) Numeration Systems and Number Theory -- Number theory is a basis for all areas of mathematics. Number theory and sense are precludes to computation, to estimate, and to have an understanding of the ways numbers are represented and interrelated. Fluency of also understanding the way positive and negative numbers can be visually represented on a line, or how numerical values interrelate, are essential prior to moving toward higher level concepts (Kane, 2002).

Algebraic Thinking and Problem Solving -- Rather than viewing the subject of algebra as certain sets of problems, the appropriate way to introduce it into elementary levels is as the relationship among quantities, the use of symbols, the modeling of phenomena, and the study of change. Students should be able to understand patterns, relations, and functions and how numbers may be represented in different ways. Algebraic thinking is on par with the analysis of textual materials -- the what if, the why, and the what might be. Using these concepts, as early as possible, encourages transformative thinking and the ability to apply "what if" strategies at an earlier age (Blanton, 2008).

Rational Numbers and Applications -- The basic understanding of interrelationships of numbers has already been established. Students however must understand that there are multiple models to understand place values, content, and computations. Divisions of number both whole and decimal/percentage and the use of rations and proportions are also necessary skills. In order to build on even most basic concepts of economics, other sciences (chemistry, biology, ecology, etc.) the relationships between numbers and integers is required, as is the ability to represent these numbers in verbal or graphic form. To facilitate the understanding of rational...

Whether the teacher is a mathematics specialist post Grade 6, or must include mathematical instruction Grades K-5, it is important to understand these global standards as a way to prepare students for more advanced study. These new standards reemphasize the importance of an integrated elementary school classroom -- core subjects build conceptual knowledge cross-functionally, so that as the student becomes more fluent in one, fluency in others hopefully follow. No longer is it possible to allow students to excel at reading but fail at math -- instead, the modern elementary teacher must ensure a basic fluency in all subjects.
REFERENCES

Askey, R. (1999). "Knowing and Teaching Elementary Mathematics." American

Educator. Fall 1999, Cited in:

http://www.aft.org/pubs-reports/american_educator/fall99/amed1.pdf

Blanton, M. (2008). Algebra and the Elementary Classroom. Heinemann.

Francis, A., et.al. (2008). "Using Semiotics to Teach Rational Numbers to Prospective

Elementary School Teachers." Michigan State University. Cited in:

http://meet.educ.msu.edu/pubs/pmena09/FrancisYuFrancisMcCroryPMENA09.pdf

Kane, R. (2002). "How We Teach the Teachers: New Ways to Theorize Practice

And Practice Theory." Prospectus. 32 (3): 1123.

National Council of Teachers of Mathematics. (2009). Overview: Principles for School

Mathematics. Cited in:

http://standards.nctm.org/document/chapter2/index.htm