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The concept of function has dramatically changed the
landscape of mathematics. Its introduction into
school mathematics, however, has proved to be
challenging. What might students learn about
functions if they were to answer all the functions
tasks in their seventh- and eighth-grade textbooks?
In 35 textbooks from 18 countries collected by the
Third International Mathematics and Science Study
(TIMSS), there were five distinct conceptions of
function: symbolic-rule, ordered-pair, social-data,
physical-phenomena, and controlling-image.
Symbolic-rule and ordered-pair were the most
frequent. The achievement test items in TIMSS did not
appear to address the same conceptions of function as
the tasks in the textbooks. The TIMSS test emphasized
social-data, physical-phenomena, and
controlling-image conceptions over symbolic-rule and
ordered-pair conceptions. Some textbooks had tasks
that enacted a variety of conceptions of function
whereas others only emphasized a few. These
conceptions might play an important role in making
the concept accessible if they could be used as
springboards toward a more flexible understanding of
function.
About the author
Dr. Vilma Mesa is assistant professor in the School of Educationat the University of Michigan. She studied mathematics andcomputer sciences at the University of Los Andes in Colombia andpursued graduate studies in mathematics education at theUniversity of Georgia in the USA. She investigates mathematicsteaching at the post-secondary level.
