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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.
