Comparison of lower secondary school mathematics standards
One of the project’s aims
is to show that,
in Europe, it is possible to design a curriculum for lower secondary
school
mathematics teacher training that, despite the differences between
teacher
training systems throughout Europe, includes a relevant common set of
topics to be introduced to
trainees.
Before trying to show this fact, it
is,
however, necessary to investigate which are the standards for
mathematics education
at lower secondary school level in the different European countries. If
they
turn out to be quite different, any attempt to outline a European
curriculum
will be hard or even impossible. In this chapter standards accepted in
the
project’s partner countries are compared.
The analysis of the tables below actually show that, despite some differences
between the input standards (that is the output primary schools
standards),
there is little difference, as expected, between the output lower
secondary school
mathematics standards accepted in the project’s partner
countries.
|
TOPICS
|
Czech Republic
|
Denmark
|
France
|
Italy
|
Slovak Republic
|
|
Number systems (operations
incl.)
|
|
|
|
|
|
|
Rational numbers
|
+
|
+
|
+
|
+
|
+
|
|
Fractions
|
+
|
+
|
+
|
+
|
+
|
|
Decimal numbers
|
+
|
+
|
+
|
+
|
+
|
|
Real numbers
|
+
|
+
|
+
|
+
|
+
|
|
Powers
|
+
|
+
|
+
|
+
|
+
|
|
Roots
|
+
|
+
|
+
|
+
|
+
|
|
Proportionality
|
|
|
|
|
|
|
Percent
|
+
|
+
|
+
|
+
|
+
|
|
Ratio
|
+
|
+
|
+
|
+
|
+
|
|
Proportionality, rule of three
|
+
|
+
|
+
|
+
|
+
|
|
Divisibility
|
|
|
|
|
|
|
Multiple and divisor
|
+
|
+
|
+
|
+
|
+
|
|
Prime numbers
|
+
|
+
|
-
|
+
|
+
|
|
GCD
|
+
|
-
|
+
|
+
|
+
|
|
LCM
|
+
|
-
|
-
|
+
|
+
|
|
Factorization
|
+
|
+
|
-
|
+
|
+
|
|
Expressions
|
|
|
|
|
|
|
Numerical and algebraic expressions
|
+
|
+
|
+
|
+
|
+
|
|
Polynomials
|
+
|
+
|
-
|
+
|
+
|
|
Rational expressions
|
+
|
+
|
-
|
+
|
+
|
|
Equations,
Inequalities
|
|
|
|
|
|
|
Expressions
|
+
|
+
|
+
|
+
|
+
|
|
Linear equation
|
+
|
+
|
+
|
+
|
+
|
|
Quadratic equations
|
+
|
-
|
-
|
+
|
+
|
|
Linear inequalities
|
|
+
|
+
|
+
|
+
|
|
Systems of linear equations
|
+
|
+
|
+
|
-
|
+
|
|
Functions
|
|
|
|
|
|
|
Coordinate system
|
+
|
(primary)
|
+
|
+
|
+
|
|
Properties of functions
|
+
|
+
|
-
|
-
|
+
|
|
Direct proportion
|
+
|
+
|
+
|
+
|
+
|
|
Indirect proportion
|
+
|
+
|
+
|
+
|
+
|
|
Linear function
|
+
|
+
|
+
|
+
|
+
|
|
Quadratic function
|
+
|
-
|
-
|
+
|
+
|
|
Trigonometric functions
|
+
|
-
|
-
|
-
|
+
|
|
Basic 2D notions
|
|
|
|
|
|
|
Point, straight line, plane
|
+
|
+
|
+
|
+
|
+
|
|
Half-line, segment, half-plane, angle
|
+
|
+
|
+
|
+
|
+
|
|
Circle, circumference
|
+
|
+
|
+
|
+
|
+
|
|
Triangle, quadrilateral, polygon
|
+
|
+
|
+
|
+
|
+
|
|
Sets of points of given property
|
+
|
+
|
+
|
+
|
+
|
|
Trigonometry in rectangular triangle
|
+
|
-
|
+
|
+
|
+
|
|
Basic solids
|
|
|
|
|
|
|
Polyhedron
|
+
|
-
|
+
|
+
|
+
|
|
Cube, cuboid, prism
|
+
|
+
|
+
|
+
|
+
|
|
Pyramid
|
+
|
+
|
+
|
+
|
+
|
|
Sphere, cylinder, cone
|
+
|
+
|
+
|
+
|
+
|
|
Geometric mappings
|
|
|
|
|
|
|
Congruence of geometric figures
|
+
|
+
|
-
|
+
|
+
|
|
Similarity of geometric figures
|
+
|
+
|
-
|
+
|
+
|
|
Point symmetry, line reflection, translation
|
+
|
+
|
+
|
+
|
+
|
|
Constructions
|
+
|
+
|
+
|
+
|
+
|
|
Measurement
|
+
|
+
|
+
|
+
|
+
|
Output lower secondary school
mathematics standards
Detailed descriptions for each project’s partner country can be found by following the links below:
Further
topics included in standards
The following topics are not
explicitly
mentioned in all standards, but they are implicitly present in all
mathematical
educational systems at the metacognitive[1] level. Except Statistical probability
they belong to both content knowledge and metacognitive domain. The
metacognitive level is not explicitly stated.
|
TOPICS
|
Czech Republic
|
Denmark
|
France
|
Italy
|
Slovak Republic
|
|
Data representation and organization
|
-
|
+
|
+
|
+
|
+
|
|
Estimates
|
-
|
+
|
+
|
+
|
-
|
|
Possibilities and limitations in using
mathematics as a description and a basis for decisions
|
-
|
+
|
+
|
-
|
-
|
|
Statistical probability
|
-
|
+
|
-
|
-
|
+
|
|
Communication and problem solving
|
-
|
+
|
+
|
-
|
-
|
Further topics included in
standards
Metacognition combines various
attended
thinking and reflective processes. It can be divided into five primary
components:
- preparing and planning for learning,
- selecting and
using
learning strategies,
- monitoring strategy use,
- orchestrating
various
strategies,
- evaluating strategy use and learning.
Teachers should
model strategies for learners to follow in all five areas. To be
effective,
metacognitive instruction should explicitly teach students a variety of
learning strategies and also when to use them[2].
Some theories underpinning learning strategy research:
- O’Malley and Chamot (1990)[3] classify strategies in the following way:
- cognitive strategies;
- metacognitive strategies;
- social strategies;
- affective strategies.
- Rebecca Oxford (1990)[4] distinguishes:
- Direct Strategies (memorizing, cognitive processing, compensation);
- Indirect Strategies (metacognitive, social and affective).
1 In education, the term
metacognition can be defined as "awareness of one's own knowledge or problem-solving abilities".
2 Anderson, J. (2002). The Role of Metacognition in Second Language Teaching and Learning. Available at [
http://www.cal.org/resources/digest/0110anderson.html].
3 O’Malley, J.M. & Chamot, A.U. (1990).
Learning Strategies in Second Language Acquisition. Cambridge University Press.
4 Oxford, R.L. (1990).
Language Learning Strategies: What Every Teacher Should Know. Newbury House.
