Exploring Students’ Mathematical Representation in Open-Ended Problems: A Study Based on Habits of Mind

Callista Amalia Fitri; Ade Mirza; Yulis Jamiah; Ahmad Yani T; Dona Fitriawan; Edy Yusmin

doi:10.26737/jpmi.v11i2.8868

Exploring Students’ Mathematical Representation in Open-Ended Problems: A Study Based on Habits of Mind

Callista Amalia Fitri, Ade Mirza, Yulis Jamiah, Ahmad Yani T, Dona Fitriawan, Edy Yusmin

Abstract

This scholarly inquiry seeks to: (1) identify junior high school students' mathematical representation abilities in solving open-ended problems based on their habits of mind; and (2) analyze the relationship between students' mathematical representation abilities and habits of mind. The research subjects involved 30 students in class VIII A at SMP Negeri 13 Pontianak. This investigation implemented a quantitative descriptive method within a correlational approach. The primary research instrument was a test designed in the format of open-ended questions to measure mathematical representation abilities in similarity material, as well as a habits of mind questionnaire based on four indicators, persisting, thinking flexibility, metacognition, and creating, imagining, and innovating. The analysis results reveal that: (1) Among students with high levels of habits of mind, visual, symbolic, and verbal representation abilities were recorded at 23.8%, 54.3%, and 22.2%, respectively. Students with moderate habits of mind demonstrated higher visual (47.9%), symbolic (65.4%), and verbal (34.7%) representation abilities. Conversely, students with low habits of mind exhibited 46% visual, 67.6% symbolic, and 39.7% verbal representation abilities; and (2) These results indicate a tendency that is not entirely in line with the theoretical assumption that habits of mind contribute positively to mathematical representation ability. No significant correlation exists between students’ habits of mind and their mathematical representation ability in solving open-ended problems (p = 0.246; r = −0.218), with a negative correlation. This result suggests that these two variables likely measure relatively independent dimensions and are influenced by other mediating factors, so that improvements in habits of mind do not directly lead to improvements in mathematical representation ability in solving open-ended problems.

Eksplorasi Kemampuan Representasi Matematis Siswa dalam Penyelesaian Soal Open-Ended ditinjau dari Habits of Mind

ABSTRAK
Kajian ilmiah ini dimaksudkan guna: (1) mengidentifikasi kemampuan representasi matematis siswa dalam menyelesaikan soal open-ended berdasarkan tingkat habits of mind; dan (2) menganalisis hubungan antara kemampuan representasi matematis dan habits of mind siswa. Subjek penelitian melibatkan 30 siswa kelas VIII A SMP Negeri 13 Pontianak. Studi ini menerapkan metode kuantitatif deskriptif dalam kerangka pendekatan korelasional. Instrumen penelitian terdiri atas tes berbentuk soal open-ended untuk mengukur kemampuan representasi matematis pada materi kesebangunan, serta angket habits of mind berdasarkan empat indikator, yaitu ketekunan, keluwesan berpikir, kesadaran atas proses berpikir, serta mencipta, berkhayal, dan berinovasi. Hasil penelitian mengindikasikan: (1) Di antara siswa dengan tingkat habits of mind yang tinggi, kemampuan representasi visual, simbolik, dan verbal tercatat masing-masing sebesar 23,8%, 54,3%, dan 22,2%. Siswa dengan habits of mind sedang menunjukkan kemampuan representasi visual (47,9%), simbolik (65,4%), dan verbal (34,7%) yang lebih tinggi. Sebaliknya, siswa dengan habits of mind rendah menunjukkan kemampuan representasi visual 46%, simbolik 67,6%, dan verbal 39,7%; dan (2) Temuan ini menunjukkan adanya kecenderungan yang tidak sepenuhnya sejalan dengan asumsi teoritis yang menyatakan bahwa habits of mind berkontribusi positif terhadap kemampuan representasi matematis. Hasil uji menunjukkan bahwa kemampuan representasi matematis siswa dalam menyelesaikan soal open-ended tidak berkorelasi secara signifikan dengan habits of mind (p = 0,246; r = −0,218), dengan arah hubungan yang negatif. Hasil ini mengindikasikan bahwa kedua variabel tersebut kemungkinan mengukur dimensi yang relatif independen dan dipengaruhi faktor mediasi lain, sehingga peningkatan habits of mind tidak secara langsung diikuti oleh peningkatan kemampuan representasi matematis dalam konteks penyelesaian soal open-ended.

Kata Kunci:
Representasi; Open Ended; Habits of Mind; Kesebangunan

Keywords

Representation; Open Ended; Habits of Mind; Similarity

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DOI: http://dx.doi.org/10.26737/jpmi.v11i2.8868