What are traditional algorithms? 

They are: 1) Clever strategies for computing 2) Transitions to adjacent position (regrouping) 3) Based on performing the operation on one place value at a time. 

What are three types of computational strategies? 

– Direct modeling – Student invented strategies – Traditional algorithms 


It is the use of manipulatives or drawing, along with counting, to represent directly the meaning of an operation. 

What is studentinvented strategies? 

It is any strategy other than traditional algorithm or does not involve the use of physical materials or counting by ones is an invented strategy. 

How does invented strategies contrast with traditional algorithms? 

1)Invented strategies are number orientated rather than digit oriented. 2)Invented strategies start with the largest parts of numbers those represented by the leftmost digits. 3)Invented strategies tend to change with the numbers involved in order to make the computation easier. 

What are the benefits of student invented strategies? 

– Students make fewer mistakes. – Less reteaching is required. – Students develop number sense. – Invented strategies are the basis for mental computation and estimation. – Flexible methods are often faster than traditional algorithms. – Students who invent their own strategy are involved in the process of making sense of math. 

How do you develop studentinvented strategies? 

The teacher must FACILITATE the development of strategies. 

What does a traditional algorithm require an understanding of? 

1) Regrouping 2) Trade – Younger students 

How can you help a student with the subtration algorithm? 

Use manipulatives – Ex. Ten sticks activity 

What are studentinvented strategies for multiplication? 

Ability to break numbers apart in flexible ways is even more important for multiplication. 

What can we think of division? 

We can think of division as sharing or repeated subtraction. 

Why should I remember before teaching the algorithm for ANY operation? 

Students need to have a CONCRETE understanding of WHY and HOW they work. 
