Basically, there's been a dispute over whether to emphasize "procedural" (algorithmic, memorized step-by-step processes) or "conceptual" (creative, inventive, big ideas) skills in the earliest grades. In the last 2 decades or so the "conceptual" camp has basically won the debate in teacher education schools, claiming to have research backing up the approach. Recently there have been calls for a more middle-ground approach.
Interesting articles in this month's American Educator magazine. One by cognitive psychologist Daniel T. Willingham: http://www.aft.org/pubs-reports/american_educator/issues/winter09_10/willingham.pdf
In cultivating greater conceptual knowledge, don't sacrifice procedural or factual knowledge. Procedural or factual knowledge without conceptual knowledge is shallow and is unlikely to transfer to new contexts, but conceptual knowledge without procedural or factual knowledge is ineffectual. Tie conceptual knowledge to procedures that students are learning so that the "how" has a meaningful "why" associated with it; one will reinforce the other. Increased conceptual knowledge may help the average American student move from bare competence with facts and procedures to the automaticity needed to be a good problem solver. But if we reduce work on facts and procedures, the result is likely to be disastrous.
And another article by professor E.D. Hirsh: http://www.aft.org/pubs-reports/american_educator/issues/winter09_10/hirsch.pdf
The victory of the progressive, anti-curriculum movement has chiefly occurred in the crucial early grades, and the further down one goes in the grades, the more intense the resistance to academic subject matter with the greatest wrath reserved for introducing academic knowledge in preschool. It does not seem to occur to the anti-curriculum advocates that the four-year-old children of rich, highly educated parents are gaining academic knowledge at home, while such knowledge is being unfairly withheld at school (albeit with noble intentions) from the children of the poor. For those who truly want equality, a common, content-rich core curriculum is the only option. It is the only way for our disadvantaged children to catch up to their more advantaged peers.