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ANALISIS KESALAHAN MULTIDIMENSIONAL SISWA DALAM PEMECAHAN MASALAH ALJABAR: TINJAUAN DARI PERSPEKTIF REPRESENTASI SEMIOTIK

De Fermat: Jurnal Pendidikan Matematika · Vol. 9 No. 1 (2026) · pp. 592–610

DOI
10.36277/defermat.v9i1.2494
ISSN
2621-7309, 2621-6078
Published
2026-06-26
Publisher
Program Studi Pendidikan Matematika, Fakultas Keguruan dan Ilmu Pendidikan, Universitas Balikpapan
Language
eng

Abstract

English

This study aims to uncover the multidimensional error patterns of students in solving algebra problems from the perspective of semiotic representation at various ability levels. This study used a qualitative approach involving 30 seventh-grade junior high school students. The research subjects were selected by purposive sampling, then six students were determined representing the high, medium, and low ability categories. Data were obtained through written tests and interviews, then analyzed based on Nolting's error classification, which includes misread direction error, careless error, concept error, application error, test procedure error, and transformation error. The results showed that students at all ability levels experienced difficulties in converting between representations (transformation error), especially from verbal to symbolic (algebraic expression) and symbolic to geometric expression. High-ability students were able to reason symbolically but failed to connect it to the visual context (graphical expression), while medium-ability students tended to use trial and error strategies that resulted in application errors. Students in the low-ability group showed concept errors and fundamental representation errors (transformation errors). In general, transformation errors were the most dominant type of error, followed by concept errors and application errors. These findings indicate that algebra learning needs to be designed by integrating various semiotic representations so that students' conceptual understanding can develop more deeply.

Bahasa Indonesia

Penelitian ini mengeksplorasi pola kesalahan multidimensional siswa dalam pemecahan masalah aljabar melalui perspektif representasi semiotik pada berbagai tingkat kemampuan. Data berasal dari pekerjaan tertulis siswa dan dianalisis menggunakan klasifikasi kesalahan Nolting (1994; 2002) pada tiga jenis masalah: geometri, proporsi, dan pola. Hasil menunjukkan bahwa siswa pada semua tingkat kemampuan mengalami kesulitan dalam konversi antar representasi, terutama dari bentuk verbal expression ke simbolik (algebraic expression) dan simbolik ke geometric expression. Siswa kelompok high ability mampu menalar secara simbolik namun gagal menghubungkannya dengan konteks visual (graphical expression), sedangkan siswa middle ability menggunakan strategi coba-coba yang menimbulkan Strategic Error dan application error. Siswa kelompok low ability menunjukkan miskonsepsi konseptual dan kesalahan representasi mendasar. Secara umum, kesalahan representasi merupakan kategori paling dominan, diikuti kesalahan konseptual dan strategis. Temuan ini menegaskan pentingnya pembelajaran yang mengintegrasikan berbagai representasi semiotik untuk memperkuat pemahaman konseptual dalam aljabar.

Keywords

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Affiliations come from OpenAlex; journal OAI-PMH metadata carries none. Authors without an OpenAlex ID are matched by name, which can merge or split people.

Metadata source: OAI-PMH (metadata jurnal) https://jurnal.pmat.uniba-bpn.ac.id/index.php/DEFERMAT/oai, first harvested 29 Okt 2026, last seen 1 Nov 2026.
Original metadata (oai_dc) 
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	<dc:title xml:lang="en">ANALISIS KESALAHAN MULTIDIMENSIONAL SISWA DALAM PEMECAHAN MASALAH ALJABAR: TINJAUAN DARI PERSPEKTIF REPRESENTASI SEMIOTIK</dc:title>
	<dc:title xml:lang="id">ANALISIS KESALAHAN MULTIDIMENSIONAL SISWA DALAM PEMECAHAN MASALAH ALJABAR: TINJAUAN DARI PERSPEKTIF REPRESENTASI SEMIOTIK</dc:title>
	<dc:creator xml:lang="id">Dahiana, Wa Ode</dc:creator>
	<dc:creator xml:lang="id">Tamalene, Hanisa</dc:creator>
	<dc:creator xml:lang="id">Anastasyia, Neneng</dc:creator>
	<dc:subject xml:lang="en">algebra problem solving</dc:subject>
	<dc:subject xml:lang="en">semiotic representation</dc:subject>
	<dc:subject xml:lang="en">error analysis</dc:subject>
	<dc:subject xml:lang="en">student ability levels</dc:subject>
	<dc:subject xml:lang="en">representational flexibility</dc:subject>
	<dc:subject xml:lang="id">Pemecahan Masalah Aljabar</dc:subject>
	<dc:subject xml:lang="id">Representasi Semiotik</dc:subject>
	<dc:subject xml:lang="id">Analisis Kesalahan</dc:subject>
	<dc:subject xml:lang="id">Tingkat Kemampuan Siswa</dc:subject>
	<dc:subject xml:lang="id">Fleksibilitas Representasional</dc:subject>
	<dc:description xml:lang="en">This study aims to uncover the multidimensional error patterns of students in solving algebra problems from the perspective of semiotic representation at various ability levels. This study used a qualitative approach involving 30 seventh-grade junior high school students. The research subjects were selected by purposive sampling, then six students were determined representing the high, medium, and low ability categories. Data were obtained through written tests and interviews, then analyzed based on Nolting's error classification, which includes misread direction error, careless error, concept error, application error, test procedure error, and transformation error. The results showed that students at all ability levels experienced difficulties in converting between representations (transformation error), especially from verbal to symbolic (algebraic expression) and symbolic to geometric expression. High-ability students were able to reason symbolically but failed to connect it to the visual context (graphical expression), while medium-ability students tended to use trial and error strategies that resulted in application errors. Students in the low-ability group showed concept errors and fundamental representation errors (transformation errors). In general, transformation errors were the most dominant type of error, followed by concept errors and application errors. These findings indicate that algebra learning needs to be designed by integrating various semiotic representations so that students' conceptual understanding can develop more deeply.</dc:description>
	<dc:description xml:lang="id">Penelitian ini mengeksplorasi pola kesalahan multidimensional siswa dalam pemecahan masalah aljabar melalui perspektif representasi semiotik pada berbagai tingkat kemampuan. Data berasal dari pekerjaan tertulis siswa dan dianalisis menggunakan klasifikasi kesalahan Nolting (1994; 2002) pada tiga jenis masalah: geometri, proporsi, dan pola. Hasil menunjukkan bahwa siswa pada semua tingkat kemampuan mengalami kesulitan dalam konversi antar representasi, terutama dari bentuk verbal expression ke simbolik (algebraic expression) dan simbolik ke geometric expression. Siswa kelompok high ability&amp;nbsp; mampu menalar secara simbolik namun gagal menghubungkannya dengan konteks visual (graphical expression), sedangkan siswa middle ability menggunakan strategi coba-coba yang menimbulkan Strategic Error dan application error. Siswa kelompok low ability menunjukkan miskonsepsi konseptual dan kesalahan representasi mendasar. Secara umum, kesalahan representasi merupakan kategori paling dominan, diikuti kesalahan konseptual dan strategis. Temuan ini menegaskan pentingnya pembelajaran yang mengintegrasikan berbagai representasi semiotik untuk memperkuat pemahaman konseptual dalam aljabar.</dc:description>
	<dc:publisher xml:lang="en">Program Studi Pendidikan Matematika, Fakultas Keguruan dan Ilmu Pendidikan, Universitas Balikpapan</dc:publisher>
	<dc:date>2026-06-26</dc:date>
	<dc:type>info:eu-repo/semantics/article</dc:type>
	<dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
	<dc:type xml:lang="en">Peer-reviewed Article</dc:type>
	<dc:format>application/pdf</dc:format>
	<dc:identifier>https://jurnal.pmat.uniba-bpn.ac.id/index.php/DEFERMAT/article/view/2494</dc:identifier>
	<dc:identifier>10.36277/defermat.v9i1.2494</dc:identifier>
	<dc:source xml:lang="en">De Fermat : Jurnal Pendidikan Matematika; Vol. 9 No. 1 (2026); 592-610</dc:source>
	<dc:source>2621-7309</dc:source>
	<dc:source>2621-6078</dc:source>
	<dc:source>10.36277/defermat.v9i1</dc:source>
	<dc:language>eng</dc:language>
	<dc:relation>https://jurnal.pmat.uniba-bpn.ac.id/index.php/DEFERMAT/article/view/2494/261</dc:relation>
	<dc:rights xml:lang="en">Copyright (c) 2026 De Fermat : Jurnal Pendidikan Matematika</dc:rights>
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