What is Computational Fluency?

The NCTM Principle and Standards of School Mathematics (2000) defines computational fluency as having efficient, flexible and accurate methods for computing. The key thing to note is that it does not say compute using paper and pencil methods. Students need to be fluent in mental math, paper and pencil methods and using technology such as a calculator in computing answers to situations involving numbers (both whole numbers as well as fractions and decimals). In fact one often overlooked or underdeveloped aspect of computational fluency is not only being able to compute in all three ways but also knowing which method is best based on the given task. In addition, students must be able to determine if an exact answer or a close approximation (estimate) is sufficient.

Another key idea is that just being able to compute the correct answer of estimate is not enough either. Students must be able to compute accurately in all three methods AND know when to do what operation. In other words that must be able to solve problems that involve numbers.

What are the Main Messages of Principles and Standards Regarding Computation?

1. Computational fluency is an essential goal for school mathematics (p. 152).

2. The methods that a student uses to compute should be grounded in understanding (pp. 152-55).

3. Students should know the basic number combinations for addition and subtraction by the end of grade 2 and those for multiplication and division by the end of grade 4 (pp. 32, 84, and 153).

4. Students should be able to compute fluently with whole numbers by end of grade 5 (pp. 35, 152, and 155).

5. Students can achieve computational fluency using a variety of methods and should, in fact, be comfortable with more than one approach (p. 155).

6. Students should have opportunities to invent strategies for computing using their knowledge of place value, properties of numbers, and the operations (pp. 35 and 220).

7. Students should investigate conventional algorithms for computing with whole numbers (pp. 35 and 155).

8. Students should be encouraged to use computational methods and tools that are appropriate for the context and purpose, including mental computation, estimations, calculators, and paper and pencil (pp. 36, 145, and 154).

Another resource on this topic I would highly recommend is a monograph available through the National Council of Supervisors of Mathematics called “Future Basics: Developing Numerical Power.” There is a $10 fee for this monograph. You can order it at the following web site:

http://www.ncsmonline.org/NCSMPublications/publications.html

Jenni Clock, Marleen Boone, and Nancy Kiser prepared this statement for the Seattle Public Schools Math web site.

Research into the study of children’s mathematical thinking tells us there is a continuum of strategies through which students develop computational fluency with basic facts and multi-digit numbers in all four operations. For basic facts, there are three stages before recall or memorization, in each operation. If a student has memorized without the opportunity to develop through the continuum, and then forgets the fact, he or she will have no way to solve the problem. For computations with multi-digit numbers there are four stages before the student can use the traditional algorithm with understanding. Experience along the continuum enables the student to better determine the reasonableness of an answer. Students move along the continuum at individual rates. Often it is the difficulty of the problem that determines the strategies the student will use. (Carpenter, T., Fennema, E., Franke, M., Levi, L., Empson, S. (1999) Children’s Mathematics. Portsmouth, NH: Heinemann.)

As educators {and parents are the first educators} our job is to facilitate students’ movement along the continuum of computational fluency to in-depth mathematical understanding.