Symbolic and Nonsymbolic Equivalence Tasks: The Influence of Symbols on Students with Mathematics Difficulty

Students often experience difficulty with attaching meaning to mathematics symbols. Many students react to symbols, such as the equal sign, as a command to "do something" or "write an answer" without reflecting upon the proper relational meaning of the equal sign. One method for assessing equal-sign understanding is through nonstandard equations (e.g., 3 + 4 = __ + 5) where student answers provide cues about operational or relational interpretation of the equal sign. This study investigated the influence of symbolic and nonsymbolic presentations on a measure of nonstandard equations. A representative sample of 2nd-grade students (n = 413) solved a set of nonstandard equations presented with symbols (i.e., symbolic) and the same set presented with pictures and stories (i.e., nonsymbolic). Students with and without mathematics difficulty demonstrated significantly higher scores on the nonsymbolic version without mathematics symbols. Results have implications for mathematics assessment and instruction.