Probability and statistics now form a separate content area of Uzbekistan's National Curriculum, which places interpretive and pedagogical demands on mathematics teachers. Empirical evidence on in-service teachers' stochastic competence in Uzbekistan remains limited, and continuous professional development (CPD) needs are commonly identified through self-assessment alone. This study compared self-assessed and objectively assessed stochastic competence across four curriculum-aligned components: probability–statistical thinking, data analysis and interpretation, statistical modelling, and professional-reflexive activity. A convergent mixed-methods design combined a self-assessment survey with open-ended questions (N = 175; Cronbach's α = 0.74–0.81) and an objective competence test administered to a separate, unlinked sample (N = 242; KR-20 = 0.78 for the closed items). Because the samples were independent, the two sources were compared at the group and domain level only. The mean overall self-rating was 3.49 out of 5, and prior stochastic professional development was associated with higher self-assessed competence (Mann–Whitney U = 4253.0, p = 0.005, r = 0.21; sensitivity analysis: t = 3.20, p = 0.002, d = 0.52). The mean objective competence index was 45.5% (Md = 44.4, SD = 22.3); 58.7% of teachers scored below 50%, 26.4% between 50% and 69%, and 14.9% at 70% or above. Component indices were 46.5% for probability–statistical thinking, 40.3% for data analysis and interpretation, and 50.2% for statistical modelling, with a derived estimate of 45.0% for professional-reflexive activity. Correct-response rates were 22.3% on a base-rate task, 26.9% on a truncated-axis task, and 27.3% on a correlation–causation task. The two sources showed partial convergence in conditional probabilistic reasoning but divergence in data analysis and interpretation. The findings suggest that self-assessment alone may not adequately identify CPD needs and that practice-based CPD should target data interpretation and conditional probabilistic reasoning.
Stochastic Competence of In-Service Mathematics Teachers in Uzbekistan: Comparing Self-Assessment with Objective Evidence Under the National Curriculum
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Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407. https://doi.org/10.1177/0022487108324554
Batanero, C., & Álvarez-Arroyo, R. (2024). Teaching and learning of probability. ZDM – Mathematics Education, 56(1), 5–17. https://doi.org/10.1007/s11858-023-01511-5
Batanero, C., Burrill, G., & Reading, C. (Eds.). (2011). Teaching statistics in school mathematics: Challenges for teaching and teacher education. Springer. https://doi.org/10.1007/978-94-007-1131-0
Batanero, C., & Chernoff, E. J. (Eds.). (2018). Teaching and learning stochastics: Advances in probability education research. Springer. https://doi.org/10.1007/978-3-319-72871-1
Ben-Zvi, D., & Garfield, J. (Eds.). (2004). The challenge of developing statistical literacy, reasoning and thinking. Kluwer. https://doi.org/10.1007/1-4020-2278-6
Braun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77–101. https://doi.org/10.1191/1478088706qp063oa
Desimone, L. M. (2009). Improving impact studies of teachers' professional development: Toward better conceptualizations and measures. Educational Researcher, 38(3), 181–199. https://doi.org/10.3102/0013189X08331140
Dunning, D., Heath, C., & Suls, J. M. (2004). Flawed self-assessment: Implications for health, education, and the workplace. Psychological Science in the Public Interest, 5(3), 69–106. https://doi.org/10.1111/j.1529-1006.2004.00018.x
Fetters, M. D., Curry, L. A., & Creswell, J. W. (2013). Achieving integration in mixed methods designs: Principles and practices. Health Services Research, 48(6, Pt. 2), 2134–2156. https://doi.org/10.1111/1475-6773.12117
Gal, I. (2002). Adults' statistical literacy: Meanings, components, responsibilities. International Statistical Review, 70(1), 1–25. https://doi.org/10.1111/j.1751-5823.2002.tb00336.x
Groth, R. E. (2007). Toward a conceptualization of statistical knowledge for teaching. Journal for Research in Mathematics Education, 38(5), 427–437.
Knowles, M. S. (1980). The modern practice of adult education: From pedagogy to andragogy. Cambridge Adult Education.
OECD. (2023). PISA 2022 results (Volume I): The state of learning and equity in education. OECD Publishing. https://doi.org/10.1787/53f23881-en
President of the Republic of Uzbekistan. (2022). Decree No. PF-134 of 11 May 2022 on approving the national programme for the development of school education in 2022–2026 [in Uzbek]. https://lex.uz/docs/-6008663
President of the Republic of Uzbekistan. (2024). Resolution No. PQ-231 of 21 June 2024 on additional measures to improve the system of continuous professional development of employees of preschool and school education organisations [in Uzbek]. https://lex.uz/uz/docs/-6981085
Selyutin, V. D. (2001). Nauchnye osnovy metodicheskoy gotovnosti uchitelya matematiki k obucheniyu shkol'nikov stokhastike [Scientific foundations of mathematics teachers' methodological readiness to teach stochastics to schoolchildren] [Doctoral dissertation]. [in Russian]
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14. https://doi.org/10.3102/0013189X015002004
von Davier, M., Kennedy, A., Reynolds, K., Fishbein, B., Khorramdel, L., Aldrich, C., Bookbinder, A., Bezirhan, U., & Yin, L. (2024). TIMSS 2023 international results in mathematics and science. TIMSS & PIRLS International Study Center, Boston College. https://doi.org/10.6017/lse.tpisc.timss.rs6460
Wild, C. J., & Pfannkuch, M. (1999). Statistical thinking in empirical enquiry. International Statistical Review, 67(3), 223–248. https://doi.org/10.2307/1403699
Xonqulov, U. X. (2018). Akademik litseylarda matematikaning stoxastika yo'nalishi elementlarini o'qitishning pedagogik imkoniyatlarini takomillashtirish [Improving the pedagogical possibilities of teaching elements of the stochastic strand of mathematics in academic lyceums] [Abstract of PhD dissertation in pedagogical sciences]. Tashkent. [in Uzbek]