Figuring Out Fluency in Mathematics Teaching and Learning, Grades K-8 by Jennifer M. Bay-Williams & John J. SanGiovanni

Author:Jennifer M. Bay-Williams & John J. SanGiovanni [Jennifer M. Bay-Williams & John J. SanGiovanni]
Language: eng
Format: epub
Publisher: SAGE Publications
Published: 2022-11-21T09:31:26.585378+00:00

Chapter 5 Automaticity Beyond the Basic Facts

Procedural fluency has been traditionally viewed as speed of computation and quick recall. And while we know these are not fluency, there is value in effortless recall of concepts, useful strategies, and facts. Consider these three examples:

A second grader is adding $0.75 + $0.19 + $0.25 + $0.05. She rearranges the addends without thinking about it because she “just knows” that 75 and 25 equal 100. Adding 19 and 5 is easy for her, too, so she finds the sum to be $1.24. Her classmate adds each in the order and spends time regrouping and counting. Another rearranges because she sees 5 and 75 but is then left with another problem to think about.

A fifth grader solves 3.86 + 2.28 by seeing 0.86 as 0.14 away from 1.00. She knows that 14 is half of 28, so 0.14 is half of 0.28. She rethinks the problem as 4.00 + 2.14. One classmate breaks the numbers apart by place value and recomposes. Another uses an algorithm. Both make a place value error.

A seventh grader is solving proportions. He comes across . He knows these are equivalent. He then “sees” the 7s in 42 and 35, so becomes and p is 5. His tablemate cross-multiplies and divides. He arrives at the same solution but takes significantly longer, as 6 × 35 and 210 ÷ 42 take some time to complete.

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