Interpretasi Validitas dan Reliabilitas Instrumen Kemampuan Berpikir Aljabar

Ofirenty Elyada Nubatonis, Al Jupri, Endang Cahya Mulyaning A


This research aims to interpret the validity and reliability of the items on the algebraic thinking ability instrument which are linked to content, context, question structure and students' cognitive level. The development of the algebraic thinking ability instrument was carried out in four stages by adapting the Plomp development model. The first stage (initial assessment), conducting a theoretical study of algebraic thinking abilities and curriculum analysis. The second stage (design), draft questions by paying attention to the relationship between indicators of algebraic thinking ability and learning objectives. Furthermore, this question design was validated by three experts in the field of mathematics education. The fourth stage (realization/construction) is testing the instrument which includes testing validity, reliability, distinguishability and level of difficulty. Apart from that, in the fourth stage the test results are also interpreted, evaluated and revised. The instrument was tested on 19 class VII students at one of the junior high schools in Bandung City. Interpretations of validity, reliability, distinguishability and level of difficulty are related to content, context, question structure and students' cognitive level. The results of the analysis at this stage are used as a reference for improving the instrument. The instrument produced in this research is a description question consisting of four items that are valid and reliable and can be used to measure algebraic thinking abilities, especially those related to generalization, transformation and metaglobal abilities.


algebraic thinking; instrument development; reliability; validity

Full Text:



S. Wettergren, “Lumat Special Issue 2022: Mathematical Thinking and Understanding in Learning of Mathematics Identifying and Promoting Young Students’ Early Algebraic Thinking”, 2022, doi: 10.31129/10.2.1617.

I. R. Sibgatullin, A. V. Korzhuev, E. R. Khairullina, A. R. Sadykova, R. V. Baturina, and V. Chauzova, “A Systematic Review on Algebraic Thinking in Education,” Eurasia Journal of Mathematics, Science and Technology Education, vol. 18, no. 1, pp. 1-15, Jan. 2022, doi: 10.29333/ejmste/11486.

T. Marghetis, D. Landy, and R. L. Goldstone, “Mastering algebra retrains the Visual System to Perceive Hierarchical Structure in Equations,” Cogn Res Princ Implic, vol. 1, no. 25, pp. 1 -10, Dec. 2016, doi: 10.1186/s41235-016-0020-9.

L. Puig, “Researching (Algebraic) Problem Solving from the Perspective of Local Theoretical Models,” in Procedia - Social and Behavioral Sciences, Elsevier Ltd, pp. 3–16, 2010, doi: 10.1016/j.sbspro.2010.12.002.

S. Y. Maudy, D. S., and E. M., “Student’ Algebraic Thinking Level,” International Journal of Information and Education Technology, vol. 8, no. 9, pp. 672–676, 2018, doi: 10.18178/ijiet.2018.8.9.1120.

L. A. Z. Najma and M. Masduki, “Exploration of Student Algebraic Thinking in Terms Of Implusive Reflective Cognitive Style,” Journal of Medives : Journal of Mathematics Education IKIP Veteran Semarang, vol. 7, no. 2, pp. 219-231, Jul. 2023, doi: 10.31331/medivesveteran.v7i2.2580.

D. M. Nurhayati, T. Herman, and S. Suhendra, “Analysis of Secondary School Students’ Algebraic Thinking and Math-Talk Learning Community to Help Students Learn,” J Phys Conf Ser, vol. 895, pp. 1-8, Sep. 2017, doi: 10.1088/1742-6596/895/1/012054.

H. Yansa, H. Retnawati, and M. Janna, “Misconceptions of Basic Algebra on Linear Equation in One Variable Material,” J Phys Conf Ser, vol. 1882, no. 1, pp. 1-8, May 2021, doi: 10.1088/1742-6596/1882/1/012091.

M. Mulungye, “Journal of Education and Practice ISSN,” Online, [Online]. Available:, 2016.

N. S. Utami, S. Prabawanto, and D. Suryadi, “How Students Generate Patterns in Learning Algebra? A Focus on Functional Thinking in Secondary School Students,” European Journal of Educational Research, vol. 12, no. 2, pp. 913–925, 2023, doi: 10.12973/eu-jer.12.2.913.

C. Kieran, “The Multi-Dimensionality of Early Algebraic Thinking: Background, Overarching Dimensions, and New Directions,” ZDM – Mathematics Education, vol. 54, no. 6, pp. 1131–1150, Nov. 2022, doi: 10.1007/s11858-022-01435-6.

J. J. Kaput, “1 What Is Algebra? What Is Algebraic Reasoning?,” in Algebra In The Early Grades, Routledge, pp. 5–18, 2017, doi: 10.4324/9781315097435-2.

M. L. Blanton and J. J. Kaput, “Functional Thinking as a Route Into Algebra in the Elementary Grades,” pp. 5–23 , 2011. doi: 10.1007/978-3-642-17735-4_2.

C. Pearn, M. Stephens, and R. Pierce, “Algebraic reasoning in years 5 and 6: classifying its emergence and progression using reverse fraction tasks,” ZDM - Mathematics Education, vol. 54, no. 6, pp. 1257–1271, Nov. 2022, doi: 10.1007/s11858-022-01426-7.

O. A. Alghtani and N. A. Abdulhamied, “The Effectiveness of Geometric Representative Approach in Developing Algebraic Thinking of Fourth Grade Students,” in Procedia - Social and Behavioral Sciences, Elsevier Ltd, 2010, pp. 256–263. doi: 10.1016/j.sbspro.2010.12.035.

M. Öztürk, “An Embedded Mixed Method Study on Teaching Algebraic Expressions Using Metacognition-Based Training,” Think Skills Creat, vol. 39, p. 100787, Mar. 2021, doi: 10.1016/j.tsc.2021.100787.

U. Silma, “Analisis Kemampuan Berpikir Aljabar Siswa dalam Model Pembelajaran Learning Cycle 5E,” Jurnal Pembelajaran Matematika, vol. 5, no. 3, pp. 300–319, 2018, [Online]. Available:

I. Farida, D. Lukman Hakim, U. Singaperbangsa Karawang, J. H. Ronggo Waluyo, K. Telukjambe Timur, and J. Barat, “Kemampuan Berpikir Aljabar Siswa SMP pada Materi Sistem Persamaan Linear Dua Variabel (SPLDV),” Jurnal Pembelajaran Matematika Inovatif, vol. 4, no. 5, 2021, doi: 10.22460/jpmi.v4i5.1123-1136.

A. Ihtiani and A. Agoestanto, “Analysis of Students Error in Global Meta-Level Algebraic Thinking on Problem Proving on Core Learning Assisted by Scaffolding ,” Unnes Journal of Mathematics Education, vol. 10, no. 1, pp. 27–38, 2021, doi: 10.15294/ujme.v10i1.32419.

J. J. H. van den (Jan J. H. Akker et al., Educational design research / Part A: an introduction.

C. Kieran, “Algebra Teaching and Learning,” in Encyclopedia of Mathematics Education, Cham: Springer International Publishing, 2018, pp. 1–9. doi: 10.1007/978-3-319-77487-9_6-5.

C. Kieran, “Research on the Learning and Teaching of Algebra: A Broadening of Sources of Meaning.” Accessed: Dec. 13, 2023. [Online]. Available:

J. Cai, D. Hee Chan Lew, C. Anne Morris, D. C. John Moyer, W. Swee Fong Ng, and N. Jean Schmittau, “The Development of Students’ Algebraic Thinking in Earlier Grades: A Cross-Cultural Comparative Perspective 1,” ZDM - International Journal on Mathematics Education, vol. 37, no. 1, pp. 5-15, 2005.

M. S. Britt and K. C. Irwin, “Algebraic Thinking With and Without Algebraic Representation: A three-Year Longitudinal Study,” ZDM - International Journal on Mathematics Education, vol. 40, no. 1, pp. 39–53, 2008, doi: 10.1007/s11858-007-0064-x.

K. M. Zaelani, R. Marlina, and K. N. S. Effendi, “The Algebraic Thinking Profile of Junior High School Students at Extended Abstract Level of SOLO Taxonomy,” Edumatika : Jurnal Riset Pendidikan Matematika, vol. 3, no. 2, p. 120, Nov. 2020, doi: 10.32939/ejrpm.v3i2.599.

A. C. Stephens, E. J. Knuth, M. L. Blanton, I. Isler, A. M. Gardiner, and T. Marum, “Equation Structure and The Meaning of The Equal Sign: The Impact of Task Selection in Eliciting Elementary Students’ Understandings,” The Journal of Mathematical Behavior, vol. 32, no. 2, pp. 173–182, Jun. 2013, doi: 10.1016/j.jmathb.2013.02.001.

M. L. Blanton and J. J. Kaput, “Characterizing a Classroom Practice that Promotes Algebraic Reasoning,” 2005, [Online]. Available:

E. Simsek, I. Jones, J. Hunter, and I. Xenidou-Dervou, “Mathematical Equivalence Assessment: Measurement Invariance Across Six Countries,” Studies in Educational Evaluation, vol. 70, pp. 1-11, Sep. 2021, doi: 10.1016/j.stueduc.2021.101046.

C. E. Byrd, N. M. McNeil, D. L. Chesney, and P. G. Matthews, “A Specific Misconception of The Equal Sign Acts as A Barrier to Children’s Learning of Early Algebra,” Learn Individ Differ, vol. 38, pp. 61–67, Feb. 2015, doi: 10.1016/j.lindif.2015.01.001.

M. Blanton et al., “Implementing a Framework for Early Algebra,” 2018, pp. 27–49. doi: 10.1007/978-3-319-68351-5_2.

C. Kieran, J. Pang, D. S. Swee, and F. Ng, “Early Algebra ICME-13 Topical Surveys Research into its Nature, its Learning, its Teaching.” 2016, [Online]. Available:



  • There are currently no refbacks.

Copyright (c) 2024 Jambura Journal of Mathematics Education

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Jambura Journal of Mathematics Education has been indexed by:


 Department of Mathematics, Universitas Negeri Gorontalo
Jl. Prof. Dr. Ing. B. J. Habibie, Moutong, Tilongkabila, Kabupaten Bone Bolango, Gorontalo 96554, Indonesia
 +6285255745923 (Call/SMS/WA)
 Jambura Journal of Mathematics Education (JMathEdu | eISSN: 2721-7477) by Department of Mathematics Universitas Negeri Gorontalo is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.  Powered by Public Knowledge Project OJS.