What are the advantages and disadvantages of number line and discrete object models for teaching addition and subtraction of integers? What merit might there be in a pattern-based approach? Why is it...

What are the advantages and disadvantages of number line and discrete object models for teaching addition and subtraction of integers? What merit might there be in a pattern-based approach? Why is it important for learners to develop meaningful methods for working with addition and subtraction? What are the dangers of learning rules and algorithms without understanding?