Variation of student numerical and figural reasoning approaches by pattern generalization type,strategy use and grade level

This paper explored variation of student numerical and figural reasoning approaches across different pattern generalization types and across grade level. An instrument was designed for this purpose. The instrument was given to a sample of 1232 students from grades 4 to 11 from five schools in Lebanon. Analysis of data showed that the numerical reasoning approach seems to be more dominant than the figural reasoning approach for the near and far pattern generalization types but not for the immediate generalization type. The findings showed that for the recursive strategy, the numerical reasoning approach seems to be more dominant than the figural reasoning approach for each of the three pattern generalization types. However, the figural reasoning approach seems to be more dominant than the numerical reasoning approach for the functional strategy, for each generalization type. The findings also showed that the numerical reasoning was more dominant than the figural reasoning in lower grade levels (grades 4 and 5) for each generalization type. In contrast, the figural reasoning became more dominant than the numerical reasoning in the upper grade levels (grades 10 and 11).