In Principles and Standards for School Mathematics (NCTM, 2000), the National Council of Teachers of Mathematics expressed the importance of the development of strong number skills for K-5 students.
“Understanding number and operations, developing number sense, and gaining fluency in arithmetic computations form the core of mathematics education in the elementary grades.”
Principles and Standards for School Mathematics, 2000, NCTM
Our curricula focus on a variety of skills that contribute to our students development of number sense and number skills. These skills help our students understand how numbers work and allow them to think flexibly about numbers as they perform computations and solve problems. These skills include:
- Counting
- Place value
- Composing and decomposing numbers
- Patterns and properties
- Understanding how operations work
- Understanding and fluency with basic math facts
- Understanding and fluency with multidigit computations, fractions, decimals
These skills are critical to the development of number sense. The listed skills don’t develop at one grade level, but are built on progressions and develop throughout the elementary years. Attending to these progressions as we teach math skills allows our students to build on what they know and to continue to explore increasingly complex skills and concepts using these foundational understandings.
“Students development of number sense should move through increasingly sophisticated levels of constructing ideas and skills, of recognizing and using relationships to solve problems, and of connecting new learning with old.”
Principles and Standards for School Mathematics, 2000, NCTM
Along with attention to progressions, students benefit from exploring number skills with models and lots of math talk. Lessons and practice tasks that provide opportunities for students to model number concepts and discuss their understandings allow them to build deeper understanding.
Students develop a deep understanding of numbers when we…
…focus on specific content (critical number and operation concepts).
…use instructional strategies that allow students to visualize, discuss and reflect.
…make connections to prior math learning.
…offer ongoing, targeted practice tasks that are also built on progressions and employ models and math talk.
Finding practice tasks that embrace these ideas has been difficult for K-5 teachers. I am honored to have had the opportunity to explore the development of targeted, interactive, and engaging practice tasks that support the development of K-5 numeracy skills. In collaboration with hand2Mind, I developed Navigating Numeracy Learning Progression Centers. Each grade-specific center kit contains materials and teacher directions for 15 critical numeracy skills with each skill having three distinct centers to provide practice at varied levels in the progression of the skill. The center tasks are interactive with students participating with partners to promote talk about the math concepts. The centers are hands-on, providing opportunities for students to explore the number concepts with concrete, pictorial, and abstract representations. The kits allow students to practice skills with attention to learning progressions. The centers meet students where they are and provide opportunities for their success.
To see more about the development of Navigating Numeracy:
