# JUSTIFIKASI DALAM PEMBELAJARAN MATEMATIKA

## Kata Kunci:

justification, communication, learning mathematics, reasoning.## Abstrak

Justification is a core in leaning mathematics. Justification builds up studentsâ€™ reasoning with a better way. It happens because in justifying, students are not only asked to explain their answer from solving mathematics problems, moreover, students are asked to explain whay those solution can be used and their answer is right. Albeit the purpose of justification in mathematics community has been studied, only little information can be gained about how its role in learning mathematics. This writing is an academic writing that being done by the writer based on the results of some research which implementing justification in learning process. The purposes of this writing divided into three parts, namely to know the role of justification in learning mathematics, to know the way that can be used by the teacher to support students to justify, and to know the way that can be used by the teacher in assess justification by the students.

## Referensi

Almeida, D. 1995. â€œMathematics Undergraduatesâ€™ Perceptions of Proof.â€ Teaching Mathematics and Its Applications, 14(4), p. 171-177.

Back, R-J., Mannila, L., and Wallin, S. 2010. â€œStudent justification in high school mathematics.â€ Proceedings of CERME 6, 2009, p. 291-300. Lyon Frnace INRP.

Ball, D. L and Bass, H. 2003. â€œMaking mathematics reasonable in school,â€ In J. Kilpatrick, W. G. Martin, and D. Schifter. (Eds.) A Research Companion to Principals and Standards for School Mathematics, 27-44. Reston, VA.

Bicknell, B. 1999. â€œThe Writing of explanations and justifications in mathematics: differences and dilemmas.â€ MERGA 22, pp 76-83. New Zealand.

Carpenter, T., Levi, L., Berman, P., and Pligge, M. 2005. â€œDeveloping algebraic reasoning in the elementary schoolâ€. In T. Romberg, T. Carpenter, & F. Dremock (Eds.), Understanding mathematics and science matters (pp. 81-98). Mahwah, NJ: Lawrence Erlbaum.

Cioe, M., King, S., Ostien, D., Pansa, N., and Staples, M. 2015. â€œMoving Students to â€œthe whyâ€â€. Mathematics Teaching in the Middle School. 20(8), pp. 484-491.

Cobb, P., Wood, T., and Yackel, E. 1994. Discourse, mathematical thinking, and classroom practice. In contexts for learning: Sociocultural dynamics in childrenâ€™s development. New York: Oxford University Press.

Common Core State Standards Initiative. 2010. Commmon Core State Standards for Mathematics. Washington, DC: National Governors Association Center for Besr Practices and the Council of Chief State School Officers. http://www.corestandards.org/wp- content/uploads/Math_Standards.

Dreyfus, T. 1999. â€œWhy Johnny canâ€™t prove.â€ Educational Studies in Mathematics, 38(1-3), pp.85- 109.

Herbst, P and Balacheff, N. 2009. â€œProving and knowing in public: The nature of proof in a classroomâ€. In Stylianou, D., Blanton, M., & Knuth, E. (Eds.), Teaching and Learning of Proof across the Grades: A K-16 perspective, (pp. 40-63). New York: Routledge.

Hunter, J. 2007. Developing early algebraic understanding in an inquiry classroom. Unpublished masterâ€™s thesis, Massey University, Palmerston North.

Hunter, J and Anthony, G. 2007. â€œThe development of studentsâ€™ use of justification strategies.â€ Proceedings of the 31st Annual Conference of the Mathematics Education Research Group of Australasia, p. 265-272.

Lannin, J. 2005. â€œGeneralization and justification: The challenge of introducing algebraic reasoning through patterning activities.â€ Mathematical Thinking and Learning, 7(3), 231-258.

Lithner, J. 2008. â€œA Research Framework for Creative and Imitative Reasoning.â€ Educational Studies in Mathematics, 67, 255-276.

Manoucheri, A and St John S. 2006. â€œFrom classroom discussions to group discourse.â€ Mathematics Teacher, 99(8), 544-552.

McCrone, S. 2005. â€œThe development of mathematical discussions: An investigation of a fifth-grade classroom.â€ Mathematical Thinking and Learning, 7(2), 111-133.

NCTM. 2000. Principles and Standards for School Mathematics, Reston, VA: NCTM.

NCTM. 2010. Standards for School Mathematics. Available online: http://standards.nctm.org.

Ontario Ministry of Education. 2005. The Ontario Curriculum, Grades 1 to 8: Mathematics. Toronto, ON: Queenâ€™s Printer for Ontario.

Pirie and Kieren. 1992. â€œCreating Constructivist Environments and Constructing Creative Mathematics.â€ Educational Studies in Mathematics, 23, pp. 505-528.

Skemp, R. R. 1976. â€œRelational Understanding and Instrumental Understanding.â€ Mathematics Teaching, 77, 20-26.

Thomas, S. N. 1973. Practical reasoning in natural language (3rd ed). Englewood Cliffs, NJ: Prentice-Hall.

Wood, T., Williams, G., and McNeal, B. 2006. â€œChildrenâ€™s mathematical thinking in different classroom cultures.â€ Journal for Research in Mathematics Education, 37(3), 222-252.