PERKEMBANGAN PEMAHAMAN MATEMATIS SISWA SEKOLAH DASAR KELAS V BERDASARKAN TEORI PIRIE-KIEREN PADA TOPIK PECAHAN

Nur Aida Endah Pratama

Abstract


Abstract: This study is conducted to describe and illustrate the flow of development of mathematical understanding on fifth graders in problem solving of fractions based on the theory suggested by Pirie-Kieren. The qualitative-narrative approach was used to describe clearly, in detail and comprehensively the level of development of students’ mathematical understanding with reference to Pirie-Kieren’s theory. The results of the analysis found that there are similarities within the flow of understanding developments on fifth graders in problem solving fractions, which starts from the stage of image making, moving towards the image having, then developed at the property level to the level of formalizing noticing. The difference lies in the back folding process that occurs when a less complete understanding at a certain level in the Pirie-Kieren theory.

Keywords: mathematical understanding, Pirie-Kieren theory, folding back, elementary school

Abstrak: Penelitian ini bertujuan untuk mendeskripsikan dan menggambarkan alur perkembangan pemahaman matematis siswa sekolah dasar kelas V dalam menyelesaikan masalah pecahan berdasarkan teori Pirie-Kieren. Pendekatan kualitatif-naratif digunakan untuk memaparkan secara jelas, teperinci dan menyeluruh deskrispsi level perkembangan pemahaman matematis siswa dengan mengacu pada teori Pirie-Kieren. Hasil analisis ditemukan bahwa terdapat kesamaan alur perkembangan pemahaman siswa sekolah dasar kelas V dalam menyelesaikan masalah pecahan, yaitu dimulai dari tahap image making, bergerak menuju image having, kemudian berkembang pada level property noticing sampai pada level formalizing. Perbedaannya terletak pada proses folding back yang terjadi ketika melengkapi pemahaman yang kurang pada level tertentu dalam teori Pirie-Kieren.

Kata kunci: pemahaman matematis, teori Pirie-Kieren, folding back, SD


Full Text:

PDF

References


Arends, R. I. 2004. Learning to Teach (Sixth Edition). New York: Mc Graw Hill.

Cresswell, J.W. Research Design: Qualitative, Quantitative, and Mixed Methods Approaches. USA: SAGE Publication

Droujkova, M. A., Berenson, S. B, Slaten, K., & Tombes, S. 2005. A Conceptual Framework For Studying Teacher Preparation : The Pirie-Kieren Model, Collective Understanding, and Methapor. Proceeding of the 29th Conference of the International Group for the Psychology of Mathematics Education. 2:289-296.

Gokalp, D. & Sharma, D. 2010. A Study on Addition and Subtraction of Fractions : The Use Of Pirie-Kieren Model and Hands-on Activities. Jurnal Procedia Social and Behavioral Science. 2: 5168-5171.

Hunting, R. P., & Sharpley, C. F. 1988. Fraction Knowledge in Preschool Children. Journal for Research in Mathematics Education, 19(2):175-180.

Kemendikbud. 2013. Kurikulum 2013: Kompetensi Dasar (SD) / Madrasah Ibtidaiyah (MI).

Kyriakides, A. O. 2010. Enganging Everyday Language to Enhance Comprehension Of Fraction Multiplication. Proceeding of CERME 6. January 28th – February First 2009, Lyon France.

Lawan, A. 2011. Growth of Students’ Understanding of Part-Whole Sub-Construct of Rational Number on the Layers of Pirie-Kieren Theory. Proceedings of the Seventeenth National Congress of the Association for Mathematics Education of South Africa (AMESA), Vol.1. University of the Witwatersrand Johannesburg.

Manu, S.S. 2005. Growth of Mathematical Understanding in A Bilingual Context: Analysis and Implications. Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education. 3:289-296

Martin, L., LaCroix, L., & Fownes, L. 2005. Folding Back and the Growth of Mathematical Understanding in Workplace Training. ALM International Journal. 1(1):19-35.

Martin, L. C. 2001a. Growing Mathematical Understanding : Teaching and Learning As Listening and Sharing. Proceeding of the Annual Meeting of the North American Chapter of Intenational Group for the Psychology of Mathematics Education 1 and 2. .

Martin, L.C. 2001b. Understanding as a Dynamical Process: How do They get to Where They are?. Proceeding of the Annual Meeting of the North American Chapter of Intenational Group for the Psicology of Mathematics Education 1 and 2.

Meel, D. E. 2003. Models and Theories of Mathematical Understanding: Comparing Pirie and Kieren’s Model of the Growth of Mathematical Understanding and APOS Theory. CBMS Issues in Mathematical Educations, 12:734-745

Oers, B. E. 2009. Emergent Mathematical Thinking in the Context of Play. Springer: Educ Stud Math (2010) 74 : 23-37.

Pratama, N. A. E., Sa’dijah, C., & Subanji. 2016. Teori Pirie-Kieren dalam Mendiskripsikan Perkembangan Pemahaman Matematis Siswa. Prosiding Seminar Nasional Pendidikan Dasar 2016 (Peningkatan Kualitas Pendidikan Dasar dalam Menghadapi Daya Saing Regional (ASEAN)).

Pirie, S., & Kieren, T. 1994. Beyond Metaphor: Formalizing in Mathematical Understanding within Constructivist Environments. FLM Publishing Association Vancouver, British Columbia, Canada.

Pirie, S. & Martin, L. 2000. The Role of collecting in the Growth of Mathematical Understanding. Mathematics Education Research Journal. 12 (2):127-146.

Razak, F. A., Noordin, N., Alias, R., & Dollah, R. 2012. How Do 13-years Olds in Malaysia Compare Fractions?.Procedia Social and Behavioral Science. 42:100-105.

Sa’dijah, C. 2016. Pembelajaran Matematika Secara Konstruktivis. Pidato Pengukuhan Jabatan Guru Besar dalam Bidang Ilmu Pendidikan Matematika pada Fakultas Matematika dan Ilmu Pengetahuan Alam. Malang: Universitas Negeri Malang.

Sengul, S., & Argat, A. 2015. The Analysis of Understanding Factorial concept Processes of 7th Grade Students who have Low Academic Achievement with Pirie Kieren Theory. Jurnal Procedia Social and Behavioral Science. 197: 1263-1270.

Siegler, R. S., Fazio, L. K., Bailey, D. H., & Zhou, X. 2013. Fractions: The New Frontier for Theories of Numerical Development. Trends in Cognitive Science, 17(1).

Warner, L., & Schorr, R. Y. 2004. From Primitive Knowing to Formalizing : The of Student to Student Questioning in the Development of Mathematical Understanding. Proceeding of the Twenty Sixth Annual Meeting of the North American Chapter of the International Group for Psochology of Mathematics Education: Building Connections between communities. Toronto, Ontario. 2:429-437.

Wilson, P. H., & Stein, C. C. 2007. The Role of Representations in Growth of Understanding in Pattern-Finding Task. Ninth International Conference Mathematic Education in a Global Community. Charlotte, NC.

Wong, M., & Evans, D. 2007. Student’s Conceptual Understanding of Equivalent Fractions. In J. Watson & K. Beswick (Eds.), Mathematics: Essesntial Research, essential Practice (Proceedings of the 30th Annual Conference of the Mathematics Education Research Group of Australasia). 2:824-833.

Yoshida, K. 2005. Children’s ‘Everyday Concepts of Fractions’ Based on Vygotsky’s Theory: Before and After Fraction Lessons. Proceeding of the 29th Conference of the International Group of the Psychology of Mathematics Education, 1:334.




DOI: http://dx.doi.org/10.17977/um009v26i12017p077

Refbacks

  • There are currently no refbacks.





Creative Commons License
Jurnal Sekolah Dasar is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

web
analytics View My Stats