In Chapter 8 of Van De Walle, Karp and Bay-William (2010), I agree with "Children come to school with many ideas about number.  These ideas should be built upon as we work with children and help them develop new relationships".  However in many preschool setting, this is not the case.  Teachers usually have to rush from one topics/concept to another topic/concept in order to fulfill curriculum requirement.  Concepts and more concepts are introduced to children without much focus and assessment of their understanding of the concepts before moving on.  Children are not given much practice to polish their skills and to develop new relationship on the concepts learned.  Concepts such as part-part-whole relationships, patternset set recognition are rarely given the due recognition or focus required.

Some of the concepts that are in place in most preschool are :
early counting, including addtion and subtraction,  numeral writing and recognition, counting forward and backward, concept of more/less and same.

Concept of anchoring numbers to 5 and 10 is not a common topic found in most preschool maths curriculum, though.

In my preschool, I have just taught my K2 children the use of Doubles.  I found that it is a good strategy to teach basic addition facts.  Although I have now move on to other maths concept, I will periodically at the beginning of my lesson conduct oral practices on doubling facts with my children.  They seemed to be enjoying these oral practices and thrives on the fact that they are getting very good at their doubling skill.

In Chapter 8 of Van De Walle, Karp and Bay-William (2010), I agree with "Children come to school with many ideas about number.  These ideas should be built upon as we work with children and help them develop new relationships".  However in many preschool setting, this is not the case.  Teachers usually have to rush from one topics/concept to another topic/concept in order to fulfill curriculum requirement.  Concepts and more concepts are introduced to children without much focus and assessment of their understanding of the concepts before moving on.  Children are not given much practice to polish their skills and to develop new relationship on the concepts learned.  Concepts such as part-part-whole relationships, patternset set recognition are rarely given the due recognition or focus required.

Some of the concepts that are in place in most preschool are :
early counting, including addtion and subtraction,  numeral writing and recognition, counting forward and backward, concept of more/less and same.

Concept of anchoring numbers to 5 and 10 is not a common topic found in most preschool maths curriculum, though.

In my preschool, I have just taught my K2 children the use of Doubles.  I found that it is a good strategy to teach basic addition facts.  Although I have now move on to other maths concept, I will periodically at the beginning of my lesson conduct oral practices on doubling facts with my children.  They seemed to be enjoying these oral practices and thrives on the fact that they are getting very good at their doubling skill.