Everyone has heard
of common sense. We believe
that each person has number sense as well.
What is number sense? We
define number sense in the school environment as, an understanding that
allows students to approach concepts, ideas, and problems concerning
numbers differently, according to their backgrounds, experiences, studies,
etc. These approaches
students use are often referred to as heuristics.
In Fennell and Landisí (1994) chapter, Number and Operation Sense in the book Windows of Opportunity: Mathematics for Students with Special Needs, they ask this same question. What is number sense? Throughout the chapter, they give numerous answers to this question. Fennell & Landis state: "[Number sense] is an awareness and understanding about what numbers are, their relationships, their magnitude, the relative effect of operating on numbers, including the use of mental mathematics and estimation" (p. 187). They are suggesting that students must understand how numbers relate to each other. Recognizing these relationships, as well as, the magnitude of numbers are very important aspects regarding number sense. Magnitude helps the students break down the problem and look at its relative size. In addition to these ideas, mental mathematics and estimation include the use of number sense. Students must understand and use the basic properties of numbers. For example, when students use the commutative property, they know that 20 + 10 is the same as 10 + 20. The determination, as well as, the ability of the students to estimate depends on the basic concepts of number sense. Fennell and Landis also define number sense as "the foundation from which all other mathematical concepts and ideas arise" (p. 188). They continue: "[Number sense] is good intuition about numbers and their relationships" (p. 187). Students with number sense can automatically tackle a variety of problems. They can break down the problem and use the numbers as references. In other words, they can make connections between their knowledge and newly learned mathematical concepts and skills. In general, they know how to make sense of numbers, how to apply them, and are confident that their problem solving processes will enable them to arrive at solutions.
As a teacher, one does not have to decide on an exact definition for number sense, but should be aware of it. For teachers to provide the best learning environment for their students, they must understand each studentís current number sense and address their own teaching to make sure that their students understand mathematical concepts and procedures. To do this, teachers must balance their teaching between conceptual and procedural knowledge of mathematics. In addition, teachers can have discussions with their students concerning methods of problem solving. From this teachers will recognize the level of number sense each student has and can provide students with new insights on problem solving. For example, from listening and sharing, students will see and learn how other classmates solve problems. They may use these techniques in the future to help them approach new problems.
your probability number sense or your studentís number sense, try out