Learning pythagorean theorem from ancient China: A preliminary study

Abstract

In this article, we explore how History of the Pythagorean theorem, especially from ancient China, as a source of inspiration for learning design. Based on historical examples and problem solving from the history of mathematics, we try to arrange instructional tasks for seventh-grade secondary education students and how its role in supporting students’ understanding of Pythagorean theorem. We focus on explaining the preliminary studies or the first phase of the three main phases in design research. The basic idea of instructional design is to introduce historical geometric diagrams and solve the right triangle problem in the manner of Liu Hui (3rd century CE). The purpose of introducing geometric diagrams is to connect students’ symbolic algebraic thinking with visual thinking about geometric shapes especially in the case of right triangles. In this study, we also conducted interviews and debrief sessions with teachers and tested the student’s history-based tasks to several students for initial investigation in the matter of developing the Hypothetical Learning Trajectory. Results of this study show that teachers have a positive response toward the history-based instructional task developed. On the other hand, we find the resolution of Right Triangles problems with diagrams by the students involving three steps: translation, transformation, and diagrammatic reasoning.

Profil of Students’ Mathematical Literacy in Solving AKM Task in Terms of Personality Types

“…The question contains measurement and geometry content with (1) personal context regarding the sale of hand sanitiser with the cognitive level of applying, (2) scientific about cucumber plant support wood with the cognitive level of reasoning, and (3) socio-cultural regarding damar kurung with the cognitive level of applying. Measurement and geometry content was chosen because based on the results of the 2012 PISA study on geometry content, around 70% of Indonesian students are at level 1, which means their ability is still in solving routine problems (Fachrudin et al, 2019). This test aims to determine students' mathematical literacy in solving AKM task.…”

Kemampuan Penalaran Matematis Siswa Dalam Menyelesaikan Soal Literasi Matematika Kontekstual

“…Dengan mengerjakan soal kontekstual membantu siswa dalam mensituasikan matematika kedalam konteks (Putra et al, 2016b) dan memberikan stimulus kepada siswa untuk berpikir kritis menggunakan penalaran sendiri dalam penyelesaiannya (Putra et al, 2016b) sebab matematika itu sendiri digunakan untuk memecahkan masalah di kehidupan sehari hari (Fachrudin et al, 2019), memperkuat dan mengembang-kan sains dan berhubungan dengan perkembangan teknologi sampai hari ini (Hahn, 2020); (Schoevers et al, 2020). Permasalahan literasi matematika sangat baik apabila menggunakan permasalahan kontekstual yang dekat dengan kehidupan siswa dan saat siswa menyelesaikan masalah tersebut dapat dianalisis bagaimana siswa mengeksplorasi pengetahuan baru untuk mendukung dan mendorong kemampuan penalaran matematis siswa.…”