One of our goals in the Lower School math program is to expose students to a variety of ways to perform operations and to a variety of strategies for solving problems. Students learn and understand math (like other subjects!) in vastly different ways. Children should learn there is more than one way to perform any given operation. In order to develop computational fluency, they need to learn several different approaches to all of the operations- addition, subtraction, multiplication and division. A problem-solving strategy that works for one student and in one situation may be burdensome for another student and/or difficult to apply in another circumstance. Therefore, it is imperative that students discover a wide range of approaches and strategies so that ultimately they can use those that make the most sense for them and those that are the most efficient.
Over the course of the year, we will describe a number of these approaches and strategies in this column to help you have a better sense of what your students are actually doing in the classroom. We want you to understand the ways teachers are helping your students develop computational fluency.
When working with our youngest students on addition, one very common strategy is “doubling.” As its name implies, doubling helps students understand quickly how to double single digit and simple double digit numbers. More importantly, however, when a student can double easily, he or she can then use doubling to solve more complicated problems.
For example, at some point during first grade, a student may become very comfortable knowing that 7 + 7 = 14. Then that student will be able to use that doubles fact to solve many related equations: 7 + 8 = 7 + 7 + 1 which equals 15, 7 + 6 = 7 + 7 – 1 which equals 13, or even more complicated equations like 7 + 9, 8 + 9, etc. So, from the foundation of doubles, kids can learn “neighbors,” i.e., 5+6 and 6+7. From the foundation of doubles, kids understand all their 2 as a factor multiples, e.g., 2x2, 2x3, 2x4, 2x5, 2x6…. From the foundation of doubles, kids come to understand patterns that double and even patterns that half!
When a child can apply this doubling strategy, we know that he or she is developing number sense and computational competence. This student not only knows “the facts” but understands the relationships between the numbers well enough to build on and apply that knowledge.
At some point this year, ask your child to describe doubles to you! The description will allow you to see the “thinking” behind the learning involved when it comes to those “basic facts!”
If you have any questions about this or any strategy, please stop down in the math lab or contact us at email@example.com or firstname.lastname@example.org.
Merry and Raina