Bridging informal talk and symbolic rigor: a commognitive analysis of extroverted students’ mathematical discourse

Abstract

Purpose: This study investigates how an extroverted junior high school student navigates the transition from colloquial spoken discourse to literate symbolic notation in set theory, reframing written symbolic gaps as discursive register shifts rather than cognitive deficits. Design/methodology/approach: Employing a qualitative case study design grounded in Anna Sfard’s Commognitive Framework, this research evaluated 35 eighth-grade students at SMP Islam Athirah Makassar. Focal subject SE (extroversion score 134/144) was selected via purposeful sampling. Data were collected through set-theory problem tasks and semi-structured commognitive interviews, analyzed across visual mediators, word use, routines, and endorsed narratives.Findings: SE demonstrated robust oral fluency and sound spatial logic during interviews but produced incomplete written work lacking formal set notation (∩,∪), set labels, and intermediate derivation routines. Findings confirm that extroverted learners prioritize colloquial verbal discourse, resulting in an unscaffolded symbolic realization gap in written form. Practical implications: Traditional penalization for perceived student carelessness is counterproductive. Educators should implement Oral-to-Symbolic Scaffolding Tools, such as sentence-stem templates and dynamic graphic organizers, to systematically translate oral expressiveness into rigorous mathematical notation. Originality/value: This study uniquely synthesizes personality profiling with commognitive theory, offering a novel framework that reinterprets extroverted students' symbolic omissions as discursive register misalignments rather than intrinsic psychological defects. Purpose: Penelitian ini bertujuan menganalisis bagaimana siswa SMP berkepribadian ekstrovert mengarungi transisi dari diskursus lisan kolokial ke notasi simbolis formal pada materi himpunan, merebingkai keterbatasan penulisan simbolis sebagai pergeseran register diskursus, bukan defisit kognitif. Design/methodology/approach: Menggunakan desain studi kasus kualitatif berbasis Kerangka Komognitif Anna Sfard, penelitian ini melibatkan 35 siswa kelas VIII SMP Islam Athirah Makassar. Subjek fokus SE (skor ekstrovert 134/144) dipilih melalui purposeful sampling. Data dikumpulkan melalui tes matematika materi himpunan dan wawancara komognitif semi-terstruktur, kemudian dianalisis berdasarkan mediator visual, penggunaan kata, rutinitas, dan narasi terendors. Findings: Subjek SE menunjukkan kelancaran lisan dan logika spasial yang kuat saat wawancara, namun menghasilkan lembar kerja tertulis yang tidak lengkap tanpa notasi himpunan formal (∩,∪), label diagram Venn, serta rutinitas penurunan matematis. Hasil studi mengonfirmasi bahwa siswa ekstrovert memprioritaskan diskursus lisan kolokial, sehingga menciptakan celah realisasi simbolis tertulis. Practical implications: Pemberian sanksi atau anggapan "kecerobohan" pada siswa ekstrovert terbukti tidak efektif. Pendidik perlu menerapkan Oral-to-Symbolic Scaffolding Tools (seperti pengorganisasi grafis dan templat transisi) untuk mengonversi ekspresi lisan siswa menjadi notasi simbolis yang rigorus. Originality/value: Studi ini secara unik mengintegrasikan psikologi kepribadian dengan teori komognitif, memberikan kontribusi baru yang merebingkai celah simbolis siswa ekstrovert sebagai ketidaksesuaian register diskursus, bukan hambatan kognitif.