Bénézet reasoned that elementary math instruction at that time was rote memorization that didn’t foster an understanding of the content. In fact, he believed that such instruction stifled learning math specifically and all learning in general. He believed that teaching language and reasoning skills would be a better use of time in the lower grades. Math could then be introduced at 6th grade when students could better understand it.
As superintendent in Manchester, New Hampshire, he proposed the idea to some of his principals at lower income schools populated with students whose parents were immigrants. He felt they could benefit from increased language instruction, and he also knew that parents at the more affluent schools would reject the idea.
Bénézet brought in a graduate student from Boston Universtiy to test the two groups at various times throughout the year. The test results are surprising. When tested at the beginning of the 6th grade, obviously the students in the experiment did poorly compared to those in the traditional program on basic arithmetic. However, when confronted with word problems that could be solved by reasoning, the students with no formal math instruction performed as well as those who had six years of training!
By the end of the year, the students in the experimental group had caught up with the others on basic arithmetic and were well ahead of their peers on story problems.
This research begs many questions, a few of which I pose here:
- If Bénézet’s plan worked, why isn’t it more widely known and utilized?
- Would Bénézet’s plan work today?
- Is there an even better solution?
We may never be able to answer the first question. This is not the first time that research is slow in getting into the classroom. The research and reason guiding Common Core was known decades before the political climate invited implementation. We also know that the students of many nations outperform their American counterparts in specific subject areas, but for a variety of reasons we don’t implement those changes. And perhaps one of the greatest impediments to employing so radical a plan is the same reason that Bénézet himself implemented it with such discretion; the outcry would be deafening. Yet in spite of all those factors, why have more math teachers not heard of Bénézet’s work?
In most of the research I have read on this subject, the authors agree with Bénézet’s suggestion that mathematics instruction be delayed until later grades. They often then cite anecdotes of math-phobic elementary teachers who teach mathematics by rote memory with no understanding of it themselves.
However, I don’t like to make conclusions based on anecdotes; isolated examples can be found to support any conclusion. So many of the primary and elementary teachers I know teach math for understanding in conjunction with content knowledge. This may not have been the case in American schools 80 years ago when Bénézet took umbrage with the substance of math instruction. Perhaps today math instruction has improved to the point where Bénézet’s ideas would not be necessary.
As to the third question, even if elementary math instruction is substandard—and I’m not suggesting it is—tossing it out seems a poor solution. If my car is broken, I don’t decide not to drive; I fix it. Imagine how advanced Bénézet’s sixth graders would be if they had good instruction that encouraged mathematical reasoning. I believe that if Bénézet’s view of math instruction is still valid, it begs for effective staff development, not delayed instruction. Call me an optimist, but I believe that as teachers become more fluent with teaching the Common Core Math Standards and the accompanying mathematical practices, students will make even greater gains in mathematics.
L. P. Benezet (1935/1936). The teaching of Arithmetic: The Story of an Experiment. Originally published in Journal of the National Education Association in three parts. Vol. 24, #8, pp 241-244; Vol. 24, #9, p 301-303; & Vol. 25, #1, pp 7-8
Peter Gray. Freedom to Learn. Psychology Today, March 18, 2010
Rod Judkins, MA, RCA. Why Teaching Math in Schools is Counterproductive. Psychology Today, December 8, 2014
Learning Math by Thinking. April, 2009. http://rationalmathed.blogspot.com/2009/04/learning-math-by-thinking-hassler.html