The APOS Paradigm for Research and Curriculum Development

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

doi:10.1007/978-1-4614-7966-6_6

Cited by 36 publications

(83 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The way that is used to check the process of prospective teachers is using the theory of APOS. According to Arnon et al, the theory of APOS generally consists of four stages of action, processes, objects, and schemes [4]. The action is the ability to understand concepts by using external stimuli.…”

Section: Introductionmentioning

confidence: 99%

Error Analysis on Prospective Teacher in Solving the Problem of Critical Thinking Mathematics with Apos Theory

Susandi¹,

Sa’dijah²,

As’ari³

et al. 2018

Proceedings of the 1st Annual International Conference on Mathematics, Science, and Education (ICoMSE 2017)

View full text Add to dashboard Cite

Mathematical critical thinking is an essential ability for prospective teachers. The prospective teachers must be able to use the ability to think critically well so that students who are taught can also have good mathematical critical thinking skills. However, sometimes prospective teachers have a mistake in solving the problem of critical mathematical thinking skills. The present paper aims to analyze the mistakes of prospective teachers in solving the problem of critical mathematical thinking skills. The type of research method is descriptive with the qualitative approach. The subject in this research is one student of semester VI. The methods used in this research include test method amounting to one essay question, interview method, and triangulation method. The findings show that the prospective teacher on the focus indicator can be completed well whereas the indicators of reason, inference, situation, clarity, and overview, the teacher cannot solve well. Causes of the teacher error based on APOS theory are (1) error in distinguishing between commutative and addition characteristic of multiplication on matrix, (2) error in multiplication operation on the matrix, (3) error inequality of two matrices, and (4) error in the concept of inverse equation matrix.

show abstract

Section: Introductionmentioning

confidence: 99%

Error Analysis on Prospective Teacher in Solving the Problem of Critical Thinking Mathematics with Apos Theory

Susandi¹,

Sa’dijah²,

As’ari³

et al. 2018

Proceedings of the 1st Annual International Conference on Mathematics, Science, and Education (ICoMSE 2017)

View full text Add to dashboard Cite

show abstract

“…APOS is an acronym for Action, Process, Object, and Schema. The theory borrows Piaget’s notion of reflective abstraction that was used to describe children’s construction of logico-mathematical structures and reconstructs it in the context of tertiary level mathematics education (Arnon et al., 2013). Action, Process, Object, and Schema are mental constructions that an individual might construct when learning a mathematical subject.…”

Section: Introductionmentioning

confidence: 99%

Preservice Teachers’ Introduction to Computing

Çetin

2016

Journal of Educational Computing Research

View full text Add to dashboard Cite

Computational thinking has been gaining new impetus in the academic community and in K-12 level education. Scratch is a visual programming environment that can be utilized to teach and learn introductory computing concepts. There are some studies investigating the effectiveness of Scratch for K-12 level education. However, studies that have been conducted at the collegiate level, especially in the context of preservice computing teacher education, are very rare. The present study aimed to investigate the effect of Scratch-based instruction on preservice teachers' understanding of basic programming concepts and their attitudes toward programming. In the present study, a mixed method design was utilized. In the first phase of the study, the data were collected using an achievement test, a practice test, and a computer programming attitude scale. In the second phase of the study, data were collected through a semistructured interview. The results of the study indicated that preservice teachers in Scratch-based instruction had significantly better understanding of basic computing concepts. Qualitative data indicated that Scratch-based instruction was useful in constructing a more meaningful learning environment for preservice teachers. The results of this study have implications for researchers and preservice computing teacher educators when designing an introductory computing course.

show abstract

“…From this thinking process, it can be said that both subjects performed the mechanism of encapsulation. In APOS theory, encapsulation is a mental mechanism that transforms a process so that individuals can summarize 𝑔(𝑥) into an object (Arnon et al, 2014). 𝑓(𝑥) is an element wrapped in a unitary object as a forming element of 𝑔(𝑥), which consists of 𝑓(𝑥) by k times.…”

Section: Discussionmentioning

confidence: 99%

“…The processes stage is an internal construction made by individuals through the same actions but does not have to be controlled by external stimuli (Baker et al, 2000;Planell & Delgado, 2016). Concurrently, Arnon et al (2014) also stated that individuals experience movement from relying on external cues to having internal control when repeating actions and reflecting on them. The transformation from external control to internal control involves a mental mechanism called "interiorization."…”

Section: Introductionmentioning

confidence: 99%

Students as Prospective Teachers’ Understanding of Integral Based on the APOS Theory in Terms of Gender Difference

2023

JHETP

View full text Add to dashboard Cite

The present qualitative study aims to describe the understanding of integral by college students as prospective teachers based on the APOS theory with regard to gender differences. The research subjects were one female student (FS) and one male student (MS). The data were collected through assignments on integral and interviews. The results of data analysis showed that at the actions stage, FS and MS solved the integral problem procedurally. In the processes stage, FS explained the step of determining the area using a definite integral by installing the boundaries taken from the given equation. On the other hand, MS used a definite integral while still paying attention to the influence of the area on the x-axis. In the objects stage, both subjects showed some integral relationships as the totality of the process based on integral characteristics. At the schemes stage, the coherence of the two subjects' schemes was different.

show abstract

The APOS Paradigm for Research and Curriculum Development

Cited by 36 publications

References 12 publications

Error Analysis on Prospective Teacher in Solving the Problem of Critical Thinking Mathematics with Apos Theory

Error Analysis on Prospective Teacher in Solving the Problem of Critical Thinking Mathematics with Apos Theory

Preservice Teachers’ Introduction to Computing

Students as Prospective Teachers’ Understanding of Integral Based on the APOS Theory in Terms of Gender Difference

Contact Info

Product

Resources

About