From Piaget’s Theory to APOS Theory: Reflective Abstraction in Learning Mathematics and the Historical Development of APOS Theory

Arnon, Ilana; Cottrill, Jim; Dubinsky, Ed; Oktaç, Asuman; Fuentes, Solange Roa; Trigueros, María; Weller, Kirk

doi:10.1007/978-1-4614-7966-6_2

Cited by 5 publications

(3 citation statements)

References 24 publications

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“…This is consistent with (Cooley et al, 2007) assertion that humans may execute schema thematization, as evidenced by their capacity to demonstrate the relationship between the schema's concepts and accessible and re-evaluable schema components. According to (Arnon et al, 2014b), thematization is a method that changes a schema into an object, allowing actions or processes on the schema to be performed.…”

Section: Discussionmentioning

confidence: 99%

Generalization of Patterns Drawing of High-Performance Students Based on Action, Process, Object, and Schema Theory

Firdaus¹,

Murtafiah²,

Lukitasari³

et al. 2023

EUROPEAN J ED RES

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<p style="text-align: justify;">This study is qualitative with descriptive and aims to determine the process of generalizing the pattern image of high performance students based on the action, process, object, and schema (APOS) theory. The participants in this study were high performance eighth-grade Indonesian junior high school. Assignments and examinations to gauge mathematical aptitude and interviews were used to collect data for the study. The stages of qualitative analysis include data reduction, data presentation, and generating conclusions. This study showed that when given a sequence using a pattern drawing, the subjects used a number sequence pattern to calculate the value of the next term. Students in the action stage interiorize and coordinate by collecting prints from each sequence of numbers in the process stage. After that, they do a reversal so that at the object stage, students do encapsulation, then decapsulate by evaluating the patterns observed and validating the number series patterns they find. Students explain the generalization quality of number sequence patterns at the schema stage by connecting activities, processes, and objects from one concept to actions, processes, and things from other ideas. In addition, students carry out thematization at the schematic stage by connecting existing pattern drawing concepts with general sequences. From these results, it is recommended to improve the problem-solving skill in mathematical pattern problems based on problem-solving by high performance students', such as worksheets for students.</p>

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Section: Discussionmentioning

confidence: 99%

Generalization of Patterns Drawing of High-Performance Students Based on Action, Process, Object, and Schema Theory

Firdaus¹,

Murtafiah²,

Lukitasari³

et al. 2023

EUROPEAN J ED RES

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“…Reflective abstraction includes abilities that are very important because mathematical concepts will be known, formed, and produced by students through reflective abstraction [2]. The importance of reflective abstraction is evidenced by the cognitive abilities in which students are able to develop due to reflective abstraction [5,6]. In addition, concepts built from reflective abstraction will be used as a basis for building further concepts that relate to the concept [7].…”

Section: Introductionmentioning

confidence: 99%

“…Reflective abstraction is divided into two parts which are to estimate concepts that will be formed to be used in higher thinking by using concepts that are already known / previously owned, and reorganizing/reshaping a new mathematical concept by involving concepts owned by students [2,4,6,9]. The first reflective abstraction part is to form the concepts used in higher thinking that can be seen when students from a concept in solving mathematical problems.…”

Section: Introductionmentioning

confidence: 99%

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

Wafiqoh¹,

Kusumah²,

Juandi³

2020

Proceedings of the Proceedings of the 7th Mathematics, Science, and Computer Science Education International Seminar, MSCEIS 20

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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.

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Learning AnalyTICs: Exploring the Hypothetical Learning Trajectories Through Mathematical Games

Páez

Cobos

Aguirre

et al. 2021

Methodologies and Intelligent Systems for Technology Enhanced Learning, 11th International Conference

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From Piaget’s Theory to APOS Theory: Reflective Abstraction in Learning Mathematics and the Historical Development of APOS Theory

Cited by 5 publications

References 24 publications

Generalization of Patterns Drawing of High-Performance Students Based on Action, Process, Object, and Schema Theory

Generalization of Patterns Drawing of High-Performance Students Based on Action, Process, Object, and Schema Theory

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

Learning AnalyTICs: Exploring the Hypothetical Learning Trajectories Through Mathematical Games

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