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Journal of Modern Foreign Psychology
2021. Vol. 10, no. 4, 138–146
doi:10.17759/jmfp.2021100413
ISSN: 2304-4977 (online)

Approaches to the typology of the common mistakes of younger schoolchildren in the development of mathematical concepts

322

S.P. Sanina, V.L. Sokolov

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Abstract

The review article examines the field of scientific research devoted to the analysis of errors in mathematics. The problem of mastering mathematical concepts by younger schoolchildren continues to be relevant in pedagogical psychology. Systematic work with students' mistakes is an important stage in the teacher's work. The review shows the significance of the analysis of mathematical errors. The importance of not only detecting systematic mistakes of students, but also the misconceptions about concepts behind them is substantiated. The reasons for the typology of errors are revealed in the context of a discussion about the relationship between conceptual and procedural knowledge. Various approaches to the typology of mathematical errors are described. The typology of errors based on the identification of error patterns, which has become widespread in research, is considered in detail. In this typology, three large groups of mathematical errors are distinguished: factual, procedural and conceptual. Examples of these errors are given on the material studied by younger schoolchildren.

General Information

Keywords: teaching mathematics, junior schoolchildren, mathematical errors, mathematical representations, error analysis, typology of errors

Journal rubric: Educational Psychology and Pedagogical Psychology

Article type: review article

DOI: https://doi.org/10.17759/jmfp.2021100413

Funding. The research was carried out with the financial support of the state task of the Ministry of Education of the Russian Federation No. 073-00041-21-05 dated 07/14/2021 «Formation of the psychological component of the methodological training of the future teacher necessary for the analysis of the causes of students' mistakes in order to develop their subject conceptual thinking in the process of solving educational tasks».

Received: 08.10.2021

Accepted:

For citation: Sanina S.P., Sokolov V.L. Approaches to the typology of the common mistakes of younger schoolchildren in the development of mathematical concepts [Elektronnyi resurs]. Sovremennaia zarubezhnaia psikhologiia = Journal of Modern Foreign Psychology, 2021. Vol. 10, no. 4, pp. 138–146. DOI: 10.17759/jmfp.2021100413. (In Russ., аbstr. in Engl.)

References

  1. Ketterlin-Geller L.R. et al. A Framework for Evaluating Stopping Rules for Fixed-Form Formative Assessments: Balancing Efficiency and Reliability [Elektronnyi resurs]. Practical Assessment, Research, and Evaluation, 2020. Vol. 25, article 8, 18 p. URL: https://scholarworks.umass.edu/pare/vol25/iss1/8 (Accessed 17.10.2021).
  2. Ashlock R.B. Error patterns in computation (10th ed.). Boston: Allyn & Bacon, 2010. 241 p.
  3. Baroody A.J., Feil Y., Johnson A.R. An Alternative reconceptualization of procedural and conceptual knowledge. Journal of Research in Mathematical Education, 2007. Vol. 38, no. 2, pp. 115–131. DOI:10.2307/30034952
  4. Brown J., Skow K. Mathematics: Identifying and Addressing Student Errors [Elektronnyi resurs]. [Nashville, TN]: Iris center, 2016. 34 p. 2016. URL: https://iris.peabody.vanderbilt.edu/wp-content/uploads/pdf_case_studies/ics_matherr.pdf (Accessed 17.10.2021).
  5. Chirume S. A Critical Analysis of Errors Made by Rural and Urban Students in ‘O’ Level Mathematics Paper 1 (4008/1) in Shurugwi and Gweru Districts, Zimbabwe [Elektronnyi resurs]. Asian Journal of Education and e-Learning, 2017. Vol. 5, no. 2, pp. 63–73. URL: https://ajouronline.com/index.php/AJEEL/article/view/4652 (Accessed 17.10.2021).
  6. Clements M.K. Analyzing children’s errors on written mathematical tasks. Educational Studies in Mathematics, 1980. Vol. 11, pp. 1–21. DOI:10.1007/BF00369157
  7. diSessa A.A. A Friendly Introduction to “Knowledge in Pieces”: Modeling Types of Knowledge and Their Roles in Learning [Elektronnyi resurs]. In Kaiser G., Presmeg N. (eds.), Compendium for Early Career Researchers in Mathematics Education. ICME-13 Monographs. Cham: Springer, 2019, pp. 245–265. URL: https://link.springer.com/chapter/10.1007/978-3-030-15636-7_11 (Accessed 17.10.2021).
  8. diSessa A.A. Toward an epistemology of physics [Elektronnyi resurs]. Cognition and Instruction, 1993. Vol. 10, № 2/3. pp. 105–225. URL: https://www.jstor.org/stable/3233725 (Accessed 17.10.2021).
  9. Bottge B.A. et al. Effects of Formative Assessment Strategies on the Fractions Computation Skills of Students With Disabilities. Remedial and Special Education, 2021. Vol. 42, no. 5, pp. 279–289. DOI:10.1177/0741932520942954
  10. Watson S.R. et al. Error patterns in Portuguese students’ addition and subtraction calculation tasks: Implications for teaching". Journal for Multicultural Education, 2018. Vol. 12, no. 1, pp. 67–82. DOI:10.1108/JME-01-2017-0002
  11. Fiori C., Zuccheri L. An experimental research on error patterns in written subtraction. Educational Studies in Mathematics, 2005. Vol. 60, pp. 323–331. DOI:10.1007/s10649-005-7530-6
  12. Green М., Piel J.A., Flowers С. Reversing Education Majors' Arithmetic Misconceptions with Short-Term Instruction Using Manipulatives. The Journal of Educational Research, 1993. Vol. 101, no. 4, pp. 234–242. DOI:10.3200/JOER.101.4.234-242
  13. Hwang J., Riccomini P.J. A Descriptive Analysis of the Error Patterns Observed in the Fraction-Computation Solution Pathways of Students with and Without Learning Disabilities. Assessment for Effective Intervention, 2021. Vol. 46, no. 2, pp. 132–142. DOI:10.1177/1534508419872256
  14. Justice E., Zanele N. Formative assessment: A tool for rectifying learners' errors and misconceptions in mathematics. Integrity journal of education and training, 2020. Vol. 4, no. 3, pp. 48–52. DOI:10.31248/IJET2020.085
  15. Kakoma L., Themane K.M. Misconceptions and associated errors in the learning of mathematics place value in south african primary schools: a literature review. Preprints, 2021. 24 p. DOI:10.20944/preprints202105.0456.v1
  16. Lestiana H.T., Rejeki S., Setyawan F. Identifying Students’ Errors on Fractions. Journal of Research and Advances in Mathematics Education, 2016. Vol. 1, no. 2, pp. 131–139. DOI:10.23917/jramathedu.v1i2.3396
  17. Levin M. Conceptual and Procedural Knowledge During Strategy Construction: A Complex Knowledge Systems Perspective. Cognition and Instruction, 2018. Vol. 36, no. 3, pp. 247–278. DOI:10.1080/07370008.2018.1464003
  18. Smith J.P. et al. Misconceptions Reconceived: A Constructivist Analysis of Knowledge in Transition. The Journal of the Learning Sciences, 1994. Vol. 3, no. 2, pp. 115–163. DOI:10.1207/s15327809jls0302_1
  19. Muthukrishnan P., Kee M.S., Sidhu G.K. Addition Error Patterns Among the Preschool Children. International Journal of Instruction, 2019. Vol. 12, no. 2, pp. 115–132. DOI:10.29333/iji.2019.1228a
  20. Koriakin T. et al. Patterns of Cognitive Strengths and Weaknesses and Relationships to Math Errors. Journal of Psychoeducational Assessment, 2017. Vol. 35, no. 1–2, pp. 155–167. DOI:10.1177/0734282916669909
  21. Peng A., Luo Z. A framework for examining mathematics teacher knowledge as used in error analysis [Elektronnyi resurs]. For the Learning of Mathematics, 2009. Vol. 29, no. 3, pp. 22–25. URL: https://www.jstor.org/stable/25594562 (Accessed 17.10.2021).
  22. Radatz H. Error analysis in mathematics education. Journal for Research in Mathematics Education, 1979. Vol. 10, no. 3, pp. 163–172. DOI:10.5951/jresematheduc.10.3.0163
  23. Resnick L.B., Ford W.W. Psychology of mathematics for instruction. Hillsdale, NJ: L. Erlbaum Associates, 1981. 266 p.
  24. Riccomini P.J. Identification and remediation of systematic error patterns in subtraction. Learning Disability Quarterly, 2005. Vol. 28, no. 3, pp. 233–242. DOI:10.2307/1593661
  25. Rittl-Johnson B., Schneider M. Development of conceptual and procedural knowledge in mathematics. In Kadosh R.C., Dowker A. (eds.), Oxford handbook of numerical cognition. Oxford: Oxford University Press, 2015, pp. 1102–1118. DOI:10.1093/oxfordhb/9780199642342.013.014
  26. Roelien H., Ingrid S. An error analysis in the early grades mathematics – A learning opportunity. South African Journal of Childhood Education, 2014. Vol. 4, no. 1, pp. 43–60. DOI:10.4102/sajce.v4i1.46
  27. Site Quora [Elektronnyi resurs]. Quora, Inc. 2021. URL: https://www.quora.com/Is-it-true-that-in-a-division-the-quotient-is-always-less-than-the-divisor (Accessed 17.10.2021)
  28. Fisher D. et al. Visible Learning for Mathematics, Grades K-12: What Works Best to Optimize Student Learning [Elektronnyi resurs]. Corwin Press, 2016. 304 р. https://books.google.ru/books?id=fjcbDQAAQBAJ&lpg=PP1&hl=ru&pg=PR3#v=onepage&q&f=false (Accessed 17.10.2021).

Information About the Authors

Svetlana P. Sanina, PhD in Education, Associate Professor, Chair of Pedagogical Psychology named after Professor V. A. Guruzhapov, Moscow State University of Psychology & Education, Moscow, Russia, ORCID: https://orcid.org/0000-0002-4033-3913, e-mail: saninasp@mgppu.ru

Vladimir L. Sokolov, PhD in Psychology, Associate Professor, Chair of Pedagogical Psychology named after Professor V.A. Guruzhapov, Moscow State University of Psychology & Education, Moscow, Russia, ORCID: https://orcid.org/0000-0002-6180-7567, e-mail: sokolovvl@mgppu.ru

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