ANALYSIS OF STUDENT ABILITY IN FUNCTIONAL THINKING THROUGH THE FUNCTION TABLE: THE CASE OF SQUARE FUNCTION

Suci Yuniati(1*), Suparjono Suparjono(2), Annisah Kurniati(3),

(1) Universitas Islam Negeri Suska Riau
(2) Universitas Islam Negeri Suska Riau
(3) Universitas Islam Negeri Suska Riau
(*) Corresponding Author


Abstract


One way to track students' ability to understand the concept of function can be done by analyzing their functional thinking skills. This study aims to identify and determine students' functional thinking skills through function tables. This research is an exploratory qualitative research. The research subjects were 2 out of 56 5th semester students of the Department of Mathematics Education, Suska Riau State Islamic University. The research subjects were selected purposively, namely students who correctly completed the test sheet and had fluent communication skills. Data were collected through tests and interviews. The results of the test answer sheets were analyzed based on the functional thinking framework and the results of the interviews were analyzed to explore and clarify students' functional thinking that had not been revealed on the answer sheets. The results of data analysis show that there are two stages of completion, namely the first stage, determining the number pattern and thinking about the number pattern up to the nth, determining the difference from , determining the difference from , determining the change in value between  and , generalizing the  sequence, and generalizing sequence. While the second stage, determine the change in value between  and , generalize sequence , generalize sequence , and generalize the relationship between and . Based on the results of the study, it showed that students were able to fulfill all the frameworks for solving problems through the function table


Salah satu cara untuk menelusuri kemampuan mahasiswa dalam memahami konsep fungsi dapat dilakukan dengan cara menganalisis kemampuan berpikir fungsionalnnya. Penelitian ini bertujuan untuk mengidentifikasi dan mengetahui kemampuan berpikir fungsional mahasiswa melalui tabel fungsi. Penelitian ini merupakan penelitian kualitatif yang bersifat eksploratif. Subjek penelitian adalah 2 dari 56 mahasiswa semester 5 Jurusan Pendidikan Matematika Universitas Islam Negeri Suska Riau. Subjek penelitian dipilih secara purposive yaitu mahasiswa yang menyelesaikan secara benar lembar tes dan memiliki kemampuan komunikasi yang lancar. Data dikumpulkan melalui tes dan wawancara. Hasil lembar jawaban tes dianalisis berdasarkan kerangka kerja berpikir fungsional dan hasil wawancara dianalisis untuk mendalami dan mengklarifikasi berpikir fungsional mahasiswa yang belum terungkap pada lembar jawaban. Hasil analisis data menunjukan bahwa ada dua tahapan penyelesaian yaitu tahap pertama, menentukan pola bilangan dan berpikir tentang pola bilangan sampai ke-n, menentukan beda dari , menentukan beda dari , menentukan perubahan nilai antara  dan , menggeneralisasikan barisan , dan menggeneralisasikan barisan . Sedangkan tahap kedua, menentukan perubahan nilai antara  dan , menggeneralisasikan barisan , menggeneralisasikan barisan , dan menggeneralisasikan hubungan antara dan . Berdasarkan hasil penelitian menunjukkan bahwa mahasiswa mampu memenuhi semua kerangka kerja berpikir fungsional dalam menyelesaikan masalah melalui tabel fungsi.   



Keywords


functional thinking, function table, mathematical problem solving, quadratic function

Full Text:

PDF

References


Blanton, M., Brizuela, B. M., Gardiner, A. M., Sawrey, K., Newman-owens, A., Blanton, 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.

Blanton, M. L., & Kaput, J. J. (2005). Helping Elementary Teachers Build Mathematical Generality into Curriculum and Instruction. ZDM. 37(1).

Blanton, M., Stephens, A., Knuth, E., Gardiner, A. M., Isler, I., Kim, J., … 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

Creswell, J. W. (2012). Educational Research (4th ed.). Pearson Education, Inc.

Doorman, M., Drijvers, P., Gravemeijer, K., Boon, P., & Reed, H. (2012). Concept : From Repeated Calculations to Functional. 1243–1267.

Pinto, E., & Cañadas, M. C. (2012). Functional Thinking and Generalisation in Third Year of Primary School.

Stephens, A., Blanton, M., Strachota, S., Knuth, E., & Gardiner, A. (2017). Interplay between Students’ Understandings of Proportional and Fuctional 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.

Stephens, A. C., Fonger, N., Strachota, S., Isler, I., Blanton, M., Knuth, E., … Isler, I. (2017). A Learning Progression for Elementary Students' Functional Thinking. Mathematical Thinking and Learning, 19(3), 143–166. https://doi.org/10.1080/10986065.2017.1328636

Tanişli, 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, 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

Wilkie, K. J. (2004). Learning to Like Algebra Through Looking. APMC. 19(4)

Wilkie, K. J. (2015). Learning to Teach Upper Primary School Algebra: Changes to Teachers ’ Mathematical Knowledge For Teaching Functional Thinking. Mathematics Education Research Journal. 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. https://doi.org/10.1007/s13394-015-0146-y

Yuniati, S., Nusantara, T., Subanji, & Made Sulandra, I. (2019). The use of Multiple Representation in Functional Thinking. International Journal of Recent Technology and Engineering, 8(1C2), 672–678.

Yuniati, S., Nusantara, T., Subanji, & Sulandra, I. M. (2020). Stages in Partial Functional Thinking in the form of Linear Functions: APOS Theory. Humanities and Social Sciences Reviews, 8(3), 536–544. https://doi.org/10.18510/hssr.2020.8358

Yuniati, S and Suparjono S. 2021. "Exploring Students' Ability in Functional Thinking Through Story Problems". Jurnal Cendekia: Jurnal Pendidikan Matematika 5 (1): 139-147.

Yuniati, S., & Suparjono, S. (2019). Model Representasi Matematis Siswa Kelas IV dalam Menyelesaikan Soal Cerita. MaPan: Jurnal Matematika dan Pembelajaran, 7(2), 249–260. https://doi.org/10.24252/mapan.2019v7n2a6

Yuniati, S., Nusantara, T., Subanji., Sulandra I. M. (2020). Generalisation of Relations Between Quantity Variations Through Arithmetic Sequences in Functional Thinking. IJICC, 13(2), 580–593.




DOI: http://dx.doi.org/10.24127/ajpm.v11i2.4471

Refbacks

  • There are currently no refbacks.