An Inventory of Mathematical Thinking Done by Incoming First-Grade Children

The kind of mathematical thinking that children entering first grade are capable of, if they have manipulative materials to support their thinking, is of interest to those who design and sequence learning activities for this age group. This study was made to learn how many children could do the counting, grouping, joining, separating, and distributing of objects that represent problem situations requiring the arithmetic operations of adding, subtracting, multiplying, and dividing small numbers. The situations were presented orally, and the children were not required to interpret written symbols or to write symbols. The conclusion was that most children of this age group can manipulate materials and give correct oral responses to problems involving all four operations.