Early detection of a weakness in calculation

Symptoms in a broader sense

Characteristics, symptoms, abnormalities, early warning, arithmetic weakness, arithmasthenia, acalculia, learning impairment in mathematics, learning difficulties in math lessons, arithmetic disorder.

Definition of early detection

All children who have problems (in mathematics) have a right to support - regardless of whether it is to a Dyscalculia (Partial performance disorder with at least average intelligence) or general school problems, for example in combination with a LRS (= Reading and spelling weaknesses), ADS, ADHD or one Poor concentration or similar is due.
There are opportunities to recognize arithmetic difficulties - but also reading and spelling difficulties or learning problems in general - early on, but this requires openness and requires basic knowledge that enables errors and abnormalities to be interpreted in the first place.

Children at risk

As on the Dyscalculia - mentioned on the page, the studies regarding a gender-specific distribution to the disadvantage of girls are contradictory. So it cannot be said across the board: "Girls cannot calculate!"
There is also no classic “risk child”. It has been shown, however, that children who have little self-confidence in their own achievements, do not like doing math and may even be afraid of it, can more often develop problems with arithmetic and possibly even a weakness in arithmetic.
It is the same with children who have negative attitudes towards school.
Even children with other learning problems, such as an existing one Poor concentration, with a ADS with or without hyperactivity (ADHD), but also with one LRS (= reading and writing weakness) can also tend to be a Arithmetic weakness to develop.

Learning requirements of school beginners

basic requirements

In general, it can be said that a transition - be it from kindergarten to school or from elementary school to secondary school - is generally carried out, perceived and processed differently by children. While many problems only exist initially and resolve on their own without further interference, there are children School enrollment problems solidify and can trigger real crises - up to and including school phobia. Symptoms for this can be: aggressiveness, restlessness ("fidgeting"), inattention, "unfounded" crying, learning blocks, excessive demands, ...
It is therefore of enormous importance that the transition must be designed in such a way that success in (secondary) school is likely. However, this is not only the sole task of the kindergarten and school, but also the task of the parents, who significantly influence and support the child's development and upbringing. Many problems that arise in school can - with the right sensitivity and the appropriate diagnostic measures and skills - be identified in the child's pre-school development. (see: symptomatic early detection)
The development of mathematical thinking begins long before the school enrollment. This does not mean that a child learns or should learn arithmetic long before starting school. Nor does it mean that the numbers should all be learned and written. That's what a child learns at school! This is about basic prerequisites that are being built. Basic requirements that contribute to and influence success in arithmetic and thus in mathematics lessons.

Areas of Perception

It is noticeable that similar basic requirements also apply to the Success in Reading and spelling but also developing a LRS (= reading and writing weakness) influence. Even children with a noticeable lack of concentration find it difficult to play and work. Here you have to work on perseverance in a special way and with special patience.


The diagram indicates the different sensory areas that can play a role in the perception of information in the context of mathematics. Compared to the different sensory areas that generally play a role in the perception of information, the integration of the olfactory and taste senses was dispensed with at this point, as both play a subordinate role in the context of mathematics.
The table is intended to provide information on why the areas of perception in the diagram represent essential elements in the context of mathematical learning.

Tactile perception (concerning the sense of touch)

  • Basics:
    The tactile perception is already developed in the womb. Especially in the first months of life, the child perceives his environment through this sense. Touching and “caressing”, evoke a positive basic mood in the child. The good feeling in turn has a positive effect on the child's ability to learn.
    The sense of touch is increasingly neglected with increasing age due to the strong visual and acoustic characteristics of society, although it is not insignificant and should actually be used more.
  • (Mathematical) application:
    The tactile perception takes place at / at ...
    • Touches
    • Feeling for objects
    • Sensing properties
    • ...
    and in terms of math is important for ...
    • the categorization of objects according to certain properties (round, square, oval, ...)
    • the perception of shape
    • a positive mood with regard to learning and the ability to learn

Vestibular perception (regarding balance)

  • Basics:
    The perception of equilibrium is also already developed in the womb. It is closely linked to tactile and kinaesthetic perception and is supported by visual perception.
    Problems in vestibular perception can affect visual perception and vice versa.
  • (Mathematical) application:
    Well-trained eye muscles are important for hand - eye coordination, which is ...
    • Rock
    • Climb
    • Balance
    • Catch balls
    • painting of surfaces without painting over
    • ...
    demanded and used.
    In terms of mathematics, these basics are needed when
    • Organize
    • to compare
    • Assign
    • counting
    • Mounting position (top / bottom / front / back ...)
    • Writing the numbers in the correct order (no rotators)

Visual perception

  • Basics:
    Visual perception, together with auditory perception, is probably the most frequently used. As a rule, it is fully developed by the age of eight.
  • (Mathematical) application:
    • Combination of seeing and moving (eye - hand - coordination)
    • Recognition of relevant properties (picture descriptions)
    • Error patterns
    • Look for differences

Kinesthetic perception (regarding position and movement)

  • Basics:
    The kinesthetic perception is also developed in the womb. This term means the basic perception of one's own body. So you know - without thinking about it - how the mouth has to be moved when articulating a certain word. Without worrying about it, you know how to perceive your body while sitting, walking, ...
    The kinesthetic perception is of particular importance for the development of gross and fine motor skills and can usually not be viewed in isolation (without the other areas of perception).
  • (Mathematical) application:
    • Estimating distances
    • Storage and automation
    • Form perception
    • Form distinction
    • Space concept
    • Recall symbols (numbers, operators) from memory
    • Working speed
    • Size relationships
    • Relations (... less than ..., ... greater than ..., equal / ... as large as ...)

Auditory perception

  • Basics:
    The ability to perceive acoustic stimuli enables distances and directions to be estimated.
    It also develops in the womb.
    The sense of hearing is - together with the sense of sight - the most “used” sense. Switching off the sense of sight and hearing can therefore bring about other dimensions of perception.
  • (Mathematical) application:
    • Perceiving and understanding tasks and work orders
    • understand and process
    • Acquisition of basic skills

Promotion of imagination

Listed below are a few fairly simple ways to advance a child's imagination. Under certain circumstances, these are quite "everyday":

  • Building with blocks and building blocks also promotes children's imagination and action planning in a special way. “I'm building a castle” implies an existing image in the child's head, which is to be implemented in reality with the existing building blocks.
  • Read stories or tell exciting stories. Children imagine the situation. Unlike television, it stimulates the child's imagination, creativity and imagination. The television sets the situation straight away. There is little space and freedom for the child's creativity and imagination. A ritualization in the form of a regular occurrence, for example in the form of the “bedtime story”, should be introduced and maintained. Stories also have a positive effect on the child's language ability and many other areas.
  • ...

The combination of tactile, kinesthetic and vestibular perception is particularly important for spatial orientation.
Learning with all senses promises to address the learner holistically and to consolidate and secure what has been learned in different ways through the different perception.

Promote awareness

In general, all forms of play and exercise that appeal to the senses and demand and secure perception on different levels can be used to promote perception. It is important to consciously train other senses in addition to visual and auditory perception. This can and should be done in a completely “non-mathematical” way, that is, without numbers and without ulterior motives at school, thus even in early childhood. The following are possible:

  • Baby massages
  • Feel books,
  • Playing outdoors and with natural materials (natural experiences, ...)
  • Playing with everyday objects such as marbles, building blocks, building blocks (different shapes, different colors).
  • Dice games, thereby first number perception by counting the number. Later, the dice's eyes are “simultaneously”, that is, immediately when they see the number. Counting is then no longer necessary.
  • Tactile games (feeling bags, feeling memory, ...)
  • Counting in early childhood through a memorized series of numbers and simultaneous tapping on objects
  • ...

The idea - being able to imagine something

The Ability to imagine facts and plan them in your mind, is of particular importance not only in math classes. This faculty of imagination is only given when courses of action have been internalized in this waythat they as automated apply and so to speak "by itself" run automatically could.
In the child, the ability to imagine is usually built up via the independent doing. Only what you have done and edited yourself can be integrated into your memory. While children initially imitate and imitate activities, the foundation for self-action is laid. By performing the action independently for the first time and performing one and the same activity repeatedly, one begins to mechanize, automate and accelerate processes.
It is particularly difficult for children who have an additional lack of concentration to introduce themselves.

The motor skills

In principle, any movement that is consciously and thus arbitrarily carried out falls under the area of ​​“motor skills”. There are various activities of the muscles, tensing and relaxing, but also stretching and bending.
A distinction is made between two areas:

  1. Gross motor skills
  2. Fine motor skills

In contrast to fine motor skills, gross motor skills are not limited to the hand. They affect the entire body. The following areas fall into the field of fine motor skills:

  • crawl
  • go
  • run (and the various subforms)
  • jump (also in the different variants, such as: hop, fiddle, jump rope, ...)
  • throw
  • to catch
  • climb
  • to lift
  • ...

In principle, gross motor movements are forms of movement in which several areas of the body are addressed.

In contrast, everything that is done by hand falls into the area of ​​fine motor skills. The term “hand motor skills” is often used synonymously. Fine motor skills develop at different ages. In a newborn baby, the grasping reflex is already developed, which is then further specified. The child perceives the world more and more with his hands and eventually learns to consciously reach for various objects.
As part of the development of fine motor skills, a distinction is made between different grip shapes, such as:

  • the monkey handle
  • the scissor handle
  • the tweezer handle
  • the pointed handle (which is needed when holding a pen)
  • ...
  • the ability to move fingers in isolation from one another and to be able to use different (mixed) forms of grips.

Promotion of motor skills

The promotion and training of motor skills is of elementary importance and must be encouraged in toddler age - according to the motto: What Hans does not learn, Hans never learns again, or rather difficult.

All areas that have already been mentioned in the description of the two motor sub-areas serve to promote motor skills. Movement is only learned through movement! Be a role model and avoid the merely consuming attitude under all circumstances (too much television, too much computer games, etc.). Get involved in sports activities.

If there are deficits in the morotic development, therapeutic intervention can be made. One speaks of a so-called psychomotor therapy, which addresses not only the muscle-building elements but also the different areas of perception mentioned above.

There are also different materials and devices that can train and improve the motor skills. Everything that trains the sense of balance is of enormous importance.

Storage and memory performance

Probably the most well-known differentiation of the types of memory is the distinction between short-term and long-term memory. The more recent research has led to a further development of the terms and, in some cases, a new definition. So today we differentiate between that

  • Working memory
  • and the
  • Long-term memory.

Working memory includes, on the one hand, ultra-short-term memory (= new memory) and, on the other hand, short-term memory, which stores information for a few seconds. Both forms are important in mathematics that should not be underestimated. The short-term memory is of enormous importance, especially for the short-term storage of intermediate results, memorized numbers, transfers, etc.
The capabilities of short-term storage are expanded in the child over the years, because they are significantly lower than the capabilities of an adult.
With regard to the “working memory”, a distinction is made between two sub-areas: One part is responsible for processing linguistic information while images and ideas are captured by the so-called visual-spatial sub-grouping.
When solving mathematical problems, the short-term or working memory is of enormous importance, since the requirements of learned arithmetic structures usually make intermediate storage in the brain necessary. While the structures for the solution are internalized, deepened and stuck in long-term memory as a structure, every solution to a task places high demands on the working memory and the ability to concentrate, which is actually only possible with such a form of storage.
There are various factors, such as a (child's) fear of failure, that can lead to a blockage of the memory function.

Long-term memory also consists of several components:

  • the declarative memory, which primarily stores information that is influenced by one's own feelings and experiences. It is divided into the
  • the semantic memory, for storing facts (vocabulary, ...) and the episodic memory, for storing personally important things (what was I wearing yesterday?).
  • the procedural memory, which stores routinely occurring procedures. For mathematics lessons, the procedural memory is of particular importance insofar as many areas of application and algorithms (writing of numbers, calculation methods, written calculation methods, ...) are automated and are also routinely used and carried out after understanding.

Read more on the subject here: Long-term memory