Student performance and attitudes in courses based on APOS theory and the ACE teaching cycle

Weller, Kirk; Clark, Julie; Dubinsky, Ed; Loch, Sergio; McDonald, Michael; Merkovsky, Robert

doi:10.1090/cbmath/012/05

Cited by 43 publications

(36 citation statements)

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“…APOS authors consider different conceptions: action conception, process conception, object conception and eventually schema, with three stages: intra, inter and trans (see for example Weller et al 2003). The shift from one conception to another can be considered as several stages of a transition process leading to advanced thinking.…”

Section: Thinking Modes and Knowledge's Organizationmentioning

confidence: 99%

Investigating the secondary–tertiary transition

Gueudet¹

2008

Educ Stud Math

201

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International audienceThe secondary–tertiary transition has been studied in a great amount of research in mathematics education, adopting different focuses and theoretical approaches. I present here how these focuses led the authors to identify and study different students' difficulties and to develop different means of didactical action. Individual, social, but also institutional phenomena are considered with different perspectives. Each perspective yields a particular view of transition. The association and comparison of these views makes it possible to build an organized outline of this complex object, combining several kinds of ruptures and long-term evolutions

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Section: Thinking Modes and Knowledge's Organizationmentioning

confidence: 99%

Investigating the secondary–tertiary transition

Gueudet¹

2008

Educ Stud Math

201

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“…In APOS theory, the main mental mechanisms for building the mental structures of action, process, object, and schema are called interiorization and encapsulation (Weller et al, 2003). The mental structures of action, process, object, and schema constitute the acronym APOS.…”

Section: Data Analyzementioning

confidence: 99%

Using APOS Theory Framework: Why Did Students Unable To Construct a Formal Proof?

Syamsuri

Purwanto

Subanji

et al. 2017

Int. J. Emerg. Math. Educ.

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AbstrakBerpikir matematis sangat dibutuhkan dalam belajar matematika, apalagi di perguruan tinggi. Salah satu aktifitas belajar matematika ialah pembuktian matematis. Penelitian ini mendeskripsikan proses berpikir mahasiswa yang gagal mengonstruksi bukti-matematis formal. Analisis dalam deskripsi tersebut menggunakan Teori APOS dalam menjelaskan struktur mental dan mekanisme mental yang muncul ketika melakukan pembuktian matematis. Penelitian ini menggunakan pendekatan kualitatif. Penelitian ini melibatkan 26 mahasiswa pendidikan matematika di salah satu perguruan tinggi di Banten, Indonesia. Data diperoleh melalui think-aloud ketika menyelesaikan tugas pembuktian dan dilanjutkan dengan wawancara berbasis tugas. Hasil penelitian ini menyatakan bahwa mahasiswa gagal mengonstruksi bukti matematis formal karena proses berpikir mahasiswa tersebut hanya melalui tahapan interiorisasi masalah, interiorisasi objek, dan koordinasi. Dengan demikian, mekanisme mental lainnya, seperti: enkapsulasi, de-enkapsulasi dangeneralisasi belum muncul. Hal tersebut menunjukkan bahwa struktur mental Action telah terbentuk, namun Process dan Object belum muncul. Oleh karena itu perlu dipertimbangkan suatu strategi pembelajaran yang mendukung mekanisme mental yang dibutuhkan dalam mengonstruksi bukti. Kata Kunci: proses berpikir, konstruki bukti, pembuktian, bukti matematis, teori APOS AbstractMathematical thinking is necessary for mathematics learning, especially in undergraduate level. One of the activities in undergraduate mathematics learning is proving. This article describes students' thinking process who unable to construct a mathematical formal proof. The description uses APOS Theory to explore students' mental mechanism and students' mental structure while they do proving. This research is qualitative research that conducted on 26 students majored in mathematics education in public university in Banten province, Indonesia. Data was obtained using think-aloud when solving the proving task and then interview based the task. Results show that the students could not construct a formal proof because the mental mechanism that appeared was interiorization and coordination. Based on the results, some suitable learning activities should be designed to support the construction of these mental mechanisms.

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“…In some studies (see, for example, Weller et al, 2003), these ideas were recast and applied to various topics in post-secondary mathematics. Piaget investigated the thinking of adolescents and adults, including research mathematicians.…”

Section: Description Of the Apos/ace Teachingmentioning

confidence: 99%

“…The main mental mechanisms for building the mental structures of action, process, object, and schema are called interiorisation and encapsulation (Dubinsky, 2010;Weller et al, 2003). The mental structures of action, process, object, and schema constitute the acronym APOS.…”

Section: Apos Theorymentioning

confidence: 99%

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An APOS Analysis of students’ understanding of the concept of a limit of a function

Maharaj

2010

Pythagoras

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This article reports on a study which used the APOS (Action‐Process‐Object‐Schema) theory framework to investigate university students’ understanding of limits of functions. The relevant limit concepts were taught to undergraduate science students at a university in Kwazulu‐Natal in South Africa. This paper reports on the analysis of students’ responses to four types of questions on limits of functions. The findings of this study confirmed that the limit concept is one that students find difficult to understand, and suggests that this is possibly the result of many students not having appropriate mental structures at the process, object and schema levels.

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Student performance and attitudes in courses based on APOS theory and the ACE teaching cycle

Cited by 43 publications

References 0 publications

Investigating the secondary–tertiary transition

Investigating the secondary–tertiary transition

Using APOS Theory Framework: Why Did Students Unable To Construct a Formal Proof?

An APOS Analysis of students’ understanding of the concept of a limit of a function

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