Abstract
The study of mathematics at the university level requires logical thinking and strong mathematical skills. Contemporary first-year students are not prepared for these demands and end up failing their courses. This study aims to present an instrument for enhancing mathematics teaching and promoting learning with understanding in higher education by a combination of symbolic, natural, and pictorial languages in different tasks. We analyze the 17 solutions of four languaging exercises administered in a basic calculus course for engineering students at the University of Costa Rica. The results suggest that these exercises promote the acquisition of skills necessary to be mathematically proficient and are a useful tool for revealing students’ mathematical thinking and misconceptions.
Highlights
In the last years, research in university mathematics education has increased substantially (Biza et al, 2016; Goodchild & Rønning, 2014), and the transition from high school mathematics to university mathematics has been intensely discussed (Winsløw et al, 2018; Varsavsky, 2010)
This problem was already identified in 1972, as presented by Hoyles, Newman, and Noss (2001) in this excerpt that points out that: “[students] do not understand the mathematical ideas which university teachers consider basic to their subject; they are not skillful in the manipulative processes of even elementary mathematics; they cannot grasp new ideas quickly or at all; ... and, they have no sense of purpose that is, they do not seem to realize that in order to study mathematics intensively they must work hard on their own trying to sort out ideas new and old, trying to solve test problems, and so on.” (Thwaites, 1972, as cited in Hoyles et al, 2001, p.831)
We identify the knowledge about derivatives that students understood and the misconceptions they had about some mathematical concepts
Summary
Research in university mathematics education has increased substantially (Biza et al, 2016; Goodchild & Rønning, 2014), and the transition from high school mathematics to university mathematics has been intensely discussed (Winsløw et al, 2018; Varsavsky, 2010). Several researchers (e.g., Artigue, 1995; Kilpatrick et al, 2001; Winsløw et al, 2018) point out that students enter the university without strong mathematics knowledge This problem was already identified in 1972, as presented by Hoyles, Newman, and Noss (2001) in this excerpt that points out that:. Contemporary students continue to present the same difficulties They have deficiencies in problem-solving skills, conceptual understanding, and the thinking and reasoning skills needed for the university level (Kempen & Biehler, 2014; Er, 2018; Gruenwald et al, 2004; Luk, 2005). It is evident that there is a knowledge gap between high school and university mathematics that influences the students’ performance
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