Journal of Modern Foreign Psychology
2021. Vol. 10, no. 4, 138–146
doi:10.17759/jmfp.2021100413
ISSN: 23044977 (online)
Approaches to the typology of the common mistakes of younger schoolchildren in the development of mathematical concepts
Abstract
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. 073000412105 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

KetterlinGeller L.R. et al. A Framework for Evaluating Stopping Rules for FixedForm 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).

Ashlock R.B. Error patterns in computation (10th ed.). Boston: Allyn & Bacon, 2010. 241 p.

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

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/wpcontent/uploads/pdf_case_studies/ics_matherr.pdf (Accessed 17.10.2021).

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 eLearning, 2017. Vol. 5, no. 2, pp. 63–73. URL: https://ajouronline.com/index.php/AJEEL/article/view/4652 (Accessed 17.10.2021).

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

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. ICME13 Monographs. Cham: Springer, 2019, pp. 245–265. URL: https://link.springer.com/chapter/10.1007/9783030156367_11 (Accessed 17.10.2021).

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).

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

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/JME0120170002

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/s1064900575306

Green М., Piel J.A., Flowers С. Reversing Education Majors' Arithmetic Misconceptions with ShortTerm Instruction Using Manipulatives. The Journal of Educational Research, 1993. Vol. 101, no. 4, pp. 234–242. DOI:10.3200/JOER.101.4.234242

Hwang J., Riccomini P.J. A Descriptive Analysis of the Error Patterns Observed in the FractionComputation 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

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

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

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

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

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

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

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

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).

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

Resnick L.B., Ford W.W. Psychology of mathematics for instruction. Hillsdale, NJ: L. Erlbaum Associates, 1981. 266 p.

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

RittlJohnson 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

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

Site Quora [Elektronnyi resurs]. Quora, Inc. 2021. URL: https://www.quora.com/Isittruethatinadivisionthequotientisalwayslessthanthedivisor (Accessed 17.10.2021)

Fisher D. et al. Visible Learning for Mathematics, Grades K12: 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
Metrics
Views
Total: 471
Previous month: 27
Current month: 17
Downloads
Total: 282
Previous month: 27
Current month: 16