Defining Fluency
What is the definition of procedural fluency according to the Common Core State Standards for Mathematics (CCSSM)?
“skill in carrying out procedures flexibly, accurately, efficiently, and appropriately”
What negative impact can frequent timed testing have on students' progress toward knowing facts from memory?
Children who were frequently exposed to timed testing demonstrated lower progress toward knowing facts from memory than their counterparts who had not experienced as many timed tests.
What are some formative assessment strategies mentioned for assessing basic fact fluency?
Interviews
Observations
Journaling
Quizzes
What is meant by "foundational facts" in the context of assessing basic fact fluency?
Foundational facts are so named because they can be used to generate all the other facts using a strategy.
What Stanford based professor is famous for her research on fact fluency?
Dr. Jo Boaler
Name the four tenets of fluency that must be addressed in assessments of basic fact fluency.
flexibility
appropriate strategy use
efficiency
accuracy
Which students are affected by math anxiety during timed tests?
Any and all. High achieving, struggling, ones with sophisticated strategies
How can interviews be used effectively as a formative assessment tool?
interview as a quick way to get at all four categories of fluency (as well as to see if a student just knows the fact). Accuracy is assessed as soon as the student responds, and efficiency is observed on the basis of how long it takes a student to solve the fact. Flexibility and appropriate strategy selection are addressed by such follow-up prompts as, “How did you figure it out?” or “How could you use this strategy to solve this fact?” Codes, such as those suggested in Protocol C, can facilitate recording during an interview (see fig. 1).
Describe an effective way to implement quizzes that focus on fluency rather than speed.
students are recognizing the commutativity of addition for one-more-than facts
students are recognizing the commutativity of addition for one-more-than facts.
“just know” foundational facts.
Studies found that people who used ___________ rather than just memorizing did better in different situations.
Strategies like drawing or visualizing
How does Baroody define basic fact fluency?
“the efficient, appropriate, and flexible application of single-digit calculation skills and . . . an essential aspect of mathematical proficiency”
Whose evidence suggests that timed tests may negatively influence efficiency and accuracy in mathematics?
Jo Boaler's, Ramirez and colleagues, Henry and Brown
Explain how observations can provide valuable insights into students' fact fluency.
Observation is a natural part of teaching, and recognizing which strategies students know can supply valuable insights to help support students as they learn new strategies and tackle unknown facts
How can writing prompts be used to assess students' strategy selection in basic fact fluency?
Children at any grade level can find ways to incorporate pictures, words, and numbers to communicate their strategies
Carefully review the responses, considering what they illustrate about the strategies used by the children
Math facts are held in WHAT part of the brain?
Working memory
According to recent standards, what are the expectations for students regarding summing single-digit numbers?
the first is to fluently add and subtract (or multiply and divide), and the second is to know from memory all sums (products) of two one-digit numbers
Why do many educators still rely on timed tests despite their limitations?
First, fluency is interpreted as synonymous with speed. We have already addressed that fluency is more comprehensive than speed. Second, some feel that timed tests prepare children for highstakes tests
What role does journaling play in assessing students' understanding of strategies?
Writing provides an excellent opportunity to assess flexibility and understanding of strategy selection and application.
What benefits does self-assessment provide for students in their learning of basic facts?
self-assessment practice encourages children to instinctively apply effective strategies for challenging facts they encounter
When the brain is stressed about time. . . what happens to the working memory part of the brain?
It becomes blocked.
Which grade levels have fluency expectations for addition/subtraction basic facts and which have multiplication/division basic facts?
add/subtract: k-2
Mult/divide: 3
Discuss the psychological implications of using timed tests in mathematics education.
Math anxiety
Lower progress
Reluctance to use more sophisticated strategies
How can quizzes be adapted to assess students' efficiency while avoiding the pitfalls of timed testing?
Choose one of the problems above and write about how you solved it.
Tell which helper fact you used the most on this quiz.
Circle facts you “just knew.” Highlight those for which you used a strategy.
Circle facts you are sure about. Draw a square around facts that took you longer to solve.
Discuss how assessments can be aligned with CCSSM expectations for basic fact fluency.
As the NCTM Assessment Principle states, “Assessment should support the learning of important mathematics and furnish useful information to both teachers and students”
As the NCTM Assessment Principle states, “Assessment should support the learning of important mathematics and furnish useful information to both teachers and students”
self-assessment practice encourages children to instinctively apply effective strategies for challenging facts they encounter
Jo Boaler says that speed is not important, but what IS important is thinking _________ and ____________ about maths.
Slowly and deeply