Relationships between variables in learning and modes of presenting mathematics concepts

The purpose of this study was to investigate relationships between figural and symbolic aptitudes and figural and symbolic modes of presenting mathematics concepts to secondary school students. One hundred and sixty students were measured on 11 aptitudes (five figural, five symbolic, and one semantic) from Guilford's structure‐of‐intellect cube and were randomly assigned to either a figural or symbolic instructional mode for learning the mathematical concept of function. Subjects studied the function concept using one of two sets (figural or symbolic) of programmed instructional materials during three consecutive mathematics classes. Immediately following instruction a learning test was given, which was followed by a retention test 1 week later. Data analysis showed that females scored significantly higher than males on all dependent measures, and their scores were independent of instructional mode. For male students figural instruction was superior to the symbolic mode. Significant relationships were found between instructional mode and the figural aptitude divergent production of figural systems. The symbolic aptitude cognition of symbolic systems was a predictor of success for subjects studying symbolic materials. Cognition of semantic systems was a good predictor of success for students receiving the figural instructional treatment.