Students’ understanding and application of the area under the curve concept in physics problems

Abstract

This study investigates how students understand and apply the area under the curve concept and the integral-area relation in solving introductory physics problems. We interviewed 20 students in the first semester and 15 students from the same cohort in the second semester of a calculus-based physics course sequence on several problems involving the area under the curve concept. We found that only a few students could recognize that the concept of area under the curve was applicable in physics problems. Even when students could invoke the area under the curve concept, they did not necessarily understand the relationship between the process of accumulation and the area under a curve, so they failed to apply it to novel situations. We also found that when presented with several graphs, students had difficulty in selecting the graph such that the area under the graph corresponded to a given integral, although all of them could state that ''the integral equaled the area under the curve.'' The findings in this study are consistent with those in previous mathematics education research and research in physics education on students' use of the area under the curve.

Analysis of Students’ Difficulties about Rotational Dynamic Topic Based on Resource Theory

“…However, many students have difficulty in understanding and applying physics concepts to solve the problems (Demirci 2008;Gracia et al, 2008;Nguyen & Rebello, 2011;Maries & Singh, 2016;Bollen et al, 2016). Students difficulties to solve physics problems can be explained using two different viewpoints; they are misconceptions and resource theory (Docktor & Mestre, 2014).…”

The Evaluation of Physics Students' Problem-Solving Ability Through Mauve Strategy (Magnitude, Answer, Units, Variables, and Equation)

“…Students may choose aids that match the characteristics of the physics problem (Sherin, 2006). Their difficulties are usually a way of identifying the fit between physics concepts and multi-representation (Nguyen & Rebello, 2011). Therefore, some things need to be exercised in the ability of problem-solving physics.…”

Analytical derivation: An epistemic game for solving mathematically based physics problems

“…(1), the first FTC], whereas most physics problems require finding specific values using a definite integral [Eq. (2), the second FTC], in particular physical situations. For example, defining the electric field in one dimension as the negative rate of change of electric potential with respect to position, one can write the potential difference between two any points as…”

“…Students often learn most of the mathematical concepts and skills that are required to solve physics problems in their mathematics classes. However, numerous studies suggest that they fail to access and/or apply their previously acquired mathematics knowledge in given physics contexts [1][2][3][4]. Previous studies have established various factors that contribute to this failure, such as representational inconsistencies between mathematics and physics.…”

“…Previous studies have shown a positive correlation between student difficulties with physics concepts and those with either the mathematics concepts, application of those concepts, or the representations used to connect the mathematics and the physics. Students lacking and/or failing to apply relevant mathematical knowledge and skills have shown difficulties with reasoning and/or solving problems in physics contexts [2,3,12,13].…”