Educational standards math

Educational standards mathematics called in Germany binding requirements for teaching in specialist mathematics as one of the main subjects. These educational standards were introduced in 2003 by the German Conference of Ministers of Education as a result of the PISA study .

Conception of educational standards mathematics

The conception of the mathematics educational standard takes up the distinction used in the PISA study between process-related and content-related competencies and generates three so-called dimensions in this regard. The process dimension formulates six general mathematical competencies that are to be acquired in the learning process . These can each be broken down into three requirement areas (requirement dimension). The content competence is concretized and organized by five main ideas.

Math skills

These competencies describe central aspects of mathematical work. As a rule, they appear in a group and do not claim to be clearly formulated to one another.

• Argue mathematically (K1):

This is about understanding, connecting and evaluating mathematical-logical chains of argument.

• Solve problems mathematically (K2):

If a solution structure is not obvious, a strategic approach is required to find mathematical solution ideas such as analogy, systematic testing, illustration, which must be applied, checked and evaluated with regard to their usefulness in the solution process.

• Modeling mathematically (K3):

Reality-related questions need to be translated into mathematical models as reduced, simplified images, the problem to be solved with mathematical means and this result to be assessed against the real context.

• Use mathematical representations (K4):

This competence includes both the development of suitable mathematical representations (diagrams, graphs, formulas, etc.) as well as the reflective handling of given mathematical representations.

• Dealing with symbolic, formal and technical elements of mathematics (K5):

This competence relates to the use of mathematical facts (“knowing that”) or mathematical skills (“knowing how”) and includes, among other things, knowing and applying mathematical definitions and rules, working formally with variables, terms and functions as well as Use of tools such as formulas and calculators.

• Communicate mathematically (K6):

On the one hand, this relates to the understanding of texts or oral statements on mathematics and, on the other hand, to the comprehensible written or oral representation and presentation of thoughts, solutions and results. In contrast to competence K1, value is placed here on the comprehensible representation, presentation and explanation of a solution to a, also fictitious, so-called external addressee.

Mathematical guiding principles

The six mathematical competencies mentioned can be assigned to five main ideas. These guiding principles attempt to capture the phenomena that one sees when one looks at the world through mathematical eyes.
L1 number (or upper school level: L1 algorithm and number)
L2 measurement
L3 space and form
L4 functional relationship
L5 data and chance

Requirement areas

These areas concretize the cognitive level at which the students should achieve the respective competence. A distinction is made between three requirement areas:

• Requirement area I: Reproduction

This is about the pure reproduction and application of terms, sentences and procedures in a clearly defined framework that was dealt with in the classroom.

• Requirement area II: Establishing connections

Familiar issues that are themed in class and the skills acquired there should be linked to one another and to other, sometimes unknown, areas.

• Requirement area III: Generalizing and reflecting

It is important in this area to generalize knowledge, skills and abilities acquired by way of example, to transfer them to unknown areas and to develop a personal, critical-reflective position and to defend it with arguments.

As a guideline, Area I applies when an activity can be carried out in just one step. The more complex the nature of the solution process, the higher the range of requirements. So-called operators for the subject of mathematics are assigned to the requirement areas. These are requirement verbs which, as key words, are intended to concretize the expected student performance as precisely as possible in the respective subject context and must be used in a binding manner for the Abitur exams.

The requirement areas can be related to the learning objective levels and the learning objective taxonomy according to Bloom . Verbs assigned to the learning objective levels correlate with the operators for the subject mathematics, which are assigned to the individual requirement areas.

literature

• Werner Blum, Christina Drüke-Noe, Ralph Hartung, Olaf Köller (eds.): Educational standards mathematics: concrete . Secondary level I: example exercises, suggestions for lessons, ideas for further training. Cornelsen Verlag, Berlin 2006, ISBN 3-589-22321-9 .
• Rudolf Vom Hofe, Werner Blum, Reinhard Pekrun (Eds.): Mathematik heute, Volume 1: Competence-oriented tasks and comments (PALMA). Schroedel, Braunschweig 2007, ISBN 978-3-507-83094-3 .

Web links

• Standing Conference on Education Standards in General
• Educational standards math

Individual evidence

1. ↑ Kultusministerkonferenz: Operators for the subject of mathematics. (PDF) (No longer available online.) Archived from the original on September 19, 2014 ; accessed on December 31, 2014 . Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.  
2. ^ Hessian Ministry of Culture: Operators in the subjects of biology, chemistry, computer science, mathematics and physics. (PDF) (No longer available online.) Formerly in the original ; accessed on December 31, 2014 .  ( Page no longer available , search in web archives )  Info: The link was automatically marked as defective. Please check the link according to the instructions and then remove this notice.    
3. ↑ Susanne Schewior-Popp: Planning and designing learning situations . Georg Thieme Verlag, Stuttgart 2013, ISBN 978-3-13-178602-9 , p. 55 ff . ( limited preview in Google Book search).