Investigating the 8th-grade Afghan students’ mathematics status and skills using the cognitive diagnostic model
DOI:
https://doi.org/10.12928/bamme.v3i1.8964Keywords:
Cognitive diagnosis models, DINA model, DINO model, TIMSSAbstract
Cognitive diagnostic models (CDMs) are multidimensional multivariate verification flow models with complex structure. In this research, these models were used to investigate the status of eighth grade high school students in mathematics using the TIMMS questionnaire. The cognitive diagnostic test based on 13 attributes including 32 questions was conducted on a sample of 274 students who were selected based on the multi-stage cluster sampling method among the students of Firuzkoh city. IRT and RESMA models were used to determine the psychometric properties of the questions. Data analysis using DINA and DINO models in cognitive diagnostic modeling of mathematics showed that 13 attributes explain the mathematical performance of eighth-grade students. The result shows that Afghan students have a weak mastery level in most attributes compared to 45 other countries (the countries that were included in the TIMMS questionnaire) also general results show that the examinees perform better in the field of numbers (0.49), while they perform worse in data and chance (0.12). Moreover, there exists some difference in estimating item parameters under the DINA and DINO models, such as Item 3 and Item 27. One possible explanation is that the DINA model is completely compensatory while the DINO model is fully non-compensatory. Similar to the results under the DINA model, the SEs of guessing parameters are lower than those of slipping parameters under the DINO model.
References
Chiu, C. Y., & Köhn, H. F. (2015). Consistency of cluster analysis for cognitive diagnosis: The DINO model and the DINA model revisited. Applied Psychological Measurement, 39(6), 465-479.
Choi, K. M., Lee, Y. S., & Park, Y. S. (2015). What CDM Can Tell About What Students Have Learned: An Analysis of TIMSS Eighth Grade Mathematics. Eurasia Journal of Mathematics, Science & Technology Education, 11(6).
de la Torre, J., & Chiu, C.-Y. (2016). A general method of empirical Q-matrix validation. Psychometrika, 81(2), 253–273.
De la Torre, J., & Lee, Y. S. (2013). Evaluating the Wald test for item‐level comparison of saturated and reduced models in cognitive diagnosis. Journal of Educational Measurement, 50(4), 355-373.
George, A. C., Robitzsch, A., Kiefer, T., Groß, J., & Ünlü, A. (2016). The R package CDM for cognitive diagnosis models. Journal of Statistical Software, 74(2), 1–24.
Groß, J., & George, A. C. (2014). On permissible attribute classes in noncompensatory cognitive diagnosis models. Methodology.
Halimi, N. (2013). Mathematics Education in Secondary School in Afghanistan: Teachers’ View and Practices on Teaching Problem Solving.
Huang, N. E. (2014). Hilbert-Huang transform and its applications (Vol. 16). World Scientific.
Huebner, A., & Wang, C. (2011). A note on comparing examinee classification methods for cognitive diagnosis models. Educational and Psychological Measurement, 71(2), 407–419.
Köhn, H. F., & Chiu, C. Y. (2016). A proof of the duality of the DINA model and the DINO model. Journal of Classification, 33(2), 171-184.
Lee, Y.-S., de la Torre, J., & Park, Y. S. (2012). Relationships between cognitive diagnosis, CTT, and IRT indices: An empirical investigation. Asia Pacific Education Review, 13(2), 333–345.
Liu, J. Y., Chen, C. H., Lin, C. H., Tsai, H. F., Chen, C. H., & Kamogawa, M. (2011). Ionospheric disturbances triggered by the 11 March 2011 M9. 0 Tohoku earthquake. Journal of Geophysical Research: Space Physics, 116(A6).
Liu, J., Xu, G., & Ying, Z. (2012). Data-driven learning of Q-matrix. Applied Psychological Measurement, 36(7), 548–564.
Mansory, A. M. (2010). Do Children Learn in Afghan Schools? Assessment of Math and Language Achievements of Students at the End of Grades 3 and 6 in SCA Supported Schools. Swedish Committee for Afghanistan (SCA).
Martin, M. O., Mullis, I. V. S., Foy, P., & Stanco, G. M. (2012). TIMSS 2011 International Results in Science. ERIC.
Mullis, I. V., Martin, M. O., Foy, P., & Arora, A. (2012). TIMSS 2011 international results in mathematics (pp. 139-171). Chestnut Hill, MA: TIMSS & PIRLS International Study Center.
Paek, I., & Cai, L. (2014). A comparison of item parameter standard error estimation procedures for unidimensional and multidimensional item response theory modeling. Educational and Psychological Measurement, 74(1), 58-76.
Ravand, H., Barati, H., & Widhiarso, W. (2012). Exploring diagnostic capacity of a high stakes reading comprehension test: A pedagogical demonstration. Iranian Journal of Language Testing, 3(1), 12-37..
Robitzsch, A., Kiefer, T., George, A. C., & Uenlue, A. (2014). CDM: Cognitive diagnosis modeling. R package version, 3.
Rupp, A. A., Gushta, M., Mislevy, R. J., & Shaffer, D. W. (2010). Evidence-centered design of epistemic games: Measurement principles for complex learning environments. The Journal of Technology, Learning and Assessment, 8(4).
Schmidt, W. H., & Houang, R. T. (2012). Curricular coherence and the common core state standards for mathematics. Educational Researcher, 41(8), 294-308.
Sedat, Ş. E. N., & Arican, M. (2015). A diagnostic comparison of Turkish and Korean students’ mathematics performances on the TIMSS 2011 assessment. Eğitimde ve Psikolojide Ölçme ve Değerlendirme Dergisi, 6(2).
Shu, Z., Henson, R., & Willse, J. (2013). Using neural network analysis to define methods of DINA model estimation for small sample sizes. Journal of classification, 30(2), 173-194.
Templin, J., & Henson, R. A. (2010). Diagnostic measurement: Theory, methods, and applications. Guilford Press.
Terzi, R., & Sen, S. (2019). A nondiagnostic assessment for diagnostic purposes: Q-matrix validation and item-based model fit evaluation for the TIMSS 2011 assessment. SAGE Open, 9(1), 2158244019832684.
Toker, T., & Green, K. (2012). An Application of Cognitive Diagnostic Assessment on TIMMS-2007 8th Grade Mathematics Items. Online Submission.
Wafa, M. N., Hussani, S. A. M., & Pazhman, J. (2020). Evaluation of Students' Mathematical Ability in Afghanistan's Schools Using Cognitive Diagnosis Models. Eurasia Journal of Mathematics, Science and Technology Education, 16(6).
Wafa, M. N. (2019). Assessing school students’ mathematic ability using DINA and DINO models. International Journal of Mathematics Trends and Technology (IJMTT), 65(12), 153-165
Wafa, M. N., Zia, Z., & Frozan, F. (2023). Consistency and Ability of Students Using DINA and DINO Models. European Journal of Mathematics and Statistics, 4(4), 7-13.
Wafa, M. N. (2020). 基于认知诊断模型框架评价阿富汗学生的数学能力 (Master's thesis, 东北师范大学).
Hussaini, S. A. M., & Wafa, M. N. (2021). Wettability of Femtosecond Laser Direct Fabrication of Micro and Nanostructures on Metal Surface. Turkish Online Journal of Qualitative Inquiry, 12(9).
Zhan, P., Jiao, H., & Liao, D. (2018). Cognitive diagnosis modelling incorporating item response times. British Journal of Mathematical and Statistical Psychology, 71(2), 262-286.
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