Term
What are traditional algorithms? 

Definition
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. 


Term
What are three types of computational strategies? 

Definition
 Direct modeling  Student invented strategies  Traditional algorithms 


Term

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


Term
What is studentinvented strategies? 

Definition
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. 


Term
How does invented strategies contrast with traditional algorithms? 

Definition
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. 


Term
What are the benefits of student invented strategies? 

Definition
 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. 


Term
How do you develop studentinvented strategies? 

Definition
The teacher must FACILITATE the development of strategies. 


Term
What does a traditional algorithm require an understanding of? 

Definition
1) Regrouping 2) Trade  Younger students 


Term
How can you help a student with the subtration algorithm? 

Definition
Use manipulatives  Ex. Ten sticks activity 


Term
What are studentinvented strategies for multiplication? 

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


Term
What can we think of division? 

Definition
We can think of division as sharing or repeated subtraction. 


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

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

