Students’ Understanding of the Economic Interpretation of the Derivative in the Context of Marginal Cost

Abstract

Many disciplines make use of mathematical concepts. However, there are often discrepancies between the way mathematical concepts are understood and taught in mathematics and the way they are used in other disciplines. The literature suggests that such discrepancies might make it hard for students in mathematics service courses to make a connection between the mathematical concepts taught and the way they are used in the students’ major disciplines. We investigated this hypothesis for one specific example in mathematics for economics students – the derivative and its interpretation commonly used in economics as the amount of change when increasing the production by one unit. We conducted an interview study investigating to what extent economics students can make a connection between the mathematical concept of the derivative and this common economic interpretation of the derivative. This study provides empirical evidence that it is actually difficult for economics students to make this connection, even though it was covered in their calculus course. In particular, the study reveals difficulties students have when trying to make this connection, which could be addressed in teaching.

Promoting Prospective Mathematics Teachers' Understanding of Derivative across Different Real-life Contexts

“…In the following study, Mkhatshwa and Doerr (2018) reported that business calculus students had difficulties in discriminating and interpreting the quantities of the total cost, total profit, marginal cost, and marginal profit. Similar results were reported in the studies by Feudel (2017Feudel ( , 2018 investigating calculus students' understanding of derivative in the context of economics. According to Mkhatshwa (2018), as the denominator is one, equality of the numerical values for the difference quotient (rate) and the difference (amount) quantities is the main source of this difficulty.…”

“…From the mathematical point of view, the marginal cost interpretation of derivative has some problematic aspects in terms of underestimating the infinite small differentiation (Feudel, 2016(Feudel, , 2017(Feudel, , 2018Mkhatshwa & Doerr, 2018). It emphasizes a chunky way of reasoning (change in cost by one additional unit of product) and may result in conceptualizing derivative as an amount of change as also observed in this study (Mkhatshwa, 2018;Mkhatshwa & Doerr, 2018).…”

“…A collection of recent papers investigated calculus students' understanding of derivative in non-kinematic contexts such as related rate or cost, revenue, and profit (Feudel, 2016(Feudel, , 2017(Feudel, , 2018Jones, 2017;Mkhatshwa, 2018Mkhatshwa, , 2020Mkhatshwa & Doerr, 2016. The study by Mkhatshwa (2018) evidenced that business calculus students did not see marginal change as a rate in the form of a difference quotient, rather they saw it as an amount of change (difference in only one quantity).…”