APOS analysis on cognitive process in mathematical proving activities

Syamsuri, Syamsuri; Marethi, Indiana

doi:10.18860/ijtlm.v1i1.5613

Cited by 5 publications

(9 citation statements)

References 22 publications

(32 reference statements)

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“…Learning design will use simple proof (Rocha, 2019) dan worked-example (Kirsch, 1991;Laamena et al, 2018). Learning will also be guided by the use of APOS theory (Action, Process, Object, Schema) (Arnon, Cottrill, Dubinsky, Oktaç, Fuentes, et al, 2014;Mulyono, 2011;Syamsuri & Marethi, 2018;Wijayanti et al, 2019). The development of HLT and learning instruments that had been made were consulted with experts as preliminary design.…”

Section: Preliminary Designmentioning

confidence: 99%

“…Mulyono (2011) discusses the role of APOS theory, detailing the indicators obtained from implementation in learning. Syamsuri & Marethi (2018) discusses the analysis of students' cognitive processes in proof activities. Gemander et al, (2020) and Syamsuri, et.…”

Section: Introductionmentioning

confidence: 99%

“…The students' mentality in the implementation of proof learning has not appeared which will be related to their reasoning ability. Syamsuri & Marethi (2018) the discussion about the students' unable to prove were seen from the mental structure of APOS and provided suggestions for further research. From the problems stated above, the development of proof-based learning with the APOS theory approach will be made for enhancing students' reasoning ability.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Developing Proof-Based Learning Using Apos Theory Approach in Exponential for Enhancing Students’ Reasoning Ability

Shinariko

Hartono

Darmawijoyo

2022

AJPM

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Proof-based learning is learning mathematics through proof and proving to strengthen students' concepts. The use of APOS theory (Action, Process, Object, and Schema) aims to describe students' mental structures summarized in Hypothetical Learning Trajectory (HLT). Their interest in learning mathematics requires students to have reasoning ability. This study aims to produce a mini theory of proof-based learning using the APOS theory approach about mental structure and mental mechanisms. The role of learning is to improve students' reasoning ability. The research method used is the design research validation type. The research subjects were 34 students from SMA Negeri 1 Palembang. For this reason, this study will discuss the construction of HLT which will become a mini theory. In this paper, the researcher will focus on the first lesson’s HLT proof-based learning using APOS theory approach. This study's results are to compare HLT and ALT, develop proof learning, and test the truth of the hypotheses made based on the research methodology.

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Section: Preliminary Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Developing Proof-Based Learning Using Apos Theory Approach in Exponential for Enhancing Students’ Reasoning Ability

Shinariko

Hartono

Darmawijoyo

2022

AJPM

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“…Several studies have attempted to reveal students' thinking in learning mathematics in higher education (Dreyfus, 2002;Tall, 2008;Arnon, Cottrill, Dubinsky, Oktac, Fuentes, Trigueros, & Weller, 2013;Syamsuri, Purwanto, Subanji, & Irawati, 2017;Syamsuri, 2016;Syamsuri & Marethi, 2018). Tall (2008) argues that there is a transition process towards advanced mathematical thinking.…”

Section: Introductionmentioning

confidence: 99%

“…APOS theory has been widely used in analyzing the formation of mathematical concepts at universities (Asiala, Brown, DeVries, Dubinsky, Mathews, & Thomas, 1997;Weller, Arnon, & Dubinsky, 2011;Maharaj, 2010;Syamsuri, Purwanto, Subanji, & Irawati, 2017;Syamsuri & Marethi, 2018) as well as in mathematics learning (Salgado & Trigueros, 2015;Garcia-Martinez & Parraguez, 2017). In concept construction, this theory describes the paths that students go through in constructing a mathematical concept.…”

Section: Introductionmentioning

confidence: 99%

Thinking Structure of Students’ Understanding of Probability Concept in Term of Apos Theory

Syamsuri

Santosa

2021

MaPan

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This study aims to analyze the mental structure experienced by students when understanding the concept of probability reviewed from APOS Theory and then suggests a lesson that accommodates the mental structure. APOS theory states that a learner forms a suitable mental structure when interpreting a mathematical concept. This study involved 106 third semester students who enrolled in Probability Theory. The students were given ACE (Activities, Classroom, Exercises) learning cycle treatment. After treatment, students were then given homework assignments that aim to reinforce the learning process. After the sixth week of learning, data were collected through a test. The results of this study are as follows: (1) the mental structure of students towards the concept of opportunity is still at the process level, not at the object-level, (2) Improving the learning of probability concept requires activities to improve verbal understanding, not only in the form of pictures and symbols. The alternative learning treatments are written in this article.

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