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.