The National Direction Computational Fluency Lou Maynus, Mathematics Coordinator WVDE

What is computational fluency? NCTM defines computational fluency as having efficient, flexible and accurate methods for computing. 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 . In addition, students must be able to determine if an exact answer or a close approximation (estimate) is sufficient.

Why is computational fluency important in Mathematics? All human beings have a limited information-processing capacity. That is, an individual simply cannot attend to too many things at once. Once procedures are automatic, they require little conscious effort to use, which, in turn, frees attention and working memory resources for use on other more important features of the problem.

National Math Panel Report Critical Foundations for Algebra To prepare students for Algebra, the curriculum must simultaneously develop conceptual understanding, computational fluency, and problem-solving skills. These three aspects of learning are mutually reinforcing and should not be seen as competing for class time.

The reasons for differences in the computational fluency of children in the United States and peers in countries with higher mathematics achievement are multifaceted. They include quantity and quality of practice, emphases within curricula, and parental involvement in mathematics learning. NMP

“Our classrooms are filled with students and adults who think of mathematics as rules and procedures to memorize without understanding the numerical relationships that provide the foundation for these rules.” - Number Talks

Procedures without understanding?

Procedures without understanding?

Students must learn to compute with accuracy, efficiency, and flexibility.

Number Talks A five to fifteen minute classroom conversation around purposefully crafted computation problems that are solved mentally By sharing and defending their solutions and strategies, students are provided with opportunities to collectively reason about numbers while building connections to key conceptual ideas in mathematics.

Classroom Link: Subtraction: 70-34 Classroom Clip Classroom Link: Subtraction: 70-34 Pg. 6 Number Talks Book 4 Questions

New Common Core Eight Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

Paragraph Shrinking Pairs read assigned mathematical practice. Work together to summarize the “Practice” into 25 words or less. Prepare to share with the group.

Third Grade Case Study Pgs 6-9 Read the case study, think about the student behaviors in this math class. What skills, proficiencies and mathematical practices are being developed through this number talk? 3 Documents Needed: - Note taking sheet - Venn Diagram - Mathematical Practices

Debriefing the Study Implications for Instructional Leaders I NOTICE I WONDER

Contact Information Lou Maynus, WVDE Office of Instruction lmaynus@access.k12.wv