When we say a person has “Good Number Sense” – what exactly is it that they understand and can do?

Children must have a clear understanding of our number system if they are going to be mathematically literate.  They must have some logical thinking skills that will enable them to work with numbers in a meaningful way and they must understand how our number system works.  They must be able to distinguish the four characteristics of our number system:

1.    The role of zero.

2.    The Additive Property of numbers.

3.    A base of ten.

4.    Place Value.

Students must be taught how to represent the concrete world with mathematical models such as diagrams and the open number line and eventually with numbers and other math notation.  Teachers should know that some representations are proportional models (size and number of objects grow – examples are straw bundles and base 10 blocks) and others are non-proportional (number or value grows, but no connection for size – examples are money and place value mats).  Proportional models are more concrete and therefore are better for more immature thinkers.

These understandings will not occur in one or two lessons or even in one or two grades.  The systematic study of our number system to develop “Good Number Sense” must be planned and integrated throughout the elementary school mathematics program.  Our goal is to try and further define what “Good Number Sense” is at various stages.  The Companion to the Connecticut Mathematical Frameworks is a valuable resource for this task.  Two other valuable resources are a Kathy Richardson’s 9 Critical Stages outlined in her series of assessments called Assessing Math Concepts and the series of books by Fosnot and Dolk (see the “What are some Good Resources for learning about Math?” page). We also need to further develop a bank of activities (see the “What are some ways to work on Number Sense?” page) that we can use to develop those skills and understandings and how we will assess where each child is in their personal journey towards Computational Fluency.

A technique for teaching number sense in the classroom is called “Number Talks.”  This strategy is a lot like a mini-lesson in the Writing or Reading Workshop.  It is short (usually on 5 to 10 minutes) and focused on one idea or strategy.  Since kids learn about our number system in different ways and at different times, this technique allows students long windows of opportunity for learning but because it is brief it does not bore those students who already have obtained an understanding.  In fact, it allows them the opportunity to refine their understanding and generalize it to other situations. 

Number Talks provide opportunities for children to work with computation in meaningful ways.  During Number Talks, the teacher presents various problems to groups of children and asks them to share the processes they used to figure “how many.”  Number Talks can be held either with the whole class or with small groups.  When children are working with the whole class, they will have opportunities to experience a wide range of problems and many different ways to solve them.  When working with a small group, the teacher can make sure all the children have the opportunity to share their processes if they wish, and can more easily tailor the problems to meet the needs of a particular group.

Taken from “Implementing Number Talks Helpful Hints by Cathy Young.  Available at www.mathperspectives.com

Fosnot and Dolk talk about this obtaining of Number Sense as a journey.  Most kids pass through typical phases, but they do not necessarily pass through them at the exact same time or even in the exact same order.  Their analogy of a journey is a good one.  If two people traveled in essentially the same direction, they would not necessarily follow the exact same path.  They would pass by the same landmarks along the way, but one traveler may linger at one longer than the other.  One person may double back and revisit a landmark again and again before moving on.  It is the individuality of this journey towards number sense that makes it so challenging to teach.  Different children are at different places along this journey or continuum. 

Kathy Richardson has developed a series of assessments called Assessing Math Concepts. This series attempts to assess where a child is on a continuum of critical learning phases that typical children pass through.  These assessments help teachers gather information about where their students are in this journey and therefore help guide them in their decisions about what to teach and how to teach it to best meet the needs of their students.