Substitution and sameness: Two components of a relational conception of the equals sign

Journal of Experimental Child Psychology

Volumn 113, Issue 1, 2012, Pages 166-176

  Jones, Ian ^a   Inglis, Matthew ^a   Gilmore, Camilla ^a   Dowens, Margaret ^b  

^a LOUGHBOROUGH UNIVERSITY   (United Kingdom)

^b UNIVERSITY OF NOTTINGHAM NINGBO CHINA   (China)

Author keywords

Algebra; Arithmetic; Cross cultural; Equals sign; Equivalence; Substitution

Indexed keywords

ARTICLE; CHILD; CHINA; COMPARATIVE STUDY; CONCEPT FORMATION; CULTURAL FACTOR; EDUCATION; FEMALE; HUMAN; LEARNING; MALE; MATHEMATICS; PRINCIPAL COMPONENT ANALYSIS; PROBLEM SOLVING; SEMANTICS; UNITED KINGDOM;

ASSOCIATION LEARNING; CHILD; CHINA; CONCEPT FORMATION; CROSS-CULTURAL COMPARISON; ENGLAND; FEMALE; HUMANS; MALE; MATHEMATICS; PRINCIPAL COMPONENT ANALYSIS; PROBLEM SOLVING; SEMANTICS;

EID: 84863779826     PISSN: 00220965     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jecp.2012.05.003     Document Type: Article

References (29)

1. Baroody A.J., Ginsburg H.P. The effects of instruction on children's understanding of the "equals" sign. Elementary School Journal 1983, 84:199-212.
2. Behr, M., Erlwanger, S., & Nichols, E. (1976). How children view equality sentences [PMDC Technical Report No. 3]. Tallahassee: Florida State University.
3. Carpenter T.P., Franke M.L., Levi L. Thinking mathematically: Integrating arithmetic and algebra in the elementary school 2003, Heinemann, Portsmouth, NH.
4. de Lima R.N., Tall D. Procedural embodiment and magic in linear equations. Educational Studies in Mathematics 2007, 67:3-18.
5. Denmark, T., Barco, B., & Voran, J. (1976). Final report: A teaching experiment on equality (PMDC Technical Report No. 6). Tallahassee: Florida State University.
6. Filloy E., Rojano T., Solares A. Problems dealing with unknown quantities and two different levels of representing unknowns. Journal for Research in Mathematics Education 2010, 41:52-80.
7. Holgado-Tello F.P., Chacón-Moscoso S., Barbero-García I., Vila-Abad E. Polychoric versus Pearson correlations in exploratory and confirmatory factor analysis of ordinal variables. Quality & Quantity 2008, 44:153-166.
8. Jones I., Inglis M., Gilmore C., Evans R. Using and learning the substitutive meaning of the equals sign in arithmetic contexts 2012, Loughborough University, [submitted for publication].
9. Jones I., Pratt D. A substituting meaning for the equals sign in arithmetic notating tasks. Journal for Research in Mathematics Education 2012, 43:2-33.
10. Kieran C. Concepts associated with the equality symbol. Educational Studies in Mathematics 1981, 12:317-326.
11. Knuth E.J., Stephens A.C., McNeil N.M., Alibali M.W. Does understanding the equal sign matter? Evidence from solving equations. Journal for Research in Mathematics Education 2006, 36:297-312.
12. Li X., Ding M., Capraro M.M., Capraro R.M. Sources of differences in children's understandings of mathematical equality: Comparative analysis of teacher guides and student texts in China and the United States. Cognition and Instruction 2008, 26:195-217.
13. McNeil N.M. Limitations to teaching children 2+2=4: Typical arithmetic problems can hinder learning of mathematical equivalence. Child Development 2008, 79:1524-1537.
14. McNeil N.M., Alibali M.W. Why won't you change your mind? Knowledge of operational patterns hinders learning and performance on equations. Child Development 2005, 76:883-899.
15. McNeil N.M., Alibali M.W. A strong schema can interfere with learning: The case of children's typical addition schema. Proceedings of the twenty-fourth annual conference of the Cognitive Science Society 2002, 661-666. Lawrence Erlbaum, Mahwah, NJ. C. Schunn, W. Gray (Eds.).
16. McNeil N.M., Fyfe E.R., Petersen L.A., Dunwiddie A.E., Brletic-Shipley H. Benefits of practicing 4=2+2: Nontraditional problem formats facilitate children's understanding of mathematical equivalence. Child Development 2011, 82:1620-1633.
17. McNeil N.M., Grandau L., Knuth E.J., Alibali M.W., Stephens A.C., Hattikudur S., et al. Middle-school students' understanding of the equal sign: The books they read can't help. Cognition and Instruction 2006, 24:367-385.
18. McNeil N.M., Rittle-Johnson B., Hattikudur S., Petersen L.A. Continuity in representation between children and adults: Arithmetic knowledge hinders undergraduates' algebraic problem solving. Journal of Cognition and Development 2010, 11:437-457.
19. McNeil N.M., Weinberg A., Hattikudur S., Stephens A.C., Asquith P., Knuth E.J., et al. A is for apple: Mnemonic symbols hinder the interpretation of algebraic expressions. Journal of Educational Psychology 2010, 102:625-634.
20. Molina M., Castro E., Mason J. Elementary school students' approaches to solving true/false number sentences. PNA 2008, 2:75-86.
21. Mullis I.V.S., Martin M.O., Foy P., Olson J.F., Preuschoff C., Erberber E., et al. TIMSS 2007 International Mathematics Report: Findings from IEA's Trends in International Mathematics and Science Study at the fourth and eighth grades 2008, Boston College, TIMSS and PIRLS International Study Center, Chestnut Hill, MA.
22. Organization for Economic Cooperation and Development. (2011). PISA 2009 results: What students know and can do-Student performance in reading, mathematics, and science (Vol. 1). Paris: OECD Publishing.
23. Pirie S.E.B., Lydon M. The equation, the whole equation, and nothing but the equation! One approach to the teaching of linear equations. Educational Studies in Mathematics 1997, 34:159-181.
24. Rittle-Johnson B., Alibali M.W. Conceptual and procedural knowledge of mathematics: Does one lead to the other?. Journal of Educational Psychology 1999, 91:175-189.
25. Rittle-Johnson B., Matthews P., Taylor R.S., McEldoon K.L. Assessing knowledge of mathematical equivalence. A construct-modeling approach. Journal of Educational Psychology 2011, 103:85-104.
26. Sáenz-Ludlow A., Walgamuth C. Third graders' interpretations of equality and the equal symbol. Educational Studies in Mathematics 1998, 35:153-187.
27. Seo, K. H., & Ginsburg, H. P. (2003). "You've got to carefully read the math sentence...": Classroom context and children's interpretations of the equals sign. In A. J. Baroody & A. Dowker (Eds.), The development of arithmetic concepts and skills: Constructing adaptive expertise, studies in mathematical thinking and learning (pp. 161-187). Mahwah, NJ: Lawrence Erlbaum Associates Publishers.
28. Stewart I.N., Tall D.O. The foundations of mathematics 1977, Oxford University Press, Oxford, UK.
29. Weaver J.F. The symmetric property of the equality relation and young children's ability to solve open addition and subtraction sentences. Journal for Research in Mathematics Education 1973, 4:45-56.