Previous research suggests that the Approximate Number System (ANS) allows people to approximate the cardinality of a set. This ability to discern numerical quantities may explain how meaning becomes associated with number symbols. However, recently it has been argued that ANS representations are not directly numerical, but rather are formed by…

Parents are frequently advised to use number books to help their children learn the meaning of number words and symbols. How should these resources be designed to best support learning? Previous research has shown that number books typically include multiple concrete representations of number. However, a large body of mathematics education…

A sophisticated and flexible understanding of the equals sign (=) is important for arithmetic competence and for learning further mathematics, particularly algebra. Research has identified two common conceptions held by children: the equals sign as an operator and the equals sign as signaling the same value on both sides of the equation. We argue…

A cumulative body of research has shown that children typically shift from an "operational" to a "relational" conception of the equals sign as they move through schooling. Jones (2008) argued that a truly relational conception of the equals sign comprises a "substitutive" component and a "sameness"…