The Effect of Conceptually Oriented Instruction on Students' Computational Competencies. Research Series No. 214

Does conceptually oriented instruction jeopardize students' computational competence? If it does, then why are so many reform efforts continuing to emphasize the importance of teaching for conceptual understanding? If it does not, then why are the majority of teachers at all grade levels continuing to teach for computational competence without conceptual understanding? This paper presents the results of a computational test taken by two groups of students in ninth-grade general mathematics classes. One group of students practiced computational procedures without an emphasis on the mathematical concepts. The second group of students learned the mathematical concepts underlying the procedures and spent little, if any, time on practicing computational procedures. The findings of the computational test showed that in one conceptually oriented class the average grade-level equivalence for computational competence was increased from a 6.5 grade level at the start of the school year to a 9.1 grade level at the end of the year. One computationally oriented class had an average grade level at the start of the school year of 7.1 and at the end of the school year the grade-level equivalence was 7.5. This was a gain of less than half a year, even though the students spent the whole year practicing computational procedures. Other findings showed that the students in the conceptually oriented classes attempted more items on the posttest than did students in the computationally oriented classes. Furthermore, statements made by the students at the end of the year indicated that they felt they had learned more mathematics in the conceptually oriented class than they had in any of their previous mathematics classes. The results of this study suggested that conceptual understanding enhanced students' computational competence and promoted more positive attitudes towards mathematics. The results also suggested that computational procedures are neither learned nor retained through drill-and-practice exercises without conceptual understanding. (Comparative test results are appended. The text contains 15 tables.) (Author)