Mengeksplorasi Kemampuan Siswa Dalam Berpikir Fungsional Melalui Soal Cerita
Keywords:
Berpikir fungsional, Soal cerita, Fungsi
Abstract
Pergeseran tentang kemampuan siswa dalam memecahkan aritmetika dengan operasi angka ke kemampuan siswa dalam memecahkan aljabar dengan operasi pada bilangan yang tidak diketahui sering mengalami kesulitan. Dengan demikian untuk mengatasi kesulitan siswa tersebut, maka perlu adanya latihan dan rangsangan terhadap kemampuan siswa yaitu salah satunya dengan melatih siswa dalam berpikir fungsional. Berpikir fungsional merupakan hubungan antara dua kuantitas yang digeneralisasikan ke dalam suatu bentuk fungsi. Penelitian ini bertujuan untuk mengeksplorasi kemampuan siswa berpikir fungsional melalui soal cerita. Penelitian ini merupakan penelitian kualitatif yang bersifat deskriptif eksploratif. Subjek penelitian adalah 3 siswa dari 45 siswa Sekolah Menengah Atas (SMA). Instrumen penelitian adalah lembar jawaban siswa dan pedoman wawancara. Hasil penelitian menunjukan bahwa siswa dalam berpikir fungsional melalui 3 tahap yaitu siswa menentukan pola rekursif dengan menggunakan , siswa menentukan hubungan korespondensi yaitu menentukan perubangan nilai antara variabel bebas dengan variabel terikat, dan siswa menentukan korespondesi dengan menggunakan rumus barisan aritmatika Dengan demikian dapat disimpulkan bahwa soal cerita yang diberikan dapat mengeksplorasi siswa dalam berpikir fungsional.
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References
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Blanton, M., Brizuela, B. M., Gardiner, A. M., Sawrey, K., Newman-owens, A., Blanton, M., Gardiner, A. M., & Newman-owens, A. (2016). A Learning Trajectory in 6-Year-Olds’ Thinking About Generalizing Functional Relationships. Journal for Research in Mathematics Education. 46(5), 511–558. https://doi.org/10.5951/jresematheduc.46.5.0511
Blanton, M. L., & Kaput, J. J. (2004). Elementary Grades Students’ Capacity For Functional Thinking. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education. 2. 135-142.
https://www.emis.de/proceedings/PME28/RR/RR033_Blanton.pdf
Blanton, M. L., & Kaput, J. J. (2005). Helping Elementary Teachers Build Mathematical Generality into Curriculum and Instruction. ZDM. 37(1). https://doi.org/10.1007/BF02655895
Blanton, M. L. and James J. K. (2011) . Functional Thinking as a Route Into Algebra in the Elementary Grades. https://page-one.springer.com/pdf/preview/10.1007/978-3-642-17735-4_2
Blanton, M., Stephens, A., Knuth, E., Gardiner, A. M., Isler, I., Kim, J., Blanton, M., Knuth, E., Gardiner, A. M., & Kim, J. (2015). The Development of Children ’ s Algebraic Thinking : The Impact of a Comprehensive Early Algebra Intervention in Third Grade. Journal for Research in Mathematics Education. 46(1), 39-87. https://doi.org/10.5951/jresematheduc.46.1.0039
Brizuela, B. M. (2015). Children’s Use of Variables and Variables Notation to Represent Their Algebraic Ideas. Mathematical Thinking and Learning, 1–30.
https://doi.org/10.1080/10986065.2015.981939
Carlson, M., Sally J., Edward C., Sean L., and Eric H. (2002). Applying Covariational Reasoning While Modeling Dynamic Events: A Framework and a Study. Journal for Research in Mathematics Education 33(5):352–78. https://www.jstor.org/stable/4149958
Carpenter, T. P., & Levi, L. (2000). Developing conceptions of algebraic reasoning in the primary grades. Wisconsin Center for Educational Research. 21.
https://files.eric.ed.gov/fulltext/ED470471.pdf
Cooper, T. O. M. (2006). Using Repeating Patterns to Explore Functional Thinking. 11(1):9–14. https://files.eric.ed.gov/fulltext/EJ793907.pdf
Creswell. (2012). Educational Research Fourth Edition. Pustaka Pelajar. ISBN 978-602-229-474-0
Doorman, M., Drijvers, P., Gravemeijer, K., Boon, P., & Reed, H. (2012). Tool use and Development of the Function Concept: from Repeated Calculations to Functional Thinking. International Journal of Science and Mathematics Education. 1243–1267. https://doi.org/10.1007/s10763-012-9329-0
Driscoll. M. (2003). Fostering algebraic thinking. A guide for teachers grades 6–10. Portsmouth, NH: Heinemann. https://files.eric.ed.gov/fulltext/ED476802.pdf
Kaput, J. (2000). Teaching and learning a new algebra. In E. Fennema, & T. Romberg (Eds.), Mathematics classrooms that promote understanding (pp. 133–155). Mahwah, NJ: Lawrence Erlbaum Associates.
http://www.educ.fc.ul.pt/docentes/jponte/DA/DA-TEXTOS/Kaput_99AlgUnd.pdf
Koedinger, K. R. and Nathan, M. J. (2004). The Real Story Behind Story Problems : Effects of Representations on Quantitative Reasoning. The Journal of the Learning Sciences. 13(2):129–64. https://www.researchgate.net/profile/Kenneth_Koedinger2/publication/280786796_The_Real_Story_behind_Story_Problems_Effects_of_Representations_on_Quantitative_Reasoning/inline/jsViewer/568bdda308ae8445f58dbd11?inViewer=1&pdfJsDownload=1&origin=publication_detail&previewAsPdf=false
Machmurotun, S. (2014). The Thinking Ability of Students in Solving Mathematics. Journal Pendidikan Matematika. 2(2): 237–48.
http://seminar.uny.ac.id/icriems/sites/seminar.uny.ac.id.icriems/files/proceeding2018/ME86_Eva%20Dwi%20Minarti.pdf
Markworth, K. A. (2010). Growing and Growing: Promoting Functional Thinking With Geometric Growing Patterns. A Dissertation Submitted to the Faculty of the University of North Carolina at Chapel Hill in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in the School of Education. Chapel Hill
Mceldoon, K. L., and Rittle-Johnson. (2010). Assessing Elementary Students Functional Thinking Skills.The Case of Function Tables
https://peabody.vanderbilt.edu/docs/pdf/PRO/ATME_McEldoonandRittle-JohnsonPME-NApaper_2010.pdf
Muir, T. & Livy, S. (2015). Two of Everything Developing Functional Thinking in Primary Grades Through Children’s Literature. In APMC. Vol. 20 (1).
https://files.eric.ed.gov/fulltext/EJ1093237.pdf
Stephens, A., Blanton, M., Strachota, S., Knuth, E., & Gardiner, A. (2017). The Interplay between Students’ Understandings of Proportional and Functional Relationships. Proceedings of the 39th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Indianapolis, IN Hoosier Association of Mathematics Teacher Educators. 251–258. https://files.eric.ed.gov/fulltext/ED581309.pdf
Stephens, A. C., Blanton, M. L., Knuth, E. J., Marum, T., & Gardiner, A. M. (2011). From Recursive Pattern To Correspondence Rule: Developing Students’ Abilities To Engage in Functional Thinking. Proceedings of the 34th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Kalamazoo, MI: Western Michigan University.
https://www.researchgate.net/profile/Isil_Isler-Baykal/publication/304526974_From_recursive_pattern_to_correspondence_rule_Developing_students%27_abilities_to_engage_in_functional_thinking/inline/jsViewer/5772691508aeef01a0b62a99?inViewer=1&pdfJsDownload=1&origin=publication_detail&previewAsPdf=false
Stephens, A. C., Fonger, N., Strachota, S., Isler, I., Blanton, M., Knuth, E., & Murphy Gardiner, A. (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. (2011). Teori Berpikir Pseudo Penalaran Kovariasional. Universitas Negeri Malang. ISBN: 979.495.963.4
Tanişli, D. 2011. “Functional Thinking Ways in Relation to Linear Function Tables of Elementary School Students.” Journal of Mathematical Behavior 30(3):206–23
Tanıs, D. (2011). Functional Thinking Ways in Relation to Linear Function Tables of Elementary School Students. Journal of Mathematical Behavior, 30(3), 206–223. https://doi.org/10.1016/j.jmathb.2011.08.001
Warren, E. A., & Cooper. (2012). Exploring Young Students Functional Thinking. Proceeding of the 35th Conference of the International Group for the Psychology of Mathematics Education. 4. 75–84. https://dialnet.unirioja.es/descarga/articulo/4268866.pdf
Warren, E. A., Cooper, T. J., & Lamb, J. T. (2006). Investigating Functional Thinking in the Elementary Classroom : Foundations of Early Algebraic Reasoning. 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. In Contemporary Issues in Early Childhood. 6(2), 150–162. https://doi.org/10.2304/ciec.2005.6.2.5
Wilkie, K. J. (2004). Learning to like Algebra through Looking. APMC. 19(4). https://files.eric.ed.gov/fulltext/EJ1093277.pdf
Wilkie, K. J. (2014). Upper Primary School Teachers’ Mathematical Knowledge for Teaching Functional Thinking in Algebra. Journal of Mathematics Teacher Education. 17(5). https://doi.org/10.1007/s10857-013-9251-6
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. (2015). Developing Students’ Functional Thinking in Algebra Through Different Visualisations of a Growing Pattern’s Structure. Mathematics Education Research Journal, 223–243. https://doi.org/10.1007/s13394-015-0146-y
Yuniati, S., Nusantara, T., Subanji, & Made S., I. (2019). The use of Multiple Representation in Functional Thinking. International Journal of Recent Technology and Engineering, 8(1C2), 672–678. https://www.ijrte.org/wp-content/uploads/papers/v8i1C2/A11120581C219.pdf
Yuniati, S., & Suparjono. (2019). Model Representasi Matematis Siswa Kelas IV dalam Menyelesaikan Soal Cerita. MaPan 7(2):249–60. https://www.researchgate.net/publication/338508181_MODEL_REPRESENTASI_MATEMATIS_SISWA_KELAS_IV_DALAM_MENYELESAIKAN_SOAL_CERITA/inline/jsViewer/5e1876ba299bf10bc3a109bb?inViewer=1&pdfJsDownload=1&origin=publication_detail&previewAsPdf=false
Blanton, M., Brizuela, B. M., Gardiner, A. M., Sawrey, K., Newman-owens, A., Blanton, M., Gardiner, A. M., & Newman-owens, A. (2016). A Learning Trajectory in 6-Year-Olds’ Thinking About Generalizing Functional Relationships. Journal for Research in Mathematics Education. 46(5), 511–558. https://doi.org/10.5951/jresematheduc.46.5.0511
Blanton, M. L., & Kaput, J. J. (2004). Elementary Grades Students’ Capacity For Functional Thinking. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education. 2. 135-142.
https://www.emis.de/proceedings/PME28/RR/RR033_Blanton.pdf
Blanton, M. L., & Kaput, J. J. (2005). Helping Elementary Teachers Build Mathematical Generality into Curriculum and Instruction. ZDM. 37(1). https://doi.org/10.1007/BF02655895
Blanton, M. L. and James J. K. (2011) . Functional Thinking as a Route Into Algebra in the Elementary Grades. https://page-one.springer.com/pdf/preview/10.1007/978-3-642-17735-4_2
Blanton, M., Stephens, A., Knuth, E., Gardiner, A. M., Isler, I., Kim, J., Blanton, M., Knuth, E., Gardiner, A. M., & Kim, J. (2015). The Development of Children ’ s Algebraic Thinking : The Impact of a Comprehensive Early Algebra Intervention in Third Grade. Journal for Research in Mathematics Education. 46(1), 39-87. https://doi.org/10.5951/jresematheduc.46.1.0039
Brizuela, B. M. (2015). Children’s Use of Variables and Variables Notation to Represent Their Algebraic Ideas. Mathematical Thinking and Learning, 1–30.
https://doi.org/10.1080/10986065.2015.981939
Carlson, M., Sally J., Edward C., Sean L., and Eric H. (2002). Applying Covariational Reasoning While Modeling Dynamic Events: A Framework and a Study. Journal for Research in Mathematics Education 33(5):352–78. https://www.jstor.org/stable/4149958
Carpenter, T. P., & Levi, L. (2000). Developing conceptions of algebraic reasoning in the primary grades. Wisconsin Center for Educational Research. 21.
https://files.eric.ed.gov/fulltext/ED470471.pdf
Cooper, T. O. M. (2006). Using Repeating Patterns to Explore Functional Thinking. 11(1):9–14. https://files.eric.ed.gov/fulltext/EJ793907.pdf
Creswell. (2012). Educational Research Fourth Edition. Pustaka Pelajar. ISBN 978-602-229-474-0
Doorman, M., Drijvers, P., Gravemeijer, K., Boon, P., & Reed, H. (2012). Tool use and Development of the Function Concept: from Repeated Calculations to Functional Thinking. International Journal of Science and Mathematics Education. 1243–1267. https://doi.org/10.1007/s10763-012-9329-0
Driscoll. M. (2003). Fostering algebraic thinking. A guide for teachers grades 6–10. Portsmouth, NH: Heinemann. https://files.eric.ed.gov/fulltext/ED476802.pdf
Kaput, J. (2000). Teaching and learning a new algebra. In E. Fennema, & T. Romberg (Eds.), Mathematics classrooms that promote understanding (pp. 133–155). Mahwah, NJ: Lawrence Erlbaum Associates.
http://www.educ.fc.ul.pt/docentes/jponte/DA/DA-TEXTOS/Kaput_99AlgUnd.pdf
Koedinger, K. R. and Nathan, M. J. (2004). The Real Story Behind Story Problems : Effects of Representations on Quantitative Reasoning. The Journal of the Learning Sciences. 13(2):129–64. https://www.researchgate.net/profile/Kenneth_Koedinger2/publication/280786796_The_Real_Story_behind_Story_Problems_Effects_of_Representations_on_Quantitative_Reasoning/inline/jsViewer/568bdda308ae8445f58dbd11?inViewer=1&pdfJsDownload=1&origin=publication_detail&previewAsPdf=false
Machmurotun, S. (2014). The Thinking Ability of Students in Solving Mathematics. Journal Pendidikan Matematika. 2(2): 237–48.
http://seminar.uny.ac.id/icriems/sites/seminar.uny.ac.id.icriems/files/proceeding2018/ME86_Eva%20Dwi%20Minarti.pdf
Markworth, K. A. (2010). Growing and Growing: Promoting Functional Thinking With Geometric Growing Patterns. A Dissertation Submitted to the Faculty of the University of North Carolina at Chapel Hill in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in the School of Education. Chapel Hill
Mceldoon, K. L., and Rittle-Johnson. (2010). Assessing Elementary Students Functional Thinking Skills.The Case of Function Tables
https://peabody.vanderbilt.edu/docs/pdf/PRO/ATME_McEldoonandRittle-JohnsonPME-NApaper_2010.pdf
Muir, T. & Livy, S. (2015). Two of Everything Developing Functional Thinking in Primary Grades Through Children’s Literature. In APMC. Vol. 20 (1).
https://files.eric.ed.gov/fulltext/EJ1093237.pdf
Stephens, A., Blanton, M., Strachota, S., Knuth, E., & Gardiner, A. (2017). The Interplay between Students’ Understandings of Proportional and Functional Relationships. Proceedings of the 39th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Indianapolis, IN Hoosier Association of Mathematics Teacher Educators. 251–258. https://files.eric.ed.gov/fulltext/ED581309.pdf
Stephens, A. C., Blanton, M. L., Knuth, E. J., Marum, T., & Gardiner, A. M. (2011). From Recursive Pattern To Correspondence Rule: Developing Students’ Abilities To Engage in Functional Thinking. Proceedings of the 34th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Kalamazoo, MI: Western Michigan University.
https://www.researchgate.net/profile/Isil_Isler-Baykal/publication/304526974_From_recursive_pattern_to_correspondence_rule_Developing_students%27_abilities_to_engage_in_functional_thinking/inline/jsViewer/5772691508aeef01a0b62a99?inViewer=1&pdfJsDownload=1&origin=publication_detail&previewAsPdf=false
Stephens, A. C., Fonger, N., Strachota, S., Isler, I., Blanton, M., Knuth, E., & Murphy Gardiner, A. (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. (2011). Teori Berpikir Pseudo Penalaran Kovariasional. Universitas Negeri Malang. ISBN: 979.495.963.4
Tanişli, D. 2011. “Functional Thinking Ways in Relation to Linear Function Tables of Elementary School Students.” Journal of Mathematical Behavior 30(3):206–23
Tanıs, D. (2011). Functional Thinking Ways in Relation to Linear Function Tables of Elementary School Students. Journal of Mathematical Behavior, 30(3), 206–223. https://doi.org/10.1016/j.jmathb.2011.08.001
Warren, E. A., & Cooper. (2012). Exploring Young Students Functional Thinking. Proceeding of the 35th Conference of the International Group for the Psychology of Mathematics Education. 4. 75–84. https://dialnet.unirioja.es/descarga/articulo/4268866.pdf
Warren, E. A., Cooper, T. J., & Lamb, J. T. (2006). Investigating Functional Thinking in the Elementary Classroom : Foundations of Early Algebraic Reasoning. 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. In Contemporary Issues in Early Childhood. 6(2), 150–162. https://doi.org/10.2304/ciec.2005.6.2.5
Wilkie, K. J. (2004). Learning to like Algebra through Looking. APMC. 19(4). https://files.eric.ed.gov/fulltext/EJ1093277.pdf
Wilkie, K. J. (2014). Upper Primary School Teachers’ Mathematical Knowledge for Teaching Functional Thinking in Algebra. Journal of Mathematics Teacher Education. 17(5). https://doi.org/10.1007/s10857-013-9251-6
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. (2015). Developing Students’ Functional Thinking in Algebra Through Different Visualisations of a Growing Pattern’s Structure. Mathematics Education Research Journal, 223–243. https://doi.org/10.1007/s13394-015-0146-y
Yuniati, S., Nusantara, T., Subanji, & Made S., I. (2019). The use of Multiple Representation in Functional Thinking. International Journal of Recent Technology and Engineering, 8(1C2), 672–678. https://www.ijrte.org/wp-content/uploads/papers/v8i1C2/A11120581C219.pdf
Yuniati, S., & Suparjono. (2019). Model Representasi Matematis Siswa Kelas IV dalam Menyelesaikan Soal Cerita. MaPan 7(2):249–60. https://www.researchgate.net/publication/338508181_MODEL_REPRESENTASI_MATEMATIS_SISWA_KELAS_IV_DALAM_MENYELESAIKAN_SOAL_CERITA/inline/jsViewer/5e1876ba299bf10bc3a109bb?inViewer=1&pdfJsDownload=1&origin=publication_detail&previewAsPdf=false
Published
2021-02-14
How to Cite
Yuniati, S., & Suparjono, S. (2021). Mengeksplorasi Kemampuan Siswa Dalam Berpikir Fungsional Melalui Soal Cerita. Jurnal Cendekia : Jurnal Pendidikan Matematika, 5(1), 139-147. https://doi.org/10.31004/cendekia.v5i1.475
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Articles
Copyright (c) 2021 Suci Yuniati
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