Undergraduate Students’ Difficulties in Conceptual Understanding of Derivation

Abstract

Derivation is one of the fundamental concepts in the learning of university mathematics. It is a prerequisite for other concepts in undergraduate level and its traces are visible in the majority of mathematical courses at university level. Students have difficulties in the learning of this concept which mostly come back to lack of conceptual understanding. The purpose of this study is to investigate the reasons of difficulties, which faced students in conceptual understanding of derivation. The design of this study is qualitative analysis of open-ended questions, and its subjects consisted of 63 undergraduate students. The findings showed students have serious difficulties in understanding conceptually of derivation. The students' responds indicated that main reasons of difficulties in conceptual understanding of derivation come back to focusing on symbolic aspect more than embodied aspect, lack of making logical connection between these aspects, and weakness of dealing with generalized question. Findings of this study provide information to undergraduate instructors and students to overcome learning difficulties of derivation.

Li̇sans Öğrenci̇leri̇ni̇n Türev Tanimiyla İlgi̇li̇ Yorumlari Ve Türeve Yükledi̇kleri̇ Anlamlar

“…Bazı kavramlar ne kadar basit ya da temel kavramlar olursa olsun ya da ne kadar kesin bir şekilde tanımlanırsa tanımlansın öğrenciler bu kavramlara yönelik informel anlamalara sahip olabilir ya da kendilerine özgü bir anlayış geliştirebilirler (Orton, 1983). Bu konuda öğrencilerin türevi kavramsal ve sezgisel olarak anlayamadıkları (Hashemi, Abu, Kashefi & Rahimi, 2014;Orton, 1983) daha çok yüzeysel (Açıkyıldız, 2013) ve türevin tanımı ile sınırlanan cebirsel anlamaya sahip oldukları (Orhun, 2012) belirtilmiştir. Araştırmalarda öğrencilerin çoğu zaman işlemsel ve prosedürel tarzda hareket ettiği görülmüştür (Kertil, 2014).…”

Students’ understanding of calculus-based kinematics and the arguments they generated for problem-solving: The case of understanding physics

“…In the literature, learning about the application of calculus-based kinematics equally requires formal modes of understanding, using precisely defined symbolic notations and explicit rules for their manipulation (Hashemi et al, 2014;Mason, Stacey, & Burton, 2010;Tall, 2012). From maths-in-physics perspective, formal modes of understanding involve exploiting mathematics and logic (or arguments) that are widely used in physics (Govender, 2007;Kiray & Kaptan, 2012;Reif, 1995).…”

“…As such their understanding of the interconnectedness provided by the tenets of calculus-kinematic equations is missing. Both fundamental and derived calculuskinematic equations can potentially support and complement each other (Hashemi, Abu, Kashefi & Rahimi, 2014) and allow fuller understanding of problems inspired by mathematical physics (Bing & Redish, 2009). The level of understanding of application of calculus in vector-kinematics and the extent, to which they are applied, of course, vary according to the type of instruction given and the students" abilities to use relevant knowledge resources to construct sound arguments.…”

Development of High School Students' Understanding and Confidence skills with VBA for Excel Shapes Games

“…From the findings of the difficulties there are several causes of students' difficulties in understanding abilities related to statistics, first, students are not able to clearly understand the definition of statistics, second, students have not been able to develop mathematical concepts so students can explain the steps in solving statistical problems, third make conclusions in the form of a formula based on students' observations in statistics. To overcome the difficulties of students' comprehension skills, researchers support students to form mathematical concepts in statistical learning with one of the mathematical media through computers, although they can also without using a computer [6], researchers make learning strategies that are able to collaborate between students and instructors, so that there are active learning and teaching in the classroom [7].…”