Enhancing Creative Reasoning through Mathematical Task: The Quest for an Ideal Design

Kusaeri Kusaeri, Siti Lailiyah, Yuni Arrifadah, Siti Asmiyah

Abstract


This study aims to: (i) identify the types of completion and ways of completing mathematical tasks carried out by students based on the type of their educational institution (Junior High School (SMP) and Junior Islamic High School (MTs)), and (ii) explore the tendency of the type of reasoning students use in completing the tasks. This study involved 93 students at grade 8 of prominent SMP and MTs in Sidoarjo Regency, East Java. Variety of ways and solutions to mathematical tasks and the tendency to type of students’ reasoning are explored through creative reasoning tests. Interview techniques by telephone are implemented to further explore the types of student reasoning (Local Creative Reasoning (LCR) or Global Creative Reasoning (GCR)). The results show that in comparison to MTs students, SMP students have more varied answers and ways to solve mathematical tasks. In certain cases; however, MTs students show some unique answers. The type of creative reasoning that students tend to use is of the LCR. These findings indicate the importance for mathematics teachers to design mathematics tasks that develop GCR-type creative reasoning. Examples and exercises in mathematics textbooks should also be directed at developing this type of creative reasoning.


Keywords


Mathematical Task, Creative Reasoning, Local Creative Reasoning, Global Creative Reasoning

References


J. Sidenvall, J. Lithner, and J. Jäder,"Students’ reasoning in mathematics textbook task solving," International Journal of Mathematical Education in Science and Technology, vol. 46, no. 4, pp. 533-552, 2015, https://doi.org/10.1080/0020739X.2014.992986.

C.S. Ayal, Y.S. Kusuma, J. Subandar and J.A. Dahlan, "The enhancement of mathematical reasoning ability of junior high school students by applying mind mapping strategy," Journal of Education and Practice, vol. 7, no. 25, pp. 50-58, 2016.

S. Lailiyah, T. Nusantara, C. Sa’Dijah, E. B. Irawan, Kusaeri, and A. H. Asyhar, “Structuring students’ analogical reasoning in solving algebra problem,” in IOP Conference Series: Materials Science and Engineering, 2018, vol. 296, no. 1, doi: 10.1088/1757-899X/296/1/012029.

L.P.W. Adnyani, I. Kurniawan, and E.A.R. Pinahayu,"Development of creative-thinking instrument in mathematics problem solving based on logical mathematics intelligence,"Journal of Research and Advances in Mathematics Education, vol. 3, no. 1, pp. 1-12, 2018, doi: 10.23917/jramathedu.v3i1.5201.

J. Jäder, J. Lithner, and J. Sidenvall,"Mathematical problem solving in textbooks from twelve countries," International Journal of Mathematical Education in Science and Technology, vol. 51, no. 7, pp. 1120-1136, 2019. https://doi.org/10.1080/ 0020739X. 2019.1656826.

J. Boesen, O. Helenius, J. Lithner, E. Bergqvist, T. Bergqvist, T. Palm and B. Palmberg,"Developing mathematical competence: from the intended to the enacted curriculum," Journal of Mathematical Behavior, vol. 33, pp. 72–87, 2014, doi: 10.1016/j.jmathb.2013.10.001.

J.D. Davis, D.O. Smith, A. R. Roy, and Y.K. Bilgic,"Reasoning-and-proving in algebra: The case of two reform-oriented U.S. Textbooks,"International Journal of Educational Research, vol. 64, 92–106, 2014, http://dx.doi.org/10.1016/j.ijer.2013.06.012.

K. Kusaeri and A. Ridho, “Learning outcome of mathematics and science: Features of Indonesian madrasah students,” Jurnal Penelitian dan Evauasi Pendidikan, vol. 23, pp. 95–105, 2019, doi: 10.21831/pep.v23i1.24881.

B. Kaur, "Mathematics education in Singapore - An insider’s perspective," Journal on Mathematics Education, vol. 5, no. 1, pp. 1-16, 2014.

H. Krzywacki, L. Pehkonen and A. Laine,"Promoting Mathematical Thinking in Finnish Mathematics Education" In: Niemi H., Toom A., Kallioniemi A. (eds), Miracle of Education. Rotterdam: Sense Publishers, 2016, https://doi.org/10.1007/978-94-6300-776-4_8.

M.S. Salim, "Reasoning-and-proving and world-related problems in the mathematics textbook of Kurikulum 2013 revised in 2017," IOP Conf. Series: Journal of Physics: Conference Series, vol. 1317, pp. 1-6, 2018, doi:10.1088/1742-6596/1317/1/012126.

J. Boesen, J. Lithner, and T. Palm, "The relation between types of assessment task and the mathematical reasoning student uses," Education Studies in Mathematics, vol. 75, pp. 89-105, 2010, https://www.jstor.org/stable/40928548.

S. Lailiyah, K. Kusaeri and W.Y. Rizki, "Identifikasi proses berpikir siswa dalam menyelesaikan masalah aljabar dengan menggunakan representasi graf," Jurnal Riset Pendidikan Matematika, vol. 7, no. 1, pp. 25-44, 2020, https://doi.org/10.21831/jrpm.v7i1.32257.

K. Kusaeri and A. Aditomo, “Pedagogical Beliefs about Critical Thinking among Indonesian Mathematics Pre-service Teachers,” International Journal of Instruction, vol. 12, pp. 573–590, 2019, doi: 10.29333/iji.2019.12137a.

R. Nyman, "What makes a mathematical task interesting?" Educational Research and Reviews, vol. 11, no. 16, pp. 1509-1520, 2016, doi: 10.5897/ERR2016.2919.

A. Kolouvou, M. van den Heuvel-Panhizen, and A. Bakker, "Non-routine problem-solving task in primary school mathematics textbook – a needle in a haystack," Mediterranean Journal for Research in Mathematics Education, vol. 8, no. 2, pp. 31-68, 2009.

A. Wijaya, M. van den Heuvel-Panhizen, and M. Doorman,"Opportunity to learn context-based tasks provided by mathematics textbooks,"Educational Studies in Mathematics, vol. 89, pp. 41 – 65, 2015, https://doi.org/10.1007/ s10649-015-9595-1.

R. Johar, S. Yusniarti and S. Saminan, "The analysis of proportional reasoning problem in the Indonesian mathematics textbook for the junior high school," Journal on Mathematics Education, vol. 9, no. 1, pp. 55-68, 2018, http://dx.doi.org/10.22342/jme.9.1.4145.55-68.

R.I.I. Putri and Z. Zulkardi, "Designing PISA-like mathematics task using Asian Games context," Journal on Mathematics Education, vol. 11, no.1, pp. 135-144, 2020, http://doi.org/10.22342/ jme.11.1.9786.135-144.

I.V.S. Mullis, M.O. Martin, P. Foy and A. Arora, "TIMSS 2011 international results in mathematics," Chestnut Hill, MA: Boston College, 2012.

A.H. Alajmi,"Addressing computational estimation in the Kuwaiti curriculum: Teachers’ views," Mathematics Teacher Education, vol. 12, no. 4, pp. 263–283, 2009, https://doi.org/ 10.1007/s10857-009-9106-3.

D.C. Yang and I.A. Sianturi,"An analysis of Singaporean versus Indonesian textbooks based on trigonometry content," Eurasia Journal of Mathematics Science and Technology Education, vol. 13 no. 7, pp. 3829-3848, 2017, https://doi.org/10.12973/ eurasia. 2017.00760a

V.Berisha, and R. Bytyqi,"Types of mathematical tasks used in secondary classroom instruction," International Journal of Evaluation and Research in Education (IJERE), vol. 9, no. 3, pp.751- 758, 2020, doi: 10.11591/ ijere.v9i3.20617.

J. Lithner,"Principles for designing mathematical tasks that enhance imitative and creative reasoning," ZDM Mathematics Education, vol. 49, pp. 937-949, 2017, https://doi.org/10.1007/ s11858-017-0867-3.

B. Koichu, O. Zaslavsky and L. Dolev, "Effects of variations in task design on mathematics teachers’ learning experiences: A case of sorting task,"Journal of Mathematics Teacher Education, vol. 19, pp. 349-370, 2016, https://doi.org/10.1007/s10857-015-9302-2.

B. Jonsson, Y.C. Kulaksiz, and J. Lithner, "Creative and algorithmic mathematical reasoning: effects of transfer-appropriate processing and effortful struggle," International Journal of Mathematical Education in Science and Technology, vol. 47, no. 8, pp. 1206-1225, 2016, doi:10.1080/0020739X.2016.1192232.

E. Thanheiser, "Developing prospective teachers’ conceptions with well-designed tasks: Explaining successes and analyzing conceptual difficulties," Journal of Mathematics Teacher Education, vol. 18, pp. 141–172, 2014, https://doi.org/10. 1007/s10857-014-9272-9.

E. Bergqvist, "Types of reasoning required in university exams in mathematics," The Journal of Mathematical Behavior, vol. 26, no. 4, pp. 348-370, 2007, doi: 10.1016/j.jmathb.2007.11.001.

J. Lithner,"A research framework for creative and imitative reasoning," Educational Studies in Mathematic, vol. 67, no. 3, pp. 255-276, 2008, doi:10.1007/sl0649-007-91.

N.R.W. Sari, M. Asikin, and M. Mulyono, "Imitative and creative reasoning abilities viewed from locus of control on guided inquiry model react strategy," Unnes Journal of Mathematics Education Research, vol. 9, no. 1, pp.19-25, 2020.

L. Biza, G. Joel and E. Nardi, "Balancing classroom management with mathematical learning: Using practiced-based task design in mathematica teacher education," Mathematics Teacher Education and Development, vol. 17, No. 2, pp. 182-198, 2015.

L. P. W. Adnyani, I. Kurniawan and E.A. R. Pinahayu,"Development of creative-thinking instrument in mathematics problem solving based on logical mathematics intelligence," Journal of Research and Advances in Mathematics Education, vol.3, no. 1, pp. 1-12, 2018, doi: 10.23917/jramathedu.v3i1.5201.

T. Masfingatin, W. Murtafiah and S. Maharani, "Exploration of creative mathematical reasoning students in solving geometric problem," Jurnal Pendidikan Matematika, vol. 14, no. 2, pp, 155-168, 2020, https://doi.org/ 10.22342/ jpm.14.2.7654.155-168.

M.A. Simon, "Reconstructing mathematics pedagogy from a constructivist perspective," Journal for Research in Mathematics Education,vol. 26, pp. 114–145, 1995, doi: 10.2307/749205.

P. Ivars, C. Fernández, S. Linares and B.H. Choy, "Enhancing noticing: Using a hypothetical learning trajectory to improve pre-service primary teachers’ professional discourse," Eurasia Journal of Mathematics, Science and Technology Education, vol. 14, no. 11, pp. 1-16, 2018, doi://doi.org/10.29333/ejmste/93421

M.A. Simon and R. Tzur,"Explicating the role of mathematical tasks in conceptual learning: An elaboration of the hypothetical learning trajectory," Mathematical Thinking and Learning, vol. 6, no. 2, pp. 91-104, 2004, doi: 10.1207/s15327833mtl0602_2.

K. Gravemeijer and P. Cobb,"Design research from a learning design perspective," In J. Van den Akker, K. Gravemeijer, S. McKenney & N. Nieveen (Eds), Educational Design Research. New York: Routledge, 2006.

K. Wahyu, T.E. Kuzu, S. Subarinah, D. Ratnasari and S. Mahfudy, "Partitive Fraction Division: Revealing and Promoting Primary Students’ Understanding," Journal on Mathematics Education, vol. 11, no. 2, pp. 237-258, 2020, http://doi.org/10.22342/jme.11. 2.11062.237-258.

C. R. Reynolds, R.B. Livingston and V. Willson, "Measurement and Assessment in Education," New Jersey: Pearson Education, Inc, 2010.

L.R. Aiken, "Three coefficients for analyzing the reliability and validity of ratings," Educational and Psychological Measurement, vol. 45, no. 1, pp. 131–142, 1985, https://doi.org/10.1177/ 00131644854 51012.

C. Mann and F. Stewart, "Internet communication and qualitative research: A handbook for researching online," London: Sage Publications, 2000.

A. Irvine, P. Drew and R. Sainsbury,"Am I not answering your questions properly?Clarification, adequacy and responsiveness in semi-structured telephone and face-to-face interviews," Qualitative Research, vol. 13, no. 1, pp 87-106, 2013, https://doi.org/10.1177/ 1468794112439086.

T. Bergqvist and J. Lithner, "Mathematical reasoning in teachers’ presentations," Journal of Mathematical Behavior, vol. 31, no. 2, pp. 252–269, 2012, https://doi.org/10.1016/j.jmathb.2011.12.002.

R. Lukens-Bull,"Madrasa by any other name: Pondok, pesantren, and islamic schools in Indonesia and larger southeast Asian Region," Journal of Indonesian Islam, vol. 4, no. 1, pp. 1-21, 2010. https://doi.org/10.15642/ JIIS.2010.4.1.1-21.

K. Kusaeri, “2nd International Conference on Statistics, Mathematics, Teaching, and Research 2017,” J. Phys. Conf. Ser., vol. 1028, p. 011001, Jun. 2018, doi: 10.1088/1742-6596/1028/1/011001.

D. Newhouse and K. Beegle, "The effect of school type on academic achievement: Evidence from Indonesia," The Journal of Human Resources, vol. 41, no. 3, pp. 529 – 557, 2006, doi: 10.3368/ jhr.XLI.3.529.

S. Sunhaji,"Between social humanism and social mobilization: The dual role of madrasah in the landscape of Indonesian Islamic education," Journal of Indonesian Islam, vol. 11, no. 1, pp. 125-144, 2017, doi: 10.15642/ JIIS.2017.11.

P.W. Thompson, M.P. Carlson and J. Silverman, "The design of tasks in support of teachers’ development of coherent mathematical meanings," Journal of Mathematics Teacher Education, vol. 10, pp. 415–432, 2007. https://doi.org/10.1007/s10857-007-9054-8.




DOI: http://doi.org/10.11591/ijere.v11i2.22125

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