In the paper, I describe how my commitment to mathematics and to the teaching of mathematics evolved starting with my undergraduate years and proceeding on throughout my tenure as a professor of mathematics education. As part of this evolution, I explain how my concept of research that I developed as a graduate student changed to include mathematics teaching in teaching experiments. In discussing two events that drove the change, I explain why I changed from applying Piaget’s cognitive development theory to constructing my own explanations of children’s mathematics that I learned in teaching experiments. I then discuss using retrospective conceptual analysis of video records of the teaching experiments as the method of constructing explanations of children’s mathematics that I call the mathematics of children. I then present and discuss five mathematics of children concepts in the context of the teaching experiments from which they were constructed and argue that if school mathematics were based on the mathematics of children, school mathematics would be equitable if equity refers to fairness and justice. I close the paper by furthering the argument that the mathematics of children is a legitimate mathematics.