Research Article
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Exploring Student’s Representation Process in Solving Ill-Structured Problems Geometry

Year 2020, Volume: 7 Issue: 2, 183 - 202, 01.08.2020
https://doi.org/10.17275/per.20.28.7.2

Abstract

This study is to reveal the construction process of student representation in solving of ill-structured geometry problems. The three phases involved in the construction process are interpreting the problem, giving opinions, and concluding. A total of four high school students participated in Surabaya and Sidoarjo in this qualitative study. They used visual and symbolic representations to solve the ill-structured problems. The research data were obtained from the sheets of ill-structured geometry problems (ISGP), video recordings, and interviews. The data analysis through three stages, data identification, data presentation, and conclusion. The results of data analysis show that the process of constructing the visual and symbolic representations was carried out by the students when interpreting the problem. The subjects provide data to support problem-solving process, such as initial length and width. The construction process through the visual representation began with the process of giving meaning. They drew rectangle with a length and width. Likewise, when giving an opinion, they referred to the drawings they made with length and width of different sizes. They used symbolic representation as a length and width for the initial situation in the process of giving meaning. Through the use of variables, they could perform calculations so as to determine the proposals used as a solution. Two patterns that the students did during the process of the representation construction, are deductive and inductive. It is important for teachers to know the process of representation of students when solving ill-structured problems. It needs to be enlarged and in line with the criteria to obtain the general description of the representation of the construction process when solving the problem. Then, teachers should design meaningful learning so they can connect concepts that their students can use to solve problems. 

Supporting Institution

Lembaga Pengelola Dana Pendidikan (LPDP)

Project Number

20161141081903

References

  • Abdillah, Nusantara, T., Subanji, Susanto, H., & Abadyo. (2016). The Students Decision Making in Solving Discount Problem. International Education Studies, 9(7), 57–63. https://doi.org/10.5539/ies.v9n7p57
  • Anwar, R. B., & Rahmawati, D. (2017). Symbolic and Verbal Representation Process of Student in Solving Mathematics Problem based Polya’s Stages. International Education Studies, 10(10), 20–28. https://doi.org/10.5539/ies.v10n10p20
  • Anwar, R. B., Yuwono, I., As’ari, A. R., Sisworo, & Rahmawati, D. (2016). Mathematical Representation by Students in Building Relational Understanding on Concepts of Area and Primeter of Rectangle. Educational Research and Reviewsv, 11(21), 2002–2008. https://doi.org/10.5897/ERR2016.2813
  • Bakry, & Bakar, N. Bin. (2015). The Process of Thinking among Junior High School Students in Solving HOTS Question. International Journal of Evaluation and Research in Education, 4(3), 138–145.
  • Bal, A. P. (2014). The Examination of Representations used by Classroom Teacher Candidates in Solving Mathematical Problems. Educational Sciences: Theory & Practice, 14(6), 2349–2365. https://doi.org/10.12738/estp.2014.6.2189
  • Boonen, A. J. H., Reed, H. C., Schoonenboom, J., & Jolles, J. (2016). It’s Not a Math Lesson - We’re Learning to Draw ! Teachers’ Use of Visual Representations in Instructing Word Problem Solving in Sixth Grade of Elementary School. Frontline Learning Research, 4(5), 55–82. https://doi.org/http://dx.doi.org/10.14786/flr.v4i5.245
  • Clement, J. J. (2008). Does Decoding Increase Word Problem Solving Skills ? University of Nebraska-Lincoln. Retrieved from http://digitalcommons.unl.edu/mathmidactionresearch
  • Cooper, J. L., & Alibali, M. W. (2012). Visual Representations in Mathematical Problem-Solving: Effects of Diagrams and Illustrations. In Proceedings of the 34th Annual Meeting of The North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 281–288). Kalamazoo: Western Michigan University.
  • Creswell, J. C. (2012). Educational Research, Planning, Conducting, and Evaluating Quantitative and Qualitative Research (4th ed.). Boston: Pearson.
  • Debrenti, E. (2015). Visual Representations in Mathematics Teaching: An Experiment with Students. Acta Didactica Napocensia, 8(1), 19–26. Retrieved from eric.ed.gov
  • Erdoğan, F. (2020). The Relationship Between Prospective Middle School Mathematics Teachers’ Critical Thinking Skills and Reflective Thinking Skills. Participatory Educational Research (PER), 7(1), 220–241.
  • Gagatsis, A., & Shiakalli, M. (2004). Ability to translate from one representation of the concept of function to another and mathematical problem-solving. Educational Psychology, 24(5), 645–657. https://doi.org/10.1080/0144341042000262953
  • Goldin, G. . (2002). Representation in Mathematical Learning and Problem Solving. In Handbook of International Research In Mathematics Education (pp. 197–218). New Jersey: Lawrence Erlbaum Associates Publishers.
  • Hegarty, M., Mayer, R. E., & Monk, C. A. (1995). Comprehension of Arithmetic Word Problems : A Comparison of Successful and Unsuccessful Problem Solvers inconsistent problems with those of problem solvers who do. Journal of Educational Psychology, 87(1), 18–32.
  • Hong, N. S. (1998). The Relationship Between Well-Structured and Ill-Structured Problem Solving in Multimedia Simulation. The Pennsylvania State University.
  • Hwang, W., Chen, N., Dung, J.-J., & Yang, Y.-L. (2007). Multiple Representation Skills and Creativity Effects on Mathematical Problem Solving using a Multimedia Whiteboard System Jian-Jie Dung Yi-Lun Yang. Educational Technology & Society, 10(2), 191–212.
  • Jonassen, D. (2003). Using cognitive tools to represent problems. Journal of Research on Technology in Education, 35(3), 362–381. https://doi.org/10.1080/15391523.2003.10782391
  • Jonassen, D. H. (1997). Instructional Design Models for Well-Structured and Ill-Structured Problem-Solving Learning Outcomes. Educational Technology Research and Development, 45(1), 65–94. Retrieved from http://www.jstor.org/stable/30220169
  • Karaahmetoğlu, K., & Korkmaz, Ö. (2019). The Effect of Project-based Arduino Educational Robot Applications on Students’ Computational Thinking Skills and Their Perception of Basic Stem Skill Levels. Participatory Educational Research (PER), 6(2), 1–14. Retrieved from https://dergipark.org.tr/en/download/article-file/772664
  • Korkmaz, Ö., & Bai, X. (2019). Adapting Computational Thinking Scale (CTS) for Chinese High School Students and Their Thinking Scale Skills Level. Participatory Educational Research, 6(1), 10–26. https://doi.org/10.17275/per.19.2.6.1
  • Lesh, R., Post, T., & Behr, M. (1987). Representations and Translations among Representations in Mathematics Learning and Problem Solving in Problems of Representation in the Teaching and Learning of Mathematics of Mathematics (pp. 33–40). Hillsdale NJ: Erlbaum.
  • Miles, M. B., Huberman, A., & Saldana, J. (2014). Qualitative Data Analysis. (H. Salmon, Ed.) (Third Edit). California: SAGE Publications, Inc.
  • Murtafiah, W., Sa’dijah, C., Candra, T. D., Susiswo, & As’ari, A. R. (2018). Exploring the explanation of pre-service teacher in mathematics teaching practice. Journal on Mathematics Education, 9(2), 259–270. https://doi.org/10.22342/jme.9.2.5388.259-270
  • NCTM. (2000). Principles and Standards for School Mathematics. United States of America: The National Council of Teachers of Mathematics Inc. Retrieved from www.nctm.org
  • Özsoy, G., Kuruyer, H. G., & Çakiroglu, A. (2015). Evaluation of Students ’ Mathematical Problem-Solving Skills in Relation to Their Reading Levels. International Electronic Journal of Elementary Education, 8(1), 113–132. Retrieved from www.jejee.com
  • Pape, S. J. (2004). Middle School Children’s Problem-Solving Behavior: A Cognitive Analysis from a Reading Comprehension Perspective. Journal for Research in Mathematics Education, 35(3), 187–219.
  • Shin, N., Jonassen, D. H., & McGee, S. (2003). Predictors of well-structured and ill-structured problem-solving in an astronomy simulation. Journal of Research in Science Teaching, 40(1), 6–33. https://doi.org/10.1002/tea.10058
  • Stoltz, P. G. (2000). Adversity Quotient at Work: Make Everyday Challenges the Key to Your Success-Putting the Principles of AQ into Action. Canada: John Willey and Sons Inc. Wiley Publishers.
  • Stylianou, D. A. (2010). Teachers’ Conceptions of Representation in Middle School Mathematics. Journal of Mathematics Teacher Education, 13(4), 325–343. https://doi.org/10.1007/s10857-010-9143-y
  • Stylianou, D. A., & Silver, E. A. (2004). The Role of Visual Representations in Advanced Mathematical Problem Solving : An Examination of Expert- Novice Similarities and Differences. Mathematical Thinking and Learning, 6(4), 353–387. Retrieved from http://sci-hub.tw/10.1207/s15327833mtl0604_1#
  • Subanji, S., & Nusantara, T. (2016). Thinking Process of Pseudo Construction in Mathematics Concepts. International Education Studies, 9(2), 17. https://doi.org/10.5539/ies.v9n2p17
  • Supandi, S., Waluya, S. B., Rochmad, R., Suyitno, H., & Dewi, K. (2018). Think-Talk-Write Model for Improving Students’ Abilities in Mathematical Representation. International Journal of Instruction, 11(3), 77–90.
  • Swastika, G. T., Nusantara, T., Subanji, & Irawati, S. (2020). Alteration representation in the Process of Translation Graphic to Graphic. Humanities & Social Sciences Reviews, 8(1), 334–343. https://doi.org/http://doi.org/10/18510/hsr.2020.8144
  • Ulusoy, F., & Argun, Z. (2019). Secondary School Students’ Representations for Solving Geometric Word Problems in Different Clinical Interviews. International Journal of Education in Mathematics, Science and Technology (IJEMST), 7(1), 73–92. https://doi.org/10.18404/ijemst.328341
  • Wong, W. K., Hsu, S. C., Wu, S. H., Lee, C. W., & Hsu, W. L. (2007). LIM-G: Learner-initiating instruction model based on cognitive knowledge for geometry word problem comprehension. Computers and Education, 48(4), 582–601. https://doi.org/10.1016/j.compedu.2005.03.009
  • Xin, Y. P., Jitendra, A. K., & Buchman, A. D. (2005). Effects of Mathematical Word Problem – Solving Instruction on Middle School Students with Learning Problems. The Journal of Special Education, 39(3), 181–192.
Year 2020, Volume: 7 Issue: 2, 183 - 202, 01.08.2020
https://doi.org/10.17275/per.20.28.7.2

Abstract

Project Number

20161141081903

References

  • Abdillah, Nusantara, T., Subanji, Susanto, H., & Abadyo. (2016). The Students Decision Making in Solving Discount Problem. International Education Studies, 9(7), 57–63. https://doi.org/10.5539/ies.v9n7p57
  • Anwar, R. B., & Rahmawati, D. (2017). Symbolic and Verbal Representation Process of Student in Solving Mathematics Problem based Polya’s Stages. International Education Studies, 10(10), 20–28. https://doi.org/10.5539/ies.v10n10p20
  • Anwar, R. B., Yuwono, I., As’ari, A. R., Sisworo, & Rahmawati, D. (2016). Mathematical Representation by Students in Building Relational Understanding on Concepts of Area and Primeter of Rectangle. Educational Research and Reviewsv, 11(21), 2002–2008. https://doi.org/10.5897/ERR2016.2813
  • Bakry, & Bakar, N. Bin. (2015). The Process of Thinking among Junior High School Students in Solving HOTS Question. International Journal of Evaluation and Research in Education, 4(3), 138–145.
  • Bal, A. P. (2014). The Examination of Representations used by Classroom Teacher Candidates in Solving Mathematical Problems. Educational Sciences: Theory & Practice, 14(6), 2349–2365. https://doi.org/10.12738/estp.2014.6.2189
  • Boonen, A. J. H., Reed, H. C., Schoonenboom, J., & Jolles, J. (2016). It’s Not a Math Lesson - We’re Learning to Draw ! Teachers’ Use of Visual Representations in Instructing Word Problem Solving in Sixth Grade of Elementary School. Frontline Learning Research, 4(5), 55–82. https://doi.org/http://dx.doi.org/10.14786/flr.v4i5.245
  • Clement, J. J. (2008). Does Decoding Increase Word Problem Solving Skills ? University of Nebraska-Lincoln. Retrieved from http://digitalcommons.unl.edu/mathmidactionresearch
  • Cooper, J. L., & Alibali, M. W. (2012). Visual Representations in Mathematical Problem-Solving: Effects of Diagrams and Illustrations. In Proceedings of the 34th Annual Meeting of The North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 281–288). Kalamazoo: Western Michigan University.
  • Creswell, J. C. (2012). Educational Research, Planning, Conducting, and Evaluating Quantitative and Qualitative Research (4th ed.). Boston: Pearson.
  • Debrenti, E. (2015). Visual Representations in Mathematics Teaching: An Experiment with Students. Acta Didactica Napocensia, 8(1), 19–26. Retrieved from eric.ed.gov
  • Erdoğan, F. (2020). The Relationship Between Prospective Middle School Mathematics Teachers’ Critical Thinking Skills and Reflective Thinking Skills. Participatory Educational Research (PER), 7(1), 220–241.
  • Gagatsis, A., & Shiakalli, M. (2004). Ability to translate from one representation of the concept of function to another and mathematical problem-solving. Educational Psychology, 24(5), 645–657. https://doi.org/10.1080/0144341042000262953
  • Goldin, G. . (2002). Representation in Mathematical Learning and Problem Solving. In Handbook of International Research In Mathematics Education (pp. 197–218). New Jersey: Lawrence Erlbaum Associates Publishers.
  • Hegarty, M., Mayer, R. E., & Monk, C. A. (1995). Comprehension of Arithmetic Word Problems : A Comparison of Successful and Unsuccessful Problem Solvers inconsistent problems with those of problem solvers who do. Journal of Educational Psychology, 87(1), 18–32.
  • Hong, N. S. (1998). The Relationship Between Well-Structured and Ill-Structured Problem Solving in Multimedia Simulation. The Pennsylvania State University.
  • Hwang, W., Chen, N., Dung, J.-J., & Yang, Y.-L. (2007). Multiple Representation Skills and Creativity Effects on Mathematical Problem Solving using a Multimedia Whiteboard System Jian-Jie Dung Yi-Lun Yang. Educational Technology & Society, 10(2), 191–212.
  • Jonassen, D. (2003). Using cognitive tools to represent problems. Journal of Research on Technology in Education, 35(3), 362–381. https://doi.org/10.1080/15391523.2003.10782391
  • Jonassen, D. H. (1997). Instructional Design Models for Well-Structured and Ill-Structured Problem-Solving Learning Outcomes. Educational Technology Research and Development, 45(1), 65–94. Retrieved from http://www.jstor.org/stable/30220169
  • Karaahmetoğlu, K., & Korkmaz, Ö. (2019). The Effect of Project-based Arduino Educational Robot Applications on Students’ Computational Thinking Skills and Their Perception of Basic Stem Skill Levels. Participatory Educational Research (PER), 6(2), 1–14. Retrieved from https://dergipark.org.tr/en/download/article-file/772664
  • Korkmaz, Ö., & Bai, X. (2019). Adapting Computational Thinking Scale (CTS) for Chinese High School Students and Their Thinking Scale Skills Level. Participatory Educational Research, 6(1), 10–26. https://doi.org/10.17275/per.19.2.6.1
  • Lesh, R., Post, T., & Behr, M. (1987). Representations and Translations among Representations in Mathematics Learning and Problem Solving in Problems of Representation in the Teaching and Learning of Mathematics of Mathematics (pp. 33–40). Hillsdale NJ: Erlbaum.
  • Miles, M. B., Huberman, A., & Saldana, J. (2014). Qualitative Data Analysis. (H. Salmon, Ed.) (Third Edit). California: SAGE Publications, Inc.
  • Murtafiah, W., Sa’dijah, C., Candra, T. D., Susiswo, & As’ari, A. R. (2018). Exploring the explanation of pre-service teacher in mathematics teaching practice. Journal on Mathematics Education, 9(2), 259–270. https://doi.org/10.22342/jme.9.2.5388.259-270
  • NCTM. (2000). Principles and Standards for School Mathematics. United States of America: The National Council of Teachers of Mathematics Inc. Retrieved from www.nctm.org
  • Özsoy, G., Kuruyer, H. G., & Çakiroglu, A. (2015). Evaluation of Students ’ Mathematical Problem-Solving Skills in Relation to Their Reading Levels. International Electronic Journal of Elementary Education, 8(1), 113–132. Retrieved from www.jejee.com
  • Pape, S. J. (2004). Middle School Children’s Problem-Solving Behavior: A Cognitive Analysis from a Reading Comprehension Perspective. Journal for Research in Mathematics Education, 35(3), 187–219.
  • Shin, N., Jonassen, D. H., & McGee, S. (2003). Predictors of well-structured and ill-structured problem-solving in an astronomy simulation. Journal of Research in Science Teaching, 40(1), 6–33. https://doi.org/10.1002/tea.10058
  • Stoltz, P. G. (2000). Adversity Quotient at Work: Make Everyday Challenges the Key to Your Success-Putting the Principles of AQ into Action. Canada: John Willey and Sons Inc. Wiley Publishers.
  • Stylianou, D. A. (2010). Teachers’ Conceptions of Representation in Middle School Mathematics. Journal of Mathematics Teacher Education, 13(4), 325–343. https://doi.org/10.1007/s10857-010-9143-y
  • Stylianou, D. A., & Silver, E. A. (2004). The Role of Visual Representations in Advanced Mathematical Problem Solving : An Examination of Expert- Novice Similarities and Differences. Mathematical Thinking and Learning, 6(4), 353–387. Retrieved from http://sci-hub.tw/10.1207/s15327833mtl0604_1#
  • Subanji, S., & Nusantara, T. (2016). Thinking Process of Pseudo Construction in Mathematics Concepts. International Education Studies, 9(2), 17. https://doi.org/10.5539/ies.v9n2p17
  • Supandi, S., Waluya, S. B., Rochmad, R., Suyitno, H., & Dewi, K. (2018). Think-Talk-Write Model for Improving Students’ Abilities in Mathematical Representation. International Journal of Instruction, 11(3), 77–90.
  • Swastika, G. T., Nusantara, T., Subanji, & Irawati, S. (2020). Alteration representation in the Process of Translation Graphic to Graphic. Humanities & Social Sciences Reviews, 8(1), 334–343. https://doi.org/http://doi.org/10/18510/hsr.2020.8144
  • Ulusoy, F., & Argun, Z. (2019). Secondary School Students’ Representations for Solving Geometric Word Problems in Different Clinical Interviews. International Journal of Education in Mathematics, Science and Technology (IJEMST), 7(1), 73–92. https://doi.org/10.18404/ijemst.328341
  • Wong, W. K., Hsu, S. C., Wu, S. H., Lee, C. W., & Hsu, W. L. (2007). LIM-G: Learner-initiating instruction model based on cognitive knowledge for geometry word problem comprehension. Computers and Education, 48(4), 582–601. https://doi.org/10.1016/j.compedu.2005.03.009
  • Xin, Y. P., Jitendra, A. K., & Buchman, A. D. (2005). Effects of Mathematical Word Problem – Solving Instruction on Middle School Students with Learning Problems. The Journal of Special Education, 39(3), 181–192.
There are 36 citations in total.

Details

Primary Language English
Subjects Other Fields of Education
Journal Section Research Articles
Authors

Lydia Lia Prayitno 0000-0002-5416-8787

Purwanto - 0000-0003-0974-4068

Subanji Subanji This is me 0000-0002-4281-1923

Susiswo Susiswo 0000-0001-6461-6283

Abdur As'arı 0000-0002-4959-0043

Project Number 20161141081903
Publication Date August 1, 2020
Acceptance Date May 1, 2020
Published in Issue Year 2020 Volume: 7 Issue: 2

Cite

APA Prayitno, L. L., -, P., Subanji, S., Susiswo, S., et al. (2020). Exploring Student’s Representation Process in Solving Ill-Structured Problems Geometry. Participatory Educational Research, 7(2), 183-202. https://doi.org/10.17275/per.20.28.7.2