Equivalence in symbolic and nonsymbolic contexts: Benefits of solving problems with manipulatives.

Children's failure on equivalence problems (e. g. , 5 + 4 = 7 + _) is believed to be the result of misunderstanding the equal sign and has been tested using symbolic problems (including =). For Study I (N = 48), we designed a nonsymbolic method for presenting equivalence problems to· determine whether Grade 2 children's difficulty is due to the presence of symbols or to a more fundamental misunderstanding of equivalence. Children's superior performance on nonsymbolic versus symbolic problems suggests that children fail to map their understanding of equivalence onto problems presented with the symbols of arithmetic. For Study 2 (N = 32), we implemented a within-subject design to assess whether experience with nonsymbolic problems would facilitate performance on symbolic problems. This hypothesis was confirmed. Exposure to nonsymbolic problems may have enabled children to map their successful concepts and strategies to symbolic equivalence problems