What We Know

Number sense is a way of thinking rather than a body of knowledge and skills (Van de Walle & Watkins, 1993). Number sense can be described as good intuition about numbers and their relationships and is demonstrated by a flexibility of thinking, the ability to estimate and the ability to make judgments and inferences about numerical quantities (Greeno, 1989). Number sense, an integrated knowledge of numbers and number systems, develops gradually as a result of exploring numbers, visualizing them in different contexts and relating them in multiple ways. Number sense requires the ability and drive to connect new understanding about numbers with prior knowledge (Reys, 1994). Number sense convinces students that mathematics makes sense.

Demonstrating number sense involves whole and rational numbers and includes the ability to:

• compose and decompose numbers;
• recognize the relative magnitude of numbers;
• realize the absolute value of numbers;
• use benchmarks;
• link numeration, operation and relation symbols in meaningful ways;
• understand the effect of operations on numbers;
• perform mental computations ;
• estimate and know when an estimate is appropriate;
• make sense of numbers (Sowder, 1992).

In order for students to understand our base-ten number system, they must develop their thinking in units. Research has shown that many children's understanding of place value in second through fifth grade is delayed until grouping by ten is well established (Kamii, 1989). Thinking in units involves creating a mental image associated with a numeral, number word and set of objects. It includes the ability to flexibly use the unit in adding and subtracting and decompose the unit into other units (Wheatley & Reynolds, 1999). Students develop stronger understandings of numbers as they solve problems using two- and three-digit numbers (Fuson & Briars, 1990).

In research studies, instructional time spent fostering students' conceptual understanding of rational number concepts using multiple models and representations, translating between these representations and emphasizing the meaning of fractions positively impacted achievement rates. Research recommends using a curriculum focused on developing students' understanding of the meaning of fractions, order and equivalence before focusing on symbolic procedures for fraction operations (Cramer, Post, & del Mas, 2002).