T PD 1402297 Bibliography
DAFTAR PUSTAKA
Abidin, Y. (2011). Penelitian pendidikan dalam gamintan pendidikan dasar dan
paud. Bandung: Rizqi Press.
Alwasilah, C. (2012). Pokoknya kualitatif dasar-dasar merancang dan melakukan
penelitian kualitatif. Bandung: Pustaka Jaya.
Arikunto, S. (2010). Prosedur penelitian: Suatu pendekatan praktik. Jakarta:
Rineka Cipta.
Arnon, I., Nesher, P., & Nirenburg, R. (2001). Where do fractions encounter their
equivalents? Can this encounter take place in elementary-school?.
International Journal of Computers for Mathematical Learning, 6, 167214.
Ball, D. L. (1993). With an eye on the mathematical horizon: Dilemmas of
teaching elementary school mathematics. Elementary School Journal,
93(4), 373-397.
Ball, D. L., Lubienski, S., & Mewborn, D. S. (2001). Research on teaching
mathematics: The unsolved problem of teachers' mathematical knowledge.
Dalam V. Richardson (penyunting.), Handbook of research on teaching
(4th edition). Washington, DC: American Educational Research
Association.
Ball, D., Thames, M., & Phelps, G. (2008). Content knowledge for teaching: what
makes it special?. Journal of Teacher Education, 59(5), 389–407.
Battista, M. T. (2012). Cognition-based assessment & teaching of fraction:
building on students’ reasoning. Portsmouth: Heinemann
Bright, G. dkk. (1988). Identifying fractions on number lines. Journal for
Research in Mathematics Education, 19, 215-232.
Brousseau, G. & Warfield, V. (2014). Didactic Situations in Mathematics
Education. Dalam S. Lerman (penyunting). Encyclopedia of mathematics
education (hlm.470-476). London : springer.
Brousseau. (2002). Theory of didactical situations in mathematics. Netherlands:
Kluwer.
Brown, A. L. (1992). Design experiments: theoretical and methodological
challenges in creating complex interventions in classroom settings. The
Journal of the Learning Sciences, 2(2), 141–178.
Siti khazanatu Rohmah, 2016
DESAIN DIDAKTIS BERBASIS REALISTIC MATHEMATICS EDUCATION (RME) PADA MATERI
PECAHAN KELAS IV SEKOLAH DASAR
Universitas Pendidikan Indonesia| repository.upi.edu | perpustakaan.upi.edu
115
116
BSNP. (2006). Standar Isi Untuk Satuan Pendidikan Dasar dan Menengah.
Jakarta: BSNP.
Clements, D. H. & Sarama, J. (2007). Effects of a preschool mathematics
curriculum: summative research on the building blocks project. Journal for
Research in Mathematics Education, 38(2), 136-163.
Clements, D. H. dkk. (2011). Mathematics learned by young children in an
intervention based on learning trajectories: a large-scale cluster
randomized trial. Journal for Research in Mathematics Education, 42(2),
127–166.
Clements, D. H., Wilson, D. C., & Sarama, J. (2004). Young children's
composition of geometric figures: A learning trajectory. Mathematical
Thinking and Learning, 6(2), 163-184.
Clements, D., & Sarama, J. (2009). Learning and teaching early math: The
learning trajectories approach. New York: Routledge.
Cobb, P. (2002). Reasoning with tools and inscriptions. Journal of the Learning
Sciences, 11(2-3), 187-215.
Confrey, J. & Maloney, A. (2015). A design research study of a curriculum and
diagnostic assessment system for a learning trajectory on equipartitioning.
ZDM Mathematics Education, 47:919-932. DOI: 10.1007/s11858-0150699-y
Cortina, J. L., Visnovska, J, & Zuniga, C. (2014). Unit fractions in the context of
proportionality: Supporting students' reasoning about the inverse order
relationship. Mathematics Education Research Journal. DOI:
10.1007/s13394-013-0112-5
Cortina, J. L., Visnovska, J., & Zuniga, C.(2014). Equipartition as a didactical
obstacle in fraction instruction. Acta Didactica Universitatis Comenianae
Mathematics, Issue 14, 1-18
Creswell, J. (2012). Research design pendekatan kualitatif, kuantitatif, dan mixed
edisi ketiga. Yogyakarta: Pustaka Pelajar.
Daro, P., Mosher, F., & Corcoran, T. (2011). Learning trajectories in
mathematics: A foundation for standards, curriculum, assessment, and
instruction. (Research Report No. 68). Madison, WI: Consortium for
Policy Research in Education.
Durmus, S. & Karakirik, E. (2006). Virtual manipulatives in mathematics
education: A theoretical framework. Turkish Online Journal of
Educational
Technology,
5(1),
117-123.
http://www.tojet.net/articles/v5i1/5112.pdf
Siti Khazanatu Rohmah, 2016
DESAIN DIDAKTIS BERBASIS REALISTIC MATHEMATICS EDUCATION (RME) PADA MATERI
PECAHAN KELAS IV SEKOLAH DASAR
Universitas Pendidikan Indonesia| repository.upi.edu | perpustakaan.upi.edu
117
Ebby, C. B. dkk. (2013). Teacher analysis of student knowledge (TASK): A
measure of learning trajectory-oriented formative assessment. Paper
presented at the Annual Meeting of the American Educational Research
Association, San Francisco, April 2013.
Fajriyah, N. & Triratnawati, D. (2008). Cerdas berhitung matematika untuk
SD/MI kelas 3. Jakarta: Grahadi.
Gravemeijer, K. (1994). Educational development and educational research in
mathematics education. Journal for Research in Mathematics Education,
25 (5), 443-471.
Gravemeijer, K., Bowers, J., & Stephan, M. (2003). Chapter 4: a hypothetical
learning trajectory on measurement and flexible arithmetic. Journal for
Research in Mathematics Education, Monograph, 12, 51-66.
Gravemeijer, K.P.E. & Cobb, P. (2006). Design research from a learning design
perspective. Dalam J. van den Akker, dkk. (penyunting). Educational
design research (hlm. 17–51). London: Routledge.
Hill, H., Rowan, B., & Ball, D. L. (2005). Effects of teachers' mathematical
knowledge for teaching on student achievement. American Educational
Research Journal, 42, 371-406.
Hill, H., Schilling, S., & Ball, D. L. (2004). Developing measures of teachers'
mathematics knowledge for teaching. The Elementary School Journal,
105, 11-30.
Hurst, C. & Hurrell, D. (2014). Developing the big ideas of number. International
Journal of Educational Studies in Mathematics. ISSN: 2148 – 5984.
Izsak, A., Tillema, E., & Tunc-Pekkan, Z. (2008). Teaching and learning fraction
addition on number line. Journal for Research in Mathematics Education,
39(1), 33-62. NCTM.
Klein A. S., & Beishuizen M. (1998). The Empty Number Line in Dutch
Second Grades: Realistic Versus Gradual Program Design. Journal for
Research in Mathematics Education. 29(4), 443–464.
Lidinillah, D. A. M. (2011). Educational design research: a theoretical
framework
for
action.
[Online].
Diakses
dari:
http://file.upi.edu/Direktori/KDTASIKMALAYA/DINDIN_ABDUL_MUIZ_LIDINILLAH_(KDTASIK
MALAYA)
Lin, C. Y. dkk. (2013). Preservice teachers‘ conceptual and procedural knowledge
of fraction operations: A comparative study of the United States and
Taiwan. School Science and Mathematics, 113(1), 41-51. DOI:
10.1111/j.1949-8594.2012.00173.
Siti Khazanatu Rohmah, 2016
DESAIN DIDAKTIS BERBASIS REALISTIC MATHEMATICS EDUCATION (RME) PADA MATERI
PECAHAN KELAS IV SEKOLAH DASAR
Universitas Pendidikan Indonesia| repository.upi.edu | perpustakaan.upi.edu
118
Makonye, J. & Shingirayi, M. (2014). The obstacles faced by the learners in the
learning of quadratic inequalities. Mediterranean Journal of Social
Sciences, 5(27). MCSER Publishing, Rome-Italy.
Manno, G. (2005). Embadiment and a-didactical situation in the theachinglearning of the perpendicular straight lines concept. (Disertasi). Faculty of
Mathematics and Physics Departement of Didactic Mathematics Comenius
University Bratislava, Slovakia.
McKenney, S. & Reeves, T. (2012). Conducting educational design research.
London: Routledge.
McMillan, J. H. & Scumacher, Sally. (2010). Research education: evidence-based
inquiry (seventh edition). New Jersey. Pearson Education.
Miyakawa, T. & Winslow, C. (2009). Didactical designs for students‘
proportional reasoning: an ―open approach‖ lesson and a ―fundamental
situation‖. Educ Stud Math, 72:199–218. DOI 10.1007/s10649-009-9188-y
Moleong, L. J. (2014). Metedologi penelitian kualitatif. Bandung: PT Remaja
Rosdakarya.
Moseley, B. J., Okamoto, Y., & Ishida, J. (2007). Comparing U.S. and Japanese
elementary school teachers‘ facility for linking rational number
representations. International Journal of Science and Mathematics
Education, 5, 165-185. DOI: 10.1007/s10763-006-9040-0.
Mustaqim, B. & Astuty, A. (2008). Ayo belajar matematika jilid 4 untuk SD dan
MI kelas IV. Jakarta: Buana Raya.
Myers, M. dkk. (2015). From implicit to explicit: articulating equitable learning
trajectories based instruction. Journal of Urban Mathematics Education,
8(2), 11–22 ©JUME.
Ningsih, S. (2014). Realistic mathematics education: model alternatif
pembelajaran matematika sekolah. Jurnal Pendidikan Matematika IAIN
Antasari. 01(2), 73-94.
Nyikahadzoyi, M. R., Mapuwei, T., & Chinyoka, M. (2013). Some cognitive
obstacles faced by ‗A‘ level mathematics students in understanding
inequalities: a case study of Bindura urban high schools. International
Journal of Academic Research in Progressive Education and
Development, 2 (2). ISSN: 2226-6348
Pepin, B. & Gueudet G. (2014). Curriculum resources and textbooks in
mathematics education. Dalam S. Lerman (penyunting). Encyclopedia of
mathematics education (hlm.132-135). London : springer.
Siti Khazanatu Rohmah, 2016
DESAIN DIDAKTIS BERBASIS REALISTIC MATHEMATICS EDUCATION (RME) PADA MATERI
PECAHAN KELAS IV SEKOLAH DASAR
Universitas Pendidikan Indonesia| repository.upi.edu | perpustakaan.upi.edu
119
Pitta-Pantazi, D. (2014). Number teaching and learning. Dalam S. Lerman
(penyunting). Encyclopedia of mathematics education (hlm.470-476).
London : springer.
Pothier, Y. & Sawada, D. (1983). Partitioning: the emergence of rational number
ideas in young children. Journal for Research in Mathematics Education,
14(5), 307–317.
Prediger, S.(2008). The relevance of didactic categories for analysing obstacles in
conceptual change Revisiting the case of multiplication of fractions.
Learning and Instruction, 18(1), 3-17.
Raco, J. R. (2013). Metode penelitian kualitatif: Jenis karakteristik dan
keunggulannya. Jakarta: Grasindo.
Rangkuti, A. N. (2015). Developing a learning trajectory on fraction topics by
using realistic mathematics education approach in primary school. IOSR
Journal of Research & Method in Education, 5(5), 13-16
www.iosrjournals.org DOI: 10.9790/7388-05531316
Reys, dkk. (2012). Helping children learn mathematics. United State of America:
Wiley.
Rezat, S. & Straber, R. (2012). From didactical triangle to the socio-didactical
tetrahedron: Artifacts as fundamental constituents of the didactical
situation.
ZDM
Mathematics
Education,
44:641-651.
DOI:
10.1007/s11858-012-0448-4
Rittle-Johnson, B. & Star, J. (2007). Does comparing solution methods facilitate
conceptual and procedural knowledge? An experimental study on learning
to solve equations. Journal of Educational Psychology. 99, 561-574. DOI:
10.1037/0022-0663.99.3.561.
Sadi, A. (2007). Misconceptions in numbers. UGRU Journal, 5. hlm. 1-7.
Santrock. (2011). Life-span development jilid I. Erlangga: Jakarta. Dialih
bahasakan oleh Benedictine Widyastina.
Sarama, J., dkk. (2011). Evaluation of a learning trajectory for length in the early
years. ZDM, 43(5), 667-680.
Satori, D. & Komariah, A. (2014). Metode Penelitian Kualitatif. Bandung:
Alfabeta.
Saxe, G. B., dkk. (2005). Representing fractions with standard notations: A
developmental analysis. Journal for Research in Mathematics Education,
36, 137-157.
Siti Khazanatu Rohmah, 2016
DESAIN DIDAKTIS BERBASIS REALISTIC MATHEMATICS EDUCATION (RME) PADA MATERI
PECAHAN KELAS IV SEKOLAH DASAR
Universitas Pendidikan Indonesia| repository.upi.edu | perpustakaan.upi.edu
120
Sfard, A. (2002). The interplay of intimations and implementations: Generating
new discourse with new symbolic tools. Journal of the Learning Sciences,
11(2-3), 319-357.
Sherin, M. G. & van Es, E. A. (2009). Effects of video club participation on
teachers' professional vision. Journal of Teacher Education, 60(20).DOI:
10.1177/0022487108328155
Siegler, R. S., & Lortie-Forgues, H. (2015). Conceptual knowledge of fraction
arithmetic. Journal of Educational Psychology, 107(3), 909–918.
Simon, M. A. & Tzur, R. (2004). Explicating the role of mathematical tasks in
conceptual learning: An elaboration of the hypothetical learning trajectory.
Mathematical Thinking and Learning, 6(2), 91-104.
Simon, M. A. (1995) Reconstructing mathematics pedagogy from a constructivist
perspective. Journal for Research in Mathematics Education, 26:114–145.
Simon. M. A. (2014). Hypothetical learning trajectories in mathematics education.
Dalam S. Lerman (penyunting). Encyclopedia of mathematics education
(hlm. 470-476). London: springer.
Sonnabend T. (2010). Mathematics for teachers an interactive approach for
grades K-8. USA: Belmont.
Steffe, L. P. (2003). Fractional commensurate, composition, and adding schemes:
Learning trajectories of Jason and Laura: Grade 5. The Journal of
Mathematical Behavior, 22(3), 237-295.
Steffe, L. P. (2004). On the contruction of learning trajectories of children: the
case of commensurate fractions. Mathematical Thinking and Learning,
6(2):129-162.
Steinbring, H. (2008). Changed views on mathematical knowledge in the course
of didactical theory development—independent corpus of scientific
knowledge or result of social constructions?. ZDM Mathematics
Education, 40:303-316.
Sugiono. (2012). Metode Penelitian Kuantitatif Kualitatif dan R&D. Bandung:
Alfabeta.
Sumanto, Y. D., Kusumawati, H., & Aksin, N. (2008). Gemar matematika 5 untuk
SD/MI kelas V. Jakarta: Intan Pariwara.
Suryadi, D. (2010). Menciptakan proses belajar aktif: kajian dari sudut pandang
teori belajar dan teori didaktik. Makalah disajikan pada seminar
pendidikan nasional di UNP.
Siti Khazanatu Rohmah, 2016
DESAIN DIDAKTIS BERBASIS REALISTIC MATHEMATICS EDUCATION (RME) PADA MATERI
PECAHAN KELAS IV SEKOLAH DASAR
Universitas Pendidikan Indonesia| repository.upi.edu | perpustakaan.upi.edu
121
Tobias, J. (2013). Prospective elementary teachers‘ development of fraction
language for defining the whole. Journal of Mathematics Teacher
Education, 16, 85-103. DOI: 10.1007/s10857-012-9212-5.
Untari, E. (2013). Diagnosis kesulitan belajar pokok bahasan pecahan pada siswa
kelas V Sekolah Dasar. Jurnal Ilmiah STKIP PGRI Ngawi. (13)1. Hlm. 18.
Usdiyana, D. dkk. (2009). Meningkatkan kemampuan berpikir logis siswa SMP
melalui pembelajaran matematika realistik. Jurnal Pengajaran MIPA,
13(1). ISSN: 1412-0917
van de Walle, J. A., dkk. (2010). Elementary and middle school mathematics:
Teaching developmentarlly. United State : Pearson.
van den Akker, J. dkk. (penyunting). (2006). Educational design research.
London: Routledge.
van den Heuvel-Panhuizen M & Drijvers P. (2014) Realistic mathematics
education. Dalam S. Lerman (penyunting). Encyclopedia of mathematics
education (hlm. 521-525. London : springer.
van den Heuvel-Panhuizen, M. (2000). Mathematics education in the
Netherlands: A guided tour. Freudenthal Institute Cd-rom for ICME9.
Utrecht: Utrecht University.
van den Heuvel-Panhuizen, M. (2003). The didactical use of models in realistic
mathematics education: an example from a longitudinal trajectory on
percentage. Educational Studies in Mathematics, 54: 9–35.
van Oers, B. (2014). Scaffolding in mathematics education. Dalam S. Lerman
(penyunting). Encyclopedia of mathematics education (hlm.535-538).
London : springer.
Vinner, S. (2014). Concept development in mathematics education. Dalam S.
Lerman (penyunting). Encyclopedia of mathematics education (hlm.9195). London : springer.
Wahyudin. (2013). Matematika Dasar Pengetahuan Bermuatan pedagogis:
gagasan yang kuat untuk para guru. (interpreter). Bandung: Mandiri.
Warfield, V. M. (2006). Invitation to didactique. [online]. Diakses dari:
http://www.math.washington.edu/∼warfield/Inv%20to%20Did66%20722-06.pdf.
Webb, D. C., van der Kooij, H., & Gist, M. R. (2011). Design research in the
netherlands: introducing logarithms using realistic mathematics education.
Journal of Mathematics Education at Teachers College Spring–Summer,
Volume 2.
Siti Khazanatu Rohmah, 2016
DESAIN DIDAKTIS BERBASIS REALISTIC MATHEMATICS EDUCATION (RME) PADA MATERI
PECAHAN KELAS IV SEKOLAH DASAR
Universitas Pendidikan Indonesia| repository.upi.edu | perpustakaan.upi.edu
122
Weber, E. (2015). Expanding notions of “learning trajectories” in mathematics
education. College of Education, Oregon State University. 541-737-1305.
Westenskow, A.(2012). Equivalent fraction learning trajectories for students with
mathematical learning difficulties when using manipulatives. All Graduate
Theses
and
Dissertations.
Paper
1368.
http://digitalcommons.usu.edu/etd/1368
Wheeldon, D. A. (2008). Developing mathematical practices in a social
context:an instructional sequence to support prospective elementary
teachers’ learning of fractions. (Disertasi). Department of Teaching and
Learning Principles in the College of Education at the University of
Central Florida, Orlando.
Wijayanti, M. (2007, februari). Alternatif mengatasi kesulitan belajar. Gemari.
Edition
73/VIII/2007,
hlm.
37.
Diakses
dari:
http://www.gemari.or.id/artikel/2546.shtml
Wilson, P. H. dkk. (2014). Teachers‘ use of their mathematical knowledge for
teaching in learning a mathematics learning trajectory. Journal of
Mathematics Teacher Education, 17(2), 149-175.DOI: 10.1007/s10857013-9256-1.
Wilson, P. H., Mojica, G. F., & Confrey, J. (2013). Learning trajectories in
teacher education: Supporting teachers‘ understandings of students‘
mathematical thinking. Journal of Mathematical Behavior, 32.103– 121
Wright R. J., Ellemor-Collins D., & Tabor P. D. (2012). Developing number
knowledge: assessment, teaching & intervention with 7 – 11-year-olds.
Sage Publications Ltd, London.
Wu, H. (1998). Teaching fractions in elementary school: A manual for teachers.
[online]. Diakses dari: https://math.berkeley.edu/~wu/fractions1998.pdf
Wu, H. (2014). Teaching fractions according to the common core standards.
[online].
Diakses
dari:
https://math.berkeley.edu/~wu/CCSSFractions_1.pdf
Siti Khazanatu Rohmah, 2016
DESAIN DIDAKTIS BERBASIS REALISTIC MATHEMATICS EDUCATION (RME) PADA MATERI
PECAHAN KELAS IV SEKOLAH DASAR
Universitas Pendidikan Indonesia| repository.upi.edu | perpustakaan.upi.edu
Abidin, Y. (2011). Penelitian pendidikan dalam gamintan pendidikan dasar dan
paud. Bandung: Rizqi Press.
Alwasilah, C. (2012). Pokoknya kualitatif dasar-dasar merancang dan melakukan
penelitian kualitatif. Bandung: Pustaka Jaya.
Arikunto, S. (2010). Prosedur penelitian: Suatu pendekatan praktik. Jakarta:
Rineka Cipta.
Arnon, I., Nesher, P., & Nirenburg, R. (2001). Where do fractions encounter their
equivalents? Can this encounter take place in elementary-school?.
International Journal of Computers for Mathematical Learning, 6, 167214.
Ball, D. L. (1993). With an eye on the mathematical horizon: Dilemmas of
teaching elementary school mathematics. Elementary School Journal,
93(4), 373-397.
Ball, D. L., Lubienski, S., & Mewborn, D. S. (2001). Research on teaching
mathematics: The unsolved problem of teachers' mathematical knowledge.
Dalam V. Richardson (penyunting.), Handbook of research on teaching
(4th edition). Washington, DC: American Educational Research
Association.
Ball, D., Thames, M., & Phelps, G. (2008). Content knowledge for teaching: what
makes it special?. Journal of Teacher Education, 59(5), 389–407.
Battista, M. T. (2012). Cognition-based assessment & teaching of fraction:
building on students’ reasoning. Portsmouth: Heinemann
Bright, G. dkk. (1988). Identifying fractions on number lines. Journal for
Research in Mathematics Education, 19, 215-232.
Brousseau, G. & Warfield, V. (2014). Didactic Situations in Mathematics
Education. Dalam S. Lerman (penyunting). Encyclopedia of mathematics
education (hlm.470-476). London : springer.
Brousseau. (2002). Theory of didactical situations in mathematics. Netherlands:
Kluwer.
Brown, A. L. (1992). Design experiments: theoretical and methodological
challenges in creating complex interventions in classroom settings. The
Journal of the Learning Sciences, 2(2), 141–178.
Siti khazanatu Rohmah, 2016
DESAIN DIDAKTIS BERBASIS REALISTIC MATHEMATICS EDUCATION (RME) PADA MATERI
PECAHAN KELAS IV SEKOLAH DASAR
Universitas Pendidikan Indonesia| repository.upi.edu | perpustakaan.upi.edu
115
116
BSNP. (2006). Standar Isi Untuk Satuan Pendidikan Dasar dan Menengah.
Jakarta: BSNP.
Clements, D. H. & Sarama, J. (2007). Effects of a preschool mathematics
curriculum: summative research on the building blocks project. Journal for
Research in Mathematics Education, 38(2), 136-163.
Clements, D. H. dkk. (2011). Mathematics learned by young children in an
intervention based on learning trajectories: a large-scale cluster
randomized trial. Journal for Research in Mathematics Education, 42(2),
127–166.
Clements, D. H., Wilson, D. C., & Sarama, J. (2004). Young children's
composition of geometric figures: A learning trajectory. Mathematical
Thinking and Learning, 6(2), 163-184.
Clements, D., & Sarama, J. (2009). Learning and teaching early math: The
learning trajectories approach. New York: Routledge.
Cobb, P. (2002). Reasoning with tools and inscriptions. Journal of the Learning
Sciences, 11(2-3), 187-215.
Confrey, J. & Maloney, A. (2015). A design research study of a curriculum and
diagnostic assessment system for a learning trajectory on equipartitioning.
ZDM Mathematics Education, 47:919-932. DOI: 10.1007/s11858-0150699-y
Cortina, J. L., Visnovska, J, & Zuniga, C. (2014). Unit fractions in the context of
proportionality: Supporting students' reasoning about the inverse order
relationship. Mathematics Education Research Journal. DOI:
10.1007/s13394-013-0112-5
Cortina, J. L., Visnovska, J., & Zuniga, C.(2014). Equipartition as a didactical
obstacle in fraction instruction. Acta Didactica Universitatis Comenianae
Mathematics, Issue 14, 1-18
Creswell, J. (2012). Research design pendekatan kualitatif, kuantitatif, dan mixed
edisi ketiga. Yogyakarta: Pustaka Pelajar.
Daro, P., Mosher, F., & Corcoran, T. (2011). Learning trajectories in
mathematics: A foundation for standards, curriculum, assessment, and
instruction. (Research Report No. 68). Madison, WI: Consortium for
Policy Research in Education.
Durmus, S. & Karakirik, E. (2006). Virtual manipulatives in mathematics
education: A theoretical framework. Turkish Online Journal of
Educational
Technology,
5(1),
117-123.
http://www.tojet.net/articles/v5i1/5112.pdf
Siti Khazanatu Rohmah, 2016
DESAIN DIDAKTIS BERBASIS REALISTIC MATHEMATICS EDUCATION (RME) PADA MATERI
PECAHAN KELAS IV SEKOLAH DASAR
Universitas Pendidikan Indonesia| repository.upi.edu | perpustakaan.upi.edu
117
Ebby, C. B. dkk. (2013). Teacher analysis of student knowledge (TASK): A
measure of learning trajectory-oriented formative assessment. Paper
presented at the Annual Meeting of the American Educational Research
Association, San Francisco, April 2013.
Fajriyah, N. & Triratnawati, D. (2008). Cerdas berhitung matematika untuk
SD/MI kelas 3. Jakarta: Grahadi.
Gravemeijer, K. (1994). Educational development and educational research in
mathematics education. Journal for Research in Mathematics Education,
25 (5), 443-471.
Gravemeijer, K., Bowers, J., & Stephan, M. (2003). Chapter 4: a hypothetical
learning trajectory on measurement and flexible arithmetic. Journal for
Research in Mathematics Education, Monograph, 12, 51-66.
Gravemeijer, K.P.E. & Cobb, P. (2006). Design research from a learning design
perspective. Dalam J. van den Akker, dkk. (penyunting). Educational
design research (hlm. 17–51). London: Routledge.
Hill, H., Rowan, B., & Ball, D. L. (2005). Effects of teachers' mathematical
knowledge for teaching on student achievement. American Educational
Research Journal, 42, 371-406.
Hill, H., Schilling, S., & Ball, D. L. (2004). Developing measures of teachers'
mathematics knowledge for teaching. The Elementary School Journal,
105, 11-30.
Hurst, C. & Hurrell, D. (2014). Developing the big ideas of number. International
Journal of Educational Studies in Mathematics. ISSN: 2148 – 5984.
Izsak, A., Tillema, E., & Tunc-Pekkan, Z. (2008). Teaching and learning fraction
addition on number line. Journal for Research in Mathematics Education,
39(1), 33-62. NCTM.
Klein A. S., & Beishuizen M. (1998). The Empty Number Line in Dutch
Second Grades: Realistic Versus Gradual Program Design. Journal for
Research in Mathematics Education. 29(4), 443–464.
Lidinillah, D. A. M. (2011). Educational design research: a theoretical
framework
for
action.
[Online].
Diakses
dari:
http://file.upi.edu/Direktori/KDTASIKMALAYA/DINDIN_ABDUL_MUIZ_LIDINILLAH_(KDTASIK
MALAYA)
Lin, C. Y. dkk. (2013). Preservice teachers‘ conceptual and procedural knowledge
of fraction operations: A comparative study of the United States and
Taiwan. School Science and Mathematics, 113(1), 41-51. DOI:
10.1111/j.1949-8594.2012.00173.
Siti Khazanatu Rohmah, 2016
DESAIN DIDAKTIS BERBASIS REALISTIC MATHEMATICS EDUCATION (RME) PADA MATERI
PECAHAN KELAS IV SEKOLAH DASAR
Universitas Pendidikan Indonesia| repository.upi.edu | perpustakaan.upi.edu
118
Makonye, J. & Shingirayi, M. (2014). The obstacles faced by the learners in the
learning of quadratic inequalities. Mediterranean Journal of Social
Sciences, 5(27). MCSER Publishing, Rome-Italy.
Manno, G. (2005). Embadiment and a-didactical situation in the theachinglearning of the perpendicular straight lines concept. (Disertasi). Faculty of
Mathematics and Physics Departement of Didactic Mathematics Comenius
University Bratislava, Slovakia.
McKenney, S. & Reeves, T. (2012). Conducting educational design research.
London: Routledge.
McMillan, J. H. & Scumacher, Sally. (2010). Research education: evidence-based
inquiry (seventh edition). New Jersey. Pearson Education.
Miyakawa, T. & Winslow, C. (2009). Didactical designs for students‘
proportional reasoning: an ―open approach‖ lesson and a ―fundamental
situation‖. Educ Stud Math, 72:199–218. DOI 10.1007/s10649-009-9188-y
Moleong, L. J. (2014). Metedologi penelitian kualitatif. Bandung: PT Remaja
Rosdakarya.
Moseley, B. J., Okamoto, Y., & Ishida, J. (2007). Comparing U.S. and Japanese
elementary school teachers‘ facility for linking rational number
representations. International Journal of Science and Mathematics
Education, 5, 165-185. DOI: 10.1007/s10763-006-9040-0.
Mustaqim, B. & Astuty, A. (2008). Ayo belajar matematika jilid 4 untuk SD dan
MI kelas IV. Jakarta: Buana Raya.
Myers, M. dkk. (2015). From implicit to explicit: articulating equitable learning
trajectories based instruction. Journal of Urban Mathematics Education,
8(2), 11–22 ©JUME.
Ningsih, S. (2014). Realistic mathematics education: model alternatif
pembelajaran matematika sekolah. Jurnal Pendidikan Matematika IAIN
Antasari. 01(2), 73-94.
Nyikahadzoyi, M. R., Mapuwei, T., & Chinyoka, M. (2013). Some cognitive
obstacles faced by ‗A‘ level mathematics students in understanding
inequalities: a case study of Bindura urban high schools. International
Journal of Academic Research in Progressive Education and
Development, 2 (2). ISSN: 2226-6348
Pepin, B. & Gueudet G. (2014). Curriculum resources and textbooks in
mathematics education. Dalam S. Lerman (penyunting). Encyclopedia of
mathematics education (hlm.132-135). London : springer.
Siti Khazanatu Rohmah, 2016
DESAIN DIDAKTIS BERBASIS REALISTIC MATHEMATICS EDUCATION (RME) PADA MATERI
PECAHAN KELAS IV SEKOLAH DASAR
Universitas Pendidikan Indonesia| repository.upi.edu | perpustakaan.upi.edu
119
Pitta-Pantazi, D. (2014). Number teaching and learning. Dalam S. Lerman
(penyunting). Encyclopedia of mathematics education (hlm.470-476).
London : springer.
Pothier, Y. & Sawada, D. (1983). Partitioning: the emergence of rational number
ideas in young children. Journal for Research in Mathematics Education,
14(5), 307–317.
Prediger, S.(2008). The relevance of didactic categories for analysing obstacles in
conceptual change Revisiting the case of multiplication of fractions.
Learning and Instruction, 18(1), 3-17.
Raco, J. R. (2013). Metode penelitian kualitatif: Jenis karakteristik dan
keunggulannya. Jakarta: Grasindo.
Rangkuti, A. N. (2015). Developing a learning trajectory on fraction topics by
using realistic mathematics education approach in primary school. IOSR
Journal of Research & Method in Education, 5(5), 13-16
www.iosrjournals.org DOI: 10.9790/7388-05531316
Reys, dkk. (2012). Helping children learn mathematics. United State of America:
Wiley.
Rezat, S. & Straber, R. (2012). From didactical triangle to the socio-didactical
tetrahedron: Artifacts as fundamental constituents of the didactical
situation.
ZDM
Mathematics
Education,
44:641-651.
DOI:
10.1007/s11858-012-0448-4
Rittle-Johnson, B. & Star, J. (2007). Does comparing solution methods facilitate
conceptual and procedural knowledge? An experimental study on learning
to solve equations. Journal of Educational Psychology. 99, 561-574. DOI:
10.1037/0022-0663.99.3.561.
Sadi, A. (2007). Misconceptions in numbers. UGRU Journal, 5. hlm. 1-7.
Santrock. (2011). Life-span development jilid I. Erlangga: Jakarta. Dialih
bahasakan oleh Benedictine Widyastina.
Sarama, J., dkk. (2011). Evaluation of a learning trajectory for length in the early
years. ZDM, 43(5), 667-680.
Satori, D. & Komariah, A. (2014). Metode Penelitian Kualitatif. Bandung:
Alfabeta.
Saxe, G. B., dkk. (2005). Representing fractions with standard notations: A
developmental analysis. Journal for Research in Mathematics Education,
36, 137-157.
Siti Khazanatu Rohmah, 2016
DESAIN DIDAKTIS BERBASIS REALISTIC MATHEMATICS EDUCATION (RME) PADA MATERI
PECAHAN KELAS IV SEKOLAH DASAR
Universitas Pendidikan Indonesia| repository.upi.edu | perpustakaan.upi.edu
120
Sfard, A. (2002). The interplay of intimations and implementations: Generating
new discourse with new symbolic tools. Journal of the Learning Sciences,
11(2-3), 319-357.
Sherin, M. G. & van Es, E. A. (2009). Effects of video club participation on
teachers' professional vision. Journal of Teacher Education, 60(20).DOI:
10.1177/0022487108328155
Siegler, R. S., & Lortie-Forgues, H. (2015). Conceptual knowledge of fraction
arithmetic. Journal of Educational Psychology, 107(3), 909–918.
Simon, M. A. & Tzur, R. (2004). Explicating the role of mathematical tasks in
conceptual learning: An elaboration of the hypothetical learning trajectory.
Mathematical Thinking and Learning, 6(2), 91-104.
Simon, M. A. (1995) Reconstructing mathematics pedagogy from a constructivist
perspective. Journal for Research in Mathematics Education, 26:114–145.
Simon. M. A. (2014). Hypothetical learning trajectories in mathematics education.
Dalam S. Lerman (penyunting). Encyclopedia of mathematics education
(hlm. 470-476). London: springer.
Sonnabend T. (2010). Mathematics for teachers an interactive approach for
grades K-8. USA: Belmont.
Steffe, L. P. (2003). Fractional commensurate, composition, and adding schemes:
Learning trajectories of Jason and Laura: Grade 5. The Journal of
Mathematical Behavior, 22(3), 237-295.
Steffe, L. P. (2004). On the contruction of learning trajectories of children: the
case of commensurate fractions. Mathematical Thinking and Learning,
6(2):129-162.
Steinbring, H. (2008). Changed views on mathematical knowledge in the course
of didactical theory development—independent corpus of scientific
knowledge or result of social constructions?. ZDM Mathematics
Education, 40:303-316.
Sugiono. (2012). Metode Penelitian Kuantitatif Kualitatif dan R&D. Bandung:
Alfabeta.
Sumanto, Y. D., Kusumawati, H., & Aksin, N. (2008). Gemar matematika 5 untuk
SD/MI kelas V. Jakarta: Intan Pariwara.
Suryadi, D. (2010). Menciptakan proses belajar aktif: kajian dari sudut pandang
teori belajar dan teori didaktik. Makalah disajikan pada seminar
pendidikan nasional di UNP.
Siti Khazanatu Rohmah, 2016
DESAIN DIDAKTIS BERBASIS REALISTIC MATHEMATICS EDUCATION (RME) PADA MATERI
PECAHAN KELAS IV SEKOLAH DASAR
Universitas Pendidikan Indonesia| repository.upi.edu | perpustakaan.upi.edu
121
Tobias, J. (2013). Prospective elementary teachers‘ development of fraction
language for defining the whole. Journal of Mathematics Teacher
Education, 16, 85-103. DOI: 10.1007/s10857-012-9212-5.
Untari, E. (2013). Diagnosis kesulitan belajar pokok bahasan pecahan pada siswa
kelas V Sekolah Dasar. Jurnal Ilmiah STKIP PGRI Ngawi. (13)1. Hlm. 18.
Usdiyana, D. dkk. (2009). Meningkatkan kemampuan berpikir logis siswa SMP
melalui pembelajaran matematika realistik. Jurnal Pengajaran MIPA,
13(1). ISSN: 1412-0917
van de Walle, J. A., dkk. (2010). Elementary and middle school mathematics:
Teaching developmentarlly. United State : Pearson.
van den Akker, J. dkk. (penyunting). (2006). Educational design research.
London: Routledge.
van den Heuvel-Panhuizen M & Drijvers P. (2014) Realistic mathematics
education. Dalam S. Lerman (penyunting). Encyclopedia of mathematics
education (hlm. 521-525. London : springer.
van den Heuvel-Panhuizen, M. (2000). Mathematics education in the
Netherlands: A guided tour. Freudenthal Institute Cd-rom for ICME9.
Utrecht: Utrecht University.
van den Heuvel-Panhuizen, M. (2003). The didactical use of models in realistic
mathematics education: an example from a longitudinal trajectory on
percentage. Educational Studies in Mathematics, 54: 9–35.
van Oers, B. (2014). Scaffolding in mathematics education. Dalam S. Lerman
(penyunting). Encyclopedia of mathematics education (hlm.535-538).
London : springer.
Vinner, S. (2014). Concept development in mathematics education. Dalam S.
Lerman (penyunting). Encyclopedia of mathematics education (hlm.9195). London : springer.
Wahyudin. (2013). Matematika Dasar Pengetahuan Bermuatan pedagogis:
gagasan yang kuat untuk para guru. (interpreter). Bandung: Mandiri.
Warfield, V. M. (2006). Invitation to didactique. [online]. Diakses dari:
http://www.math.washington.edu/∼warfield/Inv%20to%20Did66%20722-06.pdf.
Webb, D. C., van der Kooij, H., & Gist, M. R. (2011). Design research in the
netherlands: introducing logarithms using realistic mathematics education.
Journal of Mathematics Education at Teachers College Spring–Summer,
Volume 2.
Siti Khazanatu Rohmah, 2016
DESAIN DIDAKTIS BERBASIS REALISTIC MATHEMATICS EDUCATION (RME) PADA MATERI
PECAHAN KELAS IV SEKOLAH DASAR
Universitas Pendidikan Indonesia| repository.upi.edu | perpustakaan.upi.edu
122
Weber, E. (2015). Expanding notions of “learning trajectories” in mathematics
education. College of Education, Oregon State University. 541-737-1305.
Westenskow, A.(2012). Equivalent fraction learning trajectories for students with
mathematical learning difficulties when using manipulatives. All Graduate
Theses
and
Dissertations.
Paper
1368.
http://digitalcommons.usu.edu/etd/1368
Wheeldon, D. A. (2008). Developing mathematical practices in a social
context:an instructional sequence to support prospective elementary
teachers’ learning of fractions. (Disertasi). Department of Teaching and
Learning Principles in the College of Education at the University of
Central Florida, Orlando.
Wijayanti, M. (2007, februari). Alternatif mengatasi kesulitan belajar. Gemari.
Edition
73/VIII/2007,
hlm.
37.
Diakses
dari:
http://www.gemari.or.id/artikel/2546.shtml
Wilson, P. H. dkk. (2014). Teachers‘ use of their mathematical knowledge for
teaching in learning a mathematics learning trajectory. Journal of
Mathematics Teacher Education, 17(2), 149-175.DOI: 10.1007/s10857013-9256-1.
Wilson, P. H., Mojica, G. F., & Confrey, J. (2013). Learning trajectories in
teacher education: Supporting teachers‘ understandings of students‘
mathematical thinking. Journal of Mathematical Behavior, 32.103– 121
Wright R. J., Ellemor-Collins D., & Tabor P. D. (2012). Developing number
knowledge: assessment, teaching & intervention with 7 – 11-year-olds.
Sage Publications Ltd, London.
Wu, H. (1998). Teaching fractions in elementary school: A manual for teachers.
[online]. Diakses dari: https://math.berkeley.edu/~wu/fractions1998.pdf
Wu, H. (2014). Teaching fractions according to the common core standards.
[online].
Diakses
dari:
https://math.berkeley.edu/~wu/CCSSFractions_1.pdf
Siti Khazanatu Rohmah, 2016
DESAIN DIDAKTIS BERBASIS REALISTIC MATHEMATICS EDUCATION (RME) PADA MATERI
PECAHAN KELAS IV SEKOLAH DASAR
Universitas Pendidikan Indonesia| repository.upi.edu | perpustakaan.upi.edu