Abstract
Students encounter difficulties in understanding integral because the concept of integral requires the usage of theorems, formulas, daily life practices, and interdisciplinary approaches. From this point of view, in this study we examine the effects of a teaching process consisting of modelling activities on understanding the definite integral with the help of Riemann sums. The research is designed according to the case study based on a qualitative research method. Participants consist of 28 pre-service mathematics teachers who have limited understanding of integral although they have completed a Calculus course. The modelling activities were prepared in accordance with the emergent modelling approach. Data were collected through integral test and semi-structured interviews conducted before and after the teaching process. Before the teaching process consisting of modelling activities, pre-service mathematics teachers’ knowledge about the definite integral was included in the area under a curve, inverse of derivative and integral with known boundaries. In addition, participants did not refer to Riemann sums or cumulative sums. After the teaching process consisting of modelling activities, it was seen that almost all participants could explain the following equality (lim)┬(n→∞)〖∑_(k=1)^n▒f(c_k ) ∆x_k 〗=∫_a^b▒f(x)dx. At the end of the teaching process consisting of modelling activities, this process has enabled pre-service teachers to establish the relationship between Riemann sum and definite integral. Findings revealed that teaching process of the definite integral enhanced the understanding the definite integral.
Highlights
The concept of integral is inherently closely related to the concepts of series, limit and derivative and it is used as an umbrella concept in conjunction with many subjects or situations such as functions, trigonometry, geometry, and real-life problems
Participants The participants of the study consist of 28 pre-service teachers who were enrolled in Elementary Mathematics Education Program of Faculty of Education in one of the state universities in Turkey
Pre-service teachers were engaged in eight modelling activities
Summary
The concept of integral is inherently closely related to the concepts of series, limit and derivative and it is used as an umbrella concept in conjunction with many subjects or situations such as functions, trigonometry, geometry, and real-life problems. Students generally regard integral as an area under a curve or inverse of derivative and this causes limited understanding of the integral (Sealey, 2008). Understanding the definite integral with the help of Riemann sums Ö.Ergene, A.Ş.Özdemir understanding causes not to notice the theoretical structure underlying integral concept. Dxand find the answer (e' − e() gives a response as the definite integral [DI] or inverse of derivative to the question “What does f(x)dx mean?”. This response shows limited and incomplete understanding of integral. Limited understanding of integral leads students to see integral as an abstract and difficult concept and to have high anxiety and negative attitude towards the concept of integral (Ergene, 2021a, Ergene, 2019; Ergene & Özdemir, 2020a)
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