Research Article
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Year 2020, Volume: 8 Issue: 3, 1031 - 1043, 15.09.2020

M. Syawahid Purwanto - Sukoriyanto - I Made Sulandra

https://doi.org/10.17478/jegys.765395
Cited By: 1

Abstract

References

  • Amir, M. F., Mufarikhah, I. A., Wahyuni, A., Nasrun, & Rudyanto, H. E. (2019). Developing ‘Fort Defending’ Game as a Learning Design for Mathematical Literacy Integrated to Primary School Curriculum in Indonesia. Elementary Education Online, 18(3), 1081–1092. https://doi.org/10.17051/ilkonline.2019.610145
  • Amit, M., & Neria, D. (2008). ‘“ Rising to the challenge ”’: using generalization in pattern problems to unearth the algebraic skills of talented pre-algebra students. ZDM Mathematics Education, 40(2), 111–129. https://doi.org/10.1007/s11858-007-0069-5
  • Blanton, M., Brizuela, B., Gardiner, A., Sawrey, K., & Newman-Owens, A. (2017). A progression in first-grade children’s thinking about variable and variable notation in functional relationships. Educational Studies in Mathematics, Online First. https://doi.org/doi:10.1007/s10649-016- 9745-0
  • Blanton, M. L. (2008). Algebra and the elementary classroom. Transforming thinking, transforming practice. Portsmounth, NH: Heinemann.
  • Blanton, M. L., & Kaput, J. J. (2004). Elementary Grades Students ’ Capacity for Functional Thinking. In Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 135–142).
  • Blanton, M. L., & Kaput, J. J. (2005). Characterizing a Classroom Practice That Promotes Algebraic Reasoning. Journal for Research in Mathematics Education, 36(5), 412–446.
  • Blanton, M. L., Levi, L., Crites, T., & Dougherty, B. J. (2011). Developing essential understandings of algebraic thinking, Grades 3-5. Reston, VA: The National Council of Teachers of Mathematics.
  • Bush, S. B., & Karp, K. S. (2013). Prerequisite algebra skills and associated misconceptions of middle grade students : A review. Journal of Mathematical Behavior, 32(3), 613–632. https://doi.org/10.1016/j.jmathb.2013.07.002
  • Cohen, L., Manion, L., & Morrison, K. (2000). Research methods in education (5th editio). London: Routledge.
  • Confrey, J., & Smith, E. (1991). A framework for functions: Prototypes, multiple representations, and transformations. In R. Underhill & C. Brown (Eds.), Proceedings of the thirteenth annual meeting of the north American chapter of the international group for the psychology of mathematics education (pp. 57–63). Blacksburg, VA: Virginia Polytechnic Institute & State University.
  • Creswell, J. W. (2012). Educational research: Planning, conducting, and evaluating quantitative and qualitative research. Educational Research (Vol. 4). https://doi.org/10.1017/CBO9781107415324.004
  • Eisenmann, P. (2009). A contribution to the development of functional thinking of pupils and students. The Teaching of Mathematics, (23), 73–81. Ellis, A. B. (2007). Connections Between Generalizing and Justifying : Students ’ Reasoning with Linear Relationships. Journal for Research in Mathematics Education, 38(3), 194–229.
  • Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2012). How to Design and Evaluate Research in Education. New York: McGraw-Hill.
  • Huntley, M. A., Marcus, R., Kahan, J., & Miller, J. L. (2007). Investigating high-school students ’ reasoning strategies when they solve linear equations. Journal of Mathematical Behavior, 26(2), 115–139. https://doi.org/10.1016/j.jmathb.2007.05.005
  • Jupri, A., & Drijvers, P. (2014). Difficulties in initial algebra learning in Indonesia. Mathematics Education Research Journal, 26(4), 683–710. https://doi.org/10.1007/s13394-013-0097-0
  • Kaiser, G., & Willander, T. (2005). Development of mathematical literacy: Results of an empirical study. Teaching Mathematics and Its Applications, 24(2–3), 48–60. https://doi.org/10.1093/teamat/hri016
  • Kemendikbud. Peraturan Menteri Pendidikan dan Kebudayaan Republik Indonesia Nomor 21 Tahun 2016, Pub. L. No. 21 (2016). Indonesia.
  • Kieran, C. (2007). Learning and teaching algebra at the middle school through college levels. In F. K. Lester Jr (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (p. 707). Charlotte, NC: New Age Publishing; Reston, VA: National Council of Teachers of Mathematics.
  • Knuth, E. J. (2000). Student Understanding of the Cartesian Connection : An Exploratory Study. Journal for Research in Mathematics Education, 31(4), 500–507. https://doi.org/DOI: 10.2307/749655
  • Lannin, J. K. (2005). Generalization and Justification : The Challenge of Introducing Algebraic Reasoning Through Patterning Activities. Mathematical Thinking and Learning, 7(3), 231–258. https://doi.org/DOI: 10.1207/s15327833mtl0703_3
  • Lichti, M. (2018). How to Foster Functional Thinking in Learning Environments Using Computer-Based Simulations or Real Materials. Journal for STEM Education Research, 1(1–2), 148–172.
  • Lichti, M., & Roth, J. (2019). Functional thinking: A three-dimensional construct? Journal Für Mathematik-Didaktik, 40(2), 169–195. https://doi.org/10.1007/s13138-019-00141-3
  • Mason, J., Stacey, K., & Burton, L. (2010). Thinking Mathematically. Edinburgh: Pearson.
  • Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: an Expanded Sourcebook. London: SAGE Publications Inc.
  • NCTM. (2000). Principless and Standards for School Mathematics. Reston: NCTM.
  • Smith, E. (2008). Representational thinking as a framework for introducing functions in the elementary curriculum. In J. Kaput, D. Carraher, & M. Blanton (Eds.), Algebra in the early grades (pp. 95–132). London & Newyork: Lawrence Erlbaum/Taylor & Francis Group & NCTM.
  • Stacey, K. (1989). Finding and Using Patterns in Liniar generalising Problems. Educational Studies in Mathematics, 20(2), 147–164. https://doi.org/10.1007/bf00579460
  • Stacey, K. (2011). The PISA View of Mathematical Literacy in Indonesia. Journal on Mathematics Education, 2(2), 95–126. https://doi.org/10.22342/jme.2.2.746.95-126
  • Stephens, A. C., Fonger, N., Strachota, S., Isler, I., Blanton, M. L., Knuth, E., & Gardiner, A. M. (2017). A learning progression for elementary students’ functional thinking a learning progression for elementary students’ functional. Mathematical Thinking and Learning, 19(3), 143–166. https://doi.org/10.1080/10986065.2017.1328636
  • Subanji, & Nusantara, T. (2013). Karakterisasi Kesalahan Berpikir Siswa dalam Mengonstruksi Konsep Matematika. Jurnal Ilmu Pendidikan, 33(2), 208–217. Tanıslı, D. (2011). Functional thinking ways in relation to linear function tables of elementary school students. The Journal of Mathematical Behavior, 30, 206–223. https://doi.org/10.1016/j.jmathb.2011.08.001
  • Warren, E. A., Cooper, T. J., & Lamb, J. T. (2006). Investigating functional thinking in the elementary classroom : Foundations of early algebraic reasoning. Journal of Mathematical Behavior, 25, 208–223. https://doi.org/10.1016/j.jmathb.2006.09.006
  • Warren, E., & Cooper, T. O. M. (2005). Introducing Functional Thinking in Year 2 : a case study of early algebra teaching. Contemporary Issues in Early Childhood, 6(2), 150–162.
  • Wijaya, A., Heuvel-panhuizen, M. Van Den, Doorman, M., & Robitzch, A. (2014). Difficulties in solving context-based PISA mathematics tasks : An analysis of students ’ errors. The Mathematics Enthusiast, 11(3), 555–584. https://doi.org/10.1139/t02-118
  • Wilkie, K. J. (2015). Learning to teach upper primary school algebra : changes to teachers ’ mathematical knowledge for teaching functional thinking. Mathematics Education Research Journal, 28(2), 245–275. https://doi.org/10.1007/s13394-015-0151-1
  • Wilkie, K. J., & Clarke, D. M. (2016). Developing students’ functional thinking in algebra through different visualisations of a growing pattern’ s structure. Mathematics Education Research Journal, 28(2), 223–243. https://doi.org/10.1007/s13394-015-0146-y

Elementary students’ functional thinking: From recursive to correspondence

Year 2020, Volume: 8 Issue: 3, 1031 - 1043, 15.09.2020

M. Syawahid Purwanto - Sukoriyanto - I Made Sulandra

https://doi.org/10.17478/jegys.765395
Cited By: 1

Abstract

This study aims to identify elementary students’ functional thinking processes in solving pattern problems. Previous studies showed that elementary students' functional thinking still often experience errors in solving pattern problems. The study of the functional thinking process in solving pattern problems is a fundamental key as a solution to find out the strengths and weaknesses of elementary school students, so that they are better prepared in generalizing relationships, representing and analyzing function behavior in advanced algebra classes. This study used a descriptive qualitative approach with a case study method. Participants of study was sixty-five elementary students who had not yet received generalization patterns material. The instruments were tasks and interview guidelines. Based on the task results, students who had correct answers were chosen using purposive sampling to be given an in-depth interview. The finding indicated that elementary students are able to think functionally in different ways. Students’ functional thinking begins with recursive thinking in the pre-finding formula in the entry stage. Students find the formula by corresponding thinking in the attack stage. Finally, students use the formula to get inverse in the review stage.

Keywords

Fuctional thinking Recursive Correspondence Mathematics education

References

  • Amir, M. F., Mufarikhah, I. A., Wahyuni, A., Nasrun, & Rudyanto, H. E. (2019). Developing ‘Fort Defending’ Game as a Learning Design for Mathematical Literacy Integrated to Primary School Curriculum in Indonesia. Elementary Education Online, 18(3), 1081–1092. https://doi.org/10.17051/ilkonline.2019.610145
  • Amit, M., & Neria, D. (2008). ‘“ Rising to the challenge ”’: using generalization in pattern problems to unearth the algebraic skills of talented pre-algebra students. ZDM Mathematics Education, 40(2), 111–129. https://doi.org/10.1007/s11858-007-0069-5
  • Blanton, M., Brizuela, B., Gardiner, A., Sawrey, K., & Newman-Owens, A. (2017). A progression in first-grade children’s thinking about variable and variable notation in functional relationships. Educational Studies in Mathematics, Online First. https://doi.org/doi:10.1007/s10649-016- 9745-0
  • Blanton, M. L. (2008). Algebra and the elementary classroom. Transforming thinking, transforming practice. Portsmounth, NH: Heinemann.
  • Blanton, M. L., & Kaput, J. J. (2004). Elementary Grades Students ’ Capacity for Functional Thinking. In Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 135–142).
  • Blanton, M. L., & Kaput, J. J. (2005). Characterizing a Classroom Practice That Promotes Algebraic Reasoning. Journal for Research in Mathematics Education, 36(5), 412–446.
  • Blanton, M. L., Levi, L., Crites, T., & Dougherty, B. J. (2011). Developing essential understandings of algebraic thinking, Grades 3-5. Reston, VA: The National Council of Teachers of Mathematics.
  • Bush, S. B., & Karp, K. S. (2013). Prerequisite algebra skills and associated misconceptions of middle grade students : A review. Journal of Mathematical Behavior, 32(3), 613–632. https://doi.org/10.1016/j.jmathb.2013.07.002
  • Cohen, L., Manion, L., & Morrison, K. (2000). Research methods in education (5th editio). London: Routledge.
  • Confrey, J., & Smith, E. (1991). A framework for functions: Prototypes, multiple representations, and transformations. In R. Underhill & C. Brown (Eds.), Proceedings of the thirteenth annual meeting of the north American chapter of the international group for the psychology of mathematics education (pp. 57–63). Blacksburg, VA: Virginia Polytechnic Institute & State University.
  • Creswell, J. W. (2012). Educational research: Planning, conducting, and evaluating quantitative and qualitative research. Educational Research (Vol. 4). https://doi.org/10.1017/CBO9781107415324.004
  • Eisenmann, P. (2009). A contribution to the development of functional thinking of pupils and students. The Teaching of Mathematics, (23), 73–81. Ellis, A. B. (2007). Connections Between Generalizing and Justifying : Students ’ Reasoning with Linear Relationships. Journal for Research in Mathematics Education, 38(3), 194–229.
  • Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2012). How to Design and Evaluate Research in Education. New York: McGraw-Hill.
  • Huntley, M. A., Marcus, R., Kahan, J., & Miller, J. L. (2007). Investigating high-school students ’ reasoning strategies when they solve linear equations. Journal of Mathematical Behavior, 26(2), 115–139. https://doi.org/10.1016/j.jmathb.2007.05.005
  • Jupri, A., & Drijvers, P. (2014). Difficulties in initial algebra learning in Indonesia. Mathematics Education Research Journal, 26(4), 683–710. https://doi.org/10.1007/s13394-013-0097-0
  • Kaiser, G., & Willander, T. (2005). Development of mathematical literacy: Results of an empirical study. Teaching Mathematics and Its Applications, 24(2–3), 48–60. https://doi.org/10.1093/teamat/hri016
  • Kemendikbud. Peraturan Menteri Pendidikan dan Kebudayaan Republik Indonesia Nomor 21 Tahun 2016, Pub. L. No. 21 (2016). Indonesia.
  • Kieran, C. (2007). Learning and teaching algebra at the middle school through college levels. In F. K. Lester Jr (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (p. 707). Charlotte, NC: New Age Publishing; Reston, VA: National Council of Teachers of Mathematics.
  • Knuth, E. J. (2000). Student Understanding of the Cartesian Connection : An Exploratory Study. Journal for Research in Mathematics Education, 31(4), 500–507. https://doi.org/DOI: 10.2307/749655
  • Lannin, J. K. (2005). Generalization and Justification : The Challenge of Introducing Algebraic Reasoning Through Patterning Activities. Mathematical Thinking and Learning, 7(3), 231–258. https://doi.org/DOI: 10.1207/s15327833mtl0703_3
  • Lichti, M. (2018). How to Foster Functional Thinking in Learning Environments Using Computer-Based Simulations or Real Materials. Journal for STEM Education Research, 1(1–2), 148–172.
  • Lichti, M., & Roth, J. (2019). Functional thinking: A three-dimensional construct? Journal Für Mathematik-Didaktik, 40(2), 169–195. https://doi.org/10.1007/s13138-019-00141-3
  • Mason, J., Stacey, K., & Burton, L. (2010). Thinking Mathematically. Edinburgh: Pearson.
  • Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: an Expanded Sourcebook. London: SAGE Publications Inc.
  • NCTM. (2000). Principless and Standards for School Mathematics. Reston: NCTM.
  • Smith, E. (2008). Representational thinking as a framework for introducing functions in the elementary curriculum. In J. Kaput, D. Carraher, & M. Blanton (Eds.), Algebra in the early grades (pp. 95–132). London & Newyork: Lawrence Erlbaum/Taylor & Francis Group & NCTM.
  • Stacey, K. (1989). Finding and Using Patterns in Liniar generalising Problems. Educational Studies in Mathematics, 20(2), 147–164. https://doi.org/10.1007/bf00579460
  • Stacey, K. (2011). The PISA View of Mathematical Literacy in Indonesia. Journal on Mathematics Education, 2(2), 95–126. https://doi.org/10.22342/jme.2.2.746.95-126
  • Stephens, A. C., Fonger, N., Strachota, S., Isler, I., Blanton, M. L., Knuth, E., & Gardiner, A. M. (2017). A learning progression for elementary students’ functional thinking a learning progression for elementary students’ functional. Mathematical Thinking and Learning, 19(3), 143–166. https://doi.org/10.1080/10986065.2017.1328636
  • Subanji, & Nusantara, T. (2013). Karakterisasi Kesalahan Berpikir Siswa dalam Mengonstruksi Konsep Matematika. Jurnal Ilmu Pendidikan, 33(2), 208–217. Tanıslı, D. (2011). Functional thinking ways in relation to linear function tables of elementary school students. The Journal of Mathematical Behavior, 30, 206–223. https://doi.org/10.1016/j.jmathb.2011.08.001
  • Warren, E. A., Cooper, T. J., & Lamb, J. T. (2006). Investigating functional thinking in the elementary classroom : Foundations of early algebraic reasoning. Journal of Mathematical Behavior, 25, 208–223. https://doi.org/10.1016/j.jmathb.2006.09.006
  • Warren, E., & Cooper, T. O. M. (2005). Introducing Functional Thinking in Year 2 : a case study of early algebra teaching. Contemporary Issues in Early Childhood, 6(2), 150–162.
  • Wijaya, A., Heuvel-panhuizen, M. Van Den, Doorman, M., & Robitzch, A. (2014). Difficulties in solving context-based PISA mathematics tasks : An analysis of students ’ errors. The Mathematics Enthusiast, 11(3), 555–584. https://doi.org/10.1139/t02-118
  • Wilkie, K. J. (2015). Learning to teach upper primary school algebra : changes to teachers ’ mathematical knowledge for teaching functional thinking. Mathematics Education Research Journal, 28(2), 245–275. https://doi.org/10.1007/s13394-015-0151-1
  • Wilkie, K. J., & Clarke, D. M. (2016). Developing students’ functional thinking in algebra through different visualisations of a growing pattern’ s structure. Mathematics Education Research Journal, 28(2), 223–243. https://doi.org/10.1007/s13394-015-0146-y
There are 35 citations in total.

Details

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

M. Syawahid 0000-0001-7104-5685

Purwanto - 0000-0003-0974-4068

Sukoriyanto - 0000-0003-1700-6735

I Made Sulandra 0000-0003-3023-7562

Publication Date September 15, 2020
Published in Issue Year 2020 Volume: 8 Issue: 3

Cite

APA Syawahid, M., -, P., -, S., Sulandra, I. M. (2020). Elementary students’ functional thinking: From recursive to correspondence. Journal for the Education of Gifted Young Scientists, 8(3), 1031-1043. https://doi.org/10.17478/jegys.765395
AMA Syawahid M, - P, - S, Sulandra IM. Elementary students’ functional thinking: From recursive to correspondence. JEGYS. September 2020;8(3):1031-1043. doi:10.17478/jegys.765395
Chicago Syawahid, M., Purwanto -, Sukoriyanto -, and I Made Sulandra. “Elementary students’ Functional Thinking: From Recursive to Correspondence”. Journal for the Education of Gifted Young Scientists 8, no. 3 (September 2020): 1031-43. https://doi.org/10.17478/jegys.765395.
EndNote Syawahid M, - P, - S, Sulandra IM (September 1, 2020) Elementary students’ functional thinking: From recursive to correspondence. Journal for the Education of Gifted Young Scientists 8 3 1031–1043.
IEEE M. Syawahid, P. -, S. -, and I. M. Sulandra, “Elementary students’ functional thinking: From recursive to correspondence”, JEGYS, vol. 8, no. 3, pp. 1031–1043, 2020, doi: 10.17478/jegys.765395.
ISNAD Syawahid, M. et al. “Elementary students’ Functional Thinking: From Recursive to Correspondence”. Journal for the Education of Gifted Young Scientists 8/3 (September 2020), 1031-1043. https://doi.org/10.17478/jegys.765395.
JAMA Syawahid M, - P, - S, Sulandra IM. Elementary students’ functional thinking: From recursive to correspondence. JEGYS. 2020;8:1031–1043.
MLA Syawahid, M. et al. “Elementary students’ Functional Thinking: From Recursive to Correspondence”. Journal for the Education of Gifted Young Scientists, vol. 8, no. 3, 2020, pp. 1031-43, doi:10.17478/jegys.765395.
Vancouver Syawahid M, - P, - S, Sulandra IM. Elementary students’ functional thinking: From recursive to correspondence. JEGYS. 2020;8(3):1031-43.

Cited By

Multiple pathways for developing functional thinking in elementary mathematics textbooks: a case study in China
Educational Studies in Mathematics
https://doi.org/10.1007/s10649-023-10237-w