I think we need to have both. I know this sounds like having your cake and eating it too, but concepts alone do not provide enough of a framework for all students to be able to extrapolate what to do in every situation. Conceptual approaches do not account for the more concrete thinker. Conceptual approaches do not address all learners in the classroom. Conceptual approaches alone lack a vital element.
Math is not the only subject where repetition and practice matters. This year we are spending a lot of time as a team delving into our writing curriculum. Something I have noticed is that in following the Judith Hochman approach, our school has been rightfully scaffolding the teaching of writing a five-paragraph essays. Traditionally, third grade has been the year we teach one paragraph writing. In fourth grade, traditionally we teach four-paragraph essays writing. By the end of fifth grade, students are expected to have mastered the basic five-paragraph essay. The goal was for children to have a clear understanding of the concept of essay writing, but also for them to have explicit direct instruction in how to do so.
I agreed with the approach, but I felt the specific expectations per grade level were limiting. While I do believe there is tremendous merit to any scaffolded approach where basic skills are retaught with new skills are added on each year, I think our students can do more writing. In looking at national and international standards, we now expect our third graders to write three-paragraph essays. We now expect our fourth graders to write four to five paragraph essays (albiet not nearly as fleshed out as in the older years) and we now expect our fifth graders to write five-paragraph essays. The reason for this is simple. The more students practice writing and the more they write, the better writers they will be. The "longer" they write, the better they will be.
Malcolm Gladwell writes about the 10,000 hour rule. He explains that in order to be truly great at anything, to become a master, you need to dedicate 10,000 hours of your time invested in practice. Practice is not glorious. You do not always reap immediate rewards. It is important to teaching our students to relish in the satisfaction that will come from sustained effort. The critical component here is that success will not always come immediately. This lesson is a glorious gift we need to give all children. It is a lesson of perseverance.
Somewhat related to what I have just written above is an understanding that through the practice of a discipline, the student will acquire a new language- the language embedded in that discipline. There is a dialogue that can only take place between the student and the subject when the student has mastered that language. It is the language of background knowledge, of the basics within that subject and understanding of how that subject functions as a whole. Hence, it is always important when designing lessons in any subject to not only think about engagement, but engagement in what. The "what" matters. It is what makes a subject different from another and valued as a discipline.
Concepts matter. They will always matter. Concepts frame the skills and the content, but alone concepts are hollow without skills and content. I stand for a concepts plus approach.