Adding it up- Chapter 5 and 6, Chinese base ten and language, make a 10, base-10 blocks have quanity, but chips not.

Chapter 5 THE MATHEMATICAL KNOWLEDGE CHILDREN BRING TO SCHOOL

Early research on children’s understanding of the mathematical basis for

counting focused on five principles their thinking must follow if their counting is to be mathematically useful

1. One-to-one: there must be a one-to-one relation between counting words and objects;

2. Stable order (of the counting words): these counting words must be recited in a consistent, reproducible order;

3. Cardinal: the last counting word spoken indicates how many objects are in the set as a whole (rather than being a property of a particular object in the set);

4. Abstraction: any kinds of objects can be collected together for purposes of a count; and

5. Order irrelevance (for the objects counted): objects can be counted in any sequence without altering the outcome. 

Chapter 6 DEVELOPING PROFICIENCY WITH WHOLE NUMBERS