Middle-School Students' Understanding of the Equal Sign: The Books They Read Can't Help

This study examined how 4 middle school textbook series (2 skills-based, 2 standards-based) present equal signs. Equal signs were often presented in standard operations-equals-answer contexts (e.g., 3 + 4 = 7) and were rarely presented in non-standard operations on both sides contexts (e.g., 3 + 4 = 5 + 2). They were, however, presented in other nonstandard contexts (e.g., 7 = 7). Two follow-up experiments showed that students ’ interpretations of the equal sign depend on the context. The other nonstandard contexts were better than the operations-equals-answer context at eliciting a relational understanding of the equal sign, but the operations on both sides context was best. Results suggest that textbooks rarely present equal signs in contexts most likely to elicit a relational interpretation—an interpretation critical to success in algebra. The equal sign (=) is ubiquitous in mathematics, and a sophisticated concept of the symbol is essential for understanding many topics in mathematics (e.g., algebraic equations). However, over 20 years of research in developmental psychology and mathematics education has indicated that many elementary school students (ages 7 to 11) have an inadequate understanding of the equal sign (Baroody & Ginsburg,