An International Comparison of Grade 6 Students' Understanding of the Equal Sign

Abstract

This study extends the scope of international comparisons examining students' conceptions of the equal sign. Specifically, Korean (n = 193) and Turkish (n = 334) Grade 6 students were examined to assess whether their conceptions and responses were similar to prior findings published for Chinese and U.S. students and to hypothesize relationships about problem types and conceptual understanding of the equal sign. About 59.6% of the Korean participants correctly answered all items providing conceptually accurate solutions, as compared to 28.4% of the Turkish sample. Comparison with previous studies in China and the USA indicated that the Chinese sample outperformed those from other nations, followed by Korea, Turkey, and the USA. In large-scale international studies such as Trends in International Mathematics and Science (TIMSS) and the Programme for International Student Assessment (PISA), students from China and Korea have been among the high achievers.

Grade 9 Learners’ Structural and Operational Conceptions of the Equal Sign: A Case Study of a Secondary School in Soshanguve

“…This finding is consistent with findings by other researchers (e.g. Osana, Cooperman, Adrien, Rayner, Bisanz, Watchorn, & Sherman LeVos, 2012;Prediger, 2010;Capraro, Capraro, Yetkiner, Özel, Kim, & Küçük 2010) namely that learners' conception of a variable is inadequate. Most learners' misunderstandings included viewing variables as abbreviations or labels rather than as letters that stand for quantities, assigning values to letters based on their positions in the alphabet, and being unable to operate with algebraic letters as varying quantities rather than specific values (Asquith, Stephens, Knuth, & Alibali, 2007) Sfard (1991) argues that the equal sign is usually interpreted as requiring some action rather than signifying the equivalence between two expressions, leading to the technical blunder that + 8 = 8 , as some of the learners proposed in the above excerpt.…”

A Change–Resistance Account of Children's Difficulties Understanding Mathematical Equivalence

“…Davydov (1969/1991) was the first to show that children as young as first grade could learn algebraic concepts, including mathematical equivalence. Since then, studies have shown that children in China, Korea, and Turkey better understand math equivalence than their peers of the same age in the United States (Capraro et al., ). Moreover, even in studies within the United States, extensive conceptual instruction can improve understanding of mathematical equivalence in some children (e.g., Baroody & Ginsburg, ; Jacobs et al., ; Saenz‐Ludlow & Walgamuth, ).…”

“…This is how the equal sign is introduced in China where, as stated, more than 90% of children solve mathematical equivalence problems correctly (Capraro et al., ). This discrepancy in understanding is partly due to differences in both the format and sequence of problems that children learn (Li et al., ).…”

Teaching the substitutive conception of the equals sign

“…There is widespread agreement that children's difficulties are due to how the equals sign is presented in classrooms rather than due to developmental limitations (Baroody and Ginsburg 1983;R. M. Capraro et al 2010;Cobb 1987;Li et al 2008;McNeil 2008;Rittle-Johnson et al 2011;Seo and Ginsburg 2003;Sherman and Bisanz 2009).…”