Case 3

Math Errors as a basis for Instruction

What S Doesn't Do

Make the Connection between mathematical procedures and their meaning

Says .35 is more than 10 and less than 100

Can't alter a drawing of 1/2 to show 2/4
But can add 1/4 + 1/4 to get 1/2

Can draw separate pictures of 1/3 and of 2/3
Can add 1/3 + 2/3 = 3/3
Can't draw a picture adding 1/3 and 2/3

What S Does Do

Conceptualize Difficult and Novel Problems

Problem
What time will it be 6 1/2 hours after 6:45
Solution
6:45
+6:30

Adds 45 and 30 to get 75. Says, You canıt go over 60 minutes so youıd have to carry with the 75.
STOPS HERE

Start with the Right Idea but give up easily
Error Based Diagnosis
Strong, above average conceptual abilities in math
Disconnect between concept and procedure
Poor ability independently to persist through confusions and frustrations
Error Based Individualized Instruction

Use interest and skill in drawing to represent mathematical relationships/operations/problems
Make his own materials to demonstrate equivalent fractions
Use materials to solve equivalent fractions problems
Demonstrate that creating equivalent fractions is the same as multiplying by 1
Show the relationship between all operations and the meaning that they represent
Experiment with materials as a way of working through confusion and frustration independently
Withhold explicit algorithmic steps until the fundamental operation is understood