The effect of sequence of instruction on learning algebra concepts using enactive, iconic, and symbolic materials

This study sought to verify Jerome Bruner's theory which proposes that learners grasp mathematics faster when numerical concepts are taught first with solid objects (enactive mode E), then with pictures or diagrams (iconic mode I), and finally with abstract notation (symbolic mode S). Specifically it sought to investigate whether this sequence of instructional methods, termed the E > I > S sequence, was most effective compared to the I > S > E and S > E > I sequences for learning algebraic operations. It also sought to find whether the E > I > S sequence had a greater effect on the learning of lower ability students.;Participants (N = 38) in this quasi-experimental study were seventh grade males from an urban private school. Groups receiving each instructional sequence were balanced by ability using a test of pre-algebra skills. On the first day of treatment groups of subjects began the study with an enactive (E) lesson, an iconic (I) lesson, or symbolic (S) lesson. Subjects switched instructional methods on the second and third days. The difference among the treatments was the sequence of instruction: E > I > S, I > S > E or S > E > I. All subjects took a test in the symbolic mode at the end of the third day.;The results favored the E > I > S sequence compared to the I > S > E sequence (effect size = 0.18) and the S > E > I sequence (0.36), although statistical significance was not reached. Lower ability students receiving the E > I > S sequence scored closer to the higher ability students. The difference between high and low ability students for the E > I > S sequence was 17%, compared to the differences of 19% and 40% for the I > S > E and S > E > I sequences. The implications of this study are limited by the relatively high average ability level of the subjects and the small number of comparisons.;All comparisons of the E > I > S sequence to other sequences were consistent with Bruner's predictions. Recent research has upheld the use of multiple representations in teaching algebra concepts. This study confirms those findings and gives support for the use of enactive and iconic materials prior to using purely symbolic materials.