mathematics

Number sense

Number sense is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Number sense rather than just read about it. In short: In psychology, number sense is the term used for the hypothesis that some animals, particularly humans, have a biologically determined ability that allows them to represent and manipulate large numerical quantities. The term was popularized by Stanislas Dehaene in his 1997 book "The Number Sense," but originally named by the mathematician Tobias Dantzig in his 1930 text Number: The Language of Science.

Key takeaways

Number sense belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Number sense to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Number sense from memory before moving on to harder problems.

Reference excerpt

In psychology, number sense is the term used for the hypothesis that some animals, particularly humans, have a biologically determined ability that allows them to represent and manipulate large numerical quantities. The term was popularized by Stanislas Dehaene in his 1997 book "The Number Sense," but originally named by the mathematician Tobias Dantzig in his 1930 text Number: The Language of Science. Psychologists believe that the number sense in humans can be differentiated into the approximate number system, a system that supports the estimation of the magnitude, and the parallel individuation system, which allows the tracking of individual objects, typically for quantities below 4. There are also some differences in how number sense is defined in math cognition. For example, Gersten and Chard say number sense "refers to a child's fluidity and flexibility with numbers, the sense of what numbers mean and an ability to perform mental mathematics and to look at the world and make comparisons." In non-human animals, number sense is not the ability to count, but the ability to perceive changes in the number of things in a collection. All mammals, and most birds, will notice if there is a change in the number of their young nearby. Many birds can distinguish two from three. Researchers consider number sense to be of prime importance for children in early elementary education, and the National Council of Teachers of Mathematics has made number sense a focus area of pre-K through 2nd grade mathematics education. An active area of research is to create and test teaching strategies to develop children's number sense. Number sense also refers to the contest hosted by the University Interscholastic League. This contest is a ten-minute test where contestants solve math problems mentally—no calculators, scratch-work, or mark-outs are allowed.

Concepts involved in number sense The term number sense involves several concepts of magnitude, ranking, comparison, measurement, rounding, percents, and estimation, including:

estimating with large numbers to provide reasonable approximations; judging the degree of precision appropriate to a situation; understanding the hidden meaning of numbers through analytical and critical thinking (e.g., Freakonomics); rounding (understanding reasons for rounding large numbers and limitations in comparisons); choosing measurement units to make sense for a given situation; solving real-life problems involving percentages and decimal portions; comparing physical measurements within and between the U.S. and metric systems; and comparing degrees Fahrenheit and Celsius in real-life situations. Those concepts are taught in elementary-level education.

See also Approximate number system – Innate ability to detect differences in magnitude without counting Mental calculation – Arithmetical calculations using only the human brain Number sense in animals Numeracy, innumeracy – Ability to apply numerical concepts Numerosity adaptation effect – Phenomenon in numerical cognition Order of magnitude – Scale of numbers with a fixed ratio Ordinal numerical competence Parallel individuation system – Cognitive system for number sense Numerals and grammatical number of the Pirahã language – Muran language Plant arithmetic – Form of plant intelligence Subitizing – Perception of object number without counting

References

Further reading Geary, David C. (1994). Children's Mathematical Development: Research and Practical Applications. Washington, DC: American Psychological Association. ISBN 978-1557982582.

External links Number Worlds - a site with number sense development materials

Illustrations

Worked examples

Example 1 — a first encounter with Number sense

Start with the simplest possible case. Write down what Number sense claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Number sense before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Number sense ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Number sense

In research: Number sense appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Number sense in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Number sense is common in secondary-school and first-year university syllabi. It links to neighbouring topics Cognitive science, Educational psychology, so understanding it makes those chapters shorter.
In everyday life: Look for Number sense outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Number sense in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Number sense means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Number sense out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Number sense in simple terms?

Why does Number sense matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Number sense?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Number sense.