Building Fluency

Fluency

• skill in carrying out procedures flexibly, accurately, efficiently, and appropriately
• does not necessarily emphasize time limit, though there are reasonable limits on how long computation should take
• based on deep understanding of quantity and number
• notice relationships and use strategies

Deep Understanding

• more than "how to get the answer"
• supports students' ability to access concepts from a number of perspectives
• students see math as more than a set of mnemonics or discrete procedures

Deep Understanding

• students demonstrate deep conceptual understanding of foundational mathematics by applying them to new situations, writing and speaking about their understanding

Memorization

• rapid recall of arithmetic facts or mathematical procedures
• often confused with fluency
• does not reflect understanding

Automaticity

• being able to freely make the use of knowledge in context
• deep understanding and transfer of knowledge among concepts

Number Sense

• students consider the context of the problem, look at the numbers in a problem, make a decision about which strategy would be most efficient
• not a deep understanding of a single strategy
• the ability to think flexibly among a variety of strategies in context

Fluent students...

• flexibly use a combination of deep understanding, number sense, and automaticity
• are fluent in the necessary baseline functions in mathematics allowing them to spend their thinking and processing time unpacking problems and making meaning from them

Fluent Students...

• find solutions through a number of different paths

Phases of Basic Fact Mastery

• Modeling and/or counting
• Deriving answers using reasoning strategies based on known facts
• Mastery (efficient production of answers)

"Traditional approaches to learning (facts) attempt to move students from phase 1 directly to phase 3...

This approach is ineffective- many students do not retain what they memorized in the long term,...

moving to grade 4 and beyond still not knowing their facts.

Even if students remember facts, they are unlikely to be fluent as (previously defined),...

as they will not have learned to flexibly apply strategies to find the answer to a (problem)."

Assessing Basic Fact Fluency

• interviews
• observations
• journaling

Interview

Interview

Interview

Untitled Slide

References

• Friel, Goodson-Epsy, Gleason, and Gunter (2008) "A Problem is Something You Don't Want to Have..."
• Kling and Bay-Williams (2015) Teaching Children Mathematics "Three Steps to Mastering Multiplication Facts"
• Boaler (2012) Education Week "Timed Tests and the Development of Math Anxiety"