Spatial relationship understanding is one key skill needed in an elementary math program.

Math education in the United States has received new direction in order to achieve the kinds of success seen in countries with higher achievement in mathematics performance. Two key components -- number work and spacial relationship study -- mark this shift and are the recommended goals for successful math education in the elementary school years.

### Standards and Focal Points

The Common Core State Standards Initiative gives direction on mathematical skills for all grades K-12. The elementary school years require concentrated emphasis on work with number fluency and geometric concepts. The National Council for Teachers of Mathematics also calls for specific focal points for instruction that lay a strong foundation for mastery throughout the school years. Focus on fewer skills, but with deeper exploration, is central to both of these recommended approaches.

### Number Operations

Emphasis on numbers and number sense are found across all grade levels in the Common Core. The ability to work comfortably composing and decomposing numbers in a multitude of views should be the foremost goal of a math education program. Children need to work with numbers in a variety of ways -- 36 is 3 tens and 6 ones or double 15 plus triple 2, for instance. Having fluency in computation is also central to a deep understanding of math. Knowing the algorithms to use in operations is key, however understanding why they work when manipulating numbers is critical to success in working with basic arithmetic. The use of a calculator should be a part of computational work in the elementary grades, as well as the knowledge to understand why the algorithms work as they do.

### Geometry and Spatial Awareness

Building a strong understanding of how to describe the physical world is another critical skill underpinning the Common Core math standards. Using shapes and knowing their properties help children develop a strong sense of space and assist them in knowing how to solve real-world problems such as calculating the area of a room for carpeting or a yard for grass. Drawing on paper and with computer programs should both be explored by students in the elementary grades when minds are facile, instead of postponed into the high school years.

### Measurement

Because students need to make sense of quantities and know the relationships in order to solve real-world problems, a strong sense of size and comparison skills between units of measurement is critical to the development of mathematical reasoning. Students proficient in math can work flexibly with amounts and can make sound decisions based on knowing the properties of quantities. Number skills and work with dimensional objects allow children to approach problems such as calculating the volume of a container and estimating how much it will hold.