KSM2: Essential early numeracy concepts and their development, and typical misconceptions in mathematical reasoning held by younger children
Evidence 1: VELI Workshop
Description: This training focused on building math literacy within the preschool classroom.
Analysis: In this workshop we discussed numeracy concepts including counting and cardinality, operations and algebraic thinking, geometry, and measurement and data. This discussion included development of these numeracy concepts for children ages birth to five. Most adults often think that mathematics is an abstract discipline involving complex formulas and calculations, but the foundations of math are grounded in concrete experience such as the exploration of objects and gradual understanding of their properties and relationships.
Evidence 2: Mother Goose Cares About Math and Science
Description: "Mother Goose Cares about Math and Science" is an integrated curriculum of science process skills and standards-based mathematics concepts for preschool children. The course increases science and math literacy and the ability to incorporate NCTM standards, and science process skills, into daily interactions with children.
Analysis: During this workshop we spent some time discussing development of young children, and how Piaget's theory of cognitive development can affect mathematical reasoning. Young children rely heavily upon their perceptions of the world around them. Because of this, young children might think that if objects are rearranged or changed in form that their amount has also been changed. Reliance upon the observable rather than the internal understanding that materials do not change unless something is added or taken away is a characteristic of children in the preoperational period. As children explore and manipulate materials, they gradually move to the concrete operational period.
Evidence 3: More Than Counting
Hieronymus, Brenda and Sally Moomaw (1995). More Than Counting: Math Activities for Young Thinkers. St. Paul, Minnesota:Redleaf Press.
Description: This book provides direction for a math curriculum and instructions for improving the math experiences of young children. There are many games and activities that promote facilitating children's construction of mathematical knowledge.
Analysis: This resource again describes Piaget's theory of cognitive development as mentioned above. This resource describes the developmental stages of quantification that preschool and Kindergarten aged children progress through including global, one-to-one correspondence and counting. As children move through these stages, mistakes will be made. Quantification mistakes are developmentally appropriate, and can be made by individual children over a prolonged period of time as they expand and refine their thinking skills.
