Students’ difficulties in productive connective thinking to solve mathematical problems

Abstract

[English]: The purpose of this study was to identify students’ difficulties in establishing mathematical connections in productive connective thinking to solve mathematical problems. Students’ difficulties were identified from which the students did not develop connection ideas after reflection at the stages of Toshio’s (2000) cognition scheme. The purposive sampling was used to select 2 out of 85 11th-grade students who had taken the initial test in order to measure their connective thinking. Students’ works and the transcript of think-aloud and interviews with two students were analyzed using a qualitative descriptive approach. It reveals that students indicate various difficulties in developing connections. At the cognition stage, students had difficulty establishing a connection idea for solutions, since they were not able to collect appropriate data and did not verify the initial data to understand the direction of solving the problem. At the inference stage, students were difficult to establish a procedure connection because they could not plan an effective strategy of problem-solving. At the formulation stage, students had difficulty establishing numerical connections since they did not verify the data and did not have sufficient understanding of the concepts to formulate the problem. At the reconstruction stage, students found it difficult to establish generalization connections because of being not motivated to solve the problems and not doing a comprehensive generalization and evaluation towards the problem-solving. Keywords: Connective thinking, Mathematical connections, Reflection, Toshio thinking scheme [Bahasa]: Penelitian ini bertujuan mengidentifikasi kesulitan siswa membangun koneksi matematis dalam berpikir konektif produktif untuk memecahkan masalah matematika. Kesulitan siswa membangun koneksi matematis diidentifikasi dari tidak berkembangnya ide-ide koneksi setelah refleksi pada setiap tahapan kognitif Toshio (2000). Tehnik purposive sampling digunakan untuk memilih 2 dari 85 orang siswa kelas 11 yang telah mengikuti tes awal untuk mengukur kemampuan berpikir konektif. Lembar kerja, rekaman think aloud dan wawancara dari dua orang siswa dianalisis dengan pendekatan deskriptif kualitatif. Hasil analisis menunjukkan siswa mengalami berbagai kesulitan membangun koneksi. Pada tahap kognisi, siswa mengalami kesulitan membangun koneksi ide solusi karena siswa tidak mampu mengumpulkan data yang sesuai dan tidak melakukan verifikasi terhadap data awal yang dikumpulkan untuk memahami dan memikirkan arah penyelesaian masalah. Pada tahap inferensi, siswa mengalami kesulitan membangun koneksi prosedur karena siswa tidak menyusun rencana penyelesaian yang efektif. Pada tahap formulasi, siswa mengalami kesulitan membangun koneksi numerik karena siswa tidak melakukan proses verifikasi data dan tidak memiliki pemahaman konsep yang memadai untuk melakukan proses formulasi. Pada tahap rekonstruksi, siswa mengalami kesulitan membangun koneksi generalisasi karena siswa tidak memiliki motivasi untuk memecahkan masalah dan tidak melakukan proses generalisasi dan evaluasi secara menyeluruh terhadap proses pemecahan masalah. Kata kunci: Berpikir konektif, Koneksi matematis, Refleksi, Skema berpikir Toshio

Keywords

• connective thinking
• mathematics connections
• reflection
• toshio scheme