- PK.1 Children begin to develop processes and strategies for solving mathematical problems.
- PK.2 Children begin to develop skills of comparing and classifying objects, relationships and events in their environment.
- PK.3 Children begin to develop the ability to seek out and to recognize patterns in everyday life.
- PK.4 Children begin to develop skills of sorting and organizing information and using information to make predictions and solve new problems.
- PK.5 Children explore and discover simple ways to measure.
- PK.6 Children can translate a problem or activity into a new form (e.g., a picture, diagram, model, symbol, or words) by applying emerging skills in representing, discussing, reading, writing, and listening.
- PK.7 Children begin to develop an understanding of numbers and explore simple mathematical processes (operations) using concrete materials.
- PK.8 Children build their visual thinking skills through explorations with shape and the spaces in their classrooms and neighborhoods.
Children vary considerably in how good they are at receiving and sending precise sets of directions. With appropriate instruction and practice, children can improve in this area. When the instructions and expected actions are related to math, then improvements are an indication of an increasing level of math maturity.
Human natural language-learning capabilities are so great that if a child is raised in a bilingual or a trilingual oral environment, the child will become bilingual or trilingual in oral communication. Moreover, think about children raised in a musical home environment. Music is a type of language, and music is innate to humans. Children raised in a musical home environment will learn a great deal of music before they reach school age. Now, consider mathematics. Math can be considered as a type of language. It is a discipline specific language developed by humans. Based on the research of Devlin (2000) and others, we know that a child with an intact brain has the capacity to learn a great deal of mathematics. The extent to which this learning occurs depends on the quality and extent of the informal and formalmath education the child receives.The mathematical richness of the environments that children are raised in vary considerably—probably much more than the linguistic environments. In any case, for most children, the mathematical richness is poor relative to the linguistic environment. Based on this line of reasoning, the premise of this book is that math education can be substantially improved by increasing the math richness of the life of a child both at the preschool level and continuing on through the informal and formal education as the child grows toward adulthood.