Abstract
This study aims at understanding the role of the tools chosen throughout the processes of solving a non-routine mathematical problem and communicating its solution. In assuming that problem-solving is a synchronous activity of mathematization and expression of mathematical thinking we take our proposed Mathematical Problem Solving with Technology (MPST) model to analyze the processes of solving-and-expressing-problems. Resorting to qualitative methods for data collection and analysis, we report on the case of an 8th grader working on a covariation problem to examine the role that paper-and-pencil and digital tools play in the development of a conceptual model of the situation. We found that the resources used throughout the solving-and-expressing activity influenced the depth of the conceptual model developed, within a process of progressive mathematization. Whereas paper-and-pencil led to the emergence of a conceptual model based on exploring particular cases, the digital transformation of the solution was triggered by the process of communicating its mathematical justification and expanded the previous model. Moreover, the complexity of this activity is evidenced by its multiple sequences of processes. Finally, the integration process seems crucial as the concomitant use of technological and mathematical resources precedes major advancements in the expansion of the conceptual model.
Highlights
Abstrak Penelitian ini bertujuan untuk memberikan memahami tentang peran pemilihan media teknologi dalam proses pemecahan masalah matematika non-rutin dan mengkomunikasikan solusinya
Barrera-Mora and Reyes-Rodriguez (2013) concluded that dynamic geometry environment (DGE) act as reorganizers of mathematical thinking, allowing cognitive activities only possible due to the dynamism embedded in the tool, leading to explore variation and covariation, and to different forms of justifying a conjecture and expressing it with the tool
Other studies point that the mathematics used by students working on a paper-and-pencil task is different from the one they apply when using a touchscreen device (Bairral, Arzarelo, & Assis, 2017); students use similar strategies both with paper-and-pencil and an applet in solving equations (Jupri, Drijvers, & van den HeuvelPanhuizen, 2016); there are benefits in both environments (Koyuncu, Akyuz, & Cakiroglu, 2015), or the two environments play a complementary role in mathematical learning, in conjecturing and proving activities (Komatsu & Jones, 2020)
Summary
Abstrak Penelitian ini bertujuan untuk memberikan memahami tentang peran pemilihan media teknologi dalam proses pemecahan masalah matematika non-rutin dan mengkomunikasikan solusinya. Diasumsikan bahwa pemecahan masalah adalah sinkronisasi aktivitas matematika dan ekspresi pemikiran matematis, kami menawarkan model Mathematical Problem Solving with Technology (MPST) untuk menganalisis proses pemecahan-danpengungkapan-masalah. Berdasarkan penggunaan metode kualitatif dalam pengumpulan dan analisis data, kami melaporkan kasus seorang siswa kelas 8 yang mengerjakan masalah kovarian untuk mengidentifikasi peran penggunaan kertas dan pensil serta alat digital dalam pengembangan model konseptual dari aktivitas ini. Kami menemukan bahwa sumber daya yang digunakan selama aktivitas pemecahan dan pengungkapan mempengaruhi kedalaman model konseptual yang dikembangkan dalam proses matematisasi progresif. Barrera-Mora and Reyes-Rodriguez (2013) concluded that DGEs act as reorganizers of mathematical thinking, allowing cognitive activities only possible due to the dynamism embedded in the tool, leading to explore variation and covariation, and to different forms of justifying a conjecture and expressing it with the tool. The successful experiences with particular digital tools and their affordances integrate and reshape cognition, reconfigure the essence of mathematical thinking and activity, and can be transferred to other situations (Barrera-Mora & Reyes-Rodriguez, 2013; Borba & Villarreal, 1998)
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