Promoting problem solving, critical thinking, creativity, and oral communication through math

Kelly Gallagher, Consultant for School Improvement/MathFor most of us growing up, learning math was about solving problems the “right” way based on the steps our teacher taught. A lot has changed in the teaching of math, including support for encouraging students to find many ways of solving problems using a strategy known as Number Talks.

Number Talks involves the use of mental math strategies to promote flexible thinking, visualization, and problem solving. It can be delivered as part of the math block or in addition to learning to support or extend mathematical standards at any level of education.

Consider the problem 18 x 5. Some of you immediately reach for the nearest pencil, ready to scratch out an algorithm because that’s what you’re accustomed to doing. We trust that process because it’s been there for us so many times. However, flexible thinking and more efficient problem solving may suggest ways to solve this problem mentally in ways you’ve never imagined.

You may think 10 x 5 is 50 and 8 x 5 is 40. 50 + 40 = 90

You may also break 18 into parts, knowing that 9 and 9 makes 18. Therefore, knowing that 9 x 5 = 45 and 9 x 5 = 45. 45 + 45 = 90

You may think about repeated addition by doing 18 + 18 + 18 + 18 + 18 = 90 in your head.

Another common way to consider this problem efficiently is to take 18 x10 and divide by 2. Students using this strategy know that 10 is 5 doubled, therefore needing to divide the final product in half to get the correct answer. 18 x 10 = 180 and 180 / 2 = 90

Some use what we call a doubling and halving strategy to change 18 x 5. Students that solve this way recognize that half of 18 (9) and twice 5 (10) forms a new equation of 10 x 9, which also equals 90.

There are other ways students may approach this equation. The key to the Number Talks is that the teacher honors all the ways! When students hear their peers solve in different ways, it promotes growth, academically and socially. Oftentimes students who are quick to recall and repeat their math facts, lack conceptual understanding and/or struggle to articulate strategies. On the contrary, students that are using flexible strategies may take time to solve as they strengthen their fluency and mental math skills. The goal is to move all students forward regardless of their entry point. Number Talks builds effective, efficient, and collaborative problem solvers who honor multiple viewpoints and approaches.

The Number Talks routine is intended to be a short portion of the day, lasting only five to 15 minutes.

As the most desirable employability skills shift from reading, writing and computation, a higher emphasis is being placed on interpersonal skills, problem solving, critical thinking, creativity, and oral communication. The Number Talks instructional routine is designed to promote complex thinkers who are also creative problem solvers – future ready skills that all students will benefit from as they enter the workforce!

Kelly Gallagher is a School Improvement and Math Consultant for Central Rivers Area Education Agency. Kelly can be reached at Central Rivers Area Education Agency, based in Cedar Falls, provides innovative leadership and support for public and accredited non-public school districts in an 18-county area of Iowa. Learn more at