Basic Skills Versus Conceptual Understanding: A Bogus Dichotomy in Mathematics Education

By H. Wu, American Educator, Fall 1999

Education seems to be plagued by false dichotomies. Until recently, when research and common sense gained the upper hand, the debate over how to teach beginning reading was characterized by many as ``phonics vs. meaning.'' It turns out that, rather than a dichotomy, there is an inseparable connection between decoding --- what one might call the skills part of reading --- and comprehension. Fluent decoding, which for most children is best ensured by the direct and systematic teaching of phonics and lots of practice reading, is an indispensable condition of comprehension.

``Facts vs. higher order thinking'' is another example of a false choice that we often encounter these days, as if thinking of any sort --- high or low --- could exist outside of content knowledge. In mathematics education, this debate takes the form of ``basic skills or conceptual understanding.'' This bogus dichotomy would seem to arise from a common misconception of mathematics held by a segment of the public and the education community: that the demand for precision and fluency in the execution of basic skills in school mathematics runs counter to the acquisition of conceptual understanding. The truth is that in mathematics, skills and understanding are completely intertwined. In most cases, the precision and fluency in the execution of the skills are the requisite vehicles to convey the conceptual understanding. There is not ``conceptual understanding'' and ``problem-solving skill'' on the one hand and ``basic skills'' on the other. Nor can one acquire the former without the latter. ...

This false dichotomy impedes efforts to improve math education.

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