Excerpts from What Should Be Taught in the Elementary Mathematics Curriculum, by H. Wu,
June 2, 2007:
“Insofar as the mathematics in elementary school is the foundation of all of K-12 mathematics and beyond, it should, in a grade-appropriate manner, respect the basic characteristics of mathematics. This sounds simple, but its implementation is anything but that, as the available evidence in the education literature shows. My personal conviction is that the essence of the elementary school curriculum consists of coherence, precision, and reasoning. In fact, the same is true of the mathematics curriculum for all grades, not just the elementary grades.
First of all, the elementary curriculum is surprisingly coherent. If you dig beneath the surface, you will find that the main topics of this curriculum are not a collection of facts unrelated to each other like caged animals in a zoo; rather, they form a whole tapestry where each item exists as part of a larger design.
Children should learn about this mathematics tapestry in a language that does not leave room for misunderstanding or guesswork. It should be a language sufficiently precise, so that they can reconstruct the tapestry step by-step if necessary. Too often, such precision of language is not achieved.
Above all, I would like to illustrate why it is important that elementary school mathematics, like all mathematics, be built on reasoning. Reasoning is the power that propels each move from one step to the next. When students are given this power, they learn that mathematics is something they can do, because it is done according to some objective criteria, in the same way that video games are played according to some objective criteria.
Learning cannot take place in the classroom if students are kept in the dark about why they must do what they are supposed to do.
Recall that the main goal of the elementary mathematics curriculum is to provide children with a good foundation for mathematics.
Sometimes, progress in mathematics is achieved, not by looking forward, but by looking back and understanding what we have done a little better.
So regardless of the difference in the preponderance of skills or the pedagogical needs in the primary grades, the principal concern is still with building a robust foundation for children’s learning of mathematics. Even little kids need mathematics that is coherent, precise, and logical."