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256. Regulation of the Federal Minister for Education, the Arts and Culture, with which the regulation on the curriculum of the educational institution for kindergarten education and the regulation on the curricula for the educational institute for social education are amended

Article 1

Amendment of the regulation on the curriculum of the educational institute for kindergarten pedagogy

Because of

1. |
of the School Organization Act, BGBl. No 242/1962, as last amended by the Federal Law BGBl. I n ° 36/2012, in particular § § 6 and 96 thereof, and |
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2. |
§ 7 (1) of the Federal Teacher's Teacher Training Act, BGBl. No 244/1965, as last amended by the Federal Law BGBl. I No 55/2012, |
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Is prescribed: |

The regulation of the Federal Minister of Education and Arts on the curriculum of the educational institution for kindergarten pedagogy, BGBl. No 514/1992, as last amended by the BGBl Regulation. II No 256/2006, shall be amended as follows:

(1) In Article I, Article 3 of the following paragraph 8 is added:

" (8) Sections V and VII of the Annex to this Regulation, as amended by the BGBl Regulation. II No 256/2012 are to be found in relation to the 1st, 2nd and 2nd and 3. Class with 1. September 2012 and with respect to the other classes with 1 September of the following years in class ascending into force. "

2. In the appendix (curriculum of the educational institution for kindergarten pedagogy) Section V (hour table) Z 10 is called the name "Mathematics" by the name "Applied Mathematics" shall be replaced and shall be the subject matter of "Applied Mathematics" line in question:

" 10. |
Applied mathematics |
2 |
2 |
2 |
2 |
2 |
10 |
(I) " |

3. In the Appendix V Z 16, the subject shall be the subject matter of "Rhythmisch-Musical Education" line in question:

" 16. |
Rhythmical Music Education |
- |
1 |
1 |
- |
1 |
3 |
IV " |

4. In the Appendix Section V Z 22, the subject matter shall be the subject matter of: "Informatics and Media" line in question:

" 22. |
Computer science and media |
1 |
1 |
- |
- |
- |
2 |
II " |

5. In the Appendix V Z 23, the subject matter shall be the subject matter of: "Seminar Organization, Management and Law" line in question:

" 23. |
Seminar Organization, Management and Law |
- |
- |
- |
1 |
1 |
2 |
II " |

6. In Annex VII (educational and teaching duties of the individual subjects, didactical principles, teaching material) Subsection A (compulsory items), Z 10, together with the heading, reads:

" 10. APPLIED MATHEMATICS

Education and teaching tasks:

The pupils achieve the following learning goals:

- |
Translate problems into the mathematical symbol language, |
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- |
accurate work and reasoning, |
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- |
Plan and consistent approach to solving tasks, |
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- |
precise presentation of results, |
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- |
Prepare the transfer of skills and methods that have already been learned to new tasks, |
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- |
appropriate handling of technical aids, |
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- |
correct application of the computational laws, |
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- |
exact graphic representation of mathematical relationships, |
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- |
Review and estimate the accuracy of results, |
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- |
Develop logical thinking structures by solving mathematical problems, |
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- |
Acquisition of knowledge about the development of mathematical understanding (principles and principles of early pedagogical action in relation to mathematical progenitor skills), |
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- |
Establish relationships between mathematical structures and the early basic skills underlying them, |
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- |
To be familiar with the content dimensions Figures and dimensions, algebra and geometry, functional relationships, analysis and stochastics and the dimensions of action Argumentation and communication, operating and technology use (minimum requirement is a graphic calculator), interpreters and documenting, modelling and transferring. |

The students develop the following insights:

- |
The conviction that mathematical basic knowledge and thinking should be done in the same way as early childhood and in girls and boys, |
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- |
the recognition that argumentation and communication are characteristic of applied mathematics, |
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- |
the experience that solving tasks can bring joy and self-confidence, |
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- |
The awareness that mathematical thinking and mathematical knowledge can be applied in the different areas of life, knowledge, and professions. |

Teaching material:

1st Class:

Competence Area "Numbers and Measures"

Counting with numbers and numbers

- |
Know the numerical ranges of the natural, whole, rational, real and complex numbers and can argue their relationships; |
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- |
Represent numbers and intervals on the number line; |
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- |
Express numbers in the decimal system in fixed and floating-point representation, and thus perform basic computing operations; |
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- |
To understand and apply figures in percentage; |
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- |
Control round and over-the-top calculation. |

Math with Maces

- |
Understand numbers as measures of sizes that convert measures between different units, |
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- |
Multiples and parts of units with the corresponding powers of ten can represent. |

Competence Area "Algebra and Geometry"

Variables and terms

- |
Can be expected with variables and terms (brackets, binomics formulas and breaks); |
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- |
Understand potential laws with integer exponents, justify them and apply them. |

Equations and Formulas

- |
Resolve linear equations and inequality in a variable and interpret the solution set; |
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- |
Can reshape formulas according to one of their variables; |
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- |
Model problems from different application areas in the form of an equation and can interpret and document the results with regard to the problem situation. |

Linear Equation Systems

- |
Can set up and solve systems of equations for application; |
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- |
The conditions for the solderability of linear equation systems with two variables can be argued, graphically illustrated and interpreted. |

Competence Area "Functional coherences"

Functions

- |
Know and argue the definitions of function and relation; |
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- |
Understand and interpret functions as models to describe the dependency between two sizes. |

Linear functions

- |
Know the function equation for the linear function (f (x) = k x + d), represent the graph in the coordinate system and can calculate the increase k as well as the ordinates section d computationally and graphically; |
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- |
know the term reverse function and calculate the equation of the inverse function computationally and graphically; |
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- |
calculate the zero position of the linear function, determine graphically, and interpret it as a solution of a linear equation; |
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- |
Graphically determine and calculate the intersection of two linear functions. |

School-specific competence area

Empirical functions

- |
can be graphically represented by occupational field-related investigations; |
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- |
Can interpret and argue graphic representations of empirical occupational functions. |

Quantities

- |
Identify, graphically represent and interpret combinations of quantities (average, unification and difference); can apply and interpret volume charts. |

Models for early mathematical education (forerunner skills)

- |
Understanding, describing, applying and presenting numbers and quantities |
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- |
Models for the development of counting, counting strategies; counting principles in infancy; |
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- |
Components of the early quantity and payment concept (classification, seriation, quantity comparison, counting skills, number knowledge, first computational skills), skills of weighing, measuring and comparison. |

School work: Two one-hour schoolwork

Portfolio on early mathematical education

2nd class

Competence Area "Numbers and Measures"

Complex numbers

- |
in the Gaussian plane, and the addition or Perform subtraction and illustrate it. |

Competence Area "Algebra and Geometry"

Equations

- |
Establish quadratic equations, solve and argue the different real and complex solutions; apply formulas of elementary geometry and reshape; |
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- |
for solving equations of higher degree of technology appropriately. |

Potenzlaws

- |
Understand the potential laws with rational exponents, explain them and illustrate them in examples and apply them; |
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- |
Potent and root notation can be converted into one another. |

Competence Area "Functional coherences"

Functions

- |
Quadratic functions, power functions (of type f (x) = x N with integer n) and the Root function (f (x) = x 1/2 ) and can interpret their properties. |
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- |
Graphically determine and calculate intersection points of two functions |

Competence area "Stochastics"

Descriptive statistics

- |
Graphically represent and interpret frequencies (absolute, relative and percentage), and can argue the selection of a certain style of presentation in application tasks; |
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- |
Calculate and interpret mean values and scatter measures (arithmetic mean, median, mode, standard deviation, span, quartile and quartile distance); |
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- |
Graphically explain the regression and correlation of two-dimensional data sets, determine the use of technology, and interpret the results. |

School-specific competence area

Statistics

- |
be able to collect data and know the difference in the processing of qualitative and quantitative characteristics; |
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- |
be able to argue data manipulation; |
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- |
the descriptive statistics can be applied to occupational field-related investigations. |

Models for early mathematical education (forerunner skills)

- |
Understand, describe, apply and present shapes and patterns; |
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- |
Visual-spatial abilities, comparisons of patterns and structures for understanding of geometric terms, spatial and temporal orientation, symmetry. |

School work: Two one-hour schoolwork

Portfolio on early mathematical education

3rd Class

Competence Area "Algebra and Geometry"

Vectors and matrices

- |
Know the definitions of vector and matrix; |
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- |
can represent two-dimensional vectors in the coordinate system; |
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- |
The addition, subtraction, multiplication with a scalar as well as scalar product of two-dimensional vectors can be interpreted geometrically and can be applied in practical tasks; |
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- |
Represent systems of equations in matrix form and can be solved by means of technology use. |

Exponential equations and logarithms

- |
Exponential equations (of type a X = b or e λx = c, where a, b, λ, c can be real numbers) with logarithmation; |
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- |
to know and apply logarithmic computational laws; |
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- |
can be used adequately for solving complex exponential equations. |

Trigonometry

- |
Can interpret the sinus, cosine and tangent of an angle in the right angle triangle as side relationships; |
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- |
resolving right-angled triangles; |
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- |
Can solve equations with trigonometric functions using technology. |

Competence Area "Functional coherences"

Exponential function and logarithmic function

- |
Graphene of exponential functions (of type f (x) = a-b) X ; b is a positive real number) with its characteristic properties and can be interpreted in the context; |
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- |
know the terms "half-life" and "doubling time", identify and interpret in context; |
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- |
The logarithmic function is known as the inverse function of the exponential function. |

Sequences and series

- |
Be able to know and apply the educational law of arithmetic and geometric consequences; |
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- |
the definition of the series. |

School-specific competence area

Models for intake and acceptance processes

- |
Compare linear functions and exponential functions as models for the description of supply and take-off processes and use them in a meaningful way; |
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- |
may argue the connection of linear functions with arithmetic sequences and exponential functions with geometric consequences in the description of ingestion and acceptance processes; |
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- |
Perform calculations of practice-relevant supply and acceptance processes and can document and interpret the results. |

Models for early mathematical education (forerunner skills)

- |
Understand, describe, apply and present seriation and model presentations on numerical processing and mathematical competence development. |

School work: two school works, at least one of them two hours

Portfolio on early mathematical education

4. Class

Competence Area "Algebra and Geometry"

Trigonometry

- |
Solve simple tasks with sine and cosine sets and can interpret the results. |

Competence Area "Functional coherences"

Trigonometric functions

- |
Visualize trigonometric functions (degrees and radians), and can argue with the unit circle. |

Analysis Capability Area

Differential invoice

- |
Have an intuitive interface concept and an intuitive concept of continuity of a function; |
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- |
monotony and pole positions of the function can be discussed; |
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- |
understand the terms difference quotient (mean rate of change) and the differential quotient ("momentary" rate of change) and can use it to solve tasks; |
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- |
know the concept of the discharge function; |
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- |
Differentiate potent, polynomial, and simple exponential functions and interpret the result; |
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- |
Calculate the derivation of composite power, polynomial and simple exponential functions with the help of the derivation rules (bottom, factor, product and chain rule); |
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- |
local extrema, curvature behavior, turning points of potency and polynomial functions can be calculated and described using the derivation (sfunction); |
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- |
Perform function equations from application-related contexts (reverse tasks). |

Competence area "Stochastics"

Probability Invoice

- |
Use and interpret the classical and statistical probability term; |
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- |
to exclude the addition and multiplication rule to each other, apply independent events; |
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- |
present probabilities for simple facts about tree diagrams, and can calculate; |
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- |
Know and apply the concept of random variables, determine the distribution function and the characteristics (expectation value and variance) of a random variable, and can argue. |

School-specific competence area

Extreme value issues

- |
Model and transfer extreme value problems, carry out calculations and argue results (side conditions: text, similarity, and Pythagoreischer teaching rate). |

Models for early mathematical education (forerunner skills)

- |
To understand, describe, apply and present the basic experiences of young children with the duration of time, time sequences and rhythms. |

School work: Two two-hour schoolwork

Portfolio on early mathematical education

5. Class

Analysis Capability Area

Integral Accounting

- |
Know the term "root function" and recognize and describe the relationship between function and root function in its graphical representation; |
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- |
Calculate the root functions of potency and polynomial functions; |
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- |
may interpret the concept of a given integral on the basis of an intuitive limit value term as a limit value of a top and subtotal; |
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- |
the specific integral can be interpreted as an oriented area; |
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- |
Use the specific integral of power and polynomial functions to calculate the area content. |

Competence area "Stochastics"

Probability Invoice

- |
Know and use and interpret the binomial distribution in context; |
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- |
Model random experiments using binomial distribution, calculate probabilities, represent graphs, and interpret the results. |

School-specific competence area

Continuous probability distribution

- |
Know and use and interpret the normal distribution in context; |
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- |
be able to understand and illustrate the importance of expectation and standard deviation in relation to the normal distribution curve; |
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- |
identify and describe situations in which binomial distribution and/or can be modeled with normal distribution; |
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- |
can apply the probability calculation to job-related problems. |

Models for early mathematical education (forerunner skills)

- |
Understand, describe, apply and present experience in terms of chance, probability and abundance. |

Repetition of all thematic areas

School work: Two two-or three-hour school work

Portfolio on early mathematical education

7. In Annex VII, subsection A, Z 16, together with the heading, reads:

" 16. RHYTHMICAL MUSICAL EDUCATION

Education and teaching tasks:

The pupils achieve the following learning goals:

- |
Perceive, understand and express the interaction of music and movement in the artistic-educational and communicative context, |
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- |
Acquisition of theoretical foundations and reflection on the implementation of rhythmical and musical content in the pedagogical professional field, |
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- |
Raising awareness of the senses and differentiating perception as a basis for observation and action processes, |
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- |
development and use of the individual artistic expression in music and movement, |
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- |
Conscious of the networking of motor, social-affective and cognitive learning processes. |

Teaching material:

2nd class

Competence area "perception and body consciousness"

- |
Be able to consciously perceiuse your own body; |
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- |
Sensitize different senses and differentiate perceptual areas; |
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- |
Relationship and interrelation of music and movement (time/force/space/form) can be recorded. |

Competence Area "Creativity and Expression"

- |
develop expressiveness through music and movement and expand the movement repertoire; |
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- |
With the means of rhythm (music/instruments, movement, language/voice, material/objects) can improvise and shape under guidance; |
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- |
To be able to capture and express the metrum, clock, rhythm, form, dynamics; |
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- |
be able to move under the guidance of free and bound dance forms; |
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- |
can develop simple choreographies in different social forms. |

Competence Area "Interaction and Communication"

- |
Interact with other classmates in different forms of social interaction and find solutions together; |
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- |
can take various roles (leading/following, co-operating, leading) in creative and pedagogical processes; |
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- |
can perceim the effect of voice in communication. |

Competence area "Transfer to the pedagogical professional field"

- |
Even experienced rhythm units can reflect. |

3rd Class

Competence area "perception and body consciousness"

- |
Free and bound forms of movement to different music can be executed in a differentiated way. |

Competence Area "Creativity and Expression"

- |
Be able to use different instruments and materials creatively (e.g. for improvisations, sound stories, movement/song accompaniment, design of picture books); |
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- |
Use the voice and language in a variety of ways and can invent and shape different types of text (non-sensation, texts and sayings); |
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- |
continue to be able to distinguish themselves, differentiated and concentrated with rhythmic musical tasks; |
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- |
to know and implement intercultural elements from music, movement and language. |

Competence Area "Interaction and Communication"

- |
Use elementary musical instruments and rhythmic materials to promote interaction and non-verbal communication. |

Competence area "Transfer to the pedagogical professional field"

- |
understand and discuss the aims and content of rhythmical and musical education; |
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- |
to use different materials to work with children and adolescents; |
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- |
methodical basic knowledge of the construction of songs, texts, sound stories and dances can be applied by way of example; |
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- |
can handle introductory specialist literature; |
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- |
In the case of hospice exercises in the practice kindergarten, practice hort, specific tasks and observation tasks can be fulfilled by means of reflection criteria; |
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- |
It is possible to plan and perform rhythmic units by way of example. |

5. Class

Competence area "perception and body consciousness"

- |
It is possible to integrate tension and relaxation in the sense of the psychohygienes in a personal and professional context. |

Competence Area "Creativity and Expression"

- |
To be able to use and reflect on their creative potential in an improvisatory and creative way with voice, language, movement, music and material. |

Competence Area "Interaction and Communication"

- |
Can act empathically and appreciably; |
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- |
Bring and accept personal opinions in an appropriate manner; |
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- |
emotional and factual agation; |
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- |
Acting in a cooperative, communicative and team-oriented way, and assuming responsibility. |

Competence area "Transfer to the pedagogical professional field"

- |
Using rhythmics as a method to promote children in their emotional, social, cognitive and motor skills; |
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- |
Can offer rhythmics as a learning aid in the Hort (also interdisciplinary); |
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- |
Can integrate children of different ages with different developmental conditions and behavioural dispositions with the means of music and movement in group processes; |
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- |
Know similarities and differences of related subjects (Psychomotor/Motopädagogik, Elementary Music Pedagogy, Sensor-Integration, Music Therapy); |
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- |
deal independently with specialist literature, assess it critically and use it adequately; |
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- |
Planning, carrying out and presenting projects (including cross-disciplinary). " |

8. In Appendix Section VII, subsection A, Z 22, together with the heading, reads:

" 22. COMPUTER SCIENCE AND MEDIA

Education and teaching tasks:

The pupils achieve the following learning goals:

- |
Knowledge of computer and information technology basic knowledge to solve simple problems. |
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- |
Self-determined and goal-oriented use of information technologies and media. |
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- |
Ability to support children and young people professionally in the critical handling of information technologies. |
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- |
Ability to obtain information in a targeted way, to prepare and to present it in a media-friendly way. |
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- |
Acquisition of media skills in order to be able to apply and develop them in the teaching of other subjects. |

Teaching material:

1st Class

"Text Processing" Competence Area

- |
You can create formatting and layout of simple documents according to defined standards. |

Competence area "Managing and presenting data"

- |
Can perform simple calculations using standard programs (spreadsheet calculation); |
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- |
Make data readable and can be displayed in diagrams. |

Competence area "Fundamentals of EDP"

- |
Create a simple file organization; |
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- |
data backups can be performed; |
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- |
know basic file formats and their meaning;. |
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- |
Identify and operate key components of the hardware; |
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- |
Know the basics of the operation and use of software. |

Presentation of the Competence Area "Presentation"

- |
be able to perform a simple presentation by means of suitable media; |
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- |
be able to know and apply essential quality criteria for presentations. |

Competence Area "Networks" (Web, Internet, Networks)

- |
Knowing the possibilities of searching the Internet and taking into account its limitations. |

Competence area "Media"

- |
Basic tools of image processing can apply. |

2nd class

"Text Processing" Competence Area

- |
It is possible to design a multi-page document in a suitable way. |

Competence area "Managing and presenting data"

- |
Can create practical applications in the field of data processing. |

Competence area "Fundamentals of EDP"

- |
Be able to deal responsibly with your own and foreign data; |
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- |
Solve simple problems with hard-and software. |

Presentation of the Competence Area "Presentation"

- |
Create and present a multi-media presentation. |

Competence Area "Networks" (Web, Internet, Networks)

- |
Platforms for communication and knowledge acquisition can be used. |

Competence area "Media"

- |
A media project can be carried out. " |

9. In Annex VII, subsection A, Z 23, together with the heading:

" 23. SEMINAR ORGANISATION, MANAGEMENT AND LAW

Education and teaching tasks:

The pupils achieve the following learning goals:

- |
Acquisition of basic knowledge of company management-in particular social pedagogical institutions-and application in the occupational field. |
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- |
Assessment of fundamental legal issues in the social pedagogical environment by acquiring knowledge of occupational areas of law. |
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- |
Get to know and learn about the special features of the management of service organisations with a strong leadership. |
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- |
Enable targeted action in organisations for the conscious organisation of professional development. |

Teaching material:

4. Class

Competence Area "Law"

- |
Know the essential legal regulations from the professional field. |

Competence Area "Project Management"

- |
Know and apply the elements and methods of project management. |

Competence area "Marketing and Management"

- |
know the tools of evaluation and quality management; |
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- |
can assess various forms of personnel development; |
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- |
can use different instruments of further information and storage of information. |

5. Class

Competence area "Marketing and Management"

- |
Be able to know and organise various forms of public relations; |
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- |
Corporate culture, goals, mission statement can analyze. |

Competence area "Organization and Management"

- |
Define and explain the concept of organization in its various meanings; |
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- |
be able to know and explain basic organisational concepts; |
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- |
Know and understand management and management tasks in the social pedagogical field. |

Competence area "Business fundamentals"

- |
To apply basic knowledge of accounting in a professional context. " |

Article 2

Amendment of the Regulation on curricula for the educational institute for social pedagogy

Because of

1. |
of the School Organization Act, BGBl. No 242/1962, as last amended by the Federal Law BGBl. I n ° 36/2012, in particular § § 6 and 96 thereof, and |
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2. |
§ 7 (1) of the Federal Teacher's Teacher Training Act, BGBl. No 244/1965, as last amended by the Federal Law BGBl. I No 55/2012, |
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Is prescribed: |

The Federal Minister of Education, Arts and Sport's Regulation on the curricula for the educational institute for social pedagogy, BGBl. No 355/1985, as last amended by the BGBl Regulation. II No 256/2006, shall be amended as follows:

(1) In Article III, Article 3 of the following paragraph 4 is added:

" (4) Sections IV and VI of Appendix 1 to this Regulation, as amended by the BGBl Regulation. II No 256/2012 are to be found in relation to the 1st, 2nd and 2nd and 3. Class with 1. September 2012 and with respect to the other classes with 1 September of the following years in class ascending into force. "

2. In Annex I (curriculum of the educational institute for social pedagogy) Section IV (timetable), the name shall be: "Mathematics" by the name "Applied Mathematics" shall be replaced and shall be the subject matter of "Applied Mathematics" line in question:

" |
Applied mathematics |
2 |
2 |
2 |
2 |
2 |
10 |
(I) " |

3. In Annex I, Section VI [Education and teaching tasks of the individual teaching subjects, division of the teaching material on the individual school levels (classes), didactic principles] Subsection A (compulsory subject matters) shall be the subject of the compulsory subject matter. "Mathematics" by the compulsory subject "Applied Mathematics" is replaced and is:

" APPLIED MATHEMATICS

Education and teaching tasks:

The pupils achieve the following learning goals:

- |
Translate problems into the mathematical symbol language, |
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- |
accurate work and reasoning, |
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- |
Plan and consistent approach to solving tasks, |
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- |
precise presentation of results, |
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- |
Prepare the transfer of skills and methods that have already been learned to new tasks, |
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- |
appropriate handling of technical aids, |
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- |
correct application of the computational laws, |
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- |
exact graphic representation of mathematical relationships, |
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- |
Check and estimate the accuracy of results, |
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- |
Develop logical thinking structures by solving mathematical problems, |
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- |
Acquisition of knowledge about the development of mathematical understanding (principles and principles of early pedagogical action in relation to mathematical progenitor skills), |
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- |
Establish relationships between mathematical structures and the early basic skills underlying them, |
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- |
To be familiar with the content dimensions Figures and dimensions, algebra and geometry, functional relationships, analysis and stochastics and the dimensions of action Argumentation and communication, operating and technology use (minimum requirement is a graphic calculator), interpreters and documenting, modelling and transferring. |

The students develop the following insights:

- |
Can use key findings for mathematical early education and learning help, |
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- |
the recognition that argumentation and communication are characteristic of applied mathematics, |
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- |
the experience that solving tasks can bring joy and self-confidence, |
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- |
The awareness that mathematical thinking and mathematical knowledge can be applied in the different areas of life, knowledge, and professions. |

Teaching material:

1st Class

Competence Area "Numbers and Measures"

Calculate with numbers and numbers:

- |
Know the numerical ranges of the natural, whole, rational, real and complex numbers and can argue their relationship; |
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Represent numbers and intervals on the number line; |
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Express numbers in the decimal system in fixed and floating-point representation, and thus perform basic computing operations; |
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To understand and apply figures in percentage; |
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Control round and over-the-top calculation. |

Calculate with Maßen:

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To understand numbers as measures of sizes, to convert the measures between units; |
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Multiples and parts of units with the corresponding powers of ten can represent. |

Competence Area "Algebra and Geometry"

Variables and terms

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Can be expected with variables and terms (brackets, binomics formulas and breaks); |
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Understand potential laws with integer exponents, justify them and apply them. |

Equations and Formulas

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Resolve linear equations and inequality in a variable and interpret the solution set; |
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Can reshape formulas according to one of their variables; |
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Model problems from different application areas in the form of an equation and can interpret and document the results with regard to the problem situation. |

Linear Equation Systems

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Can set up and solve systems of equations for application; |
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The conditions for the solderability of linear equation systems with two variables can be argued, graphically illustrated and interpreted. |

Competence Area "Functional coherences"

Functions

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Know and argue the definitions of function and relation; |
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Understand and interpret functions as models to describe the dependency between two sizes. |

Linear functions

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Know the function equation for the linear function (f (x) = k x + d), represent the graph in the coordinate system and can calculate the increase k as well as the ordinates section d computationally and graphically; |
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know the term reverse function and calculate the equation of the inverse function computationally and graphically; |
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calculate the zero position of the linear function, determine graphically, and interpret it as a solution of a linear equation; |
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Graphically determine and calculate the intersection of two linear functions. |

School-specific competence area

Empirical functions

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can be graphically represented by occupational field-related investigations; |
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Can interpret and argue graphic representations of empirical occupational functions. |

Quantities

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Identify, graphically represent and interpret combinations of quantities (average, unification and difference); can apply and interpret volume charts. |

Models for mathematical learning aid in the elementary school

In selected examples, the students develop models for the learning support and create mathematical-oriented learning games and illustrative material for the development of counting, counting strategies, numerical processing and for the development of the counting strategies, the numerical processing and the numerical methods. the mathematical development of skills in elementary school and learning aids for the acquisition of numbers and payment methods, learning aids for recording quantities, learning aids for computing with measures and in the skills of weighing, measuring and Comparison.

School work: Two one-hour schoolwork

Portfolio on the mathematical learning aid

2nd class

Competence Area "Numbers and Measures"

Complex numbers

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in the Gaussian plane, and the addition or Perform subtraction and illustrate it. |

Competence Area "Algebra and Geometry"

Equations

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Create quadratic equations, solve and argue the different real and complex solutions; |
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Apply and reshape formulas of elementary geometry; |
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for solving equations of higher degree of technology appropriately. |

Potenzlaws

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Understand the potential laws with rational exponents, explain them and illustrate them in examples and apply them; |
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Potent and root notation can be converted into one another. |

Competence Area "Functional coherences"

Functions

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Quadratic functions, power functions (of type f (x) = x N with integer n) and the Root function (f (x) = x 1/2 ) and can interpret their properties; |
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You can graphically determine and calculate the intersection points of two functions. |

Competence area "Stochastics"

Descriptive statistics

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Graphically represent and interpret frequencies (absolute, relative and percentage), and can argue the selection of a certain style of presentation in application tasks; |
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Calculate and interpret mean values and scatter measures (arithmetic mean, median, mode, standard deviation, span, quartile and quartile distance); |
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Graphically explain the regression and correlation of two-dimensional data sets, determine the use of technology, and interpret the results. |

School-specific competence area

Statistics:

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be able to collect data and know the difference in the processing of qualitative and quantitative characteristics; |
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be able to argue data manipulation; |
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the descriptive statistics can be applied to occupational field-related investigations. |

Models for mathematical learning aids in elementary school

In selected examples, the students develop models, learning aids and illustrative material for the learning accompaniment for the understanding of spatial orientation, spatial orientation, comparison of surfaces, shape, size, symmetries, patterns and Structures and of general geometric terms.

School work: Two one-hour schoolwork

Portfolio on the mathematical learning aid

3rd Class

Competence Area "Algebra and Geometry"

Vectors and matrices

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Know the definitions of vector and matrix; |
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can represent two-dimensional vectors in the coordinate system; |
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The addition, subtraction, multiplication with a scalar as well as scalar product of two-dimensional vectors can be interpreted geometrically and can be applied in practical tasks; |
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Represent systems of equations in matrix form and can be solved by means of technology use. |

Exponential equations and logarithms

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Exponential equations (of type a X = b or e λx = c, where a, b, λ, c can be real numbers) with logarithmation; |
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to know and apply logarithmic computational laws; |
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can be used adequately for solving complex exponential equations. |

Trigonometry

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Can interpret the sinus, cosine and tangent of an angle in the right angle triangle as side relationships; |
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resolving right-angled triangles; |
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Can solve equations with trigonometric functions using technology. |

Competence Area "Functional coherences"

Exponential function and logarithmic function

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Graphene of exponential functions (of type f (x) = a-b) X ; b is a positive real number) with its characteristic properties and can be interpreted in the context; |
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know the terms "half-life" and "doubling time", identify and interpret in context; |
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The logarithmic function is known as the inverse function of the exponential function. |

Sequences and series

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Be able to know and apply the educational law of arithmetic and geometric consequences; |
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the definition of the series. |

School-specific competence area

Models for intake and acceptance processes

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Compare linear functions and exponential functions as models for the description of supply and take-off processes and use them in a meaningful way; |
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may argue the connection of linear functions with arithmetic sequences and exponential functions with geometric consequences in the description of ingestion and acceptance processes; |
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Perform calculations of practice-relevant supply and acceptance processes and can document and interpret the results. |

Models for mathematical learning aids in the transition from adult education to secondary education

In selected examples, the students develop the mathematical learning accompaniment and create mathematically oriented learning games and illustrative material for the processing of numbers and of relations: "larger, smaller, equal", for the basic computational skill with numbers and for understanding the elementary geometry.

School work: two school works, at least one of them two hours

Portfolio on the mathematical learning aid

4. Class

Competence Area "Algebra and Geometry"

Trigonometry

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Solve simple tasks with sine and cosine sets and can interpret the results. |

Competence Area "Functional coherences"

Trigonometric functions

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Visualize trigonometric functions (degrees and radians), and can argue with the unit circle. |

Analysis Capability Area

Differential invoice

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Have an intuitive interface concept and an intuitive concept of continuity of a function, |
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monotony and pole positions of the function can be discussed; |
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understand the terms difference quotient (mean rate of change) and the differential quotient ("momentary" rate of change) and can use it to solve tasks; |
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know the concept of the discharge function; |
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Differentiate potent, polynomial, and simple exponential functions and interpret the result; |
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Calculate the derivation of composite power, polynomial and simple exponential functions with the help of the derivation rules (bottom, factor, product and chain rule); |
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local extrema, curvature behavior, turning points of potency and polynomial functions can be calculated and described using the derivation (sfunction); |
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Perform function equations from application-related contexts (reverse tasks). |

Competence area "Stochastics"

Probability Invoice

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Use and interpret the classical and statistical probability term; |
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to exclude the addition and multiplication rule to each other, apply independent events; |
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present probabilities for simple facts about tree diagrams, and can calculate; |
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Know and apply the concept of random variables, determine the distribution function and the characteristics (expectation value and variance) of a random variable, and can argue. |

School-specific competence area

Extreme value issues

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Model and transfer extreme value problems, carry out calculations and argue results (side conditions: text, similarity, and Pythagoreischer teaching rate). |

Models of mathematical learning aids in the transition from upper secondary to secondary level 2

In selected examples, the students develop the mathematical learning accompaniment and create mathematically oriented learning games and illustrative material in the area of numbers, geometric forms and simple functions and Relations.

School work: Two two-hour schoolwork

Portfolio on the mathematical learning aid

5. Class

Analysis Capability Area

Integral Accounting

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Know the term "root function" and recognize and describe the relationship between function and root function in its graphical representation; |
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Calculate the root functions of potency and polynomial functions; |
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may interpret the concept of a given integral on the basis of an intuitive limit value term as a limit value of a top and subtotal; |
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the specific integral can be interpreted as an oriented area; |
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Use the specific integral of power and polynomial functions to calculate the area content. |

Competence area "Stochastics"

Probability Invoice

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Know and use and interpret the binomial distribution in context; |
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Model random experiments using binomial distribution, calculate probabilities, represent graphs, and interpret the results. |

School-specific competence area

Continuous probability distribution

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Know and use and interpret the normal distribution in context; |
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be able to understand and illustrate the importance of expectation and standard deviation in relation to the normal distribution curve; |
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identify and describe situations in which binomial distribution and/or can be modeled with normal distribution; |
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can apply the probability calculation to job-related problems. |

Models of mathematical learning aids in upper secondary education

In selected examples, the students develop the general mathematical learning accompaniment and create suitable mathematically oriented learning games and illustrative material, and it should be noted that the quantity and number-related Pre-knowledge influence on the later achievements in mathematics education. Young people with computational difficulties often have uncertainties in the prenumic foundations of the infant and pre-school age.

Repetition of all thematic areas

School work: Two two to three hours of school work

Portfolio on the mathematical learning aid "

Schmied