Number talks
• Instructional routine – 10 minutes
In a study of forty-four mathematicians’ computation
strategies, Ann Dowker (1992) found that “mathematicians
tended to use strategies involving the understanding of
arithmetical properties and relationships rather than
strategies involving the use of school-taught techniques”.
To these mathematicians, solving these problems “seemed to
involved an enjoyment of thinking about and playing with
numbers, rather than rote memorization”.
For all the mathematicians and all the problems, they only
used an algorithm 4% of the time. “Most mathematicians
used a wide variety of strategy types during the task and, if
retested, often used a different strategy for the same problem
on two occasions”.
Goals of Number Talks
• Helping children to make sense of quantity
and the mathematical relationships inherent
in arithmetic operations.
• Helping children to understand that there can
be many ways to solve a mathematics
problem.
• Helping children to learn to trust their own
reasoning; this builds intellectual autonomy.
Problems created by instrumental
instruction of algorithms for addition,
subtraction, multiplication, and
division:
• The focus is on individual digits, not on quantities
and relationships among the quantities.
• The central learning goal is to master a series of
steps rather than understanding the meaning and
use of the mathematical operation.
When recording, be sure not to
violate the equals sign!
e.g, 10 x 3 = 30 + 6 = 36
Planning the Number Talk
(20 minutes)
• Anticipate different methods students might
use for solving the problem.
• Plan how you will record student methods.
• Generate the kinds of questions you will need
to be prepared to ask to fully understand and
represent a student’s method.
• Think about what you might do if very few
strategies emerge from the class.