# COGNITIVE LEVEL PROFILE AT THE TENTH GRADE OF SENIOR HIGH SCHOOL STUDENTS IN MATHEMATICS PROBLEM SOLVING ON THREE VARIABLES OF LINEAR EQUATION SYSTEM

## Main Article Content

## Abstract

Problem solving is significant skill in facing 21st century. Students have different levels of problem solving. The levels that explain individual abilities in solving mathematics problems are called as cognitive level. It consists of three levels; cognition, metacognition, and epistemic cognition. The cognitive level influences individual in understanding the problem and deciding the right strategies to solve it. The material used to obtain the data is three variables linear equation system, by involving two high ability students at the tenth grade from one of the state senior high schools in Pati. This research employs qualitative method, which the data are collected through task-based interview and time triangulation is applied to validate the data. The results reveal that at the cognition level, students with high ability have an understanding related to conceptual and procedural knowledge, but the ability of students in factual knowledge is low, especially in terminology skill; at the metacognition level, the students are able to write down each strategy in each method, but it is not detail; while at the epistemic cognition level, they are able to explain the weaknesses of a method, but they have not been able to provide a solution to overcome its weaknesses.

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## References

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Sullivan, P., Borcek, C., Walker, N., & Mick, R. (2016). Exploring a Structure for Mathematics Lessons that Initiate Learning by Activating Cognition on Challenging Tasks. Journal of Mathematical Behavior. 41., 159-170.

Anderson, L., & Karthwohl, D. (2001). A Taxonomy for Learning Teaching and Assesing. New York: Longman.

Ameliah, I. H., Munawaroh, M., Muchyidin, A. (2016). The Influence of Curiosity and Self-Confidence of Students Toward Outcome Studied Mathematics Grade VII MTs Negeri 1 Cirebon. Mathematics Education Learning and Teaching. 5 (1). 9-21

Baimba, Brown, & Hardimah. (2008). The Mismatch Between Science Teachers’ Beliefs and Classroom Practices. Jurnal of Aplied Research and Education (JARE). Vol 12, 194-203.

Bandura, A. (2006a). Autobiography. MG Lindzey & WM Runyan (Eds.), A History of Psychology in Autobiography (Vol. IX). Washington, DC: American Psychological Association.

Benjafield, J. G. (1992). Cognition. Englewood Cliffs: NJ: Prentice-Hall.

Berger, P., & Luckmann, T. (2005). Interpersonal Intellegence. Jakarta: Amara Books.

Budiyono. (2003). Educational Research Methodology. Surakarta: Sebelas Maret University Press.

Carlson, M.P. and Bloom, I. (2005). The Cyclic Nature of Problem Solving: An Emergent Multidimensional Problem-Solving (MPS) Framework. Educational Studies in Mathematics, 58(1), 45 – 75.

Chinn, C., Buckland, L., & Samarapungavan, A. (2011). Expanding the Dimensions of Epistemic Cognition: Arguments from Philosophy and Psychology. Educational Psychologist, 46, 141–167.

Cleopatra, M. (2015). The Effect of Life Style towards Mathematics Learning Motivation. Jurnal Formatif. 5 (2). 168-181.

National Education Department. (2003). The Law of National Education System. Jakarta: National Education Department.

Downing K.J. (2009).Self-Efficacy And Metacognitive Development. The International Journal Of Learning, 16 (4).

Ferguson, L., Brathen, I., & Stromso, H. (2012). Epistemic Cognition when Students Read Multiple Documents Containing Conflicting Scientific Evidence: A Think-aloud Study. Learning and Instruction 22, 103-120.

Hofer, B., & Pintrich, P. (1997). The Development of Epistemological Theories: Beliefs about Knowledge and Knowing and Their Relation to Learning. Review of Educational Research, 67, 88–140.

Kamaleswaran, J., Rohaida, M., & Rose, A. (2014). A Review of Science, Technology, Engineering & Mathematics (STEM) Education Research from 1999–2013. Eurasia Journal of Mathematics, Science & Technology Education, 10(3), 155-163.

Kim, Y., Park, M. S., Moore, T., & Sasha. (2013). Multiple Levels of Metacognition and Their Elicitation Complex Problem-Solving Tasks. Journal of Mathematical Behavior,32, 377-396.

Kitchener, K. S. (1983). Cognition, Metacognition, and Epistemic Cognition: A three-Level Model of Cognitive Processing. Hum. Dev. 26, 222-232.

Knight, S., & Littleton, K. (2017). A Discursive Approach to the Analysis of Epistemic Cognition. Learning, Culture and Social Interaction, 03.

Kuhn, D. & Dean Jr, D. (2004). Metacognition: A Bridge Between Cognitive Psychology and Educational Practice. Theory into Practice, 43(4), 268 – 273.

Mason, L., Boldrin, A., & Ariasi, N. (2009). Epistemic Metacognition in Context: Evaluating and Learning Online Information. Metacognition and Learning. 5, 67-90.

Moleong, L. J. (2007). Qualitatif Research Methodology. Bandung: PT Remaja Rosdakarya.

OECD. (2010). PISA 2012 Mathematical Framework. Paris: OECD.

Polya, G. (1973). How to Solve I. New Jersey: Princeton University Press.

Reed, S. K. (2004). Educational Psychology: Theory and Practice (9th ed.). USA: Thomson Learning.

Sciefele, U., & Csikszentmihalyit, M., (1995). Motivation and Ability as Factors in Mathematic Experience and Achievement. Journal for Research in Mathematics Education. 26 (2). 163-181.

Setianingrum, A., Sujadi, I., & Pramudya, I. (2017). The Process of Reflective Thinking in Mathematics Problem Solving Review from Cognitive Style. International Conferens Mathematics and Science Education (p. 358). Bandung: Universitas Pedidikan Indonesia.

Sternberg, R. J. (2006). Cognitive Psychology. (4th ed.). Belmont: Thompson Wodswort.

Sugiyanto. (2009). The Contribution of Achievement Motivation towards Students’ Learning Motivation at the Eleventh Grade of SMAN 10 Semarang. Paradigma. 8 (4). 19-34.

Sullivan, P., Borcek, C., Walker, N., & Mick, R. (2016). Exploring a Structure for Mathematics Lessons that Initiate Learning by Activating Cognition on Challenging Tasks. Journal of Mathematical Behavior. 41., 159-170.