In the never-ending dialogue about math education that has come to be known as the “math wars”, proponents of reform-based math tend to characterize math as it was taught in the 60’s (and prior) as “skills-based”. The term connotes a teaching of math that focused almost exclusively on procedures and facts in isolation to the conceptual underpinning that holds math together. The “skills-based” appellation also suggests that those students who may have mastered their math courses in K-12 were missing the conceptual basis of mathematics and were taught the subject as a means to do computation, rather than explore the wonders of mathematics for its own sake.I'm beginning to believe less and less in the "math for its own sake" mentality. I don't know that that can be taught, and to be quite honest, I'm not sure there are enough people out there who are willing to put in enough effort to get to the point where they can see the beauty, wonder, and interconnectedness of the mathematical mosaic. I now lean towards the "teach to fluency" mode, which is "necessary but not sufficient" to get to the "beauty and wonder" mode. Oh, I'll take my students to "beauty and wonder" if they want to go there, and plenty do, but that's not where I focus my classes.
Without delving too far into the math wars, I and others have written that while traditional math may sometimes have been taught poorly, it also was taught properly. In fact, a view of the textbooks in use at that time reveal that they provided both procedures and concept. Missing perhaps were more challenging problems, but also missing from the reformers’ arguments is the fact that not only are procedures and concepts taught in tandem but that computational fluency leads to conceptual understanding.
Too much "beauty and wonder" and not enough "fluency" puts the cart before the horse.