Scoring rubric design to measure the ability to prove plane geometry problems not accompanied by image visualization
DOI:
https://doi.org/10.29408/jel.v10i1.22550Keywords:
image visualization, plane geometry, proof, scoring rubricAbstract
Proof of the type of problem not accompanied by image visualization will require a longer flow and process than proof of the kind of problem accompanied by image visualization. The ability of students to prove problems, especially problems not accompanied by image visualization, must be adequately expressed and objectively. For that, we need an instrument that can reveal the ability to prove the case of these problems. This research has successfully designed a scoring rubric that can be explicitly used to measure students' proving abilities on problems not accompanied by image visualization. Aspects developed in the scoring rubric include making image visualizations according to the information in the questions. These include sub-aspects of image accuracy and completeness of labels, initial steps of proving, preparation of conjectures, flow of proving, and support for valid arguments for statements made. Based on the validation from the experts, the scoring rubric developed was declared valid and ready to be used to measure the student's proving ability on plane geometry, proving problems not accompanied by image visualization.References
Anhar. L. N.. Triyanto. & Henny. E. C. (2019). Analisis kemampuan pemecahan masalah matematika pada materi geometri berdasarkan langkah polya ditinjau dari kemampuan representasi matematis siswa kelas VIII SMPN 2 plupuh tahun 2018/2019 [Analysis of mathematical problem solving abilities on geometric material based on polya steps in terms of the students' mathematical representation abilities of class VIII SMPN 2 plupuh year 2018/2019]. Jurnal Pendidikan Matematika Dan Matematika. III(1). 515–524. https://jurnal.uns.ac.id/JMMS/article/view/38027/25104
Arcavi. A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics. 52(3). 215–241. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.126.6579&rep=rep1&type=pdf
Arifin. S. A. N. (2021). Analisis jawaban mahasiswa dalam menyelesaikan soal pembuktian geometri berdasarkan teori newman [Analysis of student answers in solving geometric proof problems based on Newman's theory]. Edukatif : Jurnal Ilmu Pendidikan. 3(4). 1395–1408. http://dx.doi.org/10.31004/edukatif.v3i4.564%0Ahttps://edukatif.org/index.php/edukatif/article/viewFile/564/pdf
Azizah. I. N.. Amri. M. K.. Ikashaum. F.. & Mispani. M. (2021). Pengembangan modul kalkulus dengan pemanfaatan software geogebra [Development of calculus modules using geogebra software]. JRPM (Jurnal Review Pembelajaran Matematika). 6(1). 13–23. https://doi.org/10.15642/jrpm.2021.6.1.13-23
Brown. G. T. L. (2018). Assessment of student achievement. Routledge.
Budiarti. E. (2014). Alur berpikir siswa SMP dalam membuktikan teorema pythagoras melalui tugas pengajuan soal ditinjau dari perbedaan jenis kelamin [The thinking flow of junior high school students in proving the pythagorean theorem through the task of submitting questions in terms of gender differences]. MATHEdunesa: Jurnal Ilmiah Pendidikan Matematika. 3(3). 47–54. https://doi.org/10.26740/mathedunesa.v3n3.p%25p
Cahyani. H.. Suyitno. H.. Junaidi. I.. & Jl Unnes. K. (2020). The student’s errors in mathematical problem solving based on NEA judging from the self efficacy on learning CORE. Unnes Journal of Mathematics Education Research. 9(1). 2020–2069. http://journal.unnes.ac.id/sju/index.php/ujmer
Cirillo. M.. & Hummer. J. (2021). Competencies and behaviors observed when students solve geometry proof problems: An interview study with smartpen technology. ZDM - Mathematics Education. 53(4). 861–875. https://doi.org/10.1007/s11858-021-01221-w
Clements. K.. & Ellerton. N. (1996. May 1st ). The Newman Procedure for analysing errors on written mathematical tasks. 1978. 1–7. http://compasstech.com.au/ARNOLD/PAGES/newman.htm
Fallo. S. K.. Fitriani. F.. & Amsikan. S. (2021). Prosedur newman: Analisis kesalahan siswa dalam menyelesaikan soal bangun ruang prisma [Newman's procedure: Analysis of student errors in solving prism space problems]. MATH-EDU: Jurnal Ilmu Pendidikan Matematika. 6(3). 89–99. https://doi.org/10.32938/jipm.6.3.2021.89-99
Firdaus. (2021). Analisis kesalahan berdasarkan teori newman dalam menyelesaikan masalah luas dan keliling bidang datar [Error analysis based on newman's theory in solving the problem of area and perimeter of a plane]. Urnal Publikasi Pendidikan. 11. 3. http://ojs.unm.ac.id/index.php/pubpend
Gagatsis. A.. Elia. I.. Geitona. Z.. Deliyianni. E.. & Gridos. P. (2022). How could the presentation of a geometrical task influence student creativity? Journal of Research in Science. Mathematics and Technology Education. 5(1). 93–116. https://doi.org/10.31756/jrsmte.514
Gridos. P.. Avgerinos. E.. Mamona-Downs. J.. & Vlachou. R. (2021). Geometrical figure apprehension. construction of auxiliary lines. and multiple solutions in problem solving: Aspects of mathematical creativity in school geometry. International Journal of Science and Mathematics Education. https://doi.org/10.1007/s10763-021-10155-4
Hadi. W.. Handayani. I.. & Noviana. W. (2021). Analisis kemampuan pembuktian matematis pada proposisi geometri euclid menggunakan geogebra online [Analysis of mathematical proof ability on euclidean geometrical propositions using geogebra online]. Indonesian GeoGebra Journal. 1(1). 40–49. https://journal.geogebra.id/index.php/IndonesianGeoGebraJournal/article/view/6/2
Haj-Yahya. A. (2019). Do prototypical construction and self-attributes of presented drawings afect the construction and validation of proofs? Mathematics Education Research Journal. 32. 685–718. https://link.springer.com/article/10.1007/s13394-019-00276-z
Hanna. G.. & Sidoli. N. (2007). Visualisation and proof: A brief survey of philosophical perspectives. ZDM - International Journal on Mathematics Education. 39(1–2). 73–78. https://doi.org/10.1007/s11858-006-0005-0
Indrayany. E. S.. & Lestari. F. (2019). Analisis kesulitan siswa SMP dalam memecahkan masalah geometri dan faktor penyebab kesulitan siswa ditinjau dari teori van hiele [Analysis of the difficulties of junior high school students in solving geometric problems and the factors causing students' difficulties in terms of van hiele's theory]. Jurnal Math Educator Nusantara: Wahana Publikasi Karya Tulis Ilmiah Di Bidang Pendidikan Matematika. 5(2). 109–123. https://doi.org/10.29407/jmen.v5i2.13729
Jaelani. A. K.. & Hasbi. M. (2022). Development of authentic assessment in geometry learning. JRPM (Jurnal Review Pembelajaran Matematika). 7(1). 1–19. https://doi.org/10.2991/ictvet-18.2019.78
Jonsson. A. (2014). Rubrics as a way of providing transparency in assessment. Assessment and Evaluation in Higher Education. 39(7). 840–852. https://doi.org/10.1080/02602938.2013.875117
Jupri. A. (2022). Strategi pemecahan masalah geometri mahasiswa calon guru matematika: Antara prediksi dan kenyataan [Prospective mathematics teachers geometry problem solving strategy: Between prediction and reality]. Jurnal Gantang. 6(2). 141–149. https://doi.org/10.31629/jg.v6i2.3539
Krajcevski. M.. & Sears. R. (2019). Common visual representations as a source for misconceptions of preservice teachers in a geometry connection course. International Journal for Mathematics Teaching and Learning. 20(1). 85–106. https://digitalcommons.usf.edu/cgi/viewcontent.cgi?article=1206&context=tal_facpub
Kurniawan. A.. Setiawan. D.. & Hidayat. W. (2019). Analisis kemampuan pemecahan masalah matematis siswa SMP berbantuan soal kontekstual pada materi bangun ruang sisi datar [Analysis of mathematical problem solving abilities of junior high school students with the help of contextual questions on the material of flat side space]. NUMERICAL: Jurnal Matematika Dan Pendidikan Matematika. 2(5). 63–76. https://journal.ikipsiliwangi.ac.id/index.php/jpmi/article/view/2976/1016
Maarif. S.. Perbowo. K. S.. Noto. M. S.. & Harisman. Y. (2019). Obstacles in constructing geometrical proofs of mathematics-teacher-students based on boero’s proving model. Journal of Physics: Conference Series. 1315(1). 1–14. https://doi.org/10.1088/1742-6596/1315/1/012043
Maarif. S.. Wahyudin. W.. Alyani. F.. & Pradipta. T. R. (2020). Kemampuan mengkonstruksi bukti geometri mahasiswa calon guru matematika pada perkuliahan geometri [The ability to construct proofs of prospective teacher mathematics students in geometry lectures]. Jurnal Elemen. 6(2). 211–227. https://doi.org/10.29408/jel.v6i2.2012
Mahfuddin. M.. & Caswita. C. (2021). Analisis kemampuan pemecahan masalah pada soal berbasis high order thinking ditinjau dari kemampuan spasial [Analysis of problem-solving skills on high-order thinking-based questions in terms of spatial abilities]. AKSIOMA: Jurnal Program Studi Pendidikan Matematika. 10(3). 1696. https://doi.org/10.24127/ajpm.v10i3.3874
Mariotti. M. A.. & Pedemonte. B. (2019). Intuition and proof in the solution of conjecturing problems’. ZDM: The International Journal on Mathematics Education. 51(1). 1–19. https://link.springer.com/article/10.1007/s11858-019-01059-3
Mithalal. J.. & Balacheff. N. (2019). The instrumental deconstruction as a link between drawing and geometrical figure. Educational Studies in Mathematics. 100(2). 161–176. https://doi.org/10.1007/s10649-018-9862-z
Moleko. M. M. (2021). Teachers’ perspectives on addressing linguistic factors affecting visualisation of mathematics word problems. Eurasia Journal of Mathematics. Science and Technology Education. 17(11). 1–18. https://doi.org/10.29333/ejmste/11248
Mudaly. D. V.. & Reddy. L. (2016). The role of visualisation in the proving process of euclidean geometry problems. PONTE International Scientific Researchs Journal. 72(8). https://doi.org/10.21506/j.ponte.2016.8.13
Mwadzaangati. L. (2019). Comparison of geometric proof development tasks as set up in the textbook and as implemented by teachers in the classroom. Pythagoras. 40(1). 1–14. https://doi.org/10.4102/PYTHAGORAS.V40I1.458
Naidoo. J.. & Kapofu. W. (2020). Exploring female learners’ perceptions of learning geometry in mathematics. South African Journal of Education. 40(1). 1–11 https://doi.org/10.15700/saje.v40n1a1727
Nieveen. N. (1999). Prototyping to reach product quality. In J. Van den Akke. R. Branch. K. Gustafson. N. Nieveen. & T. Plom (Eds.). Design Approach and Education and Training (pp. 125–135). Kluer Academic Publishers
Nitko. A. J. (2001). Educational assessment of students. Prentice Hall
Nitko. A. J.. & Brookhart. S. M. (2014). Educational Assessment of Students. Pearson
Noto. M. S.. Priatna. N.. & Dahlan. J. A. (2019). Mathematical proof: The learning obstacles of pre-service mathematics teachers on transformation geometry. Journal on Mathematics Education. 10(1). 117–125. https://doi.org/10.22342/jme.10.1.5379.117-126
Nurikawai. D.. Sagita. L.. & Setiyani. S. (2021). Analisis kesulitan pemahaman konsep matematis siswa dalam menyelesaikan soal bentuk aljabar dengan prosedur newman [Analysis of the difficulty of understanding students' mathematical concepts in solving algebraic questions with the newman procedure]. Journal of Honai Math. 4(1). 49–66. https://doi.org/10.30862/jhm.v4i1.157
Ozturk. M. (2021). Cognitive and metacognitive skills performed by math teachers in the proving process of number theory. Athens Journal of Education. 8(1). 53–72. https://doi.org/10.30958/aje.8-1-4
Pachemska. T. A.. Gunova. V.. & Lazarova. L. K. (2016). Visualization of the geometry problems in primary math education (Needs and challenges). IMO-Istrazivanje Matematickog Obrazovanja. 8(15). 33–37. http://www.imvibl.org/dmbl/meso/imo/imo_vol_8__br_15/imo_vol_8_br_15_33_37.pdf
Panadero. E.. & Jonsson. A. (2020). A critical review of the arguments against the use of rubrics. Educational Research Review. 30. 1–112. https://doi.org/10.1016/j.edurev.2020.100329
Patac. A. V. Patac. L. P.. & Crispo. N. E. (2022). Students’ understanding of a geometric theorem: A case of grade 9 problem posing. JRAMathEdu (Journal of Research and Advances in Mathematics Education). 7(2). 105-115. https://doi.org/10.23917/jramathedu.v7i2.16394
Peligro. R. M.. Luna. C. A.. Ph. D.. Lomibao. L. S.. & Ph. D. (2018). Students’ error analysis on a given geometric proofs and solutions : Its effect on their achievement and conceptual understanding. International Journal of Research in Social Sciences. 8(1). 664–673. https://bit.ly/3DdmoQD
Polit. D. F.. Beck. C. T.. & Owen. S. V. (2007). Is the CVI an acceptable indicator of content validity? : Appraisal and recommendations. Research in Nursing & Health. 30. 459–467. https://doi.org/10.1002/nur.20199
Ramírez-Uclés. R.. & Ruiz-Hidalgo. J. F. (2022). Reasoning. representing. and generalizing in geometric proof problems among 8th grade talented students. Mathematics. 10(5). https://doi.org/10.3390/math10050789
Riyadi. Syarifah. T. J.. & Nikmaturrohmah. P. (2021). Profile of students’ problem-solving skills viewed from polya’s four-steps approach and elementary school students. European Journal of Educational Research. 10(4). 1625–1638. https://pdf.eu-jer.com/EU-JER_10_4_1625.pdf
Scristia. S.. Meryansumayeka. M.. Safitri. E.. Araiku. J.. & Aisyah. S. (2022). Development of teaching materials based on two-column proof strategy on congruent triangle materials. Proceedings of the 2nd National Conference on Mathematics Education 2021 (NaCoME 2021). 656(NaCoME 2021). 189–193. https://doi.org/10.2991/assehr.k.220403.027
Singh. P.. Rahman. A. A.. & Hoon. T. S. (2010). The newman procedure for analyzing primary four pupils errors on written mathematical tasks: A malaysian perspective. Procedia - Social and Behavioral Sciences. 8(December). 264–271. https://doi.org/10.1016/j.sbspro.2010.12.036
Siskawati. E. (2020). Analisis kesalahan peserta didik dalam menyelesaikan soal matematika problem solving berdasar newman’s error analysis (NEA) [Analysis of student errors in solving mathematical problem solving based on newman's error analysis (NEA)]. Prosiding Panelitian Nasional Pendidikan Matematika. 19. 401–408. http://www.proceeding.unindra.ac.id/index.php/DPNPMunindra/article/view/4771
Sommerhoff. D.. & Ufer. S. (2019). Acceptance criteria for validating mathematical proofs used by school students. university students. and mathematicians in the context of teaching. ZDM: The International Journal on Mathematics Education. 51(5). 717–730. https://link.springer.com/article/10.1007/s11858-019-01039-7
Suhaini. M.. Ahmad. A.. & Bohari. N. M. (2021). Assessments on vocational knowledge and skills: A content validity analysis. European Journal of Educational Research. 10(3). 1529–1540. https://doi.org/10.12973/EU-JER.10.3.1529
Sutama. S.. & Indriyani. Y. P. (2021). Newman error analysis (NEA): Detection of student learning barriers in PPKM in mathematics subjects. AKSIOMA: Jurnal Program Studi Pendidikan Matematika. 10(4). 2901. https://doi.org/10.24127/ajpm.v10i4.4221
Thiagarajan. S.. Semmel. D. S.. & Semmel. M. I. (1974). Instructional development for training teachers of exceptional children: A sourcebook. University Of Minnesota
Tripathi. P. N. (2020). Exploring the use of deductive logic in geometry as a tool for cognitive growth. International Conference to Review Research in Science. Technology and Mathematics Education. 2. 91–100. https://bit.ly/3L3GZJ2
Urhan. S.. & Bülbül. A. (2022). Analysis of mathematical proving in geometry based on habermas’ construct of rationality. Mathematics Education Research Journal. Issue May. https://doi.org/10.1007/s13394-022-00420-2
VanSpronsen. H. D. (2008). Proof processes of novice mathematics proof writers [Doctoral dissertation. The University of Montana]. The University of Montana Digital Archive. https://scholarworks.umt.edu/cgi/viewcontent.cgi?article=1797&context=etd
Vavra. K. L.. Janjic-watrich. V.. Loerke. K.. Phillips. L. M.. Norris. S. P.. & Macnab. J. (2011). Visualization in science education. ASEJ. 41(1). 22–30. https://sc.teachers.ab.ca/SiteCollectionDocuments/Vol.%2041.%20No.%201%20January%202011.pdf
Wardhani. T. A. W.. & Argaswari. D. P. A. D. (2022). High school students’ error in solving word problem of trigonometry based on newman error hierarchical model. Infinity Journal. 11(1). 87-102. https://doi.org/10.22460/infinity.v11i1.p87-102
White. A. L. (2009). A revaluation of newman’s error analysis. MAV Annual Conference 2009. 3(Year 7). 249–257. http://ww.w.mav.vic.edu.au/files/conferences/2009/08White.pdf
Yilmaz. R.. & Argun. Z. (2018). Role of visualization in mathematical abstraction: The case of congruence concept. International Journal of Education in Mathematics. Science and Technology. 6(1). 41–57. https://doi.org/10.18404/ijemst.328337
Žakelj. A.. & Klančar. A. (2022). The role of visual representations in geometry learning. European Journal of Educational Research. 11(3). 1393–1411. https://doi.org/https://doi.org/10.12973/eu-jer.11.3.1393
Zarzycki. P. (2004). From visualizing to proving. Teaching Mathematics and Its Applications. 23(3). 108–118. https://doi.org/10.1093/teamat/23.3.108
Zimmermann. W.. & Cunningham. S. (1991). Editors’ introduction: What is mathematical visualization? MAA Notes : Visualization in Teaching and Learning Mathematics. 19. 1–7. http://www.hitt.uqam.ca/mat7191_fich/Zimmermann_Cunningham_1991.pdf
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