Percentages versus Rasch estimates: alternative methodological strategies for replication studies in mathematics education

References

• Andrich, D., & Marais, I. (2019). A course in Rasch measurement theory. Measuring in the Educational, Social and Health Sciences, 41–53.
   Google Scholar
• Arnup, J. L., Murrihy, C., Roodenburg, J., & McLean, L.A. (2013). Cognitive style and gender differences in children’s mathematics achievement. Educational Studies, 39(3). 355–368. https://doi.org/10.1080/03055698.2013.767184
   Web of Science ®Google Scholar
• Baird, K. (2012). Class in the classroom: The relationship between school resources and math performance among low socioeconomic status students in 19 rich countries. Education Economics, 20(5), 484–509. https://doi.org/10.1080/09645292.2010.511848
   Google Scholar
• Bell, A., Greer, B., Grimison, L., & Mangan, C. (1989). Children's performance on multiplicative word problems: Elements of a descriptive theory. Journal for Research in Mathematics Education, 20(5), 434–449. https://doi.org/10.2307/749419
   Web of Science ®Google Scholar
• Bolondi, G., & Ferretti, F. (2021). Quantifying solid findings in mathematics education: Loss of meaning for algebraic symbols. International Journal of Innovation in Science and Mathematics Education, 29(1), 1–15. https://doi.org/10.30722/IJISME.29.01.001
   Google Scholar
• Cai, J., Morris, A., Hohensee, C., Hwang, S., Robison, V., & Hiebert, J. (2018). The role of replication studies in educational research. Journal for Research in Mathematics Education, 49(1), 2–8. https://doi.org/10.5951/jresematheduc.49.1.0002
   Web of Science ®Google Scholar
• Cascella, C. (2019). How much ‘home possession’ affect educational attainment? Empirical evidence towards a simpler socio-economic status index. In L. Gómez Chova, A. López Martínez, I. Candel Torres (Eds.) Iceri2019 proceedings (pp. 5809-5814). IATED.
   Google Scholar
• Cascella, C. (2020a). Exploring the complex relationship between students’ Reading skills and their performance in mathematics: a population-based study. Educational Research and Evaluation, 26(3-4), 126–149. https://doi.org/10.1080/13803611.2021.1924790
   Web of Science ®Google Scholar
• Cascella, C. (2020b). Intersectional effects of Socioeconomic status, phase and gender on Mathematics achievement. Educational Studies, 46(4), 476–496. https://doi.org/10.1080/03055698.2019.1614432
   Web of Science ®Google Scholar
• Clemens, M. A. (2017). The meaning of failed replications: A review and proposal. Journal of Economic Surveys, 31(1), 326–342. https://doi.org/10.1111/joes.12139
   Web of Science ®Google Scholar
• Coleman, J. S. (1966). Equality of educational opportunity [summary report] (Vol. 1). US Department of Health, Education, and Welfare, Office of Education.
   Google Scholar
• Daroczy, G., Wolska, M., Meurers, W.D., & Nuerk, H.C. (2015). Word problems: A review of linguistic and numerical factors contributing to their difficulty. Frontiers in Psychology, 6, 348. https://doi.org/10.3389/fpsyg.2015.00348
   PubMed Web of Science ®Google Scholar
• De Corte, E., Verschaffel, L., & Van Collie, V. (1988). Influence of number size, problem structure, and response mode on children’s solution of multiplication problems. Journal of Mathematics Behaviour, 7, 197–216.
   Google Scholar
• De Mauro, T., & Chiari, I. (2016). Il Nuovo vocabolario di base della lingua italiana. Internazionale. https://www.internazionale.it/opinione/tullio-de-mauro/2016/12/23/il-nuovo-vocabolario-di-base-della-lingua-italiana
   Google Scholar
• Deri, M., Nello, M., & Marino, M. (1983). Il ruolo dei modelli primitivi per la moltiplicazione e la divisione. L’insegnamento Della Matematica e Delle Scienze Integrate, 6(6), 6–27.
   Google Scholar
• Dreyfus, T. (2017). What are solid findings in mathematics education? In T. Dooley, & G. Gueudet (Eds.), Proceedings of the tenth congress of the European society for research in mathematics education (pp. 57–62). DCU Institute of Education & ERME.
   Google Scholar
• Engelhard, G. (2009). Using item response theory and model—Data fit to conceptualize differential item and person functioning for students With disabilities. Educational and Psychological Measurement, 69(4), 585–602. https://doi.org/10.1177/0013164408323240
   Web of Science ®Google Scholar
• Engelhard, G. (2013). Invariant measurement: Using Rasch models in the social, behavioral, and health sciences. Routledge. https://doi.org/10.4324/9780203073636
   Google Scholar
• Erickson, S.A., & Lockwood, E. (2021). Investigating combinatorial provers’ reasoning about multiplication. International Journal of Research in Undergraduate Mathematics Education, 7(1), 77–106. https://doi.org/10.1007/s40753-020-00123-8
   Google Scholar
• Falorsi, P. D., Falzetti, P., & Ricci, R. (2019). Le metodologie di campionamento e di scomposizione della devianza nelle rilevazioni nazionali dell’INVALSI.
   Google Scholar
• Fanelli, D. (2018). Is science really facing a reproducibility crisis, and do we need it to? Proceedings of the National Academy of Sciences, 115(11), 2628–2631. https://doi.org/10.1073/pnas.1708272114
   PubMed Web of Science ®Google Scholar
• Fischbein, E., Deri, M., Nello, M., & Marino, M. (1985). The role of implicit models in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 16(1), 3–17. https://doi.org/10.2307/748969
   Google Scholar
• Frias-Navarro, D., Pascual-Llobell, J., Pascual-Soler, M., Perezgonzalez, J., & Berrios-Riquelme, J. (2020). Replication crisis or an opportunity to improve scientific production? European Journal of Education, 55(4), 618–631. https://doi.org/10.1111/ejed.12417
   Web of Science ®Google Scholar
• Giberti, C. (2022). NewData_FischbeinIntuitiveModels. Mendeley Data – V3. https://doi.org/10.17632/4gmd9xnwhs.3
   Google Scholar
• Giberti, C., & Maffia, A. (2022). Primitive model of partitive division: A replication of the fischbein et al. Study. Implementation and Replication Studies in Mathematics Education, 2(2), 149–173. https://doi.org/10.1163/26670127-bja10007
   Google Scholar
• Given, L. (2012). Quota sampling. The SAGE Encyclopedia of Qualitative Research Methods, 2008, 1–3.
   Google Scholar
• Graeber, A. O., & Tirosh, D. (1990). Insights fourth and fifth graders bring to multiplication and division with decimals. Educational Studies in Mathematics, 21(6), 565–588. https://doi.org/10.1007/BF00315945
   Google Scholar
• Hambleton, R. K. (2000). Emergence of item response modeling in instrument development and data analysis. Medical Care, II, 60–65.
   Google Scholar
• Harel, G., Behr, M., Post, T., & Lesh, R. (1994). The impact of the number type on the solution of multiplication and division problems: further investigations. In G. Harel, & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 365–384). State University of New York Press.
   Google Scholar
• Impara, J. C., & Plake, B. S. (1998). Teachers’ ability to estimate item difficulty: A test of the assumptions in the Angoff standard setting method. Journal of Educational Measurement, 35(1), 69-81. https://doi.org/10.1111/j.1745-3984.1998.tb00528.x
   Web of Science ®Google Scholar
• INVALSI. (2018). Rapporto risultati [Tr. Results Report].
   Google Scholar
• Izsák, A., & Beckmann, S. (2019). Developing a coherent approach to multiplication and measurement. Educational Studies in Mathematics, 101(1), 83–103. https://doi.org/10.1007/s10649-019-09885-8
   Web of Science ®Google Scholar
• Jabrayilov, R., Emons, W. H., & Sijtsma, K. (2016). Comparison of classical test theory and item response theory in individual change assessment. Applied Psychological Measurement, 40(8), 559–572. https://doi.org/10.1177/0146621616664046
   PubMed Web of Science ®Google Scholar
• Kolen, M. J., & Brennan, R. L. (2014). Test equating, scaling, and linking. Springer.
   Google Scholar
• Kouba, V. L. (1989). Children’s solution strategies for equivalent set multiplication and division word problems. Journal for Research in Mathematics Education, 20(2), 147–158. https://doi.org/10.2307/749279
   Web of Science ®Google Scholar
• Lewis-Beck, M. S., Bryman, A., & Futing Liao, T. (2004). The SAGE encyclopedia of social science research methods (Voll. 1–0). Sage Publications, Inc.
   Google Scholar
• Linacre, J. M. (2022). Winsteps® (Version 5.2.3) [Computer Software]. https://www.winsteps.com/
   Google Scholar
• Maclean, R., Watanabe, R., Baker, R., Boediono., Cheng, Y. C., Duncan, W., Keeves, J., Mansheng, Z., Power, C., Rajput, J. S., Thaman, K. H., Alagumalai, S., Curtis, D. D., & Hungi, N. (2005). Applied rasch measurement: A book of exemplars. Springer. https://doi.org/10.1007/1-4020-3076-2
   Google Scholar
• Maffia, A., & Mariotti, M.A. (2018). Intuitive and formal models of whole number multiplication: Relations and emerging structures. For the Learning of Mathematics, 38(3), 30–36. https://www.jstor.org/stable/26548509
   Google Scholar
• Moser, C. A. (1952). Quota sampling. Journal of the Royal Statistical Society. Series A (General), 115(3), 411–423. https://doi.org/10.2307/2980740
   Web of Science ®Google Scholar
• Polotskaia, E., & Savard, A. (2021). Some multiplicative structures in elementary education: a view from relational paradigm. Educational Studies in Mathematics, 106(3), 447–469. https://doi.org/10.1007/s10649-020-09979-8
   Web of Science ®Google Scholar
• Primi, C. (2017). Solid findings in mathematics education: A psychometric approach. In T. Dooley, & G. Gueudet (Eds.), Proceedings of the tenth congress of the European society for research in mathematics education (pp. 63–67). DCU Institute of Education & ERME.
   Google Scholar
• Qu, C., Szkudlarek, E., & Brannon, E.M. (2021). Approximate multiplication in young children prior to multiplication instruction. Journal of Experimental Child Psychology, 207, 105116–116. https://doi.org/10.1016/j.jecp.2021.105116
   PubMed Web of Science ®Google Scholar
• Rasch, G. (1960). Probabilistic models for some intelligence and achievement tests. Copenhagen: Danish institute for educational research (Expanded edition, 1980). University of Chicago Press.
   Google Scholar
• Sanchez-Aguilar, M. (2020). A foucauldian analysis of representations of mathematicians in lower secondary Mexican mathematics textbooks International Journal of Science and Mathematics Education, 18(4), 753–770. https://doi.org/10.1007/s10763-019-09986-z
   Web of Science ®Google Scholar
• Schmidt, K. M., & Embretson, S. E. (2003). Item Response Theory and measuring abilities. In J. A. Schinka, & W. F. Velicer (Eds.), Handbook of psychology, 2, research method in psychology (pp. 429–445). John Wiley and sons.
   Google Scholar
• Schmidt, S. (2009). Shall we really do it again? The powerful concept of replication is neglected in the social sciences. Review of General Psychology, 13(2), 90–100. https://doi.org/10.1037/a0015108
   Web of Science ®Google Scholar
• Schoenfeld, A. H. (2018). Research commentary: On replications. Journal for Research in Mathematics Education, 49(1), 91–97. https://doi.org/10.5951/jresematheduc.49.1.0091
   Web of Science ®Google Scholar
• Sidanius, J., & Pratto, F. (1999). Social Dominance. https://doi.org/10.1017/cbo9781139175043
   Google Scholar
• Simon, M. A., Kara, M., Norton, A., & Placa, N. (2018). Fostering construction of a meaning for multiplication that subsumes whole-number and fraction multiplication: A study of the Learning Through Activity research program. The Journal of Mathematical Behavior, 52, 151–173. https://doi.org/10.1016/j.jmathb.2018.03.002
   Web of Science ®Google Scholar
• Vest, F. R. (1971). A catalog of models for multiplication and division of whole numbers. Educational Studies in Mathematics, 3(2), 220–228. https://doi.org/10.1007/BF00305450
   Google Scholar
• Wright, B. D., & Stone, M. H. (1979). Best test design. Mesa Press.
   Google Scholar
• Yang, K., & Banamah, A. (2014). Quota sampling as an alternative to probability sampling? An experimental study. Sociological Research Online, 19(1), 56–66. doi:10.5153/sro.3199
   Web of Science ®Google Scholar