# Symptoms of a weakness in numeracy

## Synonyms in a broader sense

Features, symptoms, abnormalities, early warning, arithmetic weakness, arithmasthenia, acalculia, learning impairment in mathematics, learning difficulties in mathematics lessons, arithmetic disorder, partial performance disorder, dyscalculia, dyslexia, reading and spelling weakness, LRS.

## early detection

In order to be able to define deviations from the norm, it is necessary to know what is actually called the norm. In the area of arithmetic weaknesses (but also every other learning problem, such as reading and spelling weaknesses) this means that you first learn which standards should be achieved when and where.

Defining this in the school area is not particularly difficult due to the defined learning goals and standards to be achieved, which have to be achieved specifically in each school year.

But what about performance deviations in the preschool area?

Are there any indications here that suggest that learning problems are likely?

If so: What can be done diagnostically and therapeutically so that the probability of a learning disability is kept as low as possible?

## Developmental problems in kindergarten

The basic idea of the kindergarten goes back to Friedrich Fröbel, who in 1840 filled his basic idea with content and turned it into reality. He had the vision of a place for children that accepted and supported all children regardless of their social background and based on the principle of an extended family. The focus was always on playing together, social interaction and looking after the child. The kindergarten should also be a place of contact between families and encourage interaction.

The kindergarten and the basic idea of Froebel were subject - as well as other educational areas - to various influences. Pedagogical concepts were changed and adapted to social conditions and changes. Political influences can also be proven if you look for them.

As a result of the changed living conditions, especially because of the changed childhood, the kindergarten or daycare center is becoming more and more important as an important care institution for young children.

As in the context of the **Early detection of weaknesses in numeracy** addressed, the essentials are formed **Requirements how**: **Perception - storage - motor skills and imagination** after the foundation stone was laid in the womb through interaction with the environment in toddler and thus in preschool age. They influence learning in a special way and are often jointly responsible for the development of learning problems (poor numeracy, poor concentration, poor reading and spelling, ...). These components can be promoted through various exercises.

The kindergarten, which in its ideal form integrates education, care and upbringing with one another, can have a fundamental influence. The child's own experiences form the most essential basis *free* according to the saying of Confucius:

Tell me and I'll forget!

Show me and I'll remember!

Let me do it myself and I will understand!

Developmental problems can already be found in the preschool area. However, caution is advised here, because not every deviation from the norm means that learning problems in the school sector will definitely develop. A “healthy” vigilance cannot hurt, however. Tackling problems when you notice them doesn't do any harm if it doesn't result in excessive actionism. In any case, it must be prevented that abnormalities are “over-treated”. For example, if you find an abnormality in the visual perception of a child, this ability must not be trained 24 hours a day. It should then be integrated primarily into the playful confrontation of the child and the child's progress should be checked from time to time.

Some serious abnormalities may require consultation with the pediatrician. As a preschool institution, your kindergarten can provide you with further information on this.

The following list assigns the underlying ability to the various abnormalities. It does not claim to be complete. The assignment of anomalies to ability is not always clear. Sometimes there are several underlying skills, which is why abnormalities are mentioned twice.

The following problems are not limited to the preschool area either. They can certainly still exist in school age. The only rule here is: If abnormalities occur: be vigilant!

The following abnormalities may indicate learning problems:

**perception**:

- Problems touching objects while blindfolded.
- Problems naming the parts of the body that were touched with eyes closed.
- Problems hearing out certain sounds and / or combinations of sounds
- Finger agnosia (inability to distinguish between certain fingers on the hand and to show them on request)
- Problems with the visual detection of smaller quantities up to a number of six objects (e.g. points of the cube image; Muggle stones that are out of order; turning plates, stones ...); Quantity has to be counted!
- Associated with this also: Problems with the acquisition of relations: greater than / less than; more than / less than; the same number of, ... .
- Problems in the area of combining certain areas of perception, e.g. Problems in hand - eyes - coordination (tapping certain objects)
- Problems with coloring (crossing the lines)
- Problems sorting items according to certain criteria.
- Problems imitating rhythms (clapping, ...)
- Problems in the area of spatial orientation

**storage**:

- Problems naming items you've seen before but then removed or covered.
- Problems with adding rows (red circle, blue triangle, green square, yellow rectangle, ...) or with reconstructing figures from memory.
- Problems memorizing
- Problems with repeating words, syllables and numbers, but also: Problems repeating nonsense words / syllables, but also repeating rows of numbers.

**Motor skills**:

- Problems in the area of gross motor skills (when running, crouching, catching, balancing, ...)
- Problems in fine motor skills (coloring, holding a pen, finger games, tying shoes, ...)
- Problems with clapping or clapping at given rhythms
- Problems imitating movements / sequences of movements.
- Problems mimicking gestures and / or facial expressions.
- Problems with crossing the midline (for example, when children are supposed to make cross movements, e.g. moving forwards / backwards or sideways, touching the left knee with the right hand or vice versa

**idea**:

- Problems retelling stories due to lack of imagination (creating images in the head)
- Problems extending logical series
- Problems with coloring (crossing the lines)
- Problems with planning activities (determining the order: first ..., then ...)

## primary school

The principle of self-acting should of course also be anchored as an essential element in primary school.

Recognizing weaknesses in calculation requires an expansion of the perspective. Not only the fact whether a task has been calculated correctly is important, but also the path taken to solve a task. Correct solutions do not necessarily say something about a child's numeracy and skills. Especially in the first years of school, pupils can count towards their goal. The ability of poorly performing children to hide their problems should not be underestimated.

The development of mathematical thinking is at the center of complex studies. Piaget carried out investigations in this regard in the 1960s and found that the development of the concept of number depends largely on the ability of a visual - spatial imagination.

The development of the concept of numbers, the step-by-step expansion of the number range up to a million (in the fourth year of school) and the gradual penetration of the same is the focus of mathematics lessons in elementary school.

The development of the number ranges takes place step by step, subdivisions can be made and transitions can be made fluent at the end of the school year. For example, the number range can be extended to 100 at the end of the first school year. A mathematical penetration of the number range then takes place in the second school year.

**Number range up to 20**

*Learning areas:*

- Traits and relationships
- Numbers - addition and subtraction
- Sizes
- geometry

**Number range up to 100**

*Learning areas:*

- Extension of the number range
- Addition and subtraction
- Multiplication and division
- Properties of numbers / number sets
- Sizes
- geometry

**Number range up to 1,000**

*Learning areas:*

- Extension of the number range
- Addition and subtraction / written calculation methods
- Multiplication and division
- Properties of numbers / number sets
- Sizes
- geometry

**Number range up to 1,000,000**

*Learning areas:*

- Extension of the number range
- Addition and subtraction
- Multiplication and division / written calculation methods
- Properties of numbers / number sets
- Sizes
- geometry

The development of the concept of numbers and the orientation in the number space is given special importance, since penetration and an ability to orientate in the respective number space is of particular importance for all other areas of responsibility. Which also includes:

- the bundling to build up the decadal place value system,
- working with the value board
- Orientation on the number line, the number band, the scoreboard, the hundreds / thousands field, ... to build up numerical relationships (successor, predecessor, neighboring tens, hundreds, thousands, ...
- writing and reading numbers (number dictations, ...)
- Compare and order (relations: ... less than ..., ... greater than ..., ...
- the different numerical aspect (cardinal number (number), ordinal number (sequence: first, second, ...), measure (number in connection with a quantity), operator number (number in connection with a calculation command), ...)
- the structure of number properties (even / odd; divisible / not divisible; ...
- Rounding Numbers
- ...

## class 1

Even in the preschool area, children have diverse experiences with numbers, quantities and sizes, as well as with space and time. These knowledge and skills are taken up and further developed in the initial lessons.

In mathematics lessons in the first year of school, the correct spelling of digits is also introduced and, in addition to taking up and developing various previous experiences, the first operations (addition and subtraction) are introduced. In order to gain insight into the mathematical operations, the operations are first introduced at the level of action. The addition is nothing more than an addition (enlarge, add, fill in, ...), the subtraction is represented by removing (reducing, shortening, ...).

Most children find it easy to transition to the symbolic level through understanding and a variety of exercises, but there are also deviations and abnormalities that are shown below.

**Traits and relationships**

- Problems with pairing.
- Problems determining quantities (how many are 6 bears?)
- Problems checking the perceptual correspondence of the elements of two sets
- Problems when completing relations (... less than ..., ... greater than ..., equal)

**Numbers addition subtraction**

- Number rotator (12 instead of 21) when reading and writing.

Rotating numbers can also symbolize problems in capturing the place value. - Spatial instability: 9 and 6 are swapped, the numbers (especially 3 or 1) are written the wrong way round (analogies to spatial instability in the case of reading and spelling weaknesses)
- Problems counting, especially counting down
- Problems with determining predecessor and successor (orientation in number space)
- Problems understanding addition and / or subtraction
- Problems solving task, reversal task and / or supplementary task
- Problems when exceeding the tens (remembering intermediate results)

**Sizes**

- Problems capturing quantities
- Problems with entering relations (e.g. when calculating with money: 3 euros> 4 cents.

**geometry**

- Problems naming features
- Problems with the identification of square, rectangle, triangle, circle.
- Problems with touching and sorting according to certain criteria.

## 2nd grade

**Extension of the number range:**

- Problems in understanding the place value system P
- Problems reading numbers
- Problems jotting down numbers by ear

**Addition and subtraction**:

- Calculating with fingers is retained
- Small one plus tasks (addition and subtraction tasks in the ZR up to 20) are not yet automated
- Addition and subtraction are only carried out with the help of counting (also on the hundred table)
- Problems with building calculation schemes. (Add to the next ten and then continue: FIRST ..., THEN)
- Problems with factual arithmetic that are not due to deficiencies / weaknesses in meaningful reading
- Problems in understanding task, reversal and supplementary task
- Problems with making transfer payments

**Multiplication and division**:

- Problems learning and automating multiplication tables
- Problems capturing the multiplication as multiple addition
- Problems in understanding task, reversal and supplementary task

**Properties of numbers and sets of numbers**:

- Problems understanding the place value system
- Problems reading numbers
- Problems jotting down numbers by ear

**Sizes**:

- Problems introducing sizes
- Problems capturing quantities

## Class 3

**Extension of the number range:**

- Problems understanding the place value system.
- Problems reading numbers
- Problems jotting down numbers by ear.

**Addition and subtraction:**

- Calculating with fingers is retained.
- Small one plus tasks (addition and subtraction tasks in the ZR up to 20) are not yet automated.
- Addition and subtraction are only done with the help of counting.
- Problems in understanding task, reversal and supplementary task
- Problems building up written addition
- Problems with completing (supplementary tasks) and thus also problems with setting up the written subtraction
- Problems with the written subtraction of multiple minuends (= numbers that should be subtracted from a number)
- Problems saving intermediate results
- Problems with factual arithmetic that are not due to deficiencies / weaknesses in meaningful reading
- Problems with making transfer payments

**Multiplication and division:**

- Problems learning and automating multiplication tables.
- Problems capturing the multiplication as multiple addition.
- Problems in understanding task, reversal and supplementary task

**Properties of numbers and sets of numbers:**

- Problems understanding the place value system.
- Problems reading numbers
- Problems jotting down numbers by ear.

**Sizes:**

- Problems introducing sizes
- Problems capturing quantities

## Grade 4

**Extension of the number range:**

- Problems understanding the place value system.
- Problems reading numbers
- Problems jotting down numbers by ear.

**Addition and subtraction:**

- Calculating with fingers is retained.
- Small one plus tasks (addition and subtraction tasks in the ZR up to 20) are not yet automated.
- Addition and subtraction are only done with the help of counting.
- Problems in understanding task, reversal and supplementary task
- Problems building up written addition
- Problems with completing (supplementary tasks) and thus also problems with setting up the written subtraction
- Problems with the written subtraction of multiple minuends (= numbers that should be subtracted from a number)
- Problems saving intermediate results
- Problems with factual arithmetic that are not due to deficiencies / weaknesses in meaningful reading
- Problems with making transfer payments

**Multiplication and division:**

- Problems learning and automating multiplication tables.
- Problems capturing the multiplication as multiple addition.
- Problems in understanding task, reversal and supplementary task

**Properties of numbers and sets of numbers:**

- Problems understanding the place value system.
- Problems reading numbers
- Problems jotting down numbers by ear.

**Sizes:**

- Problems introducing sizes
- Problems capturing quantities