Designing Learning Strategy to Improve Undergraduate Students’ Problem Solving in Derivatives and Integrals: A Conceptual Framework

Abstract

Derivatives and integrals are two important concepts of calculus which are precondition topics for most of mathematics courses and other courses in different fields of studies. A majority of students at the undergraduate level have to master derivatives and integrals if they want to be successful in their studies However, students encounter difficulties in the learning of derivatives and integrals. Most of these difficulties arise from the students' weakness in problem solving. This paper presents a learning strategy which has been designed to overcome these difficulties based on mathematical thinking and generalization strategies with prompts and questions.

A Conceptual and Procedural Research on the Hierarchical Structure of Mathematics Emerging in the Minds of University Students: An Example of Limit-Continuity-Integral-Derivative

“…It was noticed that the participants did not have enough conceptual knowledge of the existence of solving derivative and definite integral problems defined with the help of limit and limit concept. This result reports similarity with the results showing the students have learning difficulties in the concepts of limit, continuity, derivative, integral (Baki and Çekmez, 2012;Biber and Argün, 2015;Cornu, 1991;Davis and Vinner, 1986;Hashemi, Abu, Kashefi, Mokhtar and Rahimi, 2015;Kula and Bukova Güzel, 2015;Özkaya, Işık and Konyalıoğlu, 2014;Sağlam and Bülbül, 2012;Szydlik, 2000;Tall and Vinner, 1981;Tangül, Barak and Özdaş, 2015;Williams, 1991) or misconceptions (Akbulut and Işık, 2005;Baştürk and Dönmez, 2011;Bergthold, 1999;Bezuidenhout, 2001;Cornu, 1991;Davis and Vinner, 1986;Dönmez, 2009;Gray and Tall,1991;Jordaan, 2005;Orton, 1983;Szydlik, 2000;Tall and Vinner, 1981;Tall, 1993;Williams,1989Williams, , 1991. As the situation handled in this study for the solutions of relevant concepts originates from the accumulation point, which can be considered as basic, similarly, in the study by Çetin, et al (2012), it was pointed out that the students did not understand this concept at all.…”

Polytechnic Students' Mathematical Thinking Processes in Linear Algebra: A Qualitative Approach

“…This means that, specializing, generalizing, and conjecturing were the successful mathematical thinking processes in this study as evident in the study of [24] where the Cohen's d values for the test appeared to have an effect size that is large in the difference of mean [39,40]. The results are in line with the findings of [41,42] whom characterized mathematical thinking as a way to improve students' understanding and expand their mastery level of mathematics problems. The analysis of the findings in Table 1 revealed a positive result of a significant difference in the first three mathematical thinking processes (specializing, generalizing, and conjecturing) with a non-significant outcome in the last mathematical thinking process (convincing).…”

“…This may be attributed to the fact that convincing is associated to an in-depth examination of trying to establish and justify why something is true. The studies of [27], [41], [43] argued that the first three mathematical thinking processes can be achieve if the specialization process is properly designed through a useful conjecturing, then it can be helpful in making generalization. Thus, the results in this qualitative analysis may be attributed to what [44] calls "the notion of a monitor."…”

Mathematics learning strategies of high school students in Nepal

“…Studies on learning strategies in the last decade focused interventions on learning strategies. For example, Berger and Karabenick (2011) related motivation and learning strategies and Hashemi et al (2015) interrelated effects of designing learning strategies on students' problem-solving in calculus. Cho and Heron (2015) investigated students' self-regulated learning with reference to affective aspects by using different learning strategies.…”