Spatial representations of numbers in children and their connection with calculation abilities

Jan Lonnemann1, Helga Krinzinger, André Knops

  • 1Section Neuropsychology, Department of Neurology, University Hospital, RWTH Aachen University, Aachen, Germany. lonnemann@neuropsych.rwth-aachen.de

Related Concept Videos

Real Number Operations01:27

Real Number Operations

The concept of real numbers includes all the values that can be represented on a continuous number line. The system began with basic counting values used for enumeration. It later expanded to include values that represent the absence of quantity and opposites of the counting values. When situations required expressing parts of a whole or dividing quantities evenly, values capable of representing such proportions were developed. When written using decimal notation, these values can end or repeat...
Piaget's Stage 3 of Cognitive Development01:17

Piaget's Stage 3 of Cognitive Development

During Piaget's concrete operational stage, from ages 7 to 11, children exhibit a marked increase in logical thinking skills, specifically in relation to tangible, real-world events. This stage is characterized by the development of several essential cognitive concepts, including conservation, reversibility, and classification, all of which support the child's evolving capacity for structured thought.
Conservation and Constancy of Quantity
A significant cognitive milestone in the concrete...
Numerical Calculations01:24

Numerical Calculations

In engineering applications, the representation of the numerical value is critical. Presenting or reporting the answer is one of the essential parts of engineering practices. Numerical calculations are performed using handheld calculators or computers since numerically accurate answers are always preferred.
The solution to a problem is obtained using different methods. While manually solving algebraic symbols is one of the most common methods, the graphical method is often preferred. Computers...
Piaget's Stage 2 of Cognitive Development01:14

Piaget's Stage 2 of Cognitive Development

The preoperational stage, the second of Jean Piaget's four stages of cognitive development, spans approximately ages 2 to 7 and is characterized by the emergence of symbolic thinking. During this stage, children use language, images, and symbols to represent objects and concepts, enabling them to engage in imaginative and pretend play. This symbolic thinking supports children's ability to perform make-believe actions, such as imagining a broom as a horse or their hand as a phone, blending...
Complex Numbers01:29

Complex Numbers

The real number system cannot represent the square root of a negative number, which restricts solutions for certain equations, such as quadratics with negative discriminants. To address this, the complex number system was developed, introducing the imaginary unit i, where i = √(-1). This extension allows for the representation of all roots, including those involving negative radicands.A complex number is written in the form x + yi, where x and y are real numbers. Here, x represents the real...
How Data are Classified: Numerical Data00:59

How Data are Classified: Numerical Data

Data that are countable or measurable in specific units are called numerical or quantitative data. Quantitative data are always numbers. Quantitative data are the result of counting or measuring the attributes of a population. Amount of money, pulse rate, weight, number of people living in a town, and number of students who opt for statistics are examples of quantitative data.
Quantitative data may be either discrete or continuous. All quantitative data that take on only specific numerical...