## What is number sense?

Number sense has been defined as "a well organized conceptual framework of number information that enables a person to understand numbers and number relationships and to solve mathematical problems that are not bound by traditional algorithms" (Bobis, 1996). Number sense is complex. It is the foundation for all strands of mathematics. It also facilitates problem solving, reasoning, and communication of mathematical ideas (Shumway, 2011).

Students who have a strong number sense have the following understandings and skills:

- Adapted from "Number Sense Routines" (2011)

Building number sense is a process. Each individual is in a different place in the process. As individuals grow and develop their sense of number continues to grow. We need to provide our learners with varied, rich experiences that develop their sense of number and reasoning ability which develop the understandings and skills listed above. With a well developed sense of number, learners will be more successful in junior grades where they will start to encounter: larger numbers, multiplication and division; fractions, decimals, and percents; measurement in different dimensions; and more abstract algebraic concepts.

Students who have a strong number sense have the following understandings and skills:

- Have sense of what numbers mean. (Visualizing number)
- Look at the world in terms of quantity and number. (Magnitude)
- Make comparisons among quantities. (Sense of number combined with landmark numbers)
- Flexibility, automaticity, and fluidity with number.
- Perform mental math.
- Flexibility with problems.
- Automatic use of math information.
- Determine the reasonableness of an answer.
- Uses the numbers in a problem situation to decide on a strategy that is efficient and makes most sense.

- Adapted from "Number Sense Routines" (2011)

Building number sense is a process. Each individual is in a different place in the process. As individuals grow and develop their sense of number continues to grow. We need to provide our learners with varied, rich experiences that develop their sense of number and reasoning ability which develop the understandings and skills listed above. With a well developed sense of number, learners will be more successful in junior grades where they will start to encounter: larger numbers, multiplication and division; fractions, decimals, and percents; measurement in different dimensions; and more abstract algebraic concepts.

## How does number sense develop? |
Cathy Fosnot and Maarten Dolk (2002) have described the development of number sense within a landscape of learning which includes big ideas and strategies . Douglas Clements (2007) looks at development of number sense as following a trajectory. It is important that educators know and understand the big ideas below, so that we can plan for encouraging learners development.
Subitizing - seeing a small amount as a whole and knowing the amount without counting.Magnitude - being able to tell which of two groups is largerCounting - being able to say a counting sequence without having one-to-one correspondenceOne-to-One Correspondence - saying one number for each object countedCardinality - being able to tell how many things were counted in all when asked "how much?" Individuals without cardinality will have to recount the objects again.Hierarchical Inclusion - knowing numbers build by one each time and that smaller numbers are part of bigger numbers.Part/Whole Relationships - considering parts of a number (ex.7 is made up of 3 and 4, and 6 and 1)Compensation - Seeing parts of the whole and being able to compensate (ex. 5 + 1 = 6 then 4+2=6 because 4 is 1 less than 5, and 2 is one more than 1) Unitizing - Seeing numbers in groups or units (ex. twenty is 2 groups of ten) This is the beginning of understanding place value. |

## What strategies promote number sense? |
Learners need multiple opportunities to bump into number sense ideas, use number sense, and discuss strategies with peers and adults. Educators need to provide these opportunities
daily in a responsive way that builds on learners' current developmental understandings.Some strategies that we have learned about, tried out, and observed come from "Number Senses Routines: Building Numerical Literacy Everyday in K-3" (2011). These groups of strategies include: visual routines, counting routines, and playing with quantity. The following pages will explain the routines found in Shumway's book and will dig deeper into the routines, their purpose, and other available resources to support their use in the classroom to deepen students' sense of number. |

## Bibliography

Bobis, J. (1996). Visualisation and the development of number sense with kindergarten children. In Mulligan, J. & Mitchelmore, M. (Eds.)

Clements, D. (2009)

Fosnot, C.T., & Dolk, M. (2002).

Shumway, J. (2011).

*Children's Number Learning*: A Research Monograph of the Mathematics Education Group of Australasia and the Australian Association of Mathematics Teachers. Adelaide: AAMT.Clements, D. (2009)

*Learning and Teaching Early Math: The Learning Trajectory Approach.*New York: Routledge.Fosnot, C.T., & Dolk, M. (2002).

*Young Mathematicians at Work: Constructing Fractions, Decimals, and Percents*. Portsmouth: Heinemann.

Shumway, J. (2011).

*Number sense routines: Building numerical literacy every day in grades K-3*. Portland, Me.: Stenhouse.