Modification Of The Ordinance On The Curriculum Of The Educational Institution For Kindergarten Pedagogy And The Regulation On The Curriculum For The Educational Institution For Social Pedagogy

Original Language Title: Änderung der Verordnung über den Lehrplan der Bildungsanstalt für Kindergartenpädagogik sowie der Verordnung über die Lehrpläne für die Bildungsanstalt für Sozialpädagogik

Read the untranslated law here: https://www.global-regulation.com/law/austria/2997372/nderung-der-verordnung-ber-den-lehrplan-der-bildungsanstalt-fr-kindergartenpdagogik-sowie-der-verordnung-ber-die-lehrplne-fr-die-bildungsanstalt-fr-so.html

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256. Regulation of the Federal Minister for education, art and culture, modifies the regulation about the curriculum of the educational institution for kindergarten pedagogy as well as the regulation on the curriculum for the educational institution for Social pedagogy

Article 1

Modification of the Ordinance on the curriculum of the training college for nursery

On the basis of



1 of the school Organization Act, Federal Law Gazette No 242/1962, as last amended by Federal Law Gazette I no. 36/2012, in particular its articles 6 and 96, and 2. § 7 paragraph 1 of the Federal teacher teaching obligation law, BGBl. No. 244/1965, as last amended by Federal Law Gazette I no. 55/2012, is prescribed: Ordinance of the Federal Minister for education and art about the curriculum of the training college for nursery , BGBl. No. 514/1992, as last amended by the regulation Federal Law Gazette II No. 256/2006, is amended as follows:

1. in the article I the following paragraph 8 is added § 3:

"II No. 256/2012 kick (8) sections V and VII of the plant of this Regulation as amended by regulation BGBl. with regard to the 1st, 2nd and 3rd class with September 1, 2012, and in terms of the other classes with 1st September of the subsequent years alternative ascending into force."

2. in the system (curriculum of educational institution for kindergarten Pedagogics) section V (hours Panel) Z 10 "Mathematics" is replaced by the designation "Applied mathematics" and it is the compulsory subject "Applied mathematics" that line:



"10.





Applied mathematics





2





2





2





2





2





10





(I)




3. in the section V Z 16, it is the compulsory subject "Rhythmic and musical education" that line:



"16.





Rhythmic and musical education





-





1





1





-





1





3





IV"




4. in the section V Z 22, it is the compulsory subject "Informatics and media" that line:



"22.





Informatics and media





1





1





-





-





-





2





II"




5. in the section V Z 23, which is the compulsory subject "seminar organization, management and law" that line:



"23.





Seminar organization, management and law





-





-





-





1





1





2





II"




6 in the section VII (educational and teaching tasks of individual subjects, educational principles, curriculum) under section A (compulsory subjects) is Z 10 together with the heading:



"10. APPLIED MATHEMATICS



Education and teaching task:

Students achieve the following objectives:



-Translate from problems in the mathematical language of symbols, - precise work and arguing, - planned and systematic approach to solving tasks, - accurate representation of results -, making the transfer of already learnt skills and methods on new tasks, - practical handling of technical AIDS, - correctly apply the laws of computing -, accurate graphical representation of mathematical contexts, check and estimate results for accuracy, - developing logical thinking by solving mathematical problems , - Acquisition of knowledge about the development of mathematical understanding (principles and principles of early educational action in relation to mathematical skills of precursor), - manufacture of connections between mathematical structures and the early basic skills underlying them, - trusted his contexts the content dimensions figures and mass, algebra and geometry, functional analysis and stochastics, and the plot dimensions, argumentation and communication, operate and use of technology (minimum requirement is a graphing calculator) , Interpreting and documenting, modeling, and transfer.

Students develop the following insights:



-The belief that mathematical knowledge and thinking in infancy and when girls and boys in the same way should be carried out, - the knowledge that argumentation and communication in applied mathematics are characteristic, - the experience that solving tasks can bring joy and self-confidence, - the awareness that can apply mathematical thinking and mathematical knowledge in the different life, knowledge, and professional areas.

Curriculum:



1st class:



Area of competence "Numbers and dimensions"



Computing with numbers and quantities of numbers



-Know the number ranges of the natural, whole, rational, real and complex numbers and their relationships can argue

-Numbers and intervals on the line represent;

-Express and perform this basic arithmetic numbers in the decimal system in fixed - and floating-point representation;

-Figures can understand and apply as a percentage

-Master round and rollover account.



Computing with mass



-Numbers understood as measures of sizes which can convert measures between different units, - to represent multiple and parts of units with the corresponding powers of ten.



Area of competence "Algebra and geometry"



Variables and terms



-Expect with variables and terms (parentheses, binomial formulas and fractions);

-Distributive law understand with integer exponents, they justify and can apply.



Equations and formulas



-Linear equations and inequalities can dissolve in a variable and interpret the solution set

-Formulas can transform after one of its variables

-Problems in different fields of application in the form of an equation model and interpret the results in terms of the problem and can document.



Systems of linear equations



-To set up and solve equation systems;

-the conditions for the solvability of linear equation systems with two variables can argue, graphically illustrate and interpret.



Area of competence "Functional relationship"



Functions



-Know and argue the definition of the function and relation;

-Functions can understand and interpret as models for the description of the dependency between two sizes.



Linear functions



-The function equation of the linear function (f(x) k = x + d) know, represent the graphs on the coordinate system and d computationally and graphically identify the increase in k as well as the ordinate section;

-know the concept of inverse function and the equation for the inverse function can determine computationally and graphically

-the zero point of the linear function; charge, graphically determine and interpret as a solution of a linear equation

-can graphically define and calculate the intersection of two linear functions.



School specific competence



Empirical functions



-graphically represent from professional field related studies;

-graphical representations of empirical professional field related functions can interpret and argue.



Quantities



-Mates of quantities (average, Union, and difference); identify, visualize and interpret Diagrams of amounts of can apply and interpret.



Models for early math education (skills of precursor to)



-Pay and amounts to understand, describe, apply and present models for the development of counting, counting strategies; Counting principles in infancy;

-Components of the early quantity and skills of number concept (classification, Seriation, volume comparison, counting skills, numbers knowledge, first computing skills), of weighing, measuring and comparing.

Homework: two one-hour homework

Portfolio to the early math training



2nd class



Area of competence "Numbers and dimensions"



Complex numbers



-in the Gaussian plane can represent and can illustrate and perform addition or subtraction.



Area of competence "Algebra and geometry"



Equations



-Quadratic equations set, loosen and the different cases of real and complex solution; argue Apply and transform formulas of elementary geometry;

-the solution of equations of higher degree knowing appropriate to use technology.



Distributive law



-Distributive law understand with rational exponents, they justify and demonstrate examples and can apply;

-Power - and root spelling can transform into each other.



Area of competence "Functional relationship"



Functions



-Quadratic functions, power functions (of type f(x) = xn with n integer) and the root function (f(x) = x 1/2) can represent and interpret their properties.

-Intersections of two functions can graphically define and calculate



Area of competence "Stochastic"



Descriptive statistics



-

Frequencies (absolute, relative and percentage) graphically represent the legal authority to interpret and argue the selection of a certain appearance in application tasks;

-Averages and variability can calculate and interpret (arithmetic mean, median, mode, standard deviation, range, quartiles and interquartile);

-Regression and correlation of two-dimensional data volumes explain clearly, technology usage to determine and interpret the results.



School specific competence



Statistics



-Data may collect and know the difference in the handling of qualitative and quantitative characteristics;

-Data which can be manipulated; argue

-the descriptive statistics can apply to professional field related studies.



Models for early math education (skills of precursor to)



-Shapes and patterns, understand, describe, apply, and present

-Visuo spatial skills, comparing the patterns and structures to the understanding of geometric terms, spatial and temporal orientation, symmetry.

Homework: two one-hour homework

Portfolio to the early math training



3. class



Area of competence "Algebra and geometry"



Vectors and matrices



-The definitions of vector and matrix know;

-two-dimensional vectors in coordinate system can represent

-Addition, subtraction, multiplication by a scalar and scalar product; geometrically interpret and apply in practical tasks of two-dimensional vectors

-Systems of equations in matrix form can represent and solve through technology use.



Solving exponential and logarithm



-Solving exponential (type a x = b or s λx = c, where a, b, λ, c are real numbers) roblem with Logarithmising;

-know and apply logarithmic data laws;

-Technology can adequately use for solving more complex solving exponential.



Trigonometry



-Sine, cosine, and tangent of an angle in the rectangular triangle as interpret aspect ratios;

-right triangles resolve;

-Equations with trigonometric functions using technology can solve.



Area of competence "Functional relationship"



Exponential and logarithmic function



-Graphs of exponential functions (of type f(x) = bx a·; b is a positive real number) with its characteristic properties know and suggest in the context;

-the terms "Half-life" and "Double time"; know, identify and interpret in the context

-know the logarithm function as the inverse of the exponential function.



Sequences and series



-Know and apply the Education Act of arithmetic and geometric sequences;

-know the definition of the series.



School specific competence



Models for and acceptance processes



-Linear functions and exponential functions as models; compare and meaningful use for the description and acceptance processes

-the relationship between linear functions with arithmetic sequences and of exponential functions with geometric consequences at the description and removal operations argue;

-Calculations of practice relevant to and acceptance processes perform and document and interpret the results.



Models for early math education (skills of precursor to)



-Seriation models for number crunching and mathematical competence development understand, describe, and apply present can.

Homework: two homework, at least one of them zweistündig

Portfolio to the early math training



4. class



Area of competence "Algebra and geometry"



Trigonometry



-Simple solve tasks with Sines and cosines and can interpret the results.



Area of competence "Functional relationship"



Trigonometric functions



-Trigonometric functions (degree and radian measure) can represent and argue on the basis of the unit circle.



Area of competence "Analysis"



Differential billing



-Have an intuitive notion of limit and an intuitive notion of continuity a function with;

-Discuss monotony and terminal points of the function;

-the concepts of difference quotient (average rate of change) and differential quotient ("current" rate of change) understand and use for the solution of tasks;

-the notion of inference therefrom;

-Power - and polynomial - simple exponential functions differentiate and interpret the result;

-Derivative of composite power and polynomial - simple exponential functions with the help of the calculate derivation rules (total, factor, product and chain rule);

-local extrema, curvature behavior, turning points of power - and polynomial functions with the help of calculate the Ableitung(sfunktion) and describe;

-Function equations from application-related contexts can set up (inverse problems).



Area of competence "Stochastic"



Theory of probability



-The classical and statistical probability term use and interpret;

-How to exclude the addition and multiplication rule on each other or independent events

-Conditional probabilities for simple facts about tree diagrams can represent and calculate

-the concept of random variables know and apply, define the distribution function and the parameters (mean and variance) a random variable and argue can.



School specific competence



Extreme value problems



-Model extreme value problems, transfer, perform calculations and results can argue (constraints: text similarity, Pythagorean theorem).



Models for early math education (skills of precursor to)



-Basic experiences of infants with the amount of time in temporal sequences and rhythms understand, describe, apply and present can.

Homework: two two-hour homework

Portfolio to the early math training



5th grade



Area of competence "Analysis"



Integral calculus



-The term root function know the legal authority to recognize the relationship between function and root function in their graphical representation and describe;

-Root functions; compute power - and polynomial functions

-the concept of the definite integral on the basis of an intuitive concept of limit for limit of a upper and lower sum; suggesting

-the definite integral; suggest as an oriented surface

-for the calculation of the area use the definite integral of power - and polynomial functions.



Area of competence "Stochastic"



Theory of probability



-The binomial distribution; know and use in the context and interpret

-Random experiments using the binomial distribution model, calculate probabilities, graphically display and interpret the results.



School specific competence



Continuous probability distribution



-The normal distribution; know and use in the context and interpret

-know and demonstrate the importance of mean value and standard deviation in relation to the normal distribution curve;

-Situations can identify and describe can be modeled where with binomial distribution or normal distribution

-the probability can apply to work-related problems.



Models for early math education (skills of precursor to)



-Experience with the concepts of chance, probability and frequency can understand, describe, apply and present.



Review of all subject areas



Homework: two two - or three-hour homework

Portfolio to the early math training

7. in annex VII, section A, Z 16 together with heading reads:



"16 RHYTHMIC AND MUSICAL EDUCATION



Education and teaching task:

Students achieve the following objectives:



-Perception, understanding and expression of the interaction of music and movement in the artistic educational and communicative context, acquire of theoretical basics and reflection to implement rhythmic and musical content in the educational profession, awareness of the senses and differentiation of perception as the basis for monitoring and negotiation processes, development and usage of individual artistic expression in music and movement, people aware of the networking of motor, social affective and cognitive learning processes.

Curriculum:



2nd class



Area of competence "Perception and body awareness"



-His own body consciously perceive;

-raise awareness and differentiate areas of perception different senses;

-Relationship and interaction of music and motion (time/power/space/form) can capture.



Competence "Creativity and expression"



-Develop and expand the Repertoire of movement expression through music and movement;

-by means of the rhythm (music/instruments, movement, language/voice, materials/objects) under the guidance of improvising and fashion;

-Meter, beat, rhythm, form, gather momentum and express;

-

under the guidance of free and bound forms of dance move;

-simple choreographies in different social forms can develop.



Area of competence "Interaction and communication"



-With other classmates and schoolmates in various forms of social interaction and together to find solutions;

-various roles (leader/next appears, conductive to) take in creative and educational processes;

-the effect of voice communication can perceive.



Area of competence "Transfer in the teaching profession"



-Even experienced rhythm units can reflect.



3. class



Area of competence "Perception and body awareness"



-Free and bound forms of movement to different music can perform differently.



Competence "Creativity and expression"



-Various instruments and materials can creatively use (eg for improvisations, sound stories, motion / vocal accompaniment, creating picture books);

-Voice and language varied use and invent different types of text (nonsense rhymes, lyrics and proverbs) and can make;

-enduring, differentiated and focused with rhythmic musical tasks, deal

-intercultural elements of music, movement and language to know and implement.



Area of competence "Interaction and communication"



-Elementary music instruments and rhythmic materials can use to promote interaction and non-verbal communication.



Area of competence "Transfer in the teaching profession"



-Objectives and understand and can discuss content of rhythmic musical education;

-various materials in terms of, apply to work with children and young people

-methodical basics to creating dances, songs, texts and sound stories; apply as an example

-deal with introductory literature;

-in study visits in practice kindergarten, practice Hort; meet targeted tasks and observation tasks using reflection criteria

-Rhythmic units can exemplary plan and perform.



5th grade



Area of competence "Perception and body awareness"



-Tension and relaxation can integrate within the meaning of the mental health in the context of personal and professional.



Competence "Creativity and expression"



-The own creative potential improvisational creatively can consciously insert music and material language, voice, movement, and reflect.



Area of competence "Interaction and communication"



-Act empathic and appreciative.

-bring a fine situation and accept personal opinions;

-emotional and factual actions vary;

-Act cooperative, communicative and team-oriented and can take responsibility.



Area of competence "Transfer in the teaching profession"



-Rhythm as method can use to promote the children in their emotional, social, cognitive, and motor ability of school

-Rhythm as learning aid in the Lair (also across the curriculum)

-Children of different ages with different development conditions and dispositions of behavior by means of music and movement can integrate into group processes

-Know similarities and differences between of related departments (psychomotor/Moto pedagogy, elementary music education, sensory integration, music therapy);

-to grapple with literature independently, critically evaluate and adequately; insert

-Projects (also across the curriculum) plan, perform and present."

8. in annex VII, section A, Z 22 together with the heading reads:



"22 INFORMATICS AND MEDIA



Education and teaching task:

Students achieve the following objectives:



-Knowledge of basic computer and academically knowledge to solve simple problems.

-Self-determined and purposeful use of information technologies and media.

-Ability to expertly in the critical use of information technologies to support children and young people.

-Craft, to gain information, to prepare, and to present appropriate media.

-Acquisition of media competence they apply to in the teaching of other subjects and develop.

Curriculum:



1st class



Scope of "Text processing"



-Formatting and layout of simple documents according to defined standards can create.



Area of competence "Manage and represent data"



-Simple calculations using standard programs can perform (spreadsheet);

-Data to readable prepare and present in diagrams.



Area of competence "Basics of data processing"



-A simple file organization can create

-Data backups perform;

-Basic file formats and their meaning therefrom;.

-Rename and use the main components of the hardware;

-Know basics of the operation and use of software.



Area of competence "Presentation"



-By means of appropriate media a simple presentation run;

-the main quality criteria for presentations to know and apply.



Area of competence "Networks" (Web, Internet, networks)



-Possibilities of search on the Internet can know and take into account their limits.



Area of competence "Media"



-Basic tools of image processing can apply.



2nd class



Scope of "Text processing"



-Functional design of a multi-page document can perform.



Area of competence "Manage and represent data"



-Practical applications in the field of data processing can create.



Area of competence "Basics of data processing"



-With own and foreign data responsibly;

-Easy can solve problems with hardware and software.



Area of competence "Presentation"



-Build a multimedia presentation and can perform.



Area of competence "Networks" (Web, Internet, networks)



-Platforms can use for communication and knowledge acquisition.



Area of competence "Media"



-A media project to perform."

9. in annex VII, section A, Z 23 together with the heading reads:

"23 SEMINAR ORGANIZATION, MANAGEMENT AND LAW"

Education and teaching task:

Students achieve the following objectives:



-Acquisition of fundamental knowledge of business management - in particular socio-educational institutions - and application in the field.

-Assessing basic legal issues in the social environment by acquiring knowledge of profession-specific areas of law.

-Get to know and learn the specifics of the leadership of service organizations with strong leadership.

-Enable targeted action in organizations to the conscious design of professional development.

Curriculum:



4. class



Competence area of "Law"



-Know essential statutory provisions from the professional field.



Area of competence "Project management"



-Elements and methods of project management to know and apply.



Area of competence "Marketing and management"



-Know instruments of evaluation and quality management;

-evaluate various forms of personal development.

-various instruments of share and storing information can use.



5th grade



Area of competence "Marketing and management"



-Know and organize various forms of public relations;

-Corporate culture, goals, mission statement can analyze.



Area of competence "Organization and management"



-The term organization in its various meanings, define and explain;

-know and explain organisation-theoretical concepts;

-Management and leadership in the social field, know and understand.



Area of competence "Business basics"



-Basic knowledge of accounting in the context of professional can apply."

Article 2

Modification of the Ordinance on the curriculum for the educational institution for Social pedagogy

On the basis of



1 of the school Organization Act, Federal Law Gazette No 242/1962, as last amended by Federal Law Gazette I no. 36/2012, in particular its articles 6 and 96, and 2. § 7 paragraph 1 of the Federal teacher teaching obligation law, BGBl. No. 244/1965, as last amended by Federal Law Gazette I no. 55/2012, is prescribed: Ordinance of the Federal Minister for education, art and sport, on the curriculum for the educational institution for Social pedagogy , BGBl. No. 355/1985, as last amended by the regulation Federal Law Gazette II No. 256/2006, is amended as follows:

1. in article III the following paragraph 4 is added section 3:

"II No. 256/2012 contact (4) sections IV and VI of annex 1 of this Regulation as amended by regulation BGBl. with regard to the 1st, 2nd and 3rd class with September 1, 2012, and in terms of the other classes with 1st September of the subsequent years alternative ascending into force."


2. in annex I (curriculum of the education Institute for social education) IV (hours table) section "Mathematics" is replaced by the designation "Applied mathematics" and which is the compulsory subject "Applied mathematics" that line:









Applied mathematics





2





2





2





2





2





10





(I)




3. in annex I section VI [educational and teaching tasks of individual subjects, sharing the learning on the individual school levels (classes), didactical principles] under section A (compulsory subjects) the compulsory subjects "Math" is replaced by the compulsory subjects "Applied mathematics" and is:



"APPLIED MATHEMATICS



Education and teaching task:

Students achieve the following objectives:



-Translation of problems in the mathematical language of symbols, precise work and arguing, - planned and systematic approach to solving tasks, - accurate representation of results - make the transfer of already learnt skills and methods on new tasks, - appropriate handling of technical AIDS, - check correct use of data laws, - accurate graphical representation of mathematical contexts, - and to assess results on their accuracy, - developing logical thinking by solving mathematical problems , - Acquisition of knowledge about the development of mathematical understanding (principles and principles of early educational action in relation to mathematical skills of precursor), - manufacture of connections between mathematical structures and the early basic skills underlying them, - trusted his contexts the content dimensions figures and mass, algebra and geometry, functional analysis and stochastics, and the plot dimensions, argumentation and communication, operate and use of technology (minimum requirement is a graphing calculator) , Interpreting and documenting, modeling, and transfer.

Students develop the following insights:



-Fundamental insights can use for mathematical early education and learning support, - the knowledge that argumentation and communication in applied mathematics are characteristic, - the experience that solving tasks can bring joy and self-confidence, - the awareness that can apply mathematical thinking and mathematical knowledge in the different life, knowledge, and professional areas.

Curriculum:



1st class



Area of competence "Numbers and dimensions"



Computing with numbers and quantities of numbers:



-Know the number ranges of the natural, whole, rational, real and complex numbers and their associated argue;

-Numbers and intervals on the line represent;

-Express and perform this basic arithmetic numbers in the decimal system in fixed - and floating-point representation;

-Figures can understand and apply as a percentage

-Master round and rollover account.



Computing with dimensions:



-Numbers be understood as measures of sizes, which convert measures between different units;

-Multiple and parts of units can represent with the appropriate powers of ten.



Area of competence "Algebra and geometry"



Variables and terms



-Expect with variables and terms (parentheses, binomial formulas and fractions);

-Distributive law understand with integer exponents, they justify and can apply.



Equations and formulas



-Linear equations and inequalities can dissolve in a variable and interpret the solution set

-Formulas can transform after one of its variables

-Problems in different fields of application in the form of an equation model and interpret the results in terms of the problem and can document.



Systems of linear equations



-To set up and solve equation systems;

-the conditions for the solvability of linear equation systems with two variables can argue, graphically illustrate and interpret.



Area of competence "Functional relationship"



Functions



-Know and argue the definition of the function and relation;

-Functions can understand and interpret as models for the description of the dependency between two sizes.



Linear functions



-The function equation of the linear function (f(x) k = x + d) know, represent the graphs on the coordinate system and d computationally and graphically identify the increase in k as well as the ordinate section;

-know the concept of inverse function and the equation for the inverse function can determine computationally and graphically

-the zero point of the linear function; charge, graphically determine and interpret as a solution of a linear equation

-can graphically define and calculate the intersection of two linear functions.



School specific competence



Empirical functions



-graphically represent from professional field related studies;

-graphical representations of empirical professional field related functions can interpret and argue.



Quantities



-Mates of quantities (average, Union, and difference); identify, visualize and interpret Diagrams of amounts of can apply and interpret.



Models for mathematical learning in primary school



The students develop models for tutoring on selected samples and create mathematically-oriented educational and illustrative material for the development of counting, counting strategies, the number crunching and for developing mathematical competence in elementary school, as well as learning tools for the acquisition of the digits and the number definition, learning tools to capture the Mengenbegriffs, learning aids for the computing masses and skills of weighing, measuring and comparing.

Homework: two one-hour homework

Portfolio to the mathematical learning



2nd class



Area of competence "Numbers and dimensions"



Complex numbers



-in the Gaussian plane can represent and can illustrate and perform addition or subtraction.



Area of competence "Algebra and geometry"



Equations



-Quadratic equations set, loosen and the different cases of real and complex solution; argue

-Apply and transform formulas of elementary geometry;

-the solution of equations of higher degree knowing appropriate to use technology.



Distributive law



-Distributive law understand with rational exponents, they justify and demonstrate examples and can apply;

-Power - and root spelling can transform into each other.



Area of competence "Functional relationship"



Functions



-Quadratic functions, power functions (of type f(x) = xn with n integer) and the root function (f(x) = x 1/2) represent and interpret their properties;

-Intersections of two functions can graphically define and calculate.



Area of competence "Stochastic"



Descriptive statistics



-Frequencies (absolute, relative and percentage) graphically represent the legal authority to interpret and argue the selection of a certain appearance in application tasks;

-Averages and variability can calculate and interpret (arithmetic mean, median, mode, standard deviation, range, quartiles and interquartile);

-Regression and correlation of two-dimensional data volumes explain clearly, technology usage to determine and interpret the results.



School specific competence



Statistics:



-Data may collect and know the difference in the handling of qualitative and quantitative characteristics;

-Data which can be manipulated; argue

-the descriptive statistics can apply to professional field related studies.



Models for mathematical learning in primary school



Selected examples, students develop models, teaching aids and illustrative material for tutoring to the understanding of the notion of space, spatial orientation, comparison of area, shape, size, symmetries, patterns and structures and General geometric concepts.

Homework: two one-hour homework

Portfolio to the mathematical learning



3. class



Area of competence "Algebra and geometry"



Vectors and matrices



-The definitions of vector and matrix know;

-two-dimensional vectors in coordinate system can represent

-Addition, subtraction, multiplication by a scalar and scalar product; geometrically interpret and apply in practical tasks of two-dimensional vectors

-Systems of equations in matrix form can represent and solve through technology use.



Solving exponential and logarithm



-Solving exponential (type a x = b or s λx = c, where a, b, λ, c are real numbers) roblem with Logarithmising;

-know and apply logarithmic data laws;

-Technology can adequately use for solving more complex solving exponential.



Trigonometry



-

Sine, cosine and tangent of an angle in the rectangular triangle as interpret aspect ratios;

-right triangles resolve;

-Equations with trigonometric functions using technology can solve.



Area of competence "Functional relationship"



Exponential and logarithmic function



-Graphs of exponential functions (of type f(x) = bx a·; b is a positive real number) with its characteristic properties know and suggest in the context;

-the terms "Half-life" and "Double time"; know, identify and interpret in the context

-know the logarithm function as the inverse of the exponential function.



Sequences and series



-Know and apply the Education Act of arithmetic and geometric sequences;

-know the definition of the series.



School specific competence



Models for and acceptance processes



-Linear functions and exponential functions as models; compare and meaningful use for the description and acceptance processes

-the relationship between linear functions with arithmetic sequences and of exponential functions with geometric consequences at the description and removal operations argue;

-Calculations of practice relevant to and acceptance processes perform and document and interpret the results.



Models for mathematical learning tools during the transition from the folk school in the secondary 1



Selected examples work out math tutoring students and create mathematically-oriented educational and illustrative material for the processing of numbers and relations: "bigger, smaller, equal", for the basic computer skill with numbers and for the understanding of elementary geometry.

Homework: two homework, at least one of them zweistündig

Portfolio to the mathematical learning



4. class



Area of competence "Algebra and geometry"



Trigonometry



-Simple solve tasks with Sines and cosines and can interpret the results.



Area of competence "Functional relationship"



Trigonometric functions



-Trigonometric functions (degree and radian measure) can represent and argue on the basis of the unit circle.



Area of competence "Analysis"



Differential billing



-Through an intuitive concept of limit and an intuitive notion of continuity a function have, - discuss monotony and terminal points of the function;

-the concepts of difference quotient (average rate of change) and differential quotient ("current" rate of change) understand and use for the solution of tasks;

-the notion of inference therefrom;

-Power - and polynomial - simple exponential functions differentiate and interpret the result;

-Derivative of composite power and polynomial - simple exponential functions with the help of the calculate derivation rules (total, factor, product and chain rule);

-local extrema, curvature behavior, turning points of power - and polynomial functions with the help of calculate the Ableitung(sfunktion) and describe;

-Function equations from application-related contexts can set up (inverse problems).



Area of competence "Stochastic"



Theory of probability



-The classical and statistical probability term use and interpret;

-How to exclude the addition and multiplication rule on each other or independent events

-Conditional probabilities for simple facts about tree diagrams can represent and calculate

-the concept of random variables know and apply, define the distribution function and the parameters (mean and variance) a random variable and argue can.



School specific competence



Extreme value problems



-Model extreme value problems, transfer, perform calculations and results can argue (constraints: text similarity, Pythagorean theorem).



Models for mathematical learning tools during the transition from secondary 1 to secondary 2



Selected examples, work out math tutoring students and create mathematically-oriented educational and illustrative in terms of numbers, geometrical shapes and simple functions and relations.

Homework: two two-hour homework

Portfolio to the mathematical learning



5th grade



Area of competence "Analysis"



Integral calculus



-The term root function know the legal authority to recognize the relationship between function and root function in their graphical representation and describe;

-Root functions; compute power - and polynomial functions

-the concept of the definite integral on the basis of an intuitive concept of limit for limit of a upper and lower sum; suggesting

-the definite integral; suggest as an oriented surface

-for the calculation of the area use the definite integral of power - and polynomial functions.



Area of competence "Stochastic"



Theory of probability



-The binomial distribution; know and use in the context and interpret

-Random experiments using the binomial distribution model, calculate probabilities, graphically display and interpret the results.



School specific competence



Continuous probability distribution



-The normal distribution; know and use in the context and interpret

-know and demonstrate the importance of mean value and standard deviation in relation to the normal distribution curve;

-Situations can identify and describe can be modeled where with binomial distribution or normal distribution

-the probability can apply to work-related problems.



Models for mathematical learning in secondary education 2



Selected examples, develop general math tutoring students and create appropriate mathematically-oriented educational and illustrative material, bearing in mind that the volume and numbers-related knowledge has influence on the later performances in mathematics instruction. Young people with computer problems often have uncertainties in the pre-numeric bases from the toddler and preschool.



Review of all subject areas



Homework: two two-to three-hour homework

Portfolio to the mathematical learning support"

Blacksmith