Fluency
3. Continue Fact Fluency
The following is from the 2016 Grade 5 Curriculum Framework (emphasis added):
"Mathematics instruction must develop students’ conceptual understanding, computational fluency, and problem-solving skills. The development of related conceptual understanding and computational skills should be balanced and intertwined, each supporting the other and reinforcing learning.
Computational fluency refers to having flexible, efficient, and accurate methods for computing. Students exhibit computational fluency when they demonstrate strategic thinking and flexibility in the computational methods they choose, understand, and can explain, and produce accurate answers efficiently.
The computational methods used by a student should be based on the mathematical ideas that the student understands, including the structure of the base-ten number system, number relationships, meaning of operations, and properties. Computational fluency with whole numbers is a goal of mathematics instruction in the elementary grades. Students should be fluent with the basic number combinations for addition and subtraction to 20 by the end of grade two and those for multiplication and division by the end of grade four. Students should be encouraged to use computational methods and tools that are appropriate for the context and purpose."
Real Talk
Many of us don't understand fact fluency. For most people, the ways in which we learned and practiced facts in elementary school led us to believe that fluency is all about speed. We completed timed tests, drilled flashcards, and for some, practiced with computer games, all for the purpose of being faster.
It's now time for teachers to understand that fluency is much more than automaticity. Being fluent, as the passage above describes, also means being both flexible and efficient.
Let's use 2 x 8 as an example to explore automaticity vs. flexibility and efficiency.
Student A has 1 strategy he uses when he sees a 2's fact: he counts up by twos. He sees 2x8 and counts in his head or on his fingers very quickly, "2, 4, 6, 8 , 10, 12, 14, 16". He can produce the answer 16 within 2 seconds, so his teacher counts him as fluent.
Student B has 2 strategies for solving 2's facts: she can count up by 2, and she can double. She sees 2x8, pauses for a moment to choose the doubling strategy, and thinks "8 + 8 = 16, so 2 x 8 = 16". She can also produce the answer within 2 seconds, so her teacher counts her as fluent.
Now both students are asked to solve 2 x 24.
Student A begins to count "2, 4, 6, 8, 10..." but realizes this is going to take too long. He reaches for a piece of paper to write down 24 x 2 and use the traditional algorithm.
Student B pauses, thinks about the doubling strategy, and thinks "What's 24 + 24? I know 20 + 20 is 40, and 4 + 4 is 8, so together that's 48. I know that 2 x 24 = 48."
This is why flexibility and efficiency matter! If you know more than one strategy for deriving a fact (flexibility), you can choose the best strategy for the problem at hand (efficiency). Together, these abilities demonstrate fluency.
2. It's very likely that some of your fifth graders aren't there YET. It may be tempting to draw from some of the traditional methods used to increase students' speed: timed tests, flashcards, writing out multiplication charts, or even Reflex Math. But it's important to realize that these address speed and never flexibility and efficiency. These methods also increase anxiety, erroneously teach kids that math is all about speed, and lead many students to believe "I'm not good at math". Don't go there!
So What Do We Do Instead?
Put simply: We teach multiple strategies, within contexts, and we give students authentic opportunities to practice choosing and using those strategies.
We also don't wait. Your projected pacing might have you starting multiplication on Day 1 of Week 7. But you should really start today. Start with number talks that invite students to see the strategies like doubles for x2 and doubles & double again for x4. Name the strategies as students use them and provide a few minutes of targeted strategy practice each day.
Resources
Check out the first 15 days of a multiplication fluency lessons created and implemented last year by Elicia Fleshman, with support from Tracy Proffitt. These lessons drew on data collected about students through Multiplication Running Records and game ideas presented in Math Fact Fluency.
Need more? Check out the resources below.
