My PhD research (Carruthers, 2022) focused on pedagogies that supported children's mathematics and their graphics. The findings revealed that the teachers who moved from a constructivist adult-led approach to a socio-cultural child-led approach to mathematics teaching were able to, not only uncover children's mathematics, but this led to opportunities for children to use their mathematical graphics. When the teaching was open and responsive to children's ideas and questions then it changed the teachers' understanding of mathematics education. The teachers evidenced the children's world of mathematics. As one of the teachers said “you have to understand the children's meaning rather than the child understanding the teacher's meaning. For me this is very powerful" (Carruthers, 2022).