Linear figural patterns as a teaching tool for preservice elementary teachers – the role of symbolic expressions

Abstract

International audienceFigural patterns connect several aspects of mathematical activity central to the work of teaching mathematics. In this pilot study, we investigated the solutions of 16 preservice elementary teachers to linear figural patterns of different levels of complexity after the completion of a series of six teaching sessions of a course in mathematics education. We found that a) most students were able to generalize and find the figural number of an arbitrary figure in the sequence; b) about half of the students produced mathematically imprecise formulas when translating from an arbitrary number into a general algebraic expression; c) the formulas students produced frequently lacked structural correspondence with the figural patterns and d) students had difficulties in interpreting figural patterns that are more complex. These results indicate that although the course successfully trains students to generalize with linear figural patterns, more attention to precisely formulating mathematical ideas and to interpretation of more difficult patterns can further improve the training of preservice elementary teachers