Transcript Algebra in the Czech Republic (Jarmila Novotna)

Teaching of Algebra
in the Czech Republic
Jarmila Novotná
Charles University in Prague,
Faculty of Education
Department of Mathematics and
Mathematical Education
e-mail: [email protected]
Czech Educational System
From the history
• tradition of education in Czech history (population
groups which would not achieve any education in other
countries were often educated, e.g. Hussite women in
the 15th century), the general literacy in the 1930s
was of higher standards than were common in the rest
of Europe
• Charles University was established in 1348 (the first
European University east of Germany)
• Comenius - 17th century
• compulsory six-year school attendance was enacted
in 1774
• influence of the Soviet tradition, from which schools
were only freed after 1989
Teaching of algebra in the Czech
Republic
Pre-algebra and algebra in
the compulsory education
Three programmes:
Basic School
General School
National School
Teaching of algebra in the Czech
Republic
Specific aims of mathematics
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Mathematics together with the Czech language form the
educational infrastructure of the basic school. Mathematics
provides pupils with the knowledge and skills necessary for
everyday life and prepares the foundations for successful
development through professional training and further study
at upper secondary schools. It develops pupils’ intellectual
abilities, their memory, imagination, creativity, abstract
thinking and ability to reason logically. At the same time it
contributes to the development of personal qualities, such as
patience, diligence, critical thinking.
Knowledge and skills acquired in mathematics are the
preconditions for success in the sciences, economics,
technology and the use of computers.
Teaching of algebra in the Czech
Republic
Specific aims of mathematics
Teaching of mathematics supports pupils’ learning to:
 …
 use variables, understand what they represent, solve
equations and inequalities and use them when solving word
problems
 record and express graphically relationships between
quantitative phenomena in nature and in society and work
with certain functions when solving word problems
 prove simple theorems and conclude logical results from
given assumptions
 …
Teaching of algebra in the Czech
Republic
The structure
of the schools subject mathematics
Main parts of mathematics



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Arithmetic
Algebra
Geometry
Applications of mathematics
The relation to other subjects
The language of algebra
Algebraic culture
Teaching of algebra in the Czech
Republic
Algebra in Standards
for the compulsory level

Expressions
Polynomials; Polynomial fractions

Equations
Equivalent equations; Linear equations; Quadratic
equations; Systems of linear equations

Functions
Coordinate system; Functions; Direct and indirect
proportionality; Linear functions; Quadratic
functions; Trigonometric functions
Programme: Basic School
Context
Knowledge
Skills
Programme: General School
Core of the learning programme
• Topic
 Subtopic (details)
Samples
The student
should be able to
Programme: Basic School
• 5th grade
Tables, graphs, diagrams
• 6th grade
Consolidation of knowledge and skills
• 7th grade
Direct and indirect proportions
• 8th grade
Powers with natural exponents
Expressions
Linear equations
• 9th grade
Polynomial functions, Solving equations with the unknown in the
denominator
Systems of linear equations with two variables
Functions
Programme: General School
• 6th grade
Core: Good mastering of numerical operations with natural and
decimal; drawing
Word problems
Pre-algebra (expressions, variable, function and its graph, linear
equations)
• 7th grade
Core: Dependences, functions, orientation towards applications
Linear equations and linear functions
• 8th grade
Core: Good mastering algebraic language, numerical mathematics;
geometrical constructions
Calculations with polynomials
• 9th grade
Core: Knowledge necessary for mathematical applications
Algebraic technique
Functions
Algebra in Standards for
the upper-secondary level (Gymnázium)
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Basic knowledge about sets and propositions
Expressions
Polynomials; Polynomial fractions; Expressions with
powers and roots


Algebraic equations and inequalities
Functions
Basic concepts; Rational functions; Quadratic
functions; Exponential and logarithmic functions

Trigonometry; Combinatorics, probability and
statistics; Sequences
Briefly about teaching in the Soviet Union
• Algebra started in the 6th grade (12-year old
pupils)
• In the 6th, 7th and 8th grades, it covered:
Algebraic expressions, equations,
inequalities, functions, sequences
(arithmetical, geometrical, oscillating and
Fibonacci)
• Two main approaches: calculative, scientific
Results
Entrance exams for important Universities based on
complicated manipulations with algebraic expressions
and functions
Examples
 The idea of “a big nation” can be clearly seen – only about 1.5 %
of students understood algebra, but these were excellent