Research Article
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Mathematical Argumentation Ability: Error Analysis in Solving Mathematical Arguments

Year 2020, Volume: 8 Issue: 2, 711 - 721, 15.06.2020
https://doi.org/10.17478/jegys.654460

Abstract

This study aims to analyze errors made by students in solving mathematical arguments based on Bloom’s Taxonomy. It is a quantitative descriptive study. As many as 72 students of a senior secondary school were involved as the participants. The Mathematical Argumentation Ability Test (TKAM) was developed based on the cognitive domain of Bloom’s Taxonomy (C1 to C6), and later distributed to the participants. The scores obtained from the test were analyzed. The results show that only 31% of students pass the test while 69% of students fail. Many students do not pass the test due to procedural errors and conceptual errors in solving the problems. Furthermore, based on Bloom’s Taxonomy, students who able to solve the problems only achieve the C3 level of cognitive domain, namely the ability to draw conclusion arguments

Supporting Institution

Universitas Negeri Malang

Project Number

20161141081898

Thanks

Indonesian Endowment Fund for Education (LPDP), and STKIP PGRI Pasuruan

References

  • Anderson, L., & Krathwohl, D. R. (2010). Taxonomy for Learning Teaching and Asswssing. New York: David McKay Company.
  • Anthony, G., & Walshaw, M. (2009). Characteristics of Effective Teaching of Mathematics : A View from the West, 2(2), 147–164.
  • Ayalon, M., & Hershkowitz, R. (2018). Mathematics teachers’ attention to potential classroom situations of argumentation. Journal of Mathematical Behavior, 49(May), 163–173. https://doi.org/10.1016/j.jmathb.2017.11.010
  • Ball, D. L., Thames, M. H., Phelps, G., & Ball, D. L. (2008). What Makes It Special ? https://doi.org/10.1177/0022487108324554
  • Chamundeswari. (2014). Conceptual Errors Encountered in Mathematical Operations in Algebra among Students at the Secondary Level. International Journal of Innovative Science, Engineering & Technology, 1(8), 24–38
  • Cohen, L., Manion, L., & Morrison, K. (2007). Research Methods in Education. New York: Routledge.
  • Conner, A. M., Singletary, L. M., Smith, R. C., Wagner, P. A., & Francisco, R. T. (2014). Teacher support for collective argumentation: A framework for examining how teachers support students’ engagement in mathematical activities. Educational Studies in Mathematics, 86(3), 401–429. https://doi.org/10.1007/s10649-014-9532-8
  • Cottrell, S. (2005). Critical Thinking Skills - Developing Effective Analysis and Argument. New York: Palgrave Macmillan
  • Creswell, J. (2012). Educational Research. New: Pearson.
  • Deane, P. D. (2014). A case study in principled assessment design: Designing assessments to measure and support the development of argumentative reading and writing skills. Psicología Educativa, 20(2), 99–108. https://doi.org/10.1016/j.pse.2014.10.001
  • Elbrink, M. (2007). Analyzing and Addressing Common Mathematical Errors in Secondary Education. Undergraduate Mathematics Exchange, 5(1), 2–4.
  • Foster, D. (2007). Chapter 12 Making Meaning in Algebra Examining Students ’ Understandings and Misconceptions, 53, 163–176.
  • Graydon, P. J., & Holloway, C. M. (2017). An investigation of proposed techniques for quantifying confidence in assurance arguments. Safety Science, 92, 53–65. https://doi.org/10.1016/j.ssci.2016.09.014
  • Harris, C. J., Phillips, R. S., & Penuel, W. R. (2012). Examining Teachers’ Instructional Moves Aimed at Developing Students’ Ideas and Questions in Learner-Centered Science Classrooms. Journal of Science Teacher Education, 23(7), 769–788. https://doi.org/10.1007/s10972-011-9237-0
  • Herholdt, R., & Sapire, I. (2014). An error analysis in the early grades mathematics – A learning opportunity ?, 4(October), 42–60.
  • Indrawatiningsih, N., Purwanto., As’ari, A.R., Sa’dijah, C., & Hakim, L., (2019). Identification Model for Determining Mathematical Sentences as Valid Argument, 7(9), 1839–1846. https://doi.org/10.13189/ujer.2019.070901
  • Indrawatiningsih, N., Purwanto., As’ari, A.R., Sa’dijah, Cholis., D. (2019). Students ’ mathematical argumentation ability in determining arguments or not arguments Student s ’ mathematical argumentation ability in determining arguments or not arguments. Journal of Physics: Conf. Series. https://doi.org/10.1088/1742-6596/1315/1/012053
  • Indrawatiningsih, N. (2018). Arguments in Critical Thinking Ability, 218(ICoMSE 2017), 12–15.
  • Jonassen, D. H. (2010). Research Issues in Problem Solving, 1–15.
  • Kirshner, D. (2014). Interference of Instrumental Instruction in Subsequent Relational Learning. JRME, Pages 524-540 https://doi.org/10.2307/749885
  • Krathwohl, D. R., & Anderson, L.W. (2002). A Revision of Bloom ’ s Taxonomy of Education Objective. New York: Addison Wesley Lonman Inc.
  • Krummheuer, G. (2007). Argumentation and participation in the primary mathematics classroom. Two episodes and related theoretical abductions. Journal of Mathematical Behavior, 26(1), 60–82. https://doi.org/10.1016/j.jmathb.2007.02.001
  • Krummheuer, G. (2013). The relationship between diagrammatic argumentation and narrative argumentation in the context of the development of mathematical thinking in the early years. Educational Studies in Mathematics, 84(2), 249–265. https://doi.org/10.1007/s10649-013-9471-9
  • Kuhn, D. (2010). Teaching and learning science as argument. Science Education, 94(5), 810–824. https://doi.org/10.1002/sce.20395
  • Lai, C.F. (2012). Error Analysis In Mathematics. University of Oregon: Behavioral Research and Teaching University.
  • Lee, Kosze & Smith III, J. P. (2009). Cognitive and Linguistic Challenges in Understanding Proving. Proceedings of the ICMI Study 19 Conference: Proof and Proving in Mathematics Education, 2, 2–21.
  • Legutko, M. (2008). An Analysis of Students’ Mathematical Error in The Teaching-Research Process. Mathematics Teaching-Research.
  • Li, X. (2006). Cognitive Analysis of Students’ Errors and Misconceptions in Variables, Equations, and Functions. Texas A&M University.
  • NCTM. (2000). Introduction: Perspectives on Principles and Standards for School Mathematics. School Science and Mathematics, 101(6), 277–279. https://doi.org/10.1111/j.1949-8594.2001.tb17957.x
  • Nussbaum, E. M., & Edwards, O. V. (2011). Critical questions and argument stratagems: A framework for enhancing and analyzing students’ reasoning practices. Journal of the Learning Sciences, 20(3), 443–488. https://doi.org/10.1080/10508406.2011.564567
  • Ontario Ministry of Education. (2005). Mathematics. Ontario: Ministry of Education.
  • Peraturan Pemerintah RI. (2013). Peraturan Pemerintah RI Nomor 32 Tahun 2013 tentang Standar Nasional Pendidikan. Jakarta: Kemendikbud.
  • Ruggiero, V.N. 2012. Beyond Feelings: A Guide To Critical Thinking. New York: McGraw-Hill.
  • Salma, J., & Sherwin, R. (2012). Students’ Difficulties in Comprehending. International international researchers, (1).
  • Schwarz, B. B., & Asterhan, C. (2010). Argumentation and Reasoning. International Handbook of Psychology in Education, (May), 137–176.
  • Simon, S., Erduran, S., & Osborne, J. (2006). Learning to Teach Argumentation : Research and development in the science classroom. International Journal of Science Education, (936077810). https://doi.org/10.1080/09500690500336957
  • Stylianides, A. J. (2007). The notion of proof in the context of elementary school mathematics. Educational Studies in Mathematics, 65(1), 1–20. https://doi.org/10.1007/s10649-006-9038-0
  • Stylianides, A. J., & Bieda, K. N. (2016). Proof and Argumentation in Mathematics Education Research, (Icmi), 315–351.
  • Toulmin, S. E. (2003). The Uses of Argument. Cambridge: University Press.
  • Van Ness, C. K., & Maher, C. A. (2018). Analysis of the argumentation of nine-year-olds engaged in discourse about comparing fraction models. Journal of Mathematical Behavior, (January), 0–1. https://doi.org/10.1016/j.jmathb.2018.04.004
  • Veloo, A., Krishnasamy, H. N., Shahida, W., & Abdullah, W. (2017). Types of Student Errors in Mathematical Symbols, Graphs and Problem-Solving. Asian Social Science; Vol. 11, No. 15, 324–334. https://doi.org/10.5539/ass.v11n15p324
  • Whitenack, J. W., & Knipping, N. (2002). Argumentation, instructional design theory and students’ mathematical learning: A case for coordinating interpretive lenses. Journal of Mathematical Behavior, 21(4), 441–457. https://doi.org/10.1016/S0732-3123(02)00144-X
  • Wood, T. (2013). Creating a Context for Argument in Mathematics Class. Journal for Research in Mathematics Education, 30(2), 171–191.
  • Yackel, E. (2002). What we can learn from analyzing the teacher’s role in collective argumentation. Journal of Mathematical Behavior, 21(4), 423–440. https://doi.org/10.1016/S0732-3123(02)00143-8
  • Yackel, E., & Cobb, P. (1996). Sociomathematical Norms, Argumentation, and Autonomy in Mathematics. Journal for Research in Mathematics Education, 27(4), 458. https://doi.org/10.2307/749877
  • Yackel, E., Rasmussen, C., & King, K. (2000). Social and sociomathematical norms in an advanced undergraduate mathematics course. The Journal of Mathematical Behavior, 19(3), 275–287. https://doi.org/10.1016/S0732-3123(00)00051-1
  • Yee, S. P., Boyle, J. D., Ko, Y. Y. (Winnie), & Bleiler-Baxter, S. K. (2018). Effects of constructing, critiquing, and revising arguments within university classrooms. Journal of Mathematical Behavior, 49(May 2016), 145–162. https://doi.org/10.1016/j.jmathb.2017.11.009
  • Zazkis, R., & Chernoff, E. J. (2015). What makes a counterexample exemplary ? What makes a counterexample exemplary ?. Educ Stud Math, 68: 195–208. https://doi.org/10.1007/s10649-007-9110-4
Year 2020, Volume: 8 Issue: 2, 711 - 721, 15.06.2020
https://doi.org/10.17478/jegys.654460

Abstract

Project Number

20161141081898

References

  • Anderson, L., & Krathwohl, D. R. (2010). Taxonomy for Learning Teaching and Asswssing. New York: David McKay Company.
  • Anthony, G., & Walshaw, M. (2009). Characteristics of Effective Teaching of Mathematics : A View from the West, 2(2), 147–164.
  • Ayalon, M., & Hershkowitz, R. (2018). Mathematics teachers’ attention to potential classroom situations of argumentation. Journal of Mathematical Behavior, 49(May), 163–173. https://doi.org/10.1016/j.jmathb.2017.11.010
  • Ball, D. L., Thames, M. H., Phelps, G., & Ball, D. L. (2008). What Makes It Special ? https://doi.org/10.1177/0022487108324554
  • Chamundeswari. (2014). Conceptual Errors Encountered in Mathematical Operations in Algebra among Students at the Secondary Level. International Journal of Innovative Science, Engineering & Technology, 1(8), 24–38
  • Cohen, L., Manion, L., & Morrison, K. (2007). Research Methods in Education. New York: Routledge.
  • Conner, A. M., Singletary, L. M., Smith, R. C., Wagner, P. A., & Francisco, R. T. (2014). Teacher support for collective argumentation: A framework for examining how teachers support students’ engagement in mathematical activities. Educational Studies in Mathematics, 86(3), 401–429. https://doi.org/10.1007/s10649-014-9532-8
  • Cottrell, S. (2005). Critical Thinking Skills - Developing Effective Analysis and Argument. New York: Palgrave Macmillan
  • Creswell, J. (2012). Educational Research. New: Pearson.
  • Deane, P. D. (2014). A case study in principled assessment design: Designing assessments to measure and support the development of argumentative reading and writing skills. Psicología Educativa, 20(2), 99–108. https://doi.org/10.1016/j.pse.2014.10.001
  • Elbrink, M. (2007). Analyzing and Addressing Common Mathematical Errors in Secondary Education. Undergraduate Mathematics Exchange, 5(1), 2–4.
  • Foster, D. (2007). Chapter 12 Making Meaning in Algebra Examining Students ’ Understandings and Misconceptions, 53, 163–176.
  • Graydon, P. J., & Holloway, C. M. (2017). An investigation of proposed techniques for quantifying confidence in assurance arguments. Safety Science, 92, 53–65. https://doi.org/10.1016/j.ssci.2016.09.014
  • Harris, C. J., Phillips, R. S., & Penuel, W. R. (2012). Examining Teachers’ Instructional Moves Aimed at Developing Students’ Ideas and Questions in Learner-Centered Science Classrooms. Journal of Science Teacher Education, 23(7), 769–788. https://doi.org/10.1007/s10972-011-9237-0
  • Herholdt, R., & Sapire, I. (2014). An error analysis in the early grades mathematics – A learning opportunity ?, 4(October), 42–60.
  • Indrawatiningsih, N., Purwanto., As’ari, A.R., Sa’dijah, C., & Hakim, L., (2019). Identification Model for Determining Mathematical Sentences as Valid Argument, 7(9), 1839–1846. https://doi.org/10.13189/ujer.2019.070901
  • Indrawatiningsih, N., Purwanto., As’ari, A.R., Sa’dijah, Cholis., D. (2019). Students ’ mathematical argumentation ability in determining arguments or not arguments Student s ’ mathematical argumentation ability in determining arguments or not arguments. Journal of Physics: Conf. Series. https://doi.org/10.1088/1742-6596/1315/1/012053
  • Indrawatiningsih, N. (2018). Arguments in Critical Thinking Ability, 218(ICoMSE 2017), 12–15.
  • Jonassen, D. H. (2010). Research Issues in Problem Solving, 1–15.
  • Kirshner, D. (2014). Interference of Instrumental Instruction in Subsequent Relational Learning. JRME, Pages 524-540 https://doi.org/10.2307/749885
  • Krathwohl, D. R., & Anderson, L.W. (2002). A Revision of Bloom ’ s Taxonomy of Education Objective. New York: Addison Wesley Lonman Inc.
  • Krummheuer, G. (2007). Argumentation and participation in the primary mathematics classroom. Two episodes and related theoretical abductions. Journal of Mathematical Behavior, 26(1), 60–82. https://doi.org/10.1016/j.jmathb.2007.02.001
  • Krummheuer, G. (2013). The relationship between diagrammatic argumentation and narrative argumentation in the context of the development of mathematical thinking in the early years. Educational Studies in Mathematics, 84(2), 249–265. https://doi.org/10.1007/s10649-013-9471-9
  • Kuhn, D. (2010). Teaching and learning science as argument. Science Education, 94(5), 810–824. https://doi.org/10.1002/sce.20395
  • Lai, C.F. (2012). Error Analysis In Mathematics. University of Oregon: Behavioral Research and Teaching University.
  • Lee, Kosze & Smith III, J. P. (2009). Cognitive and Linguistic Challenges in Understanding Proving. Proceedings of the ICMI Study 19 Conference: Proof and Proving in Mathematics Education, 2, 2–21.
  • Legutko, M. (2008). An Analysis of Students’ Mathematical Error in The Teaching-Research Process. Mathematics Teaching-Research.
  • Li, X. (2006). Cognitive Analysis of Students’ Errors and Misconceptions in Variables, Equations, and Functions. Texas A&M University.
  • NCTM. (2000). Introduction: Perspectives on Principles and Standards for School Mathematics. School Science and Mathematics, 101(6), 277–279. https://doi.org/10.1111/j.1949-8594.2001.tb17957.x
  • Nussbaum, E. M., & Edwards, O. V. (2011). Critical questions and argument stratagems: A framework for enhancing and analyzing students’ reasoning practices. Journal of the Learning Sciences, 20(3), 443–488. https://doi.org/10.1080/10508406.2011.564567
  • Ontario Ministry of Education. (2005). Mathematics. Ontario: Ministry of Education.
  • Peraturan Pemerintah RI. (2013). Peraturan Pemerintah RI Nomor 32 Tahun 2013 tentang Standar Nasional Pendidikan. Jakarta: Kemendikbud.
  • Ruggiero, V.N. 2012. Beyond Feelings: A Guide To Critical Thinking. New York: McGraw-Hill.
  • Salma, J., & Sherwin, R. (2012). Students’ Difficulties in Comprehending. International international researchers, (1).
  • Schwarz, B. B., & Asterhan, C. (2010). Argumentation and Reasoning. International Handbook of Psychology in Education, (May), 137–176.
  • Simon, S., Erduran, S., & Osborne, J. (2006). Learning to Teach Argumentation : Research and development in the science classroom. International Journal of Science Education, (936077810). https://doi.org/10.1080/09500690500336957
  • Stylianides, A. J. (2007). The notion of proof in the context of elementary school mathematics. Educational Studies in Mathematics, 65(1), 1–20. https://doi.org/10.1007/s10649-006-9038-0
  • Stylianides, A. J., & Bieda, K. N. (2016). Proof and Argumentation in Mathematics Education Research, (Icmi), 315–351.
  • Toulmin, S. E. (2003). The Uses of Argument. Cambridge: University Press.
  • Van Ness, C. K., & Maher, C. A. (2018). Analysis of the argumentation of nine-year-olds engaged in discourse about comparing fraction models. Journal of Mathematical Behavior, (January), 0–1. https://doi.org/10.1016/j.jmathb.2018.04.004
  • Veloo, A., Krishnasamy, H. N., Shahida, W., & Abdullah, W. (2017). Types of Student Errors in Mathematical Symbols, Graphs and Problem-Solving. Asian Social Science; Vol. 11, No. 15, 324–334. https://doi.org/10.5539/ass.v11n15p324
  • Whitenack, J. W., & Knipping, N. (2002). Argumentation, instructional design theory and students’ mathematical learning: A case for coordinating interpretive lenses. Journal of Mathematical Behavior, 21(4), 441–457. https://doi.org/10.1016/S0732-3123(02)00144-X
  • Wood, T. (2013). Creating a Context for Argument in Mathematics Class. Journal for Research in Mathematics Education, 30(2), 171–191.
  • Yackel, E. (2002). What we can learn from analyzing the teacher’s role in collective argumentation. Journal of Mathematical Behavior, 21(4), 423–440. https://doi.org/10.1016/S0732-3123(02)00143-8
  • Yackel, E., & Cobb, P. (1996). Sociomathematical Norms, Argumentation, and Autonomy in Mathematics. Journal for Research in Mathematics Education, 27(4), 458. https://doi.org/10.2307/749877
  • Yackel, E., Rasmussen, C., & King, K. (2000). Social and sociomathematical norms in an advanced undergraduate mathematics course. The Journal of Mathematical Behavior, 19(3), 275–287. https://doi.org/10.1016/S0732-3123(00)00051-1
  • Yee, S. P., Boyle, J. D., Ko, Y. Y. (Winnie), & Bleiler-Baxter, S. K. (2018). Effects of constructing, critiquing, and revising arguments within university classrooms. Journal of Mathematical Behavior, 49(May 2016), 145–162. https://doi.org/10.1016/j.jmathb.2017.11.009
  • Zazkis, R., & Chernoff, E. J. (2015). What makes a counterexample exemplary ? What makes a counterexample exemplary ?. Educ Stud Math, 68: 195–208. https://doi.org/10.1007/s10649-007-9110-4
There are 48 citations in total.

Details

Primary Language English
Subjects Other Fields of Education
Journal Section Thinking Skills
Authors

Nonik Indrawatiningsih 0000-0001-8249-4638

Purwanto -

Abdur As'ari 0000-0002-4959-0043

Cholis Sa'dijah 0000-0002-0264-8578

Project Number 20161141081898
Publication Date June 15, 2020
Published in Issue Year 2020 Volume: 8 Issue: 2

Cite

APA Indrawatiningsih, N., -, P., As’ari, A., Sa’dijah, C. (2020). Mathematical Argumentation Ability: Error Analysis in Solving Mathematical Arguments. Journal for the Education of Gifted Young Scientists, 8(2), 711-721. https://doi.org/10.17478/jegys.654460
AMA Indrawatiningsih N, - P, As’ari A, Sa’dijah C. Mathematical Argumentation Ability: Error Analysis in Solving Mathematical Arguments. JEGYS. June 2020;8(2):711-721. doi:10.17478/jegys.654460
Chicago Indrawatiningsih, Nonik, Purwanto -, Abdur As’ari, and Cholis Sa’dijah. “Mathematical Argumentation Ability: Error Analysis in Solving Mathematical Arguments”. Journal for the Education of Gifted Young Scientists 8, no. 2 (June 2020): 711-21. https://doi.org/10.17478/jegys.654460.
EndNote Indrawatiningsih N, - P, As’ari A, Sa’dijah C (June 1, 2020) Mathematical Argumentation Ability: Error Analysis in Solving Mathematical Arguments. Journal for the Education of Gifted Young Scientists 8 2 711–721.
IEEE N. Indrawatiningsih, P. -, A. As’ari, and C. Sa’dijah, “Mathematical Argumentation Ability: Error Analysis in Solving Mathematical Arguments”, JEGYS, vol. 8, no. 2, pp. 711–721, 2020, doi: 10.17478/jegys.654460.
ISNAD Indrawatiningsih, Nonik et al. “Mathematical Argumentation Ability: Error Analysis in Solving Mathematical Arguments”. Journal for the Education of Gifted Young Scientists 8/2 (June 2020), 711-721. https://doi.org/10.17478/jegys.654460.
JAMA Indrawatiningsih N, - P, As’ari A, Sa’dijah C. Mathematical Argumentation Ability: Error Analysis in Solving Mathematical Arguments. JEGYS. 2020;8:711–721.
MLA Indrawatiningsih, Nonik et al. “Mathematical Argumentation Ability: Error Analysis in Solving Mathematical Arguments”. Journal for the Education of Gifted Young Scientists, vol. 8, no. 2, 2020, pp. 711-2, doi:10.17478/jegys.654460.
Vancouver Indrawatiningsih N, - P, As’ari A, Sa’dijah C. Mathematical Argumentation Ability: Error Analysis in Solving Mathematical Arguments. JEGYS. 2020;8(2):711-2.
By introducing the concept of the "Gifted Young Scientist," JEGYS has initiated a new research trend at the intersection of science-field education and gifted education.