The development and influencing factors of Kindergarteners’ mathematics problem solving based on cognitive diagnosis assessment
Tóm tắt
In this study we investigated the development of 245 kindergarteners’ mathematics problem solving (MPS) at two time points within 7 months using a cognitive diagnostic test, which measured three cognitive components (mathematical knowledge and skills, semantic understanding, and quantitative reasoning) with eleven cognitive attributes. The effects of five influencing factors [language ability, mathematics application ability, calculation ability, approaches to learning (ATL) and socio-economic status (SES)] on the children’s MPS ability at the two time points were examined. The results indicated that the 245 children’s mastery of mathematical knowledge and skills was much better than their mastery of semantic understanding and quantitative reasoning. Furthermore, they achieved significant progress in set comparison and addition and subtraction within the range of natural numbers to ten (two of the three cognitive attributes of mathematical knowledge and skills), additive composition reasoning and one-to-many correspondence reasoning (two of the three cognitive attributes of quantitative reasoning). Only their mathematics application ability significantly predicted their mastery of the three cognitive components of MPS ability at the two-time points. Their language and calculation abilities predicted only their mastery of mathematical knowledge and skills at the two time points. Their ATL predicted their mastery of the three cognitive components of MPS only at the first time point, and their SES predicted only their mastery of semantic understanding 7 months later.
Tài liệu tham khảo
Artut, P. D. (2015). Preschool children’s skills in solving mathematical word problems. Educational Research & Reviews,10(18), 2539–2549.
Baroody, A. J. (1993). Problem solving, reasoning, and communicating, K-8: Helping children think mathematically. New York: Macmillan Publishing Company.
Baroody, A. J., Lai, M. L., Li, X., & Baroody, A. E. (2009). Preschoolers’ understanding of subtraction-related principles. Mathematical Thinking and Learning,11(1–2), 41–60.
Becker, J. (1993). Young children’s numerical use of number words: Counting in many-to-one situations. Developmental Psychology,19, 458–465.
Boora, S., Pasiphol, S., & Tangdhanakanond, K. (2015). Development of cognitive diagnostic testing on basic arithmetic operation. Procedia-Social and Behavioral Sciences,191, 769–772.
Carpenter, T. P., Hiebert, J., & Moser, J. (1979). The effect of problem structure on first graders’ initial solution processes for simple addition and subtraction problems (pp. 1–45). San Francisco: The annual meeting of the American Educational Research Association.
Charlesworth, R., & Leali, S. A. (2012). Using problem solving to assess young children’s mathematics knowledge. Early Childhood Education Journal,39(6), 373–382.
Chen, J. Q., & McNamee, G. D. (2007). Bridging: Assessment for teaching and learning in early childhood classrooms, PreK-3 (pp. 31–37). Thousand Oaks: Corwin Press.
Chen, J. Q., & McNamee, G. D. (2011). Positive approaches to learning in the context of preschool classroom activities. Early Childhood Education Journal,39(1), 71–78.
Chen, J., de la Torre, J., & Zhang, Z. (2013). Relative and absolute fit evaluation in cognitive diagnosis modelling. Journal of Educational Measurement,50(2), 123–140.
Chow, J. C., & Ekholm, E. (2018). Language domains differentially predict mathematics performance in young children. Early Childhood Research Quarterly,46, 179–186.
Cohen, J. (1977). Statistical power analysis for the behavioral sciences. Cambridge: Academic Press.
Cui, Y., Gierl, M. J., & Chang, H. H. (2012). Estimating classification consistency and accuracy for cognitive diagnostic assessment. Journal of Educational Measurement,49, 19–38.
Cummins, D. D., Kintsch, W., Reusser, K., & Weimer, R. (1988). The role of understanding in solving word problems. Cognitive Psychology,20(4), 405–438.
de la Torre, J. (2009). A cognitive diagnosis model for cognitively based multiple-choice options. Applied Psychological Measurement,33, 163–183.
de la Torre, J. (2011). The generalized DINA model framework. Psychometrika,76(2), 179–199.
de la Torre, J., & Minchen, N. (2014). Cognitively diagnostic assessments and the cognitive diagnosis model framework. Psicología Educativa,20(2), 89–97.
Decker, S. L., & Roberts, A. M. (2015). Specific cognitive predictors of early math problem solving. Psychology in the Schools,52(5), 477–488.
Denton, K., & West, J. (2002). Children's reading and mathematics achievement in kindergarten and first grade. Education Statistics Quarterly,4(1), 19–26.
Dong, S. S., Pan, Y. J., & Lin, J. M. (2014). 5–6岁儿童数学入学准备的内容分析 An analysis of the contents and requirements of 5 to 6 years old children’s mathematical school readiness. Early Childhood Education (Educational Sciences),637(11), 9–13.
George, A. C., Robitzsch, A., Kiefer, T., Gro, B. J., & Ünlü, A. (2016). The R package CDM for cognitive diagnostic models. Journal of Statistical Software,74, 1–24.
Goldin, G. A. (1982). Mathematical language and problem solving. Visible Language,16(3), 221–238.
Han, C. C., Cao, S. Y., & Chen, Y. H. (2012). 4–6 岁儿童加减法反演律概念的发展与影响因素 Four to six years old children’s understanding of inversion concept about addition and subtraction and its influencing factors. Psychological Development and Education,2, 121–130.
Hartz, S. M. (2002). A Bayesian framework for the unified model for assessing cognitive abilities: Blending theory with practicality. Urbana-Champaign: University of Illinois.
Hegarty, M., Mayer, R. E., & Monk, C. A. (1995). Comprehension of arithmetic word problems: A comparison of successful and unsuccessful problem solvers. Journal of Education Psychology,87(1), 18–32.
Hu, L. T., & Bentler, P. M. (1998). Fit indices in covariance structure modeling: Sensitivity to underparameterized model misspecification. Psychological Methods,3, 424–453.
Jordan, N. C., Kaplan, D., Ramineni, C., & Locuniak, M. N. (2009). Early math matters: Kindergarten number competence and later mathematics outcomes. Developmental Psychology,45, 850–867.
Junker, B. W., & Sijtsma, K. (2001). Cognitive assessment models with few assumptions, and connections with nonparametric item response theory. Applied Psychological Measurement,25, 258–272.
Lee, E. (2012). The relationship between approaches to learning and academic achievement among kindergarten students: an analysis using Early Childhood Longitudinal Study Kindergarten Students (ECLS-K). International Journal of Arts & Sciences,5(5), 305–313.
LeFevre, J. A., Fast, L., Skwarchuk, S. L., Smith-Chant, B. L., Bisanz, J., Kamawar, D., et al. (2010). Pathways to mathematics: Longitudinal predictors of performance. Child Development,81(6), 1753–1767.
LeFevre, J. A., Skwarchuk, S. L., Smith-Chant, B. L., Fast, L., Kamawar, D., & Bisanz, J. (2009). Home numeracy experiences and children's math performance in the early school years. Canadian Journal of Behavioural Science,41(2), 55–66.
Leighton, J. P., & Gierl, M. (2007). Why cognitive diagnostic assessment? In J. P. Leighton & M. Gierl (Eds.), Cognitive diagnostic assessment for education: Theory and applications (p. 3). Cambridge: Cambridge University Press.
Levine, S. C., Suriyakham, L. W., Rowe, M. L., Huttenlocher, J., & Gunderson, E. A. (2010). What counts in the development of young children's number knowledge? Developmental Psychology,46(5), 1309–1319.
Li, L., Zhou, X., Tu, D. P., Gao, X. L., Huang, J., Yang, Z. Y., et al. (2019). 5–6 岁儿童数学问题解决的认知诊断评估工具 Cognitive diagnosis assessment of mathematics problem solving for children aged 5 to 6. Journal of Studies in Early Childhood Education,293(5), 27–42.
Maris, E. (1999). Estimating multiple classification latent class models. Psychometrika,64(2), 187–212.
Martin, A., Ryan, R. M., & Brooks-Gunn, J. (2013). Longitudinal associations among interest, persistence, supportive parenting, and achievement in early childhood. Early Childhood Research Quarterly,28, 658–667.
McClelland, M. M., Acock, A. C., Piccinin, A., Rhea, S. A., & Stallings, M. C. (2013). Relations between preschool attention span-persistence and age 25 educational outcomes. Early Childhood Research Quarterly,28(2), 314–356.
Muthén, L. K., & Muthén, B. O. (2017). Mplus user's guide (7th ed.). Los Angeles: Muthén & Muthén.
Nortvedt, G. A., & Buchholtz, N. (2018). Assessment in mathematics education: Responding to issues regarding methodology, policy, and equity. ZDM Mathematics Education,50, 555–570.
Nunes, T., Bryant, P., Evans, D., & Barros, R. (2015). Assessing quantitative reasoning in young children. Mathematical Thinking and Learning,17(2–3), 178–196.
Purpura, D. J., & Ganley, C. M. (2014). Working memory and language: Skill-specific or domain-general relations to mathematics? Journal of Experimental Child Psychology,122, 104–121.
Ramirez, G., Chang, H., Maloney, E. A., Levine, S. C., & Beilock, S. L. (2016). On the relationship between math anxiety and math achievement in early elementary school: the role of problem solving strategies. Journal of Experimental Child Psychology,141(2006), 83–100.
Reikerås, E., Løge, I. K., & Knivsberg, A.-M. (2012). The mathematical competencies of toddlers expressed in their play and daily life activities in Norwegian kindergartens. International Journal of Early Childhood,44(1), 91–114.
Ren, X. P. (2012). 4–6 岁幼儿对数学加减逆反原则理解和运用的发展研究 Study on the development of understanding and use of the addition-subtraction inverse principle in young children aged 4–6. Shanghai: East China Normal University.
Rupp, A. A., & Templin, J. (2008). The effects of Q-matrix misspecification on parameter estimates and classification accuracy in the DINA model. Educational and Psychological Measurement,68(1), 78–96.
Sajadi, M., Amiripour, P., & Rostamy-Malkhalifeh, M. (2013). The examining mathematical word problems solving ability under efficient representation aspect. Mathematics Education Trends and Research,3, 1–11.
Sang, B., & Miao, X.-C. (1990). 皮博迪图片词汇测验修订版 (PPVT-R) 上海市区试用常模的修订 Revision of the pilot norm of peabody picture vocabulary test revised (PPVT-R) in Shanghai proper. Psychological Science,5, 22–27.
Schoenfeld, A. H. (1985). A framework for the analysis of mathematical behaviour. In A. H. Schoenfeld (Ed.), Mathematical problem solving (pp. 11–45). Cambridge: Academy Press.
Schrank, F. A., Mather, N., & McGrew, K. S. (2014). Woodcock-Johnson IV tests of achievement. Riverside: Riverside Assessments, LLC.
Shiakalli, M. A., & Zacharos, K. (2014). Building meaning through problem solving practices: The case of four-year olds. The Journal of Mathematical Behavior,35, 58–73.
Templin, J. L., & Henson, R. A. (2006). Measurement of psychological disorders using cognitive diagnosis models. Psychological Methods,11, 287–305.
Tu, D.-B., Gao, X.-L., Wang, D.-X., & Cai, Y. (2017). A new measurement of internet addiction using diagnostic classification models. Frontiers in Psychology,8, 1768.
Woodcock, R. W., McGrew, K. S., & Mather, N. (2001). Woodcock-Johnson III. Riverside: Riverside Assessments LLC.
Zhou, X. (2004). 儿童数概念的早期发展 The early development of children’s number concept. Shanghai: East China Normal University Press.
Zhou, X. (2008). 中班儿童数学认知的发展 On mathematics cognition development in children aged 4–5. Early Childhood Education (Educational Science),403(5), 43–51.