Hake relates this story in an article about Louis Paul Benezet, an educator who ran a radical experiment in the 1930′s. Benezet saw how mindlessly young children were performing mathematics, so he made a dramatic change: Almost entirely remove mathematics from grades 1-5. Start teaching mathematics in grade 6, with a focus on problem-solving (e.g., start from estimation, so that you have a sense of when an answer is reasonable). Sixth graders can understand the problems for which one should use mathematics. The point is not to introduce the solution, until students understood the problem. Remarkably, the experimental 6th graders completely caught up in just four months to the 6th graders who had had mathematics all five previous years.
Intuitively, this has always made sense to me. Elementary math should be easy to make up later.