own purposes, and that school mathematics is one of those, not the only one. He called it ethnomathematics. A few years later the Recife researchers extended their work to adults, fishermen, farmers, carpenters, and construction foremen, who solved problems of proportion and measurement at work every day and could not solve the same problems when they were written as school exercises. One study cannot settle a question this large. A pattern that holds across ages and trades is harder to dismiss.
The home as a source
The same finding turned up in the United States a few years later, in a different form, and this time the people doing the looking were the children’s own teachers.
In the early 1990s, researchers at the University of Arizona in Tucson, led by Luis Moll, worked with a group of elementary teachers on a simple idea. The teachers would not wait for a child’s knowledge to show up on a test. They would go and look for it, by visiting the homes of their own students. The project covered twenty-five households, Mexican American and Yaqui families, with about a hundred visits and interviews over one semester.
What they found they called funds of knowledge: the bodies of knowledge and skill that a household builds up over generations and needs in order to function. In those homes that meant ranching and farming, mining, construction, mechanics, trade across the border, household budgeting, and folk medicine. The parents and grandparents held it. Their children sat in classrooms every day with teachers who had never thought to ask.
Two details in that study matter for the rest of this season. The first is who did the looking. Moll and his colleagues were direct about it: the teacher, not the anthropologist, is the bridge between a family’s knowledge and the classroom. The second is what the project did not mean. It did not mean a festival day with crafts and dances. It meant the specific, working knowledge of people in a particular place, brought into how children are taught.
In Recife the researchers went to the street. In Tucson the teachers went to the home. In both places the knowledge had been there all along.
Two adults, and a village
Going to the home is one way to see what a child brings. Putting an adult in the classroom who already shares the child’s world is another. Two programs in Southeast Asia have tried it and measured it.
The first is in the far south of Thailand, where about a million people speak Patani Malay at home and send their children to schools where Thai is the language of instruction. In 2008, 42 percent of third graders in that region failed the national Thai writing test. Across the rest of the country the figure was about six percent.
That year a research institute at Mahidol University, working with the Ministry of Education, began teaching in four government schools in Patani Malay for kindergarten and first grade, with Thai added from second grade. Every early-years classroom had a teacher who spoke Patani Malay. Where a primary classroom had a Thai teacher who did not, the program placed a Patani Malay-speaking assistant beside her, so some rooms held two adults, one for each language. The Thai teachers worried at first that they were being replaced, and it took long discussion to show them they were still needed.
By 2012 the program had grown to sixteen schools. A longitudinal study by a nearby university compared its children with children in Thai-only classrooms and found them scoring 40 to 60 percent higher across subjects. Parents and grandparents who could not help with homework in Thai could help with homework in Patani Malay.
The second program is in the highlands of northeastern Cambodia, where children grow up speaking Tampuan, Kreung, Brao, Kavet, or Bunong. A national survey around 2000 found literacy there lower than anywhere else in the country. In 2002 an aid organization and the provincial education office opened community schools that taught in Tampuan and Kreung. The teachers came from the villages. They spoke the children’s languages because they were the children’s neighbors.
In 2015 Cambodia’s Ministry of Education adopted a national plan to bring those schools into the state system and to recognize community teachers as government teachers, and provincial offices have since moved many of them onto the state payroll. The model moves children to Khmer by fourth grade, and the people who built it will say that three years is too short. They call it a foot in the door.
Both programs did what the teachers in Tucson did. They found a way to see what children already knew. In Thailand that meant a second adult beside the teacher. In Cambodia it meant hiring from the village.
Who decides what counts
Underneath all of this sits a rule that almost nobody states out loud. People read the results of a test built in one context as the truth about children from another.
A written test is not a neutral measure of what a child knows. It is a record of what the people who designed it expected a child to show, in the form they expected to see it. When a teacher judges children only by those written answers, she can mistake knowledge she has not measured for knowledge the child does not have.
So who benefits? When the test is the only measure, the institutions built on it benefit, because they never have to learn what they cannot see. The children who share the test’s context benefit, because their knowledge is the kind it was built to count. When someone goes to the street, or the home, or hires from the village, the children whose knowledge finally gets counted benefit, and so does the teacher, who now has something to build on.
On this show I have called the cost the misrecognition tax. Here it is charged in a subject almost everyone assumes has no culture in it. If it is charged in arithmetic, it is charged everywhere.
A second objection should be named too. Children in Recife still need the written procedures taught in school, because those procedures open doors that street arithmetic does not. That is true, and nothing in this research says otherwise. The research does not take a political side. It takes an empirical one. What it shows is that a child who misses a written problem may hold the mathematics anyway, and that a teacher who knows this starts from a different place. The aim is to build on what the child has, and not to build over it.
Last season I spent eleven episodes showing that a teacher who shares a child’s background reads that child differently. This episode finds the same pattern in a subject most people assume has no background in it at all.
What children already know
I have argued for a long time that children do not arrive at school empty. The idea that they do, and that a teacher’s job is to fill them, is what Paulo Freire called banking education, and it is still the working assumption of a great deal of schooling. The work in this episode points the other way. Children arrive with a way of making sense of the world that was built in the context where they live, and they have already learned a great deal from the people and the work around them.
The question is never whether the knowledge is there. The question is whether the teacher in the classroom can recognize it.
That is what a match does at its best. A teacher who shares a child’s world is not automatically a better teacher. She is more likely to see what the child brought with her, and to build on it.
Would it take root?
Each episode this season ends on the same question: would it take root? It comes from Michael Sadler, who argued in 1900 that you cannot lift a practice from one country’s schools and plant it in another without understanding the conditions that let it grow.
What travels here is the method of looking. Go where children use their knowledge and find out how they learned it. Researchers did that in the street markets of Recife, teachers did it in the homes of Tucson, and educators in southern Thailand and the Cambodian highlands did it by bringing in adults who shared the children’s languages and backgrounds.
What stays local is what gets found. A coconut vendor’s arithmetic is not a Yaqui household’s knowledge of ranching, and neither one is Patani Malay. The method travels. The content never does. A teacher cannot bring a child’s knowledge in from somewhere else. It has to be found where the child is.
If you teach, here is one thing to try this week. Ask one student what they are good at outside of school, and then ask how they learned it. If you do not teach, ask a child in your life the same two questions. Then find out whether the child’s teachers know.
Next week the adult in the classroom is joined by software, and the software was built by people the child will never meet. The question this season keeps asking comes with it.
