13th International Congress on Mathematical Education Hamburg, 24-31 July 2016 1 - 1 A JOURNEY TO INTEGRATION: PROMOTING A ROBUST CONCEPTION OF INTEGRAL Tolga KABACA 1 , Ali DELICE 2 , Mahmut KERTIL 2 , Gulseren KARAGOZ AKAR 3 1 Pamukkale University, 2 Marmara University, 3 Bogazici University Research studies show students’ weaknesses in conceptual understanding of the integration. The aim of this paper is offering a sequence of activities to reach a mature conceptual understanding of integral. The journey is started from exploring an area calculation method by partitioning, forming an algebraic sequence, and taking the limit of that sequence for obtaining the formal concept of integration. We also planned the usage of spreadsheet program. During the journey, we make an effort to support students for quantitative reasoning. At the end of the journey, we hypothesize that students can reach the big idea that “Integral is a special continuous sum and antiderivative is a genius method to calculate this sum” instead of “integral is an operation which is the inverse of derivative”. Consequently, the effect of this learning journey was tested on 47 students and some clues were found showing the positive effect understanding the integration conceptually. INTRODUCTION Integration is one of the basic concepts of calculus which requires the robust understanding of many prior concepts such as limit, derivative, rate, and rate of change. In an earlier study, Orton (1983) determined students’ weak understanding of integration and he pointed out that students’ main difficulty was considering it as the limit of the sequence of areas under a curve. The review of literature have also pointed out that general understanding of calculus concepts by students from different grades levels and from different countries were limited to rote application of algebraic rules in artificial and pure-symbolic situations (Orton, 1983; Tall, 1992; White & Mitchelmore, 1996; Stroup, 2002; Berry & Nyman, 2003). In the study by White and Mitchelmore, (1996), students’ difficulties in interpreting the symbols used for variables and their weak understanding of the contextual meaning calculus concepts were reported. The teaching orientation of the integration is also dominated by introducing integration as the inverse of derivative, or mastering the techniques of integration in pure-symbolic situations (Tall, 2002; Delice & Sevimli, 2011). However, this way of teaching does not support conceptual understanding, and students have difficulties in understanding the limiting idea behind the area under a curve (Orton, 1983), or they had difficulties in reversing between derivative and antiderivative graphs (Berry & Nyman, 2003; Ubuz, 2007). Many researchers emphasized the need for focusing on change, rate of change (derivative), and accumulation of change (integration) for the conceptual understanding of calculus concepts (Stroup, 2002; Tall, 1992; Thompson, 1994a; 1994b). Stroup (2002) stressed that qualitative aspects of calculus concepts are as important as well as the formal representations of them. According to Stroup (2002), qualitative aspects of calculus ideas assumed to be developed by the formal instruction. However, this is not the case in practice as evidenced by many research studies (i.e., Berry & Nyman, 2003; Thompson, 1994). Students’ conceptual understanding of integration necessitates the ability of considering this concept as accumulation of change or cumulative growth in different contexts (Stroup, 2002; Thompson, 1994). The relationship between “how much” (amount) and “how fast”