An Overview of the Calculus Curriculum Reform Effort: Issues for Learning, Teaching, and Curriculum Development

How students use mathematical resources in an electrostatics context

“…[5][6][7][8] This conclusion is similar to findings of student work in physics: Students can carry out the calculations, but many lack the associated conceptual understanding. 9 A central concept of an integral is as the limit of a Riemann sum.…”

Relieving of Misconceptions of Derivative Concept with Derive

“…Students have misconceptions that they did not consider the intervals while finding the derivative of the functions (Orton, 1980), 3. Students experienced difficulty in doing the geometric interpretation of derivative and they had misconception by thinking the distance (Ferrini-Mundy & Graham, 1991;Ubuz, 2001), 4. The misconception rooted from thinking the derivative of the function as the derivative at a specific point (Amit & Vinner, 1990;Orton, 1980;Özkan & Ünal, 2009;Ubuz, 2007), 5.…”

“…They have misconceptions rooted from not knowing the physical interpretation of the derivative (Bezuidenhout, 1998;Bingölbali, 2010), 7. They cannot construct a relation between the slopes of the tangent and the normal (Bingölbali, 2010;Ferrini-Mundy & Graham, 1991;Gür & Barak, 2007;Orton, 1983;Ubuz, 2001). …”

“…When examine of literature show that there are several studies investigate of misconceptions toward derivative subject (Aksoy, 2007;Amit & Vinner, 1990;Bezuidenhout, 1998;Bingölbali, 2010;Gür & Barak, 2007;Ferrini-Mundy & Graham, 1991;Hӓhkiöniemi, 2005;Orton, 1980;1983;Özkan & Ünal, 2009;Ubuz, 2001;. Seen these studies that students have got misconceptions such as given derivative function of derivative in a point, considered as if derivative function of tangent equations, given tangent equations of derivative in a point.…”

On Understanding the Notion of Limits and Infinitesimal Quantities

“…Ferrini-Mundy & Graham (1991) argue that the students' understanding of central concepts of calculus is exceptionally Fprimitive_: Bstudents demonstrate virtually no intuition about the concepts and processes of calculus; they diligently mimic examples and their attempts to adapt prior knowledge to a new situation usually result in very persistent and often inadequate conceptions whose change the students firmly resist.Ŵ hile attempting to reach a wide range of students in teaching calculus, it is perhaps more practicable to appeal to one's intuition to convey mathematical concepts and ideas, building on what they have already learned, without making heavy demands on their aptitude for abstract and rigorous mathematical understanding. The author is broadly in agreement with the following opinion expressed by Koirala (1997): BAn introductory calculus course should be informal, intuitive and conceptually based mainly on graphs and functions... Formulas and rules should not be given as granted but they should be carefully developed intuitively on the basis of students' previous work in mathematics and sciences^(see also Heid, 1988;Orton, 1983).…”