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Analysis of Preservice Teachers' Understanding of Solving Trigonometric Equations: A Perspective through Actions, Processes, Objects, and Schemas Theory

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Title: Analysis of Preservice Teachers' Understanding of Solving Trigonometric Equations: A Perspective through Actions, Processes, Objects, and Schemas Theory
Language: English
Authors: Angel Mukuka (ORCID 0000-0003-0292-1324), Benjamin Tatira (ORCID 0000-0002-0118-3676)
Source: Pythagoras. 2025 46(1).
Availability: AOSIS. 15 Oxford Street, Durbanville, Cape Town, 7550 South Africa. Tel: +27-21-975-2602; Fax: +27-21-975-4635; e-mail: publishing@aosis.co.za; Web site: https://sajce.co.za/index.php/pythagoras
Peer Reviewed: Y
Page Count: 15
Publication Date: 2025
Document Type: Journal Articles
Reports - Research
Education Level: Higher Education
Postsecondary Education
Secondary Education
High Schools
Descriptors: Foreign Countries, Preservice Teachers, Knowledge Level, Trigonometry, Equations (Mathematics), College Freshmen, Problem Solving, Barriers, Teacher Education Programs, Mathematics Teachers, Mathematical Concepts, Mental Computation, Secondary School Mathematics, High Schools
Geographic Terms: South Africa
ISSN: 1012-2346
2223-7895
Abstract: This study analysed first-year preservice teachers' understanding of trigonometric equations at a South African university in the Eastern Cape province. We employed the Action-Process-Object-Schema (APOS) framework to analyse the mental constructions made by preservice teachers in solving trigonometric equations. A qualitative case study design was employed to analyse test scripts from 223 preservice teachers, complemented by follow-up interviews with eight of these participants. Findings show that the success rate in the two analysed items was low. Students who had not developed specific mental structures could not solve the given problems. Only 15.5% of the participants reached the Object level, while 76% remained at the Action or Process stages. Conversely, 8.5% of the participants were at the pre-Action stage, having not shown evidence of action mental structures conjectured in the genetic decomposition. Challenges encountered include difficulties with algebraic manipulations, reference angles, angle relationships across quadrants, and conversions between degrees and radians. The analysis further revealed a lack of understanding of the periodic nature of trigonometric functions and the general solution derivation.
Abstractor: As Provided
Entry Date: 2025
Accession Number: EJ1478285
Database: ERIC
FullText Text:
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  Data: AOSIS. 15 Oxford Street, Durbanville, Cape Town, 7550 South Africa. Tel: +27-21-975-2602; Fax: +27-21-975-4635; e-mail: publishing@aosis.co.za; Web site: https://sajce.co.za/index.php/pythagoras
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  Data: This study analysed first-year preservice teachers' understanding of trigonometric equations at a South African university in the Eastern Cape province. We employed the Action-Process-Object-Schema (APOS) framework to analyse the mental constructions made by preservice teachers in solving trigonometric equations. A qualitative case study design was employed to analyse test scripts from 223 preservice teachers, complemented by follow-up interviews with eight of these participants. Findings show that the success rate in the two analysed items was low. Students who had not developed specific mental structures could not solve the given problems. Only 15.5% of the participants reached the Object level, while 76% remained at the Action or Process stages. Conversely, 8.5% of the participants were at the pre-Action stage, having not shown evidence of action mental structures conjectured in the genetic decomposition. Challenges encountered include difficulties with algebraic manipulations, reference angles, angle relationships across quadrants, and conversions between degrees and radians. The analysis further revealed a lack of understanding of the periodic nature of trigonometric functions and the general solution derivation.
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  Data: EJ1478285
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      – Text: English
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      Pagination:
        PageCount: 15
    Subjects:
      – SubjectFull: Foreign Countries
        Type: general
      – SubjectFull: Preservice Teachers
        Type: general
      – SubjectFull: Knowledge Level
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      – SubjectFull: Trigonometry
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      – SubjectFull: Barriers
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      – SubjectFull: Teacher Education Programs
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      – SubjectFull: Mathematics Teachers
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      – SubjectFull: Mathematical Concepts
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      – SubjectFull: Mental Computation
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      – SubjectFull: South Africa
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      – TitleFull: Analysis of Preservice Teachers' Understanding of Solving Trigonometric Equations: A Perspective through Actions, Processes, Objects, and Schemas Theory
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