|
What Error Happened To Inferences Of Senior High School Students Using Mathematical Critical Thinking Ability?
[Full Text]
AUTHOR(S)
Ardi Dwi Susandi, Cholis Sa’dijah, Abdur Rahman As’ari, Susiswo
KEYWORDS
Error Analysis, Inference, Mathematical Critical Thinking Ability, APOS Theory.
ABSTRACT
Critical thinking is one of important factors in learning mathematics because it is used as one of the tools to solve mathematical problems. In the process of mathematical critical thinking, students experience the process of making inferences i.e. in the process of making conclusions of the premises given so that the premises and the conclusions form valid arguments. However, students sometimes make mistakes in giving reasons to the inferences made. The objective of this research was to analyze the error of a high school student in making inferences using mathematical critical thinking ability based on APOS theory. The type of research used was descriptive with qualitative approach. The subjectof this research was a student of twelfth grade. The methods used in the study included two test of essays, interview, and triangulation methods. The findings showed that the student was able to make inferences of given problems. However, the student had not been able to give the reasons of the inferences made. The causes of student errors in working on the questions of inferences based on APOS theory were: (1) errors in manipulating the application of the rules of making conclusion on logical thinking, (2) misconceptions (SPLDV) about the equation of coinciding lines, (3) errors dealing with kinds of numbers in mathematics (4) difficulties in changing given premises in the forms of mathematical symbols (5) difficulties in remembering the wayof eliminating and substituting of SPLDV principles, (6) difficultiesin changing SPLDV matrix forms into SPLDV algebra.
REFERENCES
[1]. Aizikovitsh, E., & Amit, M. (2010). Evaluating an infusion approach to the teaching of critical thinking skills through mathematics. Procedia Social and Behavioral Sciences, 2(2), 3818–3822. https://doi.org/10.1016/j.sbspro.2010.03.596
[2]. Aksu, G. (2015). Determination the Effects of Vocational High School Students ’ Logical and Critical Thinking Skills on Mathematics Success. Eurasian Journal of Educational Research, (59), 181–206.
[3]. Arnon, I, Cottrill, J, Dubinsky, E, Oktaç, A, Fuentes, SR, Trigueros, M, & Weller, K. (2014). APOS Theory: a framework for research and curriculum development in mathematics education. London: Springer.
[4]. Asari, A. R., Malang, U. N., Timur, J., View, B. A., View, C. T., & Asari, A. R. (2016). Variasi konstruk dalam pembelajaran matematika. Malang: CV. Bintang Sejahtera.
[5]. Brijlall, D. (2013). High school learners ’ mental construction during solving optimisation problems in Calculus : a South African case study. South African Journal of Education, 33(2), 1–18.
[6]. Carraher, D., & Martinez, M. (2008). Early algebra and mathematical generalization Early algebra and mathematical generalization. ZDM: The International Journal on Mathematics Education, 40(January), 2–22. https://doi.org/10.1007/s11858-007-0067-7
[7]. Chukwuyenum, A. N. (2013). Impact of Critical thinking on Performance in Mathematics among Senior Secondary School Students in Lagos State. IOSR Journal of Research & Method in Education (IOSR-JRME), 3(5), 18–25.
[8]. Ennis, R. H. (1996). Critical Thinking. New Jersey: Prentice-Hall Inc.
[9]. Facione, P. A. (2011). Critical Thinking : What It Is and Why It Counts. The California Academic Press: Millbrae, CA.
[10]. Fang, H., Angie, H., Ricci, F. A., & Mathematical, M. (2016). Mathematical Teaching Strategies : Pathways to Critical Thinking and Metacognition Mathematical Teaching Strategies : Pathways to Critical Thinking and Metacognition. International Journal of Research in Education and Science (IJRES), 2(1), 190–200.
[11]. Kumar, R., & James, R. (2015). Evaluation of Critical Thinking in Higher Education in Oman. International Journal of Higher Education, 4(3), 33–43. https://doi.org/10.5430/ijhe.v4n3p33
[12]. NCTM. (2000). Principles and Standards For School Mathematics. Reston, VA: NCTM.
[13]. Peter, E. E. (2012). Critical thinking : Essence for teaching mathematics and mathematics problem solving skills. African Journal of Mathematics and Computer Science Research, 5(3), 39–43. https://doi.org/10.5897/AJMCSR11.161
[14]. Rosnawati, Kartowagiran, B. . J. (2015). a formative assessment model of critical thinking in mathematics learning in junior high school. Research and Evaluation in Education Journal, 1(2), 186–198.
[15]. Saragih, S., & Napitupulu, E. (2015). Developing Student-Centered Learning Model to Improve High Order Mathematical Thinking Ability. International Education Studies, 8(6), 104–112. https://doi.org/10.5539/ies.v8n6p104
[16]. Sarpkaya, G., & Ünlü, M. (2013). Critical Thinking Skills of Teacher Candidates of Elementary Mathematics. Social and Behavioral Sciences, 93, 831–835. https://doi.org/10.1016/j.sbspro.2013.09.288
[17]. Siyepu, S. W. (2015). Analysis of errors in derivatives of trigonometric functions. International Journal of STEM Education, 2(16), 1–16. https://doi.org/10.1186/s40594-015-0029-5
[18]. Tiruneh, D. T., Verburgh, A., & Elen, J. (2014). Effectiveness of Critical Thinking Instruction in Higher Education : A Systematic Review of Intervention Studies. Higher Education Studies, 4(1), 1–17. https://doi.org/10.5539/hes.v4n1p1
[19]. Trilling, B., & Fadel, C. (2009). 21st century skills: Learning for life in Our Times. San Fransisco: Jossey-Bass.
|
