Math Instruction versus Natural Math: Benezet’s Example

Louis Benezet, natural math,

1930’s classroom (forestpark4.wikidot.com)

Children are intrinsically eager and able to learn. If we step back from our limiting preconceptions about education, we discover learning flourishes when we facilitate it rather than try to advance it through force, intimidation, and coercion.

Over 85 years ago a pioneering educator proved that delaying formal instruction, in this case of mathematics, benefits children in wonderfully unexpected ways. Louis P. Benezet, superintendent of the Manchester, New Hampshire schools, advocated the postponement of systematic instruction in math until after sixth grade. Benezet wrote,

I feel that it is all nonsense to take eight years to get children thru the ordinary arithmetic assignment of the elementary schools. What possible needs has a ten-year-old child for knowledge of long division? The whole subject of arithmetic could be postponed until the seventh year of school, and it could be mastered in two years’ study by any normal child.

While developing this rationale, Benezet spoke with eighth-grade students. He noted they had difficulties putting their ideas into English and could not explain simple mathematical reasoning. This was not only in his district; he found the same results with fourteen-year-old students in Indiana and Wisconsin. Benezet didn’t blame the children or teachers, he blamed introducing formal equations too early.  So he began an experiment, abandoning traditional arithmetic instruction below the seventh grade.

In the fall of 1929 I made up my mind to try the experiment of abandoning all formal instruction in arithmetic below the seventh grade and concentrating on teaching the children to read, to reason, and to recite – my new Three R’s. And by reciting I did not mean giving back, verbatim, the words of the teacher or of the textbook. I meant speaking the English language.

To start, he picked out five classrooms, choosing those districts where most students were from immigrant homes and the parents spoke little English. Benezet knew that in other districts the parents with greater English skills and higher education would have vehemently objected, ending the experiment before it started.

In the experimental classrooms, children were exposed to what we’d call naturally occurring math. They learned how to tell time and keep track of the date on the calendar. The students played with toy money, took part in games using numbers, and when dimension terms such as “half” or “double” or “narrower” or “wider” came up incidentally, they were discussed. Instead of math, the emphasis was on language and composition. As Benezet describes these children,

They reported on books that they had read, on incidents which they had seen, on visits that they had made. They told the stories of movies that they had attended and they made up romances on the spur of the moment. It was refreshing to go into one of these rooms. A happy and joyous spirit pervaded them. The children were no longer under the restraint of learning multiplication tables or struggling with long division.

At the end of the first school year, Benezet reported that the contrast between the experimental and traditionally taught students was remarkable. When he visited classrooms to ask children about what they were reading, he described the traditionally taught students as “hesitant, embarrassed and diffident. In one fourth grade I could not find a single child who would admit that he had committed the sin of reading.” Students in the experimental classrooms were eager to talk about what they’d been reading. In those rooms, an hour’s discussion went by with still more children eager to talk.

Benezet hung a reproduction of a well-known painting in the classrooms and asked children to write down anything the art inspired. Another obvious contrast appeared. When he showed the ten best papers from each room to the city’s seventh-grade teachers, they noted that one set of papers showed much greater maturity and command of the language. They observed that the first set of papers had a total of 40 adjectives such as nice, pretty, blue, green, and cold. The second set of papers had 128 adjectives, including magnificent, awe-inspiring, unique, and majestic. When asked to guess which district the papers came from, each teacher assumed that the students who wrote the better papers were from schools where the parents spoke English in the home. In fact, it was the opposite. Those students who wrote the most masterfully were from his experimental classes.

Yet another difference was apparent. It was something that Benezet had anticipated. He explained, “For some years I had noted that the effect of the early introduction of arithmetic had been to dull and almost chloroform the child’s reasoning faculties.” At the end of that first year, he went from classroom to classroom and asked children the same mathematical story problem. The traditionally taught students grabbed at numbers but came up with few correct results, while the experimental students reasoned out correct answers eagerly, despite having minimal exposure to formal math.

Based on these successes, the experiment expanded. By 1932, half of the third- to fifth-grade classes in the city operated under the experimental program. Due to pressure from some school principals, children in the experimental classrooms were back to learning from a math book in the second half of sixth grade. All sixth-grade children were tested. By spring of that year all the classes tested equally. When the final tests were given at the end of the school year, one of the experimental groups led the city. In other words, those children exposed to traditional math curricula for only part of the sixth-grade year had mastered the same skills as those who had spent years on drills, times tables, and exams.

In 1936, the Journal of the National Education Association published the final article by Benezet. His results showed the clear benefits of replacing formal math instruction with naturally occurring math while putting a greater emphasis on reading, writing, and reasoning. The journal called on educators to consider similar changes.

As we know, schools went in the opposite direction.

Louis Paul Bénézet

Louis Paul Bénézet

This article is an excerpt from Free Range Learning. (Next post, the extraordinary benefits of emphasizing natural math over math instruction.)

26 thoughts on “Math Instruction versus Natural Math: Benezet’s Example

  1. Thank you very much for this informative post. I am not teaching maths formally to my three children, as when I have tried with the older two it has sometimes led to tears and a dislike for maths. It’s interesting how much ‘maths’ comes up in everyday life, and it’s a lot less threatening for the children than formally taught maths. Sometimes I have a confidence wobble though, and it’s good to get a confidence boost.
    P.S. In New Zealand we say ‘maths’ instead of ‘math’ 🙂

    Liked by 1 person

  2. As with everything, following normal exposure from day-to-day life (which happens in larger amounts when home-schooled), mathematics should only be “taught” to children who want it taught to them. It is much easier and productive to satisfy a curious mind than to force-feed a child who lacks interest.

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  3. Thank you for your article. I just recently discovered Benezet myself. I read his three papers last month delineating how he did it. Actually, his 3 Rs were reading, reason, and reciting. He used oral composition in place of written composition in the early years. That too played up the natural propensity of children to tell. This reciting he called oral composition and it built up their working vocabulary and ease of expressing themselves. So both math and language arts appear to be based on incidental, real life, and skills naturally acquired that can come from real life. I love this!

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    • Good point Donna. I also think, from the little reading I’ve done about Benezet, that he understood learning intimately because he was a passion-driven learner and innovative thinker himself. People able to see beyond boundaries put up by cultural conditioning are often the ones to break down those boundaries.

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  4. I’m sharing it with my Gifted and Talented group today, as well. WONDERFUL article. I’ve squabble about this for years, especially as it pertains to the horrid experience we give Kindergarteners nowadays.

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  5. Very interesting and it rings true to me. And for the handful of kids who are drawn to math at an early age, this method of teaching still opens that door for them.

    It seemed to us that a lot of the recommended curriculum in the early grades was unnecessary. Third grade just looked like a repeat of second grade, so for our daughter we skipped it. It all makes you wonder how much of our institutional education is dictated more by traditional or institutional inertia than by its effectiveness.

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    • I feel a lot of the built in redundancy of our current methods in elementary school is due to the natural unfolding of child development. The first reason I believe the repetition is there to catch those who were not developmentally ready the first time. The second reason is that skills not needed in daily life grow rusty. But we repeat the idea that children’s brain slide during the summer. The first reason would be totally unnecessary if formal instruction was given when most children attain that level of brain development. The second reason would be unnecessary if we waited to teach certain concepts until they were more likely to be reinforced by the need in real life.The brain changes at puberty and cognitive development blossoms, abstract learning blossoms at that time too. Math when taught in books is abstract. Those squiggly characters mean what we tell children they mean. Common core tries to rectify it with hands on first. But that still ignores both brain development and practical daily use.

      It appears that Bezenet was building on concrete thinking, which is what most children do best in their years before puberty. Taking this natural strength of children he taught them to think and reason with what they learned concretely with math that was practical for them. He builds on children’s ability to tell what they see and know, helping them refine that through reciting. Even their oral expression was based on the concrete experience of what they saw, experienced, and read. Once these powers of reading, reasoning, and reciting were developed and then at puberty, he was able to take advantages of cognitive development and teach the more abstract concepts found in rote learning.

      Delayed formal math instruction was nothing new. How he did it was. In the late 1800s there were one year math courses. Children in one room school houses were often taught in one school year what children in city schools spent about eight years to learn. These were usually taught about junior high age. The second year was Euclidean Geometry or Surveying. I own two such math books, one used in Kentucky by my grandfather and his older brothers, and one used in New York by my husband’s grandfather. Country children naturally worked and helped on the farm and lived math in a way city children did not. Most country children learned math by living it, before formal instruction. It appears that Bezenet tried to teach practical math experientially in the classroom and math reasoning, to make up for the lack of experience on the farm.

      I love that he actually carried out an experiment and demonstrated the soundness of building on how children naturally develop. He also said in the lower grades his math each day was about 20 minutes. That matches the attention span of children that age.

      It is amazing what children can do when we focus on building on their strengths and recognizing where they are developmentally.

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  6. Hi, Laura.
    I have a B. Sc. in Mathematics and couldn’t agree more. A huge mistake is lying in the current way of teaching Math, yet poor performance seems not to be enough to prompt a change.
    Maybe you know the book “Why Johnny Can’t Add: The Failure of the New Math” by Morris Kline.

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  7. Pingback: Wiskunde leren van moeder natuur | Heb jij iets geleerd vandaag? – Een Sudbury school perspectief op leren

  8. Pingback: How I’d Change Grade School | Mark's Daily Apple

    • Curriculum based on Benezet’s approach isn’t possible because it’s learning unique to the child and the situation. Kids learned math in the Benezet experiment as it naturally occurred in their daily lives. That’s possible in the classroom, home, or community today too. If you’re playing a board game, kids end up learn counting and scoring. If you’re making plans, it kids end up learning to tell time and track dates on the calendar. If you’re building something or baking something, kids learn to measure.

      The next article in this series, The Benefits of Natural Math, talk about the rationale behind this approach in greater detail: https://lauragraceweldon.com/2014/11/19/the-benefits-of-natural-math/

      And the final article in this series, “Natural Math: 100+ Activities & Resources” provides all sorts of open-ended, hands-on ways to learn math without a curriculum. https://lauragraceweldon.com/2014/11/26/natural-math-100-activities-resources/

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