Two Parts of Reflective abstraction: For New Problem Solving and Mathematical Concept

Abstract

This research aimed to describe the reflective abstraction exhibited by each of part of reflective abstraction. The research question was about How is students' reflective abstraction in reflecting their prior knowledge into higher thought and reorganizing the new mathematical concept. We performed a qualitative research approach with a study case design as the research method. This study involved 36 11 ℎ grade students and 36 12 ℎ grade students. The data was analyzed qualitatively by using hyperRESEARCH application. The first part of the students' reflective abstraction could be seen from how the students developed the concept of mathematical problem solving on the mathematical problem testing, while the second part of the reflective abstraction could be seen on the process of developing core concepts of mathematics learning.

The relation of complex problem solving with reflective abstraction: a systematic literature review

“…Relation CPS to prior knowledge i) the ability to apply prior knowledge when solving complex problems is of the utmost importance [6], [33], [47]- [49]; ii) students with high CPS use prior knowledge when learning new problems [50]; iii) prior knowledge affects one's CPS ability [22], [50], [51]; iv) applying previous knowledge when solving complex problems was most important [48]; v) the CPS process tends to develop existing ideas rather than create new ones [52]; vi) prior knowledge as a moderation between intelligence and CPS [53]; vii) prior knowledge interacts with reasoning abilities to be utilized effectively for CPS [54]- [56]; viii) in CPS, existing information is integrated with prior knowledge [57]; ix) the level of proficiency in CPS interacts with a dynamically changing problem environment, and prior knowledge is not predominant [58]; x) in CPS, real-world experience complements prior knowledge [59]; xi) in addition to prior knowledge, CPS is influenced by additional cognitive aspects such as searching for relevant information, mindfulness, and the ability to organize mental operations [60]; xii) differences in prior knowledge and experience have an impact on CPS [61]; xiii) prior knowledge or the context of the problem can influence CPS [62]; xiv) in CPS, there is a step in forming a hypothesis based on prior knowledge [63]; and xv) in CPS, prior knowledge is used to define the problem [64]. Relation of prior knowledge to reflective abstraction i) reflective abstraction is a process of building new concepts based on previous ideas or new knowledge based on prior knowledge [15]; ii) reflective abstraction as a tool to support and contribute to building knowledge based on previous knowledge [65], [66]; iii) there is an influence between reflective abstraction and prior knowledge, and reflective abstraction must be supported by prior knowledge [67]; iv) reflective abstraction constructs new concepts through prior knowledge; [68], [69]; v) prior mathematical knowledge supports constructing knowledge through a process of reflective abstraction [70]; vi) through assimilation g...…”

“…Relation of prior knowledge to reflective abstraction i) reflective abstraction is a process of building new concepts based on previous ideas or new knowledge based on prior knowledge [15]; ii) reflective abstraction as a tool to support and contribute to building knowledge based on previous knowledge [65], [66]; iii) there is an influence between reflective abstraction and prior knowledge, and reflective abstraction must be supported by prior knowledge [67]; iv) reflective abstraction constructs new concepts through prior knowledge; [68], [69]; v) prior mathematical knowledge supports constructing knowledge through a process of reflective abstraction [70]; vi) through assimilation generalization based on prior knowledge gives rise to reflective abstraction [71]; vii) construction of new knowledge as the dissemination of prior knowledge through reflective abstraction [72]; viii) the need for connection to prior knowledge in the process of reflective abstraction [73]; ix) the learning objectives largely determine the prior knowledge involved in the reflective abstraction process [74]; x) task and learning design can build on prior knowledge concepts and encourage reflective abstraction [75]; xi) the lack of concepts from prior knowledge that cannot be overcome will limit reflective abstraction [76]; xii) reflective abstraction describes the construction of new high-level knowledge starting from prior knowledge [14]; xiii) student's reflective abstractions can more readily appear using apperception or exploring prior knowledge in the learning process [77]; xiv) reflective abstraction reflects prior knowledge into new mathematical concepts [70]; xv) at the level of reflective abstraction representation, prior knowledge is used to plan problem-solving [10]; xvi) reflective abstraction as a reflection to expand on previous structures or prior knowledge [78]; and xvii) reflective abstraction as a constructive process of prior knowledge [79]. Reflective abstraction in problem-solving i) problem-solving ability can be described based on reflective abstraction [67]; ii) reflective abstraction ability of students in problem solving is required [80]; iii) reflective abstraction can be used for problem-solving and solving thinking [11]; iv) the importance of reflective abstraction is the ability to understand problems, find solutions, and solve problems [81]; v) reflective abstraction can develop the concept of solving mathematical problems…”

“…Knowledge addition is related to prior learning. So how do previous skills and knowledge affect the ability to solve complex problems, and reflective abstraction can reflect their prior knowledge into higher-order thinking and reorganization of new mathematical concepts [70] included in solving problems. Reflective abstraction leads the subject to constructive generalizations and generates new synthesis to acquire new knowledge [81].…”

“…However, prior knowledge through reflective abstraction is essential because students will know, form, and produce mathematical concepts. The importance of reflective abstraction is evidenced by the cognitive abilities that students can develop because of reflective abstraction [70].…”

Modifikasi Permainan Caklingking Untuk Meningkatkan Kemampuan Pemahaman Konsep Berhitung Siswa

“…Siswa lebih banyak berjuang dan berusaha dalam proses memahami konsep matematis (Colomeischi & Colomeischi, 2015;Mikheeva et al, 2019). Konsep matematis saling berhubungan satu sama lain (R. Wafiqoh & Kusumah, 2019), serta konsep matematis merupakan poin utama dalam belajar matematika (Wafiqoh et al, 2020a), sehingga siswa dituntut tidak pernah mengabaikan pemahaman mereka dalam mempelajari suatu konsep matematis. Konsep matematis yang dimiliki sebelumnya dapat menjadi suatu bahan untuk membentuk struktur matematika yang baru berdasarkan hasil identifikasi, pembangunan, dan pengaturan (Budiarto et al, 2017;Djasuli et al, 2017).…”