To what Kind of Mathematical Problems are Calculus Students Exposed? A Textbook Analysis

Adriana Berenice Valencia Álvarez
Jaime Ricardo Valenzuela González

Abstract. Given the importance of solving mathematical problems placed in
real contexts and given the influence of the textbook in the teaching and
learning of mathematics, it is important to study to what kind of mathematical
problems students are exposed. In this article, we present a distinction between
conventional mathematical problems and mathematical modeling problems in
terms of nine aspects related to the problem statement and its solution (Green
and Emerson, 2010). Using these nine criteria, we analyzed and classified a
total of 188 examples and 1,114 exercises found in the unit about functions in
a sample of Calculus textbooks from Mexican and American publishing companies.
As a result, the analysis showed that between 65% and 87% of the
examples and exercises in the books studied were classified as completely
conventional problems. Modeling problems were found in only three of the
books analyzed and these correspond to merely 1% or 2% of the examples and
exercises of the unit.

Keywords: Analysis of textbooks, mathematical modeling problems, conventional
problems, solving problems, Calculus.

DOI: 10.24844/EM2903.02

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