Doing the Math - JHU Mathematics - Johns Hopkins University

Introduction
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Background
Mathematics education is an enormously controversial subject in the United States.
The quality of the education offered to elementary, middle school, high school, and
college students is a subject of much debate. The two most salient topics at the heart
of the debate are the role of arithmetic and the level of abstraction present in math
curricula.
One faction in the debate was fueled largely by an influential, and now controversial,
1989 National Council of the Teachers of Mathematics publication entitled
Curriculum and Evaluation Standards for School Mathematics. This group
maintains that traditional mathematics education is overly focused on routine
procedures and does not foster higher-order thinking skills and conceptual
understanding. It believes that mathematics should be made relevant and engaging
to students and that the ubiquity of calculators justifies a de-emphasis on arithmetic
skills and procedures. Curricula were developed to implement these ideas, and in
some of them the standard algorithms of arithmetic and memorization of basic math
facts are neither emphasized nor practiced. The use of these kinds of curricula has
become widespread, and this gave rise to the other side of the debate. Parents, who
were taught traditional arithmetic, were shocked to find that their children were not
learning basic math facts and procedures in school.
The second group—which now includes parents, teachers, mathematics professors,
engineers, and scientists—favors the teaching of mathematics in more traditional
forms, without relying on calculators to perform arithmetic. This group argues that
mathematics has an internal, hierarchical logic, and that this structure needs to be
preserved and emphasized in mathematics curricula. It believes that arithmetic
fluency is an essential component of mathematics education, both for general
computational literacy and for proceeding to the next level of mathematics. It points
out that students who do not learn basic skills thoroughly are not prepared to study
and understand more advanced mathematics, and that this may preclude them from
pursuing careers in technical fields such as science and engineering. Equally
deplored is American students’ relatively poor performance on math tests that are
administered on an international basis in order to compare math achievement in
different countries.
Meanwhile, statistics show that there is a broad, national lack of alignment between
the expectations of college professors and the mandates of high school educators.
Many post-secondary institutions are testing incoming students and determining that
many of them require remedial mathematics. According to a 2008 report issued by
the National Mathematics Advisory Panel, there is a “vast and growing demand for
remedial mathematics education among arriving students in four-year colleges and
community colleges across the nation.” 3 For students, this means that successful
completion of high school mathematics requirements does not necessarily lead to
Doing the Math 3