Looking for a pattern: Error analysis as a diagnostic assessment for making instructional decisions to promote academic success

References

• Aksoy, N. C., & Yazlik, D. O. (2017). Student errors in fractions and possible causes of these errors. Journal of Education and Training Studies, 5(11), 219–233. https://doi.org/10.11114/jets.v5i11.2679
   Google Scholar
• Arslan, S. (2010). Traditional instruction of differential equations and conceptual learning. Teaching Mathematics and Its Applications, 29(2), 94–107. https://doi.org/10.1093/teamat/hrq001
   Google Scholar
• Ashlock, R. B. (2010). Errors patterns in computation: Using error patterns to help each student learn (10th ed.). Allyn & Bacon.
   Google Scholar
• Benjamini, Y., & Hochberg, Y. (1995). Controlling the false discovery: A practical and powerful approach to multiple testing. Journal of the Royal Statistical Society: Series B (Methodological), 57(1), 289–300. https://doi.org/10.1111/j.2517-6161.1995.tb02031.x
   Web of Science ®Google Scholar
• Brown, J. S., & Burton, R. R. (1978). Diagnostic models for procedural bugs in basic mathematical skills. Cognitive Science, 2(2), 155–192. https://doi.org/10.1016/S0364-0213(78)80004-4
   Google Scholar
• Callejo, M. L., & Zapatera, A. (2017). Prospective primary teachers’ noticing of students’ understanding of pattern generalization. Journal of Mathematics Teacher Education, 20(4), 309–333. https://doi.org/10.1007/s10857-016-9343-1
   Web of Science ®Google Scholar
• Cathcart, W. G., Pothier, Y. M., Vance, J. H., & Bezuk, N. S. (2011). Learning mathematics in elementary and middle schools: A learner-centered approach (5th ed.). Pearson.
   Google Scholar
• Cebulski, L. (1984). Children’s errors in subtraction: An investigation into causes and remediation. Report Research/Technical, 143, 27 p.
   Google Scholar
• Cooper, S. (2009). Preservice teachers’ analysis of children’s work to make instructional decisions. School Science and Mathematics, 109(6), 355–362. https://doi.org/10.1111/j.1949-8594.2009.tb18105.x
   Google Scholar
• Dunn, O. J. (1964). Multiple comparisons using rank sums. Technometrics, 6(3), 241–252. https://doi.org/10.1080/00401706.1964.10490181
   Web of Science ®Google Scholar
• Engelhardt, J. M. (1977). Analysis of children computational errors: A qualitative approach. British Journal of Educational Psychology, 47(2), 149–154. 8279.1977.tb02340.x https://doi.org/10.1111/j.2044-
   Google Scholar
• Foley, T. E., & Cawley, J. F. (2003). About the mathematics of division: Implications for students with disabilities. Exceptionality, 11(3), 131–149. https://doi.org/10.1207/S15327035EX1103_02
   Google Scholar
• Geary, D. C. (2011). Cognitive predictors of achievement growth in mathematics: A 5-year longitudinal study. Developmental Psychology, 47(6), 1539–1552. https://doi.org/10.1037/a0025510
   PubMed Web of Science ®Google Scholar
• Gojak, L. M. (2012, November 1). Fluency: Simply fast and accurate? I think not! NCTM Summing Up. https://www.nctm.org/News-and-Calendar/Messages-from-the-President/Archive/Linda-M_-Gojak/Fluency_-Simply-Fast-and-Accurate_-I-Think-Not!/
   Google Scholar
• Higgins, J. J. (2004). Introduction to modern nonparametric statistic. Thompson Brooks/Cole.
   Google Scholar
• Jordan, N. C., Glutting, J., & Ramineni, C. (2010). The importance of number sense to mathematics achievement in first and third grades. Learning and Individual Differences, 20(2), 82–88. https://doi.org/10.1016/j.lindif.2009.07.004
   PubMed Web of Science ®Google Scholar
• Jordan, N. C., Hanich, L. B., & Kaplan, D. (2003). A longitudinal study of mathematical competencies in children with specific mathematics difficulties versus children with comorbid mathematics and reading difficulties. Child Development, 74(3), 834–850. https://doi.org/10.1111/1467-8624.00571
   PubMed Web of Science ®Google Scholar
• Lopes, J., & Bueno, M. (2014). Construção e validação de uma prova de mathemática para alunos do primeiro ao quarto ano de escolaridade [Development and validation of a math test for first to fourth grade students]. Psicologia: Reflexão e Crítica, 27(3), 434–442. https://doi.org/10.1590/1678-7153.201427303
   Google Scholar
• Lortie-Forgues, H., Tian, J., & Siegler, R. S. (2015). Why is learning fraction and decimal so difficult? Developmental Review, 38, 201–221. https://doi.org/10.1016/j.dr.2015.07.008
   Web of Science ®Google Scholar
• Mehmetlioglu, D. (2014). Misconceptions of elementary school students about comparing decimals numbers. Procedia – Social and Behavioral Sciences, 152, 569–574. https://doi.org/doi: https://doi.org/10.1016/j.sbspro.2014.09.245
   Google Scholar
• Mercer, C. D., & Miller, S. P. (1991–1994). The strategic math series. Edge Enterprises.
   Google Scholar
• Namkung, J. M., & Fuchs, L. S. (2012). Early numerical competencies of students with different forms of mathematics disabilities. Learning Disabilities Research & Practice, 27(1), 2–11. https://doi.org/10.1111/j.1540-5826.2011.00350.x
   PubMed Web of Science ®Google Scholar
• National Mathematics Advisory Council. (2008). Foundations for success. The final report of the National Mathematics Advisory Panel. U.S. Department of Education.
   Google Scholar
• Nelson, G., & Powell, S. R. (2018). Computation error analysis: Students with mathematics difficulty compared to typically achieving students. Assessment for Effective Intervention, 43(3), 144–156. https://doi.org/10.1177/1534508417745627
   Web of Science ®Google Scholar
• Ogle, D. H., Wheeler, P., & Dino, A. (2018). FSA: Fisheries stock analysis (R package Version 0.8.22.9000 Retrieved from https://github.com/droglenc/FSA.
   Google Scholar
• R Core Team. (2017). R: A language and environment for statistical computing. R Foundation for Statistical Computing. https://www.R-project.org/
   Google Scholar
• Riccomini, P. J. (2005). Identification and remediation of systematic error patterns in subtraction. Learning Disability Quarterly, 28(3), 233–242. https://doi.org/10.2307/1593661
   Web of Science ®Google Scholar
• Roberts, G. H. (1968). The failure strategies of third grade arithmetic pupils. The Arithmetic Teachers, 15, 442–446. http://www.jstor.org/stable/41185806
   Google Scholar
• Sapire, I., Shalem, Y., Wilson-Thompson, B., & Paulsen, R. (2016). Engaging with learners’ errors when teaching mathematics. Pythagoras-Journal of the Association for Mathematics Education of South Africa, 37, 1012–2346. https://doi.org/10.4102/Pythagoras.v37i1.331
   Google Scholar
• Skagerlund, K., & Traff, U. (2014). Development of magnitude processing in children with developmental dyscalculia: Space, time, and number. Frontiers in Psychology, 5, 675–615. https://doi.org/10.3389/fpsyg.2014.00675
   PubMed Web of Science ®Google Scholar
• Skwarchuk, S.-L., & Betts, P. (2006). An error analysis of elementary school children’s number production abilities. Australian Journal of Educational & Developmental Psychology, 6, 1–11. http://newcastle.edu.au/group/ajedp/
   Google Scholar
• Stefanich, G. P., & Rokusek, T. (1992). An analysis of computational errors in the use of division algorithms by fourth-grade students. School Science and Mathematics, 92(4), 201–205. https://doi.org/10.1111/j.1949-8594.1992.tb12173.x
   Google Scholar
• Thanheiser, E. (2009). Preservice elementary school teachers’ conceptions of multidigit whole numbers. Journal for Research in Mathematics Education, 40, 251–281. http://www.jstor.org/stable/40539337
   Web of Science ®Google Scholar
• Thanheiser, E. (2012). Understanding multidigit whole numbers: The role of knowledge components connections, and context in understanding regrouping 3 +- digit numbers. The Journal of Mathematical Behavior, 31(2), 220–234. https://doi.org/10.1016/j.jmathb.2011.12.007
   Google Scholar
• Tolar, T. D., Lederberg, A. R., & Fletcher, J. M. (2009). A structural model of algebra achievement: Computational fluency and spatial visualization as mediators of the effect of working memory on algebra achievement. Educational Psychology, 29(2), 239–266. https://doi.org/10.1080/01443410802708903
   Web of Science ®Google Scholar
• Traff, U., & Samuelson, J. (2013). Analysis of errors in multi-digit arithmetic and arithmetic word problem solving in children with mathematics learning difficulties. Special Education, 1, 121–132.
   Google Scholar
• Wood, D. K., & Frank, A. R. (2000). Memory-enhancing strategies to learn multiplication facts. Teaching Exceptional Children, 32(5), 78–82. https://doi.org/10.1177/004005990003200511
   Google Scholar
• Yorulmaz, A., & Önal, H. (2017). Examination of the views of class teachers regarding the errors primary school students make in four operations. Universal Journal of Educational Research, 5(11), 1885–1895. https://doi.org/10.13189/ujer.2017.051105
   Google Scholar
• Zhang, D., Ding, Y., Barrett, E. D., Xin, Y. P., & Liu, R. (2014). A comparison of strategic development of multiplication skills in low-achieving, average achieving, and high achieving students. European Journal of Psychology of Education, 29(2), 195–214. https://doi.org/10.1007/s10212-013-0194-1
   Web of Science ®Google Scholar