All mathematics is comprised of three elements: symbols, nominalizations, and images, and the combination of these three elements determine the mathematical meaning. However, adolescents may not be aware of these three elements. When asked to describe mathematical language, they will often name equations and images, two of the three elements. Over…

Successful algebraic problem solving entails adaptability of solution methods using different representations. Prior research has suggested that students are more likely to prefer symbolic solution methods (equations) over graphical ones, even when graphical methods should be more efficient. However, this research has not tested how representation…

Are numerals estranged from a sense of the actual quantities they represent? We demonstrate that, irrespective of numerical size or distance, direct comparison of the relative quantities represented by symbolic and nonsymbolic formats leads to performance markedly worse than when comparing 2 nonsymbolic quantities (Experiment 1). Experiment 2…