The Development of Courseware Based on Mathematical Representations and Arguments in Number Theory Courses

Abstract

Courseware have an important role in the achievement of the objectives of education. Nevertheless, it does not mean any learning resources can be used for a type of learning. The teacher should provide and develop materials appropriate to the characteristics and the social environment of its student. Number Theory courses is one of the basic subjects that would be a prerequisite for courses at the next level, such as Linear Algebra, Complex Analysis, Real Analysis, Transformation Geometry, and Algebra Structure. Thus, the student's understanding about the essential concepts that exist in this course will determine their success in studying subjects that mentioned above. In trying to understand most of the topics in Number Theory required the abilities of mathematical argumentation and representation. The ability of argumentation is required in studying the topic of complex number system, special operations, mathematical induction, congruence and divisibility. Ability representation especially verbal representations and symbols required by almost all the topics in this course. The purpose of this paper is to describe the development of teaching and learning Number Theory materials which facilitate students to develop the ability of mathematical argumentation and representation. The model used is a Thiagarajan development model consisting phases of defining, planning, development, and deployment. This paper is restricted to the analysis of the results of the materials validation from number theory experts. Keywords: Courseware, Numbers Theory, Argumentation, Representation AbstrakBahan ajar memiliki peranan penting dalam pencapaian tujuan pendidikan. Meskipun demikian, tidak berarti sebarang sumber belajar dapat digunakan untuk suatu jenis pembelajaran. Pengajar hendaknya menyediakan dan mengembangkan bahan ajar yang sesuai dengan karakteristik dan lingkungan sosial mahasiswanya. Mata kuliah Teori Bilangan merupakan salah satu mata kuliah dasar yang akan menjadi prasyarat bagi mata kuliah-mata kuliah keprodian pada tingkat selanjutnya, seperti mata kuliah Aljabar Linear, Analisis Kompleks, Analisis Real, Geometri Transformasi, dan Struktur Aljabar. Dengan demikian, pemahaman mahasiswa secara utuh terhadap konsep-konsep esensial yang ada pada mata kuliah ini akan sangat menentukan keberhasilan mereka dalam mempelajari mata kuliah-mata kuliah tersebut di atas. Dalam memahami sebagian besar topik yang terdapat dalam mata kuliah Teori Bilangan diperlukan kemampuan argumentasi dan representasi matematis. Kemampuan argumentasi diperlukan mahasiswa dalam mempelajari topik sistem bilangan kompleks, operasi khusus, induksi matematika, kekongruenan dan keterbagian. Kemampuan representasi terutama representasi verbal dan simbol dibutuhkan oleh hampir semua topik pada mata kuliah ini. Tujuan penulisan ini adalah untuk mendeskripsikan proses pengembangan bahan ajar Teori Bilangan yang memfasilitasi mahasiswa untuk dapat mengembangkan kemampuan argumentasi dan representasi matematisnya. Model pengembangan yang digunakan...

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