Öz
Kaynakça
- Alghtani, O. A., & Abdulhamied, N. A. (2010). The effectiveness of geometric representative approach in developing algebraic thinking of fourth grade students. Procedia - Social and Behavioral Sciences, 8(5), 256–263. https://doi.org/10.1016/j.sbspro.2010.12.035 Barbosa, E., & Borralho, A. (2011). Exploring patterns in algebraic thinking, 7, 2914–2915. Barbosa, E., & Borralho, A. (2011). Exploring patterns in algebraic thinking, 7, 2914–2915 Blanton, M., & Kaput, J. (2005) Characterizing a Classrooom Practice that Promote Algebraic Thinking. Journal for Research in Mathematics Education, 36 (5), 412-446. Booker, G., & Windsor, W. (2010). Developing algebraic thinking: Using problem-solving to build from number and geometry in the primary school to the ideas that underpin algebra in high school and beyond.Procedia - Social and Behavioral Sciences, 8(5), 411–419. https://doi.org/10.1016/j.sbspro.2010.12.057 Brousseau, G. (2002). Epistemological Obstacles, Problems, and Didactical Engineering . Theory of Didactical Situations in Mathematics: Didactique Des MathEmatiques, 1970-1990 , (1 983), 79–117. Cai, J. (2004). Developing Algebraic Thinking in the Earlier Grades : A Case Study of the Chinese Elementary School Curriculum 1. The Mathematics Educator, 8(1), 107–130. Cai, J., & J.Knuth, E. (2005). Introduction : The Development of Students’ Algebraic Thinking In Earlier Grades From Curricular, Instructional and Learning Perspectives. Zdm, 37(1), 1–4. Fong, N. S. (2004). Developing Algebraic Thinking in Early Grades: Case Study of The Singapore Primary Mathematics Curriculum. The Mathematics Educator. Vol. 8 No. 1. 39-59. Herutomo, R. A. dan Saputro, T. E. M. (2014). Analisis Kesalahan dan Miskonsepsi Siswa Kelas VII Pada Materi Aljabar. Edusentris, Jurnal Ilmu Pendidikan dan Pengajaran, Vol. 1 No. 2, hal. 134-145. Hidayati, F. (2010). Kajian Kesulitan Belajar Siswa Kelas VII SMP Negeri 16 Yogyakarta dalam Mempelajari Aljabar. Skripsi Universitas negeri Yogyakarta. Dipublikasikan Jupri, A., Drijvers, P., & Van den Heuvel-Panhuizen, M. (2014)….Difficulties in initial algebra learning in Indonesia. Mathematics Education Research Journal 26 (4), 683-710 Kilpatrick, J., Swafford, J., & Fidell, B. (2001). Adding It Up: Helping Children Learn Mathematics. Washington, DC: national Academy Press. Lew, H. C. (2004). Developing Algebraic Thinking in Early Grades: Case Study of Korean Elementary School Mathematics. The Mathematics Educator. Vol. 8 No. 1. 88-106. Marsetyorini, A. D. dan Murwaningtyas, C. E. (2012). Diagnosis Kesulitan Belajar Siswa dan Pembelajaran Remedial dalam Materi Operasi Pada Pecahan Bentuk Aljabar Di Kelas VIII SMPN 2 Jetis Bantul. Prosiding Makalah dipresentasikan dalam Seminar nasional Matematika dan Pendidikan Matematika “Kontribusi Pendidikan Matematika dan Matematika dalam Membangun Karakter Guru dan Siswa”. Jurusan Pendidikan Matematika FPMIPA UNY Mestre, C. & Oliveira, H. (2012). From Quasi-Variable Thinking to Algebraic Thinking: A Study With Grade 4 Students. [Online]. Diakses dari http://repositorio.ul.pt/bitstream/10451/7087/1/Mestre_Oliveira_ ICME12.pdf Miles, M. B. & Huberman, A. M. (1984). Qualitative Data Analysis: A Sourcebook of New Methods. California; SAGE publications Inc. Moyer, J., Huinker, D. A., & Cai, F. (2004). Developing Algebraic Thinking in the Earlier Grades: A Case Study of the U.S. Investigations Curriculum. The Mathematics Educator. Vol. 8 No. 1. 6-38. NCTM. (2000). Principles and Standards for School Mathematics. Reston, V.A: NCTM. NCTM. (2014). Principles to Actions: Ensuring Mathematical Success for All. Reston, V.A: NCTM. Permatasari, B. A. D., dkk. (2015). Analisis Kesulitan Siswa dalam Menyelesaikan Soal Materi Aljabar Siswa Kelas VIII SMP Negeri 2 Bangil. Kadikma, Vol. 6, No. 2, hal 119-130. Purwanto, M. N. (2006). Prinsip-prinsip dan teknik evaluasi pengajaran. Bandung: PT Remaja Rosdakarya. Radford, L. (2010). Elementary Forms of Algebraic Thinking in Young Students.In M. F. Pinto.& T. F. Kawasaki (Eds.).Proceedings of the 34th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4, p. 73-80. Belo Horizonte, Brazil: PME. Radford, L. (2011). Embodiment, perception and symbols in the development of early algebraic thinking.In Ubuz, B. (Ed.), Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, p. 17-24). Ankara, Turkey: PME. Radford, L. (2012). On the development of algebraic thinking.PNA 64(1), 117-133. Schmittau, J. & Morris, A. (2004). The Developing of Algebra in Elementary Mathematics Curriculum of V.V. Davydov. The Mathematics Educator. Vol. 8 No. 1. 60-87. Suryadi, D. (2010). Didactical Design Research (DDR) dalam Pengembangan Pembelajaran Matematika1. Seminar Nasional Pembelajaran MIPA Di UM Malang, 13 November 2010 SEMNAS MIPA 2010 UTAMA, (November), 1–75.
Öz
This research comes from an idea that algebraic
thinking is one of the important things in learning mathematics for elementary
school students. Algebraic thinking ability is a transitional process from
arithmetic learning to algebraic learning. Students in elementary school must
have aquired this ability as some prerequisite for advanced mathematics (at the
level of junior high school). Aside from
that, the Algebraic Thinking ability requires students to solve mathematical
problems. The main purpose of this research is to describe students’ algebraic
thinking ability based upon algebraic-thinking characteristics, knowing the
learning trajectory of learning barriers to overcome these obstacles.
Therefore, the researcher conducted the research by utilizing a descriptive
research method. The data were collected by means of test, interview and
questionnaire on students in upper grades of elementary school located in urban
areas, mid areas, also transitional regions.
Based on the analysis of the results of algebraic thinking ability
instrument test from 78 students, and having compared with the indicators of
algebraic thinking in upper grades of elementary school in Indonesia, it shows
that algebraic thinking skills of upper elementary grades in Indonesia are seemingly
less good. In addition, researchers classify the barriers of algebraic thinking
into three types, namely ontogenic obstacle, didactic obstacle, and
epistemological obstacle, therefore with the data, the researcher generates hypothetical
learning trajectory to cope with the obstacles of algebraic thinking. Learning
trajectory as a result of this study will be developed as algebraic thinking
design learning.
Anahtar Kelimeler
Algebraic thinking descriptive analysis learning obstacles mathematics
Kaynakça
- Alghtani, O. A., & Abdulhamied, N. A. (2010). The effectiveness of geometric representative approach in developing algebraic thinking of fourth grade students. Procedia - Social and Behavioral Sciences, 8(5), 256–263. https://doi.org/10.1016/j.sbspro.2010.12.035 Barbosa, E., & Borralho, A. (2011). Exploring patterns in algebraic thinking, 7, 2914–2915. Barbosa, E., & Borralho, A. (2011). Exploring patterns in algebraic thinking, 7, 2914–2915 Blanton, M., & Kaput, J. (2005) Characterizing a Classrooom Practice that Promote Algebraic Thinking. Journal for Research in Mathematics Education, 36 (5), 412-446. Booker, G., & Windsor, W. (2010). Developing algebraic thinking: Using problem-solving to build from number and geometry in the primary school to the ideas that underpin algebra in high school and beyond.Procedia - Social and Behavioral Sciences, 8(5), 411–419. https://doi.org/10.1016/j.sbspro.2010.12.057 Brousseau, G. (2002). Epistemological Obstacles, Problems, and Didactical Engineering . Theory of Didactical Situations in Mathematics: Didactique Des MathEmatiques, 1970-1990 , (1 983), 79–117. Cai, J. (2004). Developing Algebraic Thinking in the Earlier Grades : A Case Study of the Chinese Elementary School Curriculum 1. The Mathematics Educator, 8(1), 107–130. Cai, J., & J.Knuth, E. (2005). Introduction : The Development of Students’ Algebraic Thinking In Earlier Grades From Curricular, Instructional and Learning Perspectives. Zdm, 37(1), 1–4. Fong, N. S. (2004). Developing Algebraic Thinking in Early Grades: Case Study of The Singapore Primary Mathematics Curriculum. The Mathematics Educator. Vol. 8 No. 1. 39-59. Herutomo, R. A. dan Saputro, T. E. M. (2014). Analisis Kesalahan dan Miskonsepsi Siswa Kelas VII Pada Materi Aljabar. Edusentris, Jurnal Ilmu Pendidikan dan Pengajaran, Vol. 1 No. 2, hal. 134-145. Hidayati, F. (2010). Kajian Kesulitan Belajar Siswa Kelas VII SMP Negeri 16 Yogyakarta dalam Mempelajari Aljabar. Skripsi Universitas negeri Yogyakarta. Dipublikasikan Jupri, A., Drijvers, P., & Van den Heuvel-Panhuizen, M. (2014)….Difficulties in initial algebra learning in Indonesia. Mathematics Education Research Journal 26 (4), 683-710 Kilpatrick, J., Swafford, J., & Fidell, B. (2001). Adding It Up: Helping Children Learn Mathematics. Washington, DC: national Academy Press. Lew, H. C. (2004). Developing Algebraic Thinking in Early Grades: Case Study of Korean Elementary School Mathematics. The Mathematics Educator. Vol. 8 No. 1. 88-106. Marsetyorini, A. D. dan Murwaningtyas, C. E. (2012). Diagnosis Kesulitan Belajar Siswa dan Pembelajaran Remedial dalam Materi Operasi Pada Pecahan Bentuk Aljabar Di Kelas VIII SMPN 2 Jetis Bantul. Prosiding Makalah dipresentasikan dalam Seminar nasional Matematika dan Pendidikan Matematika “Kontribusi Pendidikan Matematika dan Matematika dalam Membangun Karakter Guru dan Siswa”. Jurusan Pendidikan Matematika FPMIPA UNY Mestre, C. & Oliveira, H. (2012). From Quasi-Variable Thinking to Algebraic Thinking: A Study With Grade 4 Students. [Online]. Diakses dari http://repositorio.ul.pt/bitstream/10451/7087/1/Mestre_Oliveira_ ICME12.pdf Miles, M. B. & Huberman, A. M. (1984). Qualitative Data Analysis: A Sourcebook of New Methods. California; SAGE publications Inc. Moyer, J., Huinker, D. A., & Cai, F. (2004). Developing Algebraic Thinking in the Earlier Grades: A Case Study of the U.S. Investigations Curriculum. The Mathematics Educator. Vol. 8 No. 1. 6-38. NCTM. (2000). Principles and Standards for School Mathematics. Reston, V.A: NCTM. NCTM. (2014). Principles to Actions: Ensuring Mathematical Success for All. Reston, V.A: NCTM. Permatasari, B. A. D., dkk. (2015). Analisis Kesulitan Siswa dalam Menyelesaikan Soal Materi Aljabar Siswa Kelas VIII SMP Negeri 2 Bangil. Kadikma, Vol. 6, No. 2, hal 119-130. Purwanto, M. N. (2006). Prinsip-prinsip dan teknik evaluasi pengajaran. Bandung: PT Remaja Rosdakarya. Radford, L. (2010). Elementary Forms of Algebraic Thinking in Young Students.In M. F. Pinto.& T. F. Kawasaki (Eds.).Proceedings of the 34th Conference of the International Group for the Psychology of Mathematics Education, Vol. 4, p. 73-80. Belo Horizonte, Brazil: PME. Radford, L. (2011). Embodiment, perception and symbols in the development of early algebraic thinking.In Ubuz, B. (Ed.), Proceedings of the 35th Conference of the International Group for the Psychology of Mathematics Education (Vol. 4, p. 17-24). Ankara, Turkey: PME. Radford, L. (2012). On the development of algebraic thinking.PNA 64(1), 117-133. Schmittau, J. & Morris, A. (2004). The Developing of Algebra in Elementary Mathematics Curriculum of V.V. Davydov. The Mathematics Educator. Vol. 8 No. 1. 60-87. Suryadi, D. (2010). Didactical Design Research (DDR) dalam Pengembangan Pembelajaran Matematika1. Seminar Nasional Pembelajaran MIPA Di UM Malang, 13 November 2010 SEMNAS MIPA 2010 UTAMA, (November), 1–75.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 27 Aralık 2017 |
| Gönderilme Tarihi | 5 Kasım 2017 |
| Yayımlandığı Sayı | Yıl 2017Cilt: 3 Sayı: 9 |
Cited By
Characteristics of students’ mathematical representation in solving algebraic thinking problems
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https://doi.org/10.1088/1742-6596/1521/3/032009
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