Constructing Counting and Arithmetic Learning Trajectories for Kindergarteners: A Preliminary Investigation in Taiwan

Mathematics learning trajectories (LTs) for students above elementary school level are widely investigated. Recently, LTs for kindergarteners have also attracted attention, but in those studies the LTs were based on Western samples, and it is unclear whether they also involved culture and gender differences. Therefore, the purposes of this study were twofold: (1) construct a counting and arithmetic LT based on an Eastern sample and (2) show its similarities and differences by gender. The constructed LT contains 13 hypothesized levels of mathematical concepts according to previous research, and 59 kindergarteners (26 boys and 33 girls) participated in this study and completed a counting and arithmetic test to examine empirically the theoretical LT. The results showed that empirically, there were eight and nine conceptual levels for boys and girls, respectively, and boys and girls mastered concepts in a similar order (basic arithmetic→basic counting→advanced counting→mediocre arithmetic→advanced arithmetic), with the first part differing from the hypothesized LT. Within this developmental progression, girls showed a different path from advanced counting to mediocre arithmetic. The findings show gender and culture differences for the LTs for kindergarteners, which contradicts most previous research based on Western samples.