A diagnosis of students' errors in answering the mathematics test in senior high school

Evana Gina Shantika; Edi Istiyono

doi:10.21831/pep.v23i2.16370

A diagnosis of students' errors in answering the mathematics test in senior high school

Evana Gina Shantika, Universitas Nahdlatul Wathan Mataram, Indonesia
Edi Istiyono, Universitas Negeri Yogyakarta, Indonesia

10.21831/pep.v23i2.16370

Abstract

This study aims to reveal: (1) the characteristics of diagnostic test items used in mathematics subject of the first grade of senior high school (SHS); (2) the degree of errors from several types of students’ errors in answering mathematics test; and (3) the dominant factor causing the students to make mistakes in answering mathematics test. This study used a quantitative approach involving the first graders of eight SHSs in Mataram as the population. The sample was collected by a proportionate random sampling technique, consisting of 350 students for preliminary field testing and 450 students for main field testing. The research instrument was a mathematics diagnostic test, questionnaire, and interview guidelines. The results show that: (1) the diagnostic test instrument meets the qualitative and quantitative content validity, proves empirically fit with Partial Credit Model (PCM), has reliability index of 0.92 (high category), and all items in the diagnostic test instrument are categorized in moderate difficulty; (2) misrepresentation becomes dominant errors if compared with misconceptions, the counting errors, and procedural errors. The errors dominant in the topic domain are Inequalities Linear System Two Variables if compared with Rational and Irrational Inequality One Variable, Equations and Inequalities of Absolute Value, and Linear Equations System Three Variables; and (3) most of the students do not understand how to solve the problem of inequality, determining factor quadratic equations, determining the members of the set completion, problems concerning graphs, and problems that require the capability of language interpretation into the mathematics model.

Keywords

diagnostic errors; mathematics test; Partial Credit Model

Full Text:

PDF

References

Adams, R. J., & Khoo, S.-T. (1996). Acer quest version 2.1. Camberwell, Victoria: Australian Council for Educational Research.

Blanco, L. J., & Garrote, M. (2007). Difficulties in learning inequalities in students of the first year of pre-university education in Spain. EURASIA Journal of Mathematics, Science and Technology Education, 3(3), 221–229. https://doi.org/10.12973/ejmste/75401

Bond, T. G., & Fox, C. M. (2007). Applying the Rasch model: Fundamental measurement in the human sciences (2nd ed.). Mahwah, NJ: Lawrence Erlbaum Associates.

De Ayala, R. J. (1993). Methods, plainly speaking: An introduction to polytomous item response theory models. Measurement and Evaluation in Counseling and Development, 25(4), 172–189.

Embretson, S. E. (2007). Construct validity: A universal validity system or just another test evaluation procedure? Educational Researcher, 36(8), 449–455. https://doi.org/10.3102/0013189X07311600

Embretson, S. E., & Reise, S. P. (2000). Item response theory for psychologist. London: Lawrence Erlbaum Associates.

Furr, R. M., & Bacharach, V. R. (2008). Psychometrics: An introduction. Thousand Oaks, CA: Sage Publications.

Hair, J. F., Anderson, R. E., Tatham, R. L., & Black, W. C. (2006). Multivariate data analysis (6th ed.). Upper Saddle River, NJ: Prentice-Hall.

Hambleton, R. K., Swaminathan, H., & Rogers, H. J. (1991). Fundamentals of item response theory. Newbury Park, CA: Sage Publications.

Hasselbring, T. S., Lott, A. C., & Zydney, J. M. (2005). Technology-supported math instruction for students with disabilities: Two decades of research and development. Retrieved June 10, 2017, from LD Online website: http://www.ldonline.org/article/6291/

Isgiyanto, A. (2011). Diagnosis kesalahan siswa berbasis penskoran politomus model partial credit pada matematika. Jurnal Penelitian Dan Evaluasi Pendidikan, 15(2), 308–325. Retrieved from https://journal.uny.ac.id/index.php/jpep/article/view/1099/1151

Keeves, J. P., & Masters, G. N. (1999). Partial credit model. In G. N. Masters & J. P. Kevees (Eds.), Advances in measurement in educational research and assesment. Amsterdam: Pergamon-Elsevier Science.

Kusaeri, K. (2012). Pengembangan tes diagnostik dengan menggunakan model DINA untuk mendapatkan informasi salah konsepsi dalam aljabar. Doctoral dissertation, Universitas negeri Yogyakarta, Yogyakarta.

Leighton, J. P., & Gierl, M. J. (2007). Defining and evaluating models of cognition used in educational measurement to make inferences about examinees’ thinking processes. Educational Measurement: Issues and Practice, 26(2), 3–16. https://doi.org/10.1111/j.1745-3992.2007.00090.x

Mardapi, D. (2005). Pengembangan sistem penilaian berbasis kompetensi. In Himpunan Evaluasi Pendidikan Indonesia (Ed.), Rekayasa sistem penilaian dalam rangka meningkatkan kualitas pendidikan (pp. 71–85). Yogyakarta: Himpunan Evaluasi Pendidikan Indonesia.

Mardapi, D. (2012). Pengukuran, penilaian, dan evaluasi pendidikan. Yogyakarta: Nuha Medika.

Regulation of the Minister of Education and Culture of Republic of Indonesia No. 23 of 2016 on Educational Assessment Standard. , (2016).

Retnawati, H. (2014). Teori respons butir dan penerapannya: Untuk peneliti, praktisi pengukuran dan pengujian, mahasiswa pascasarjana. Yogyakarta: Nuha Medika.

Retnawati, H. (2016a). Proving content validity of self-regulated learning scale (The comparison of Aiken index and expanded Gregory index). REiD (Research and Evaluation in Education), 2(2), 155–164. https://doi.org/10.21831/reid.v2i2.11029

Retnawati, H. (2016b). Validitas reliabilitas & karakteristik butir (Panduan untuk peneliti, mahasiswa, dan psikometrian). Yogyakarta: Nuha Medika.

Retnawati, H., Pardi, P., & Prastowo, R. (1994). Identifikasi kesulitan calon guru matematika untuk menyelesaikan persoalan matematika DIY. Yogyakarta: Universitas Negeri Yogyakarta.

Samejima, F. (1995). A cognitive method using latent trait models: Competency space approach and its relationship with Dibello and Stout’s unified cognitivepsychometric diagnosis model. In P. D. Nichols, S. F. Chipman, & R. L. Brennan (Eds.), Cognitively diagnostic assessment (pp. 391–410). Mahwah, NJ: Lawrence Erlbaum Associates.

Susetyo, B. (2015). Prosedur penyusunan dan teknik analisis tes. Bandung: Refika Aditama.

Wagiran, W. (2013). Metodologi penelitian pendidikan: Teori dan imlementasi. Yogyakarta: Budi Utama.

Warren, E. (2003). The role of arithmetic structure in the transition from arithmetic to algebra. Mathematics Education Research Journal, 15(2), 122–137. https://doi.org/10.1007/BF03217374

Wasis, W. (2011). Penskoran model partial credit pada item multiple true false bidang fisika. Doctoral dissertation, Universitas Negeri Yogyakarta, Yogyakarta.

Wells, C. S., Hambleton, R. K., & Purwono, U. (2008). Polytomous response IRT models and applications. Pelatihan Asesmen Pendidikan Dan Psikologi (Psikometri), pp. 2–10. Yogyakarta: Program Pascasarjana Universitas Negeri Yogyakarta.

White, A. L. (2005). Active mathematics in classrooms: Finding out why children make mistakes - and then doing something to help them. Square One, 4, 15–19.

DOI: https://doi.org/10.21831/pep.v23i2.16370