The Abstraction Process of Limit Knowledge

Abstract

The RBC+C abstraction model is an effective model in mathematics education because it gives the opportunity to analyze research data through cognitive actions. For this reason, we aim to examine the abstraction process of the limit knowledge of two volunteer participant students using the RBC+C abstraction model. With this aim, the students' abstraction processes were examined over recognition, building-with, construction, and consolidation. In the process, three problems that enable students to use their pre-knowledge were designed by the researchers to reveal the students' mathematical thinking levels, abstraction processes, and finally to improve a new structure. These problems were used in the application, and students' dialogues were videorecorded. The semi-constructed interview and observation data-collection methods were used in this process, and one of the researchers participated in the study as a participant observer. The data was analyzed and interpreted by transcribing the video recordings into written text and grouping them into the cognitive actions of the RBC+C model. In conclusion, these students were indicated to have managed recognizing and buildingwith their pre-knowledge on sequence, function, and infinity, and thus constructing knowledge on limits.

Analyzing students’ abstraction in learning common tangent lines of two circles based on cognitive styles

“…The transcripts were analyzed and grouped based on three abstraction activities in the RBC model. The indicators of abstraction were made by referring to abstraction activities according to Hong and Kim (2015) and Memnun et al (2017) as presented in Table 2. The interviews were conducted twice to verify that the data obtained was credible.…”

“…In RBC model, recognizing occurs when students realize that prior knowledge is attached to a given mathematical situation (Tsamir & Dreyfus, 2002;Hershkowitz et al, 2007;Dreyfus, Hershkowitz, & Schwarz, 2015;Celebioglu &Yazgan, 2015;Memnun et al, 2017). With regard to the action, recognizing involves trying to compare the results of the previous action and stating that the structure is similar or suitable.…”

“…With regard to the action, recognizing involves trying to compare the results of the previous action and stating that the structure is similar or suitable. Building-with is the activity of combining existing knowledge to meet objectives, for example, to solve problems or prove the truth of a statement (Tsamir & Dreyfus, 2002;Hershkowitz et al, 2007;Dreyfus et al, 2015;Celebioglu &Yazgan, 2015;Memnun et al, 2017). Thus, the same task can be developed by one student, but constructed by another student, depending on the student's personal history (Tsamir & Dreyfus, 2002).…”

“…Many studies have revealed abstractions using RBC models with different subjects (Dreyfus, 2007;Memnun et al, 2017;Hassan & Mitchelmore, 2006;Celebioglu & Yazgan, 2015;Katranci & Altun, 2013) but researchers have not found any research that revealed students' abstraction in constructing new knowledge based on cognitive style of students. Considering the importance of abstraction in learning mathematics (e.g., Hershkowitz et al, 2002;Ferrari, 2003), students' difficulties in geometry (Gal & Linchevski, 2010;Mutia, 2017), and the roles played by cognitive style in learning mathematics (Mayer & Massa, 2003;Chrysostomou et al, 2013), the present study aims to reveals the students' abstraction in learning common tangent lines of two circles based on their cognitive style.…”

Analysis of the Abstraction Process of Continuity Knowledge

“…One of the theories is the Recognizing(R) Building-with(B) Construction(C) + Consolidation(C) abstraction model introduced by Hershkowitz, Schwarz, and Dreyfus (2001), which provides an opportunity to study the abstraction process of knowledge through different cognitive actions (recognizing, building-with, construction, consolidation). According to the RBC+C model, the learner needs to be familiar with the old structures to reach a new structure, establish connections and reveal relationships (Sezgin-Memnun, Aydın, Özbilen, & Erdoğan, 2017). These old structures, connections, and relationships could be used to construct a new structure.…”