Children’s mathematical representations on the Blank Page: a study of graphic marks, their evolution and their combinations

This study examines the graphic marks used by kindergarten children (ages 5-6) to communicate mathematical ideas through the Blank Page: an open-ended pedagogical and research tool that invites written mathematical expression. The research involved 103 students from two schools near Barcelona and analyzed 710 representations collected during eight number decomposition workshops. Qualitative analysis identified five types of graphic marks: Pictographic, Mathematical Symbolic: Isolated Numbers, Mathematical Symbolic: Number Relationships, Mathematical Symbolic: Equations and Written Verbal. Results show a wide variety of representations and a gradual shift from pictographic to more symbolic-mathematical marks. Children also increasingly combined multiple types of marks, indicating greater representational complexity. Although workshop tasks influenced students’ choices, this relationship was not always direct. Children often incorporated symbols and numerical relationships beyond those explicitly presented , suggesting transfer of prior knowledge and growing representational autonomy. These findings support the value of open representational spaces in early childhood mathematics education.