eprintid: 66565 rev_number: 22 eprint_status: archive userid: 1290 dir: disk0/00/06/65/65 datestamp: 2019-11-07 04:12:35 lastmod: 2021-11-01 04:01:31 status_changed: 2019-11-07 04:12:35 type: thesis metadata_visibility: show creators_name: Zaini, Arina Husna creators_name: Retnawati, Heri title: Pengembangan Soal Penalaran dan Pembuktian Matematika SMA. ispublished: pub subjects: D0 divisions: pps_lit_evazdik full_text_status: restricted keywords: pembuktian, penalaran, pengembangan instrumen, reliabilitas, validitas abstract: Penelitian ini bertujuan: (1) menginvestigasi kontruksi soal penalaran dan pembuktian matematika SMA, (2) mengestimasi reliabilitas soal penalaran dan pembuktian matematika SMA, (3) mengukur kemampuan penalaran dan pembuktian matematika siswa kelas SMA. Penelitian ini merupakan penelitian pengembangan yang menggunakan langkah meliputi: (1) menentukan tujuan penyusunan instrumen, (2) mencari teori yang relevan atau cakupan materi, (3) menyusun indikator butir instrumen/soal, (4) menyusun butir instrumen, (5) validasi isi, (6) revisi berdasarkan masukan validator, (7) melakukan uji coba, (8) melakukan analisis, (9) merakit instrumen. Uji coba instrumen dilakukan di kelas XI pada tujuh sekolah, yaitu SMAN 1 Bantul, SMAN 2 Bantul, SMAN 1 Kasihan, SMAN 3 Bantul, SMAN 1 Banguntapan, SMAN 1 Pajangan, dan SMAN 1 Pleret. Jumlah keseluruhan subjek uji coba sebanyak 571 siswa. Teknik pengumpulan data yang digunakan adalah tes tertulis. Instrumen pengumpulan data berupa soal penalaran dan pembuktian matematika berbentuk uraian sebanyak 16 butir yang terdiri dari 10 soal penalaran dan enam soal pembuktian. Enam belas butir soal penalaran dan pembuktian dirakit menjadi dua paket soal yakni Paket 1 dan Paket 2 yang masing-masing paket terdiri dari lima soal penalaran dan tiga soal pembuktian. Hasil penelitian menunjukkan bahwa soal penalaran dan pembuktian matematika yang dikembangkan valid. Hal ini didasarkan pada perhitungan menggunakan rumus Aiken bahwa nilai V pada semua butir soal date: 2019-08-28 date_type: published institution: Program Pascasarjana department: Penelitian dan Evaluasi Pendidikan thesis_type: tesis referencetext: Adam, R.J. & Khoo S.T. (1996). Acer Quest: The Interactive Test Analysis System. Victoria: The Australia Council for Educational Research. Aiken, L. R. (1980). Content validity and reliability of single items or questionnaires. Education and Psychological Measurement, 40, 955-959. Retrieved form https://doi.org/10.1177/001316448004000419. Allen, M.J., & Yen, W.M. (1979). Introduction to measurement theory. Monteney: Brooks/Cole Publishing Company. Anderson, L.W. (2003). Classroom assessment: Enchancing the quality of teacher decision making. New Jersey: Lawrence Erlbaum Associates. Anisa, Zulkardi & Darmawijoyo. (2011). Pengembangan soal matematika model pisa pada konten quantity untuk mengukur kemampuan penalaran matematis siswa sekolah menengah pertama. Jurnal Pendidikan Matematika, 5(1). 1-15. DOI: https://doi.org/10.22342/jpm.5.1.333. Arbaugh, F., Smith, M., Boyle, J., Stylianides, G.J., & Steele, M. (2019). We reason & we prove for all mathematics: Building student’s critical. SAGE Publication: United Kingdom. Arends, R. I., & Kilcher, A. (2010). Teaching for student learning (become an accomplished teacer). New York, NY: Rouledge Taylor and Francis Group. DOI: 10.4324/9780203866771. Arifin, Z., & Retnawati, H. (2017). Pengembangan instrumen pengukur higher Order thinking tkills matematika siswa SMA kelas X. PYTHAGORAS: Jurnal Pendidikan Matematika, 12(1), 98-108. DOI: 10.21831/pg.v12i1.14058. Asyhar, Beni. (2015). Studi pemahaman bukti dan pembuktian dalam geometri Euclid mahasiswa jurusan tadris matematika IAIN tulungagung. Jurnal pendidikan matematika. 1(2).127-135. Azwar, S. (2017). Reliabilitas dan validitas. Yogyakarta: Pustaka Belajar Basuki, I., & Hariyanto. (2014). Asesemen pembelajaran. Bandung: PT. Remaja Rosdakarya. Bieda, K.N., Ji, X., Drweneke, J., & Picard, A. (2013). Reasoning-and-proving opportunities in elementary mathematics textbooks. International of educational Journal of educational Research, 9(46), 1-10. Retrieved from https://doi.org/10.1016/j.ijer.2013.06.005. 119 Block, E.D. (2011). Proof and fundamentals: A first cours in abstract mathematics. New York: Springer. Bragg, L.A., Herbert, S.A., Loon &g, E.Y.K., Valel, C. & Widjaja, W. (2016). Primary teachers notice the impact of language on children’s mathematical reasoning. Math Ed Res J, 1-22. Retrieved from http://dx.doi.org/10.1007/s13394-016-0178-y. Brodie, K.(2010). Teaching mathematical reasoning in secondadry school classroom. New York: Springer. Brown, Gavin & Irving, S & Keegan, Peter. (2008). An introduction to educational assessment, measurement and evaluation: Improving the quality of teacher-based assessment.2nd Edition. Auckland: Dunmore Publishing Ltd. CadwalladerOlsker, T. (2011). What do we mean by mathematical Proof?. Journal of Humanistic Mathematics, 1(1), 33-60. Retrieved from http://doi.org/10.5642/jhummath.201101.04. Cai, J., & Cirillo, M. (2014). What do we knoe about reasoning and proving? Oppoerunities and missing opportunities from curriculum analysis. Internatonal Journal of Education research, 64(1), 132-140. Chambers, P., & Timlinm, R. (2013). Teaching mathematics in the secondary school (2nd Ed). London: SAGE Publication. Retrieved from https://uk.sagepub.com/en-gb/eur/teaching-mathematics-in-the-secondary- school/book250333. Clarke, D. (1996). Assessment. Dalam A.J. Bishop, et al. (Eds.). International Handbook of Mathematics Education. Dordrecht: Kluwer Academic Publishers. Cupillari, A. (2005). The Nuts and Bolts of Proofs. Burlington: Elsevier Academic Press. De Lange, J. (2000). Assessment: No change without problems. Utrecht: Freudenthal Institute. DePascale, C.A., & Dunn, J. (2008). Simplifying psychometrics with sas. NESUG. Curran, W. S. (2015).Mathematical proof. Journal of Interdisciplinary Mathematics, 8(1), 119–125. DOI:10.1080/09720502.2005.10700395. 120 English, L.D. (2004). Mathematical and analogical reasoning in early childhood.Dalam L. English (ed). Mathematical and analogical reasoning os young leaders. Mahwah: Lawrence Erlbaum Associates, Inc. Fardillah, A.(2018). Analysis of mathematical reasoning ability of pre-service mathematics teachers in solving algebra problem based on reflective and impulsive cognitive style. Formatif: Jurnal Ilmiah Pendidikan MIPA, 8(2), 119-128. Retrieved from http://dx.doi.org/10.30998/formatif.v8i2.2333. Fox, S., & Surtees, L.(2010). Mathematics across the curriculum: Problem- solving, reasoning and numeracy in primary schools. Continuum International Publishing Group: New York. Frasier, B. & Panasuk, R. (2013). Proof in mathematics education: Expectations and reality. Journal of Curriculum and Teaching, 2(2), 76-85. DOI:10.5430/jct.v2n2p76 Gay, L.R. (1991). Educational evaluation and measurement: Competencies for analysis and application (2nd ed). New York: Macmilan Publishing Company. Goldestein, E.B. (2011). Cognitive psycology: Connecting and mind, research, and everyday experience. Belmont: Wadsworth. Goos, M., Stillman, G., & Vale, C. (2007). Teaching secondary school mathematics. Research and practice for the 21th century. Crows Nest, NSW: CMO Image Printing. Griffin, P., & Nix., P. (1991). Educational assessment and reporting. Sydney: Harcout Brace Javanovich, Publisher. Gunhan, B.C. (2014). A case study on the investigation of reasoning skills in geometry. South African Journal of Education, 34(2), 1-19. DOI: 0.15700/201412071156. Habsah, F. (2017). Developing teaching material based on realistic mathematics andoriented to the mathematical reasoning and mathematical communication. Jurnal Riset Pendidikan Matematika, 4(1), 43-55. DOI:10.21831/jrpm.v4i1.10199. Hambleton, R.K., & Swaminanth, H. (1985). Item response theory. Boston, MA: Kluwer Nijoff Publishing. Hamzah, A. H. M., & Muhlisrarini. (2014). Perencanaan dan strategi pembelajaran matematika. Depok : PT. Rajagrafindo Persada. 121 Hanna, G., Jahnke, H.N., & Pulte, H. (2010). Explanation and proof in mathematics. New York: Springer. Haylock, D., & Thangata, F. (2007). Key concept in teaching primary mathematics. London: Sage. DOI 10.1007/s10649-015-9623-1. Herman, T. (2018). Asesmen dalam pembelajaran matematika. Universitas Pendidikan Indonesia. Isgiyanto, A. (2011). Diagnosis kesalahan siswa berbasis penskoran politomus model partial credit pada matematika. Jurnal Penelitian dan Evaluasi Pendidikan, 15(2), 308-325. DOI: 10.21831/pep.v15i2.1099. Isnarto, Wahyudin, Suryadi, D., Dahlan, J.A. (2014). Student’s proof ability: exploratory studies of abstract algebra course. International Journal of Education and Research, 2(6), 215-228. Retrieved from http://www.ijern.com/journal/June-2014/18.pdf. Istiyono. (2014). Pengukuran kemampuan berpikir tingkat tinggi fisika peserta didik SMA di DIY. Disertasi, Tidak diterbitkan, Universitas Negeri Yogyakarta, Yogyakarta. Johansson, H. (2015). Mathematical reasoning in physics and real-life context .Sweden: Division of Mathematics Department of Mathematical Sciences Chalmers University of Technology and University of Gothenburg. Kennedy, L.M., Tipss, S., & Johnson, A. (2008). Guiding children’s learning of mathematics. Belmont, CA: Thomson Wadsworth. Khumaeedi, M. (2012). Reliabilitas instrumen penelitian pendidikan (the reliability of education research instruments). Jurnal pendidikan teknik mesin, 12(1), 25-30. Retrieved from https://journal.unnes.ac.id/nju/index.php/JPTM/article/view/5273/4244. DOI:10.17226/9822. Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press. Lestari, K.E. (2015). Analisis kemampuan pembuktian matematis mahasiswa menggunakan pendekatan induktif-deduktif pada mata kuliah analisis real. MENDIDIK: Jurnal Kajian Pendidikan dan Pengajaran. 1(2), 128-135. Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press. 122 Lithner, J. (2008). A research framework for creative and imitative reasoning. New York: Springer. Mardapi, D. (2017). Pengukuran, penilaian dan evaluasi pendidikan. Yogyakarta: Parama Publising. Mardapi, D. (2018). Teknik penyusunan instrument tes dan nontes. Yogyakarta: Parama Publishing. Misel & Suwangsih, E. (2016). Penerapan pendekatan matematika realistic untuk meningkatkan kemampuan representasi matematis siswa. Jurnal Metodi DIdaktik. 10(2), 27-36. Moore, R.C. (2016). Mathematics professor’s evaluation of students’ proofs: a complex teaching practice. Int. J. Res. Undergrad. Math. Ed. New York: Springer.2:246–278. DOI: 10.1007/s40753-016-0029-y. Moshman, D,. & Amsel, E,. (2015). Logical and hypothetical reasoning in adolescence. International Encyclopedia of the Social & Behavioral Sciences, Second Edition, 306–312. https://www.researchgate.net/publication/304194411_Logical_and_Hypothe tical_Reasoning_in_Adolescence_Development_of. Mubarak, M.S., Pujiastuti, E., & Suparsih. (2018). Meningkatkan kemampuan pembuktian matematis dan rasa ingin tahu siswa kelas XI MIPA SMA Negeri 6 semarang melalui model PBL. PRISMA: Prosiding Seminar Nasional Matematika, 1(1). Retrieved from https://journal.unnes.ac.id/sju/index.php/prisma/article/view/20217. Muhtaran, A. Z., & Abidin, Z. (2016). Analisis kemampuan pembuktian matematik siswa pada mata pelajaran trigonometri berdasarkan gaya belajar siswa. Makalah disajikan dalam Seminar Nasional Pendidikan Matematika, di Universitas Ahmad Dahlan Yogyakarta. Nadapdap, A., T., Y., & Istiyono, E. (2017). Developing physics problem-solving skill test for grade X students of seniar high school. REiD (Research and Evaluation in Education), 3(2). 114-123. DOI: 10.21831/reid.v3i2.14982. Naga, D.S (1992). Pengantar teori skor pada pengukuran pendidikan. Jakarta: Gunadarma. Mueller, M. & Yankelewitz, D. (2014). Fallacious argumentation in student reasoning: are the benefits?. European Journal of science and Mathematics Education. 2(1), 27-38. 123 Napitupulu, E.E. (2017). Analyzing the teaching and learning of mathematical reasoning. Asian Social Science, 13(12). 167-173. DOI:10.5539/ass.v13n12p167 National Council of The of Mathematic (NCTM). (2000). Principles and standards for school mathematics. United States of America : The National Council of Teachers of Mathematics, Inc. Nitko, A., & Brookhart S. (2011). Educational assessment of students (6th ed). Boston: Pearson Education, Inc. Novaliyosi. (2018). The Development of instruments to measure student mathematical logical thingking ability in kapita selekta. . Nunes, T., & Csapo, B. (2011). Developing and assessing mathematical reasoning.Dalam Csapo & M. Szendrei (Eds.) Framework for diagnostic assessment of mathematics. Budapest: Nemzeti Tankonyvkiado. Ozerem, A. (2012). Misconceptions in geometry and suggested solution for sevent grade student. International Journal of New Trends in Arts, Sports & Science Education, 1(4),23-35. Popham, W. (1995). Classroom Assessment. Allyn and Bacon: Boston. Purwanto. 2010. Evaluasi Hasil Belajar. Yogyakarta: Pustaka Pelajar. Ramos, J.P,. Lew, K., Torre, J. D. L., & Weber, K. (2017). Developing and validating proof comprehension tests in undergraduate mathematics. New york, NY: Rouledge Taylor and Francis Group. Retnawati, H. (2017). Validitas, reliabilitas dan karakteristik butir. Yogyakarta: Parama Publishing. Reynolds, C.R Livingston, R.B., & Wilson, V. (2010) Measurement and assessment in educational(2nd ed). Upper Saddle. River, New Jersey: Pearson Education. Reys, R., Lindquist, M.M., D.V., & Smith, N.L. (2009). Helping children learn mathematics (9th Ed). New York, NY; John Wiley & Sons, Inc. Rizta, A., Zulkardi, & Hartono, Y. (2013). Pengembangan soal penalaran model TIMSS matematika SMP. Jurnal Penelitian dan Evaluasi Pendidikan, 17(2). 230-240. Retrieved from https://journal.uny.ac.id/index.php/jpep/article/view/1697/1411. on Teaching, Assessment, and Learning in Education, 42 (2), 1-4. https://doi.org/10.1051/shsconf/20184200054 124 Global Conference Roberts, Charles. (2010). Introduction to mathematical proofs a transition. CRC Press: Francis. Romberg, T. A., & Chair. (1993). Curriculum and evaluation standards for school mathematics. NCTM: Reston, Virginia. Samejimah, F. (1994). Estimation of reliability coefficients using the test information fungction and its modifications. Applied Psycological Measurement, 18(3), 229- 224.https://doi.org/10.1177/014662169401800304. Samritin dan Suryanto. (2016). Developing an assessment instrument of junior high school student’s higher order thinking skills in mathematics. REiD (Research and Evaluation in Education), 2(1). 92-107. DOI 0.21831/reid.v2i1.8268. Santrock, J.W. (2011). Perkembangan anak edisi 7. (terjemah Sarah Genis B). Jakarta: Erlangga. Sari, D.P., & Mahendra. (2016). Developing instrument to measure mathematical Reasoning Ability. Advances in Social Science, Education and Humanities Research, 57(1), 30-33. DOI:https://doi.org/10.2991/icmsed-16.2017.7How to use a DOI?. Selden, A. & Selden, J. (2007). Teaching proving by coordinating aspects of proofs with student’s abilities. New Mexico State University: Department of Mathematical Sciences. Shadiq, Fajar. (2004). Pemecahan masalah, penalaran, dan komunikasi, Disampaikan pada diklat instruktur/pengembang matematika SMA jenjang Dasar, Widyaiswara PPPG Matematika Yogyakarta, 6 – 19 Agustus 2004. Simons, Roger. (2008). Proof and other dilemmas: Mathematics and philosophy. The Mathematical Association of America. New York. . Stefanowicz, Agata. (2014). Proofs and mathematical reasoning. Universitas od Birmingham mathematics support center: Unite Kingdom. Stylianides, A.J, & Stylianides G.J. (2009). Proof construction and evaluations. Educ Stud Math, 72, 237-253.DOI:10.1007/s10649-009-9191-3. Siswanah, E. (2016). Pengaruh pembelajaran berbasis masalah terstruktur terhadap kemampuan penalaran matematis mahasiswa pendidikan matematika UIN walisongo semarang, Jurnal Walisongo, 13-24. DOI: http://dx.doi.org/10.21580/phen.2016.6.1.941 125 Subhan. (2017). Pengambangan soal open-ended untuk mengukur kemampuan penalaran dan komunikaasi matematis siswa SMP. Tesis, Tidak diterbitkan, Universitas Negeri Yogyakarta, Yogyakarta. Suherman, Erman et al. (2003). Strategi pembelajaran matematika kontenporer. Bandung: PT Remaja Rosdakarya. Sumarmo, U. (2005). Pengembangan berpikir matematik tingkat tinggi siswa SLTP dan SMU serta mahasiswa strata satu melalui berbagai pendekatan pembelajaran. Lemlit UPI : Laporan Penelitian. Sumarsih, Budiyono, & Indriati, D. (2018). Profile of mathematical reasoning ability of 8th grade students seen from communicational ability, basic skills, connection, and logical thinking. Journal of Physics: Conference Series, 1- 10. Retrieved from https://iopscience.iop.org/article/10.1088/1742- 6596/1008/1/012078/pdf. Suprananto, Kusaeri. (2012). Pengukuran dan penelitian pendidikan. Yogyakarta: Graha Ilmu. Surapranata, S. (2009). Analisis, validitas, reliabilitas dan interpretasi hasil tes implementasi kurikulum 2004. Bandung: PT.Remaja Rosdakarya. DOI: Taylor, J., & Garnier, R. (2014). Understanding mathematical proof. CRC Press: francis. Thompson, D. R., Senk, S. l., & Johnson, G.J. (2012). Opportunities to learn reasoning and proof in high school mathematics textbooks. Journal for Research in Mathematics Education, 43(3), 253-295. Retrieved from https://www.jstor.org/stable/10.5951/jresematheduc.43.3.0253. Tesis, Tidak diterbitkan, Universitas Negeri Yogyakarta, Yogyakarta. Van de Walle, J.A (2007). Elementary and middle school mathematic:teaching developmentally (6thedition). Boston:Pearson. Syafri, F.S. (2017). Kemampuan representasi matematis dan kemampuan pembuktian matematika. E-Edumath: Jurnal Pendidikan Matematika, 3(1), 49-55. https://doi.org/10.26638/je.283.2064. Utari, Tria. (2017). Analisis muatan penalaran dan pembuktian matematis dan muatan karakter berdaya juang pada buku teks pelajaran matematika SMA kelas X kurikulum 2013. Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2013). Elementary and middle school mathematics: Teaching developmentally (8th ed.). Upper Saddle River, NJ: Pearson. 126 Wardani, R., E., A., Supriyoko & Prihatni, Y. (2018). Developing assessment model for bandel attitudes based on the teachings of Ki Hadjar Dewantara. REiD (Research and Evaluation in Education), 3(2). 117-125. DOI 10.21831/reid.v4i2.21942 Weinberg, A., Connely, T.F.,& Wiesner, E. (2015). Characterizing instructor gestures in a lecture in a proof-based mathematics class. Educ Stud Math, 90, 233–258. Widodo, P.B. (2006). Reliabilitas dan validitas konstruk skala konsep diri untuk mahasiswa Indonesia. Jurnal psikologi universitas diponegoro, 3(1), 1-9. Widyoko, E.P. (2014). Penilaian hasil pembelajaran di sekolah. Yogyakarta: Pustaka Pelajar. Yumiati, M.N. (2017). Abilities of reasoning and mathematics representation on guided inquiry learning. Journal of Education and Learning., 11(3). 283- 290. DOI: 10.11591/edulearn.v11i3.6041. Zubaidah, A., & Risnawati. (2016). Psikologi pembelajaran matematika. Yogyakarta: Aswaja Pressindo. citation: Zaini, Arina Husna and Retnawati, Heri (2019) Pengembangan Soal Penalaran dan Pembuktian Matematika SMA. S2 thesis, Program Pascasarjana. document_url: http://eprints.uny.ac.id/66565/1/LAMPIRAN.pdf document_url: http://eprints.uny.ac.id/66565/2/BAB%20I.pdf document_url: http://eprints.uny.ac.id/66565/3/BAB%20II.pdf document_url: http://eprints.uny.ac.id/66565/3/BAB%20III.pdf document_url: http://eprints.uny.ac.id/66565/4/BAB%20IV.pdf document_url: http://eprints.uny.ac.id/66565/5/DAFTAR%20PUSTAKA.pdf document_url: http://eprints.uny.ac.id/66565/6/BAB%20V.pdf document_url: http://eprints.uny.ac.id/66565/7/COVER.pdf