What that speaker is proposing sounds like the selling points of "Investigations", the math program used in the elementary schools in our district, here is a website for Investigations.

Take a look at what E.D.Hirsch says about this learning method, full story here.
Dr. E.D. Hirsch, a brilliant educator and best selling author on the subject of education has written THE book on math curriculum. His book, "The Schools We Need and Why We Don't Have Them" is a landmark work taking every major educational study into account and listing the findings of each one. When viewed as a whole, Dr. Hirsch says, "experience has shown that 'discovery learning' is the least effective method in the teacher's repertory." (page 246). Discovery learning is the same thing as Investigations Math where the students "discover" their own solutions to problems. Opposite this line of thinking is where teachers actually teach students. Dr. Hirsch says "Saxon math's approach is reasonably close to what research is telling us about how students learn--much closer, than are the progressive methods advocated by the National Council of Teachers of Mathematics." (page 131)

As Dottie says "there has to be balance between the two extremes!". Our teachers added 2 or 3 minute speed drills with little rewards to encourage the kids to memorize the facts after the kids understand the concept of adding groups of items. That has helped bring up school scores on the achievement testing.