Strategies Used By Kindergarten Children to Cover “Maximal Area” Inside a Rectangle

This qualitative study aimed to examine: 1) the manner in which kindergarten children and first graders make sense of the term “area” regarding optimization problems; 2) how this manner is manifested in their decision-making and “STEAM” (science, technology, engineering, art and math) skills; 3) how kindergarten children and first graders comprehend the concept of “cover maximal area.” Six kindergarten children and six first graders participated in the study.

To investigate the children’s knowledge objectification, a multi-semiotic data analysis was conducted; to investigate the children’s decision making an optimal model of a metacognitive process for individuals served us. Our findings indicate that all the children’s knowledge objectification process included three stages: visual, contextual, and symbolic. In the visual stage, children focused on gathering data while demonstrating basic “STEAM” skills. In the contextual stage, they focused on ergotic gestures, planned how they would cover the area using strategies of symmetry and overlapping, and demonstrated engineering and mathematics skills. The symbolic stage was demonstrated by symbolic gestures, self-evaluation, self-feedback, and mathematical skills.

The findings indicate that numeracy and geometric intuition underlie kindergarten children’s and first graders’ perception of the term “cover maximal area” and that this can and should be developed by providing geometry-based optimization activities particularly in kindergarten both when teaching mathematics in general and for STEAM subjects in particular.