THE INNOVATION OF LEARNING TRAJECTORY ON MULTIPLICATION OPERATIONS FOR RURAL AREA STUDENTS IN INDONESIA

Heris Hendriana, Rully Charitas Indra Prahmana, Wahyu Hidayat

Abstract


The rural area's student difficulties in learning the concept of number operation had been documented by several studies, especially for the case of multiplication. The teacher typically introduces the multiplication concepts using the formula without involving the concept itself. Furthermore, this study aims to design learning trajectory on multiplication operations in the Mathematics of GASING (Math GASING) by focusing more on the concept itself than the formula and by starting from the informal to a formal level of teaching. Design research used as the research method to solve this problem consisting of three phases, namely preliminary design, teaching experiment, and retrospective analysis. The research results show that the Math GASING has a real contribution for students to understanding and mastering in the concept of the multiplication operations. This research also explains the strategy and the model discovered by students in learning multiplication that the students used as a basic concept of multiplication. Finally, the students were able to understand the concept of multiplication more easily, and they showed interest in using this learning trajectory.

Keywords


multiplication; learning trajectory; design research; rural area

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References


Ahmad, N.S.B. (2010). Multiplication and the reference sum method. Procedia-Social and Behavioral Sciences, 8, 72-78. https://doi.org/10.1016/j.sbspro.2010.12.010.

Akker, J.V.D., Gravemeijer, K., McKenney, S., & Nieveen, N. (2006). Education Design Research. London: Routledge Taylor and Francis Group.

bin Syed Ismail, S.A. (2010). Multiplication with the Vedic method. Procedia-Social and Behavioral Sciences, 8, 129-133. https://doi.org/10.1016/j.sbspro.2010.12.018.

Caron, T.A. (2007). Learning multiplication: The easy way. The Clearing House: A Journal of Educational Strategies, Issues and Ideas, 80(6), 278-282. https://doi.org/10.3200/TCHS.80.6.278-282.

Chang, K. E., Sung, Y.T., Chen, Y.L., & Huang, L.H. (2008). Learning multiplication through computer-assisted learning activities. Computers in Hhuman Bbehavior, 24(6), 2904-2916. https://doi.org/10.1016/j.chb.2008.04.015.

Chung, I. (2004). A comparative assessment of constructivist and traditionalist approaches to establishing mathematical connections in learning multiplication. Education, 125(2), 271-279.

Drews, D., Dudgeon, J., Hansen, A., Lawton, F., & Surtees, L. (Eds.). (2005). Children's Errors in Mathematics: Understanding Common Misconceptions in Primary Schools. SAGE.

Freudenthal, H. (1973). Mathematics as an Educational Task. Dordrecht: Kluwer Academic Publishers.

Gravemeijer, K. (2004). Local instructional theories as means of support for teacher in reform mathematics education. Mathematical Thinking and Learning, 6(2), 105-128. https://doi.org/10.1207/s15327833mtl0602_3.

Ischebeck, A., Zamarian, L., Siedentopf, C., Koppelstätter, F., Benke, T., Felber, S., & Delazer, M. (2006). How specifically do we learn? Imaging the learning of multiplication and subtraction. Neuroimage, 30(4), 1365-1375. https://doi.org/10.1016/j.neuroimage.2005.11.016.

Kilian, L., Cahill, E., Ryan, C., Sutherland, D., & Taccetta, D. (1980). Errors that are common in multiplication. The Arithmetic Teacher, 22-25.Kilian, L., Cahill, E., Ryan, C., Sutherland, D., & Taccetta, D. (1980). Errors that are common in multiplication. The Arithmetic Teacher, 27(5), 22-25.

National Council of Teachers of Mathematics (NCTM). (2000). Principles and Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics.

Nuari, L.F., Prahmana, R.C.I., & Fatmawati, I. (2019). Learning of division operation for mental retardations' student through Math GASING. Journal on Mathematics Education, 10(1), 127-142. https://doi.org/10.22342/jme.10.1.6913.127-142.

Prahmana, R.C.I. (2013). Designing division operation learning in the mathematics of GASING. Proceeding in The First South East Asia Design/Development Research (SEA-DR) Conference 2013, 391-398.

Prahmana, R.C.I. (2015). The hypothetical learning trajectory on addition in mathematics GASING. Southeast Asian Mathematics Education Journal, 5(1), 49-61.

Prahmana, R.C.I. (2017). Design Research (Teori dan Implementasinya: Suatu Pengantar) [Design Research (Theory and Its Implementation: An Introduction)]. Depok: Rajawali Pers.

Prahmana, R.C.I., & Suwasti, P. (2014). Local instruction theory on division in mathematics GASING. Journal on Mathematics Education, 5(1), 17-26. https://doi.org/10.22342/jme.5.1.1445.17-26.

Prahmana, R. C. I., Zulkardi, & Hartono, Y. (2012). Learning multiplication using Indonesian traditional game in third grade. Journal on Mathematics Education, 3(2), 115-132. https://doi.org/10.22342/jme.3.2.1931.115-132.

Putri, R.I.I., Dolk, M., & Zulkardi. (2015). Professional development of PMRI teachers for introducing social norms. Journal on Mathematics Education, 6(1), 11-19. https://doi.org/10.22342/jme.6.1.1900.11-19.

Revina, S., Zulkardi, Darmawijoyo, & Galen, F. (2011). Spatial visualization tasks to support students' spatial structuring in learning volume measurement. Journal on Mathematics Education, 2(2), 127-146. http://dx.doi.org/10.22342/jme.2.2.745.127-146.

Reys, R.E., Suydam, M.N., Lindquist, M.M., & Smith, N.L. (1998). Helping Children Learn Mathematics. Boston: Allyn and Bacon.

Shanty, N.O., & Wijaya, S. (2012). Rectangular array model supporting students’ spatial structuring in learning multiplication. Journal on Mathematics Education, 3(2), 175-186. http://dx.doi.org/10.22342/jme.3.2.603.175-186.

Surya, Y. (2011). Petunjuk Guru: Dasar-Dasar Pintar Berhitung GASING [Teachers’ Guide: Smart Basics of Counting’s GASING]. Tangerang: PT. Kandel.

Surya, Y., & Moss, M. (2012). Mathematics education in rural Indonesia. Proceeding in the 12th International Congress on Mathematics Education: Topic Study Group 30. Korea National University of Education, Seoul, South Korea Selatan, 6223-6229.

Tanujaya, B., Prahmana, R. C. I., & Mumu, J. (2017). Mathematics instruction, problems, challenges and opportunities: A case study in Manokwari Regency, Indonesia. World Transactions on Engineering and Technology Education, 15(3), 287-291.

Unlu, M., & Ertekin, E. (2012). Why do pre-service teachers pose multiplication problems instead of division problems in fractions?. Procedia-Social and Behavioral Sciences, 46, 490-494. https://doi.org/10.1016/j.sbspro.2012.05.148.




DOI: https://doi.org/10.22342/jme.10.3.9257.397-408

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Journal on Mathematics Education
Doctoral Program on Mathematics Education
Faculty of Teacher Training and Education, Universitas Sriwijaya
Kampus FKIP Bukit Besar
Jl. Srijaya Negara, Bukit Besar
Palembang - 30139
email: jme@unsri.ac.id

p-ISSN: 2087-8885 | e-ISSN: 2407-0610

Creative Commons License
Journal on Mathematics Education (JME) is licensed under a Creative Commons Attribution 4.0 International License.


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