Analysis of Student Learning in Differential Equations Learning Area Based on Various Variables: The Case of Turkey and Ghana

Abstract

Development of mathematical models for problems experienced in study areas is important for improvement in almost all scientific fields. The solution of a problem requires development of a mathematical equation (or a mathematical model) based on the properties of the problem in certain disciplines. Such an equation is generally a function with one unknown and an equation that includes the derivative (or differential) of this function. The equation which contains a function and its finite derivatives, is called a differential equation (Pisces 2018). The present study aimed to analyze the learning of college students in differential functions based on various variables in Turkey and that of Ghana. The study was conducted in two faculties of a public university (Engineering and Education Faculties) for a year in differential equations course on 300 students’ exams and applications for Turkey. The achievements of those students were analyzed based on the problems experienced by the students, the conceptual comprehension and operational comprehension, reasoning skills, misconceptions, transition between representations, and basic mathematics knowledge variables. A similar study was carried out in a faculty of technical education in Ghana with 300 students’ examination and application and their results were analyzed as it was done in the case of Turkey. The present study for the two countries adopted a descriptive approach based on screening models. Since it was possible to reach the whole population in the study for the two countries, the complete census method was used. The main difficulties experienced by the students in each country were determined as follows: inability to conduct the operations or to conduct incorrect operations due to the lack of basic mathematical knowledge, student focus on operational comprehension instead of conceptual comprehension, inability or indecision of the students in establishing the correlation between the algebraic and graphic representations of the differential equation in transfers between representations, misconception that dependent variable should always be identified by y and independent variable should always be identified by x (this could be due to a teacher habit), and although dx-2xydy2yey2dy could be easily solved by linearization, students’ preference to attempt to find the integral multiplier, leading to calculation errors. These difficulties were similar in within the two countries as if they were taught by same instructors. It can be argued that the achievements increased in the two groups of students when the applications that would eliminate these difficulties were conducted in the following topics, however a comprehensive study should be initiated to eliminate the lack of basic mathematical knowledge, and it would even be beneficial to study the OSYM selection system. It could be suggested that calculus as a concept should be taken serious to build the two groups of students competencies in differential equations.