Nancy Anderson, EdD

Mathematics Teacher ~ Author ~ Consultant

Q: Which is more important math skills or concepts?

A: The relationship between mathematical skills or concepts is often mischaracterized as a dichotomous or competing relationship. But, in reality, skills and concepts support each other (Hiebert et al. 1997; Star, 2005).  Neither is more important than the other. Nor is there a sequential relationship between the two. Hiebert and colleagues explain that concepts support procedural development. The more connections a learner has between ideas, the more likely she or he is to learn a procedure with understanding, retain that procedure, and apply it correctly. Access to a diverse set of procedures can also help the student solve a wider range of problems which, in turn, can lead to new insights and ideas. Jon Star (2005) advises math educators to disentangle the relationship between characteristics of knowledge and how the learner holds that knowledge. He distinguishes between less robust procedural knowledge (e.g., applying procedures without understanding) and deep procedural knowledge that is rooted in conceptual understanding. For example, a student who computes 27 - 4 using "take away" but 27 - 23 by "adding on" shows conceptual understanding of two different interpretations of subtraction. In grades 4 and 5, a student who uses repeated subtraction  to solve 3 ÷ 1/3 (i.e., the number of groups of 1/3 in 3) but missing factor to solve 3 1/7 ÷ 1/2 (i.e., 1/2 of what number of 3 1/7) shows conceptual understanding of the different interpretations of division. In the middle grades, a student who can solve for x by just "looking" at the equation 2(x + 3) = 2x + 6 shows an understanding of concepts related to equality, algebraic structure, and the distributive property.  I find these examples tremendously helpful in illuminating the false dichotomy between skills and concepts. And they remind me of how important it is to always look at what the student is doing in relationship to the task rather than trying to characterize one without the other.