Math Minutes
2021/22 Quarter 3
What does being "fluent in mathematics" really mean?
Fluency is more than quickly recalling facts and smoothly performing algorithms.
Fluency is a creative process in which students are able to choose a strategy that makes sense with the numbers at hand - from basic facts all the way through fractions, decimals and even algebra.
Procedural fluency includes computational fluency (computation with the four operations) and basic fact fluency.
Procedural fluency refers to knowledge of procedures, knowledge of when and how to use them appropriately, and skill in performing them flexibly, accurately, and efficiently. This means moving beyond computation and procedures like comparing fractions, simplifying expressions and solving proportions.
There are three major components to procedural fluency:
- Efficiency: Solving a procedure in a reasonable amount of time by selecting an appropriate strategy and readily implementing that strategy.
- Flexibility: Knowing multiple procedures and applying or adapting strategies to solve procedural problems (Baroody & Dowker, 2003; Star, 2005)
- Accuracy: Correctly solving a procedure
See the image below for a deeper explanation of the three interrelated components of procedural fluency.
Source: J. Bay-Williams & J.J. SanGiovanni, Figuring Out Fluency in Mathematics Teaching and Learning: Moving Beyond Facts and Memorization, Grades K-8, Copyright 2021 by Corwin. Adapted with permission from D. Spangler & J. Wanko (Eds.), Enhancing Classroom Practice with Research behind Principles to Actions, copyright 2017, by the National Council of Teachers of Mathematics. All rights reserved.
What's New in Our Heartland AEA Library?
If you want to dig deeper, two companion books are also available. Figuring Out Fluency: Addition and Subtraction with Whole Numbers and Figuring Out Fluency: Multiplication and Division with Whole Numbers include additional activities, fluency routines and games to build procedural fluency.
Now Available at Creative Services: Concept Circles
A concept circle is a thinking routine that allows students to build conceptual understanding through making connections to a concept and discussing ideas.This rich discussion promotes the development of a deeper understanding of the mathematical concepts being presented.
You will see in the examples below that the concept circle is an organizer which is divided into 8 sections. Each of these sections hold words or symbols that are connected by a common mathematical relationship. On the outside students can include manipulatives or visual models to represent the concept in the center. This offers multiple representations of mathematical topics and offers rich discussion with the use of questioning.
Learn more in this video.
You can purchase directly from Creative Services.
Here is a direct link to Heartland AEA's Creative Services website.
I Have, You Need
“I Have, You Need” is a quick routine to help kids construct numerical relationships to 1, 10, 100, and 1,000.
Select an anchor number. (ie: 100)
Say, “For a total of 100, I have 75. You need…”
Students respond with the amount needed to get to a total of 100.
This can be done across grade levels within various strands and contexts. Examples of ways to play:
Coin Combinations (Make a dime or quarter)
Fractions and decimals (Make a whole)
Geometry (Consider angles and Make a benchmark to 90, 180, 360)
Learn more and watch an example of "I Have, You Need" in action here.
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