Linguistic competencies entailed by the concept of Mathematical Literacy Seminar on Subject literacies and the right to quality education for democratic

Linguistic competencies entailed by the concept of Mathematical Literacy

Seminar on Subject literacies and the right to quality education for democratic citizenship

and participationStrasbourg 28.09.2012

Prof. Dr. Helmut Linneweber-Lammerskitten

„Mathematical Literacy“ is more than „having basic skills in mathematics“

“Mathematical literacy is an individual's capacity to identify and understand the

role that mathematics plays in the world, to make well-founded judgements and to

use and engage with mathematics in ways that meet the needs of that individual's

life as a constructive, concerned and reflective citizen.” (OECD 2003, S. 24)

Linneweber-Lammerskitten 2

...and entails linguistic competencies

Expressions such as "identify and understand" and "well founded judgements"

refer to activities which have both cognitive and linguistic dimensions. One can

only identify, understand and judge insofar as one relates thought and language

to each other. A “life as a constructive, concerned and reflective citizen”

presupposes communication with others.

National educational standards in mathematics make abstract objectives more concrete and obligatory

3

e.g. „HarmoS educational Standards for Mathematics“ in Switzerland (cf. “Handout)”

The educational values targeted by mathematics teaching practices can only be realised if linguistic

competence is also targeted, since

• Linguistic competencies are constitutive parts of educational standards in

mathematics: Students can only reach the educational standards in mathematics at the end of compulsory

school, if they are able to name, to describe, to define, to explain, to argue etc.

• Linguistic competencies are preconditions for learning: Students can only successfully participate in learning mathematics if they have the linguistic

prerequisites to understand questions, problems, argumentations, etc. and are able to give

answers, to interact with others, etc.

• Linguistic competencies are preconditions for acting as an active, reflective and

intelligent citizen All these presuppose a certain degree of reflection, which can only be realised on a higher level of

language competence


Three aspects concerning linguistic competencies


use handout paper for cando descriptions in French and German

Cognitive and Linguisitic Aspects in Educational Standards (HarmoS)*) I

Knowing, Recognising & Describing• understanding, using and explaining technical terms• relating technical terms to mathematical objects, properties and relations and vice versa• identifying forms and pattern• naming and describing mathematical rules and laws in their own language• capturing mathematical states of affairs and describing them

…

Operating & Calculating• Carrying out calculations, transformations and constructions in written "standard form",

with notes or orally, with or without (technical) instruments

…

*) Linneweber-Lammerskitten, H. (2012). Items for a description of linguistic competence in the language of schooling necessary for teaching/learning mathematics (in secondary education). An approach

with reference points. Strasbourg: Council of Europe. Retrieved from: http://www.coe.int/t/dg4/linguistic/Source/Source2010_ForumGeneva/4_LIS-Mathematics2012_EN.pdf (August 2012)


Cognitive and Linguisitic Aspects in Educational Standards (HarmoS)*) II

Using Instruments & Tools• Using electronic instruments (calculator, Computer), works of reference, construction

instruments (compass, set square)• …

Presenting & communicating• Understanding calculations, transformations, constructions, argumentations of other

students• Presenting own calculations, transformations, constructions, argumentations in a way

that is comprehensible and traceable by others and appropriate with respect to the

mathematical object• …




Cognitive and Linguisitic Aspects in Educational Standards (HarmoS)*) III

Mathematising & Modelling• Describing, interpreting and modulating (problem) situations (of daily life) in order to

solve them by mathematical means• ...

Arguing & Justifying• Forming assertions and giving reasons for them• Making thoughts and ways of calculating transparent and justifying them • Giving illustrative explanations for mathematical phenomena and laws• understanding and reproducing proofs and counterexamples • ...




Cognitive and Linguisitic Aspects in Educational Standards (HarmoS)*) IV

Interpreting & Reflecting on Results

• Checking results for truth and for adequacy with the original problem

• Reflecting whether a result or an approach can be used for future problem solving

• …

Experimenting & Exploring

• Exploring mathematical situations and searching for mathematical laws

• Expressing conjectures and trying to support or falsify them by thought experiments

• ...




Question for presenters to address:

1) Are there any language requirements specific to your subject area?

– Natural language mixed with formal language (& formal metalanguage) and graphs,

diagrams etc.


DMK/DPK (Ed.) Fundamentum Mathematik und Physik. Bern: Orell Füssli p.15


2) How do you see the relationship between your specific subject area and the possibility

of formulating a general framework for the language of schooling?

- A general framework seems possible but only on an abstract level.

- On a less abstract level one must recognise that labels also used in ordinary

language have deviant meanings in mathematics and even within different areas of

mathematics:

- with respect to objects: Menge, Körper, Seite,

- with respect to activities: to define, to prove,



3) What do you think is the specific contribution of your subject to such a framework?

– Natural language mixed with formal language (& formal metalanguage) and graphs,

diagrams etc. (cf. 1)

– Situations, expressions, discourse functions, strategies etc. directed to “overarching

ideas” (PISA 2003)*): quantity, space and shape, change and relationships, uncertainty

– Situations, expressions, discourse functions, strategies etc. directed to “characteristic

mathematical competencies“ (PISA 2003): thinking and reasoning, argumentation,

communication, modelling, problem posing and solving, representation, using

symbolic, formal and technical language and operations, use of aids and tools


*) OECD (2003). PISA 2003 Assessment Framework: Mathematics, Reading, Science and Problem Solving Knowledge and Skills - Publications 2003. Retrieved from: http://www. oecd.org/dataoecd/46/14/33694881.pdf (June 2011).

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Linguistic competencies entailed by the concept of Mathematical Literacy Seminar on Subject literacies and the right to quality education for democratic