How one year of study can be equal to six
The famous experiment with teaching mathematics, which forces us to reconsider our views on the ratio of the quantity and quality of education.
In 1929, Frank Boynton, head of schools in Ithaca, New York, sent his educational colleagues an article on curriculum reform. Her ending sounded almost like a challenge. “We are constantly discussing what subjects should be added to the school schedule,” Boynton wrote. - But a child cannot spend all his time studying. What, in this case, needs to be removed from it? "
“Mathematician,” a month later Luis Benezet, who at the time was head of schools in Manchester (New Hampshire), answered him confidently. In his opinion, mathematics in elementary grades only makes schoolchildren stupid.
"I have noticed more than once that the only result of early learning mathematics is boredom and a real lulling of children's ability to reason"
- Louis Paul Benezet
All basic mathematical skills can be mastered in just one or two years, and before that arithmetic must be mastered through games, examples and other activities - less abstract and closer to children's thinking. “Why would a ten-year-old child know how to divide in a column? All arithmetic can be postponed until the seventh year of schooling - then any normal student will catch up with this program in a couple of years."
By this time, Benezet had already run several schools in Manchester for 5 years and earned himself not very good fame: his parents and teachers criticized him for the fact that he expelled almost all arithmetic from the school curriculum of the first two and a half years of study.
He was convinced that the ability for mathematical abstract thinking is formed closer to adolescence. Before that, teaching a child arithmetic can only be done by coaching.
Coaching discourages children from dealing with numbers and dulls their ability to think independently. The child can memorize the rules, but will not learn to understand what their meaning is. Mathematics should enter a child's life gradually, not through cramming, but through meaningful activity.
Benezet proposed to revise the classical teaching scheme, built around the three "R" (reading, writing and counting - reading, writing and arithmetic). The place of arithmetic should be taken by speaking, reciting.
Benezet was depressed that even the smartest schoolchildren did not know how to reason and correctly formulate their thoughts. As for arithmetic, they can learn the rules, but they do not know elementary mathematical logic (for example, they cannot explain why out of two fractions with the same numerator, the larger one will be the one with the lower denominator).
In the fall of 1929 Benezet set about organizing his experiment. He chose five grades (from the third to the fifth year of study), whose teachers agreed to his demands. He deliberately chose schools in which children from disadvantaged families studied: their parents, as a rule, were immigrants and did not receive a good education.
If such an experiment began in a more prestigious school, a scandal would break out.
As a compromise, arithmetic classes were postponed not until the seventh, but until the sixth year of study. Prior to that, students learned mathematics through games and practical activities in which they had to operate with dates, distances, time or money (for example, giving each other change, or calculating the time it would take to get from one place to another).
The hours that were previously devoted to mathematics were now occupied by oral classes, in which students shared their impressions of the books and films they had read, discussed recent incidents and shared some personal stories. Children, who had been gloomily silent before and could not connect even two words, could now enthusiastically talk about what was interesting to them.
“Just one visit to such a lesson - and you could be inspired. The classrooms seemed to be imbued with a joyful and free mood. [...] If earlier the children sullenly pored over the multiplication tables, now they really began to enjoy the lessons "
The results were already visible after 8 months. When researchers came to fourth-graders who studied in the traditional curriculum and asked them what they were reading now, the only reaction that could be counted on was confusion and apathy (“in one class I did not find a single child who would confess in adherence to the sin of reading, ”wrote Benezet). Now everything was different: a whole lesson would not have been enough for everyone to share their thoughts and impressions.
Mathematics was even more interesting. In 1936, the experiment ended. Benezet detailed his findings in a three-part article that was published in the Journal of the National Education Association. And they deserve to remember this now, several decades later.
By the sixth grade, children from the experimental group performed worse on arithmetic tests than schoolchildren from the control group, who continued to study according to the standard curriculum. But just a year later, they were already equal in their results. Moreover, some tasks were much easier for them.
Benezet showed that the initial mathematical skills that children learn in practice are easily transformed into a real mastery of mathematical logic.
Children who didn't spend six years on math caught up with their peers in just one year.
This becomes even more surprising when you consider that the students from the experimental group of Benezet came from not the most prosperous families and could hardly count on help with their studies outside the classroom. Children from marginalized social groups tend to do the worst because education has little or no value in the environment in which they grow up. In Benezet's experiment, the opposite was true.
When Benezet checked the results of his research, he gave students problems like the following:
The distance from Boston to Portland by water is 120 kilometers. Three steamboats left Boston for Portland at the same time. The first reached its destination in 10 hours, the second in 12, and the third in 15. How long did it take for all three ships to arrive in Portland?
It may seem strange, but in the 9th grade, only 6 out of 29 students successfully coped with this task. And children who studied under the Benezet system always gave the correct answer even in the second grade.
Benezet does not provide examples of wrong answers in his publications, but we can imagine what they were if we turn to the 1988 study. Students in the first and second grades were asked to find a solution for the following types of problems:
There are 26 sheep and 10 rams on the ship. How old is the captain of the ship?
67 out of 97 pupils "solved" the problem by simply adding 26 and 10. The children learned that mathematics is when you need to do something with numbers, but the usual school curriculum did not make them understand what was the point in these actions. And the saddest thing is that this trend is often only intensifying towards the older grades.
If Benezet's experiment was carried out correctly (and there is almost no doubt about its main results), then it tells us a lot about what is wrong with the formal school system. It is difficult to resist the temptation and not to extend the conclusions that he received in the case of mathematics, and other subjects.
As Bertrand Russell wrote, people are not born stupid. They are born ignorant, and education makes them stupid.
This short episode from the history of experimental pedagogy once again tells us how you can rebuild the learning system so that it matches the real abilities of each child; so that education does not come down to training, but turns into the education of thinking.
But for all these problems, many solutions have already been proposed. The problem, as always, is to use them.
