Numbers sense
The sense of numbers is the innate, intuitive ability to perceive and differentiate between quantities / numbers, including the ability to recognize and determine changes in quantities. The term number sense was introduced by Tobias Dantzig (1884–1956) in his book Number: The Language of Science (1930), and various scientists have since documented the number sense in more detail, for example Karen Wynn (psychology / cognition) and Stanislas Dehaene (neuroscience).
research
Even if the definitions of the sense of numbers differ in nuances, it is now accepted. The sense of numbers is the foundation for the further development of counting comprehension as well as mathematical skills based on it.
Research in this area has produced a number of important results:
- The intraparietal sulcus (IPS) is the brain area that is always active when crowds are involved. This region is “plurimodal”, ie it is activated via various sensory channels.
- This IPS region is closely networked with neurons, which are particularly active for processing size and space / location.
- Studies in the field of geometry now show that people also have a primordial intuition with regard to space / position and angle.
- In the case of brain injuries, it is possible that the sense of numbers can be lost if the ability to think and speak is otherwise intact.
- Already shortly after birth, babies show their "sense of numbers" in various experiments (cf. studies by K. Wynn and V. Izard).
- Scientific studies have also found a “sense of numbers” in mammals, birds and fish, see differentiation of quantities in animals .
Understanding the sense of numbers is essential and decisive for early childhood education and learning support. The innate, intuitive sense of numbers is, so to speak, the foundation for a solid development and constant refinement of the understanding of numbers, operations and mathematical concepts. Studies have shown that this development and refinement of mathematical skills depends on appropriate experience / teaching. As part of early childhood education, people depend on the innate sense of numbers being stimulated and strengthened (comparisons of numbers, sizes, etc., counting, becoming more / less). In early school education, he is dependent on developing a more abstract understanding in a constant dialogue between intuition and number words and building up appropriate brain circuits. After all, this childlike stimulation and education is crucial for a healthy development of math skills.
Research in the area of dyscalculia shows that such fundamental deficits in number sense are extremely rare. It is much more common to observe that the more accurate notion of numbers and operations has only been poorly developed. However, in both cases - congenital deficits in number sense / dyscalculia as well as deficits built up due to inadequate teaching - early and targeted professional interventions can contribute to sustainable improvement in mathematical skills (individualized teaching, individual support, learning therapy).
literature
Books
- B. Butterworth: The mathematical brain. Papermac, London et al. a. 2000, ISBN 0-333-76610-5 .
- Tobias Dantzig: Number: The Language of Science. Plume, 2007, ISBN 978-0-452-28811-9 (new edition of the 4th edition 1954), full text (PDF)
- Stanislas Dehaene : The sense of numbers or why we can calculate. Birkhäuser, Basel, Berlin a. a. 1999, ISBN 3-7643-5960-9 (review)
- Keith Devlin: The math gene. Or: How mathematical thinking develops + Why you can easily forget numbers. 3. Edition. German Taschenbuch-Verlag, Munich 2004, ISBN 3-423-34008-8 .
- Burkhart Fischer: hearing-seeing-looking-counting: partial performances and their disorders. Verlag Hans Huber, Bern 2007, ISBN 978-3-456-84243-1 .
Studies in professional journals
- Stanislas Dehaene, Véronique Izard, Elizabeth Spelke, Pierre Pica: Log or Linear? Distinct Intuitions of the Number Scale in Western and Amazonian Indigenous Cultures . In: Science . tape 320 , no. 5880 , May 30, 2008, ISSN 0036-8075 , p. 1217-1220 , doi : 10.1126 / science.1156540 .
- B. Fischer, A. Köngeter, K. Hartnegg: Effects of daily practice on subitizing, visual counting, and basic arithmetic skills. In: Optom Vis Dev. Volume 39, 2008, pp. 30-34.
- K. McCrink, Wynn, K .: Large-number addition and subtraction in infants. In: Psychological Science. Volume 15, 2004, S, pp. 776-781.
- Khaled Nasr, Pooja Viswanathan and Andreas Nieder: Number detectors spontaneously emerge in a deep neural network designed for visual object recognition. In: Science Advances. Volume 5, No. 5, eaav7903, doi: 10.1126 / sciadv.aav7903
- Karen Wynn: Do infants have numerical expectations or just perceptual preferences? In: Developmental Science. Volume 2, 2002, pp. 207-209.
- Karen Wynn: Findings of addition and subtraction in infants are robust and consistent: A reply to Wakeley, Rivera and Langer. In: Child Development. Volume 71, 2000, pp. 1535-1536.
Web links
- Numbers sense: this is what a 100 feels like. On: spiegel.de of March 26, 2016
- The sense of numbers arises spontaneously from the recognition of visible objects. On: idw-online.de from May 8, 2019