Preparatory Adult Education in Denmark: Some basic ideas and

some dilemmasEMMA Study Visit

Copenhagen 9 – 12 May 2007 Lena Lindenskov

10 May 2007, DPU

The study visit shows stories and voices at three levels

• At the system level: background, policy, framework, information campaigns, centrally developed material

• At the level of labour markets organisations: background and policy

• At the participants and teachers level:materials, practice, experiences, personal aims

Some background in 2000

• Adults learning mathematics mentioned in Prime Minister’s opening talk in October 1999

• Consensus in Parliament, May 2000• Results from SIALS • Employment rate is very high• International research and educational reforms• Socio-demographic trends (few young people, lots

of old people)

Danish state of the art 2007

• A growing awareness of needs and relevance - and of barriers and dilemmas

• A growing consciousness of the necessity of long term effort

• Networks between state, local authorities, institutions, and teachers

• Institutional experiences and conceptual understanding of what is relevant and accessible numeracy for the participants

Decisions in 2000 of Ministry leading to a national numeracy course for adults

• Curriculum at two levels (!!!)

• Courses are to run for 40-60 lessons (level 1), as well as 60-80 lessons (level 2).

• Curriculum is outcome-based with specific goals to be attained.

• Examinations, written and individual are national, and are non-compulsory

The two levels on a row

• level 1 : figures and quantity

• level 2: patterns and connections, including the area of “form and dimension”, as well as “data and chance”.  

Basic ideas - A

• The aim is to support adults in further developing their numeracy (NUMERALITET: functional mathematical skills and understanding that in principle all people in society need to have)

• by holding in respect at the same time– relevance of everyday mathematics – adult participants’ experienced worries and difficulties,

and their competencies, experiences and aims

Basic ideas - B

1. Oblige adult participants as co-citizens

2. Countermeasure invisibility of everyday structures and elements that can be approached by mathematical skills and understanding

– in work, in learning/studies/courses, and in everyday life, including children’s homework

3. Countermeasure invisibility of adults’ competencies and worries

– in work, in learning/studies/courses, and in everyday life, including children’s homework

To oblige adult participants as co-citizens is institutionalised as:

1. Let them play at home - flexible organisation in space

2. Flexible organisations in time

3. Special economical support

4. Pre-test as a possibility (!)

5. Non-compulsory national examination (!)

6. Requiring special education for teachers

LL&TW’s inspiration for curriculum development which countermeasures the

invisibilities

• Anthropological studies (Alan Bishop and others)

• Research on adults’ learning and thinking about education and learning

• Curriculum from other countries

• The numeracy operational model (Lindenskov & Wedege, 2001; Wedege 2004) :

- situation context

- personal intention

- media and data

- mathematical knowledge and activities (2004)

Official intented aims for Preparatory Adult Education

• to ensure participants the possibility of clarifying, improving and supplementing their functional arithmetic and mathematical skills.

• to increase the participants' possibilities of coping with, processing and producing math-containing information

and materials. 

Official intented aims for Preparatory Adult Education

1. to develop the participants' numeracy, which consists of the functional mathematical skills and understanding that in principle all people in society need to have.

Mathematical awareness

• Is part of the aims for level 1 and level 2

• It is exemplified in the Ministry’s guidelines

• Is modelled in the SPC-model (Lindenskov, 2004)

SPC-modellen

Process what exists

Construct what does not

yet exist

Sense what exists

Content – a dynamic interplay

Activities

(A.Bishop)

Data

and

media

Math con-cepts and operations

Bishop’s six activities

• Counting

• Measuring

• Locating

• Designing

• Playing

• Explaining

FVU-mathematics level 1 activities

Counting (reading numbers, sorting, comparing, calculating)Measuring (surveying, weighing, comparing, calculating, converting, sorting out)Locating (denoting place, time and direction)Playing (following rules and strategies) 

FVU-mathematics level 2 activities

• Counting

• Measuring

• Locating

• Designing

• Playing

• Explaining

FVU-mathematics level 1 goals

Read, evaluate critically, and compare numerical data, numbers and codes.

Read and understand information in simple tables

Compare, sort out and round off figures and quantities

FVU-mathematics level 1 goals (continued)

Estimate numbers and distances, heights, volumes, weight and time on the basis of a sense of units of measurements (cm/m: dl/l: g/kg: sec/min)

Add, subtract, multiply and divide whole numbers and decimals with denomination, and critically evaluate and control results with and without aids.

FVU-mathematics level 1 goals (continued)

Count and measure and both estimate and precisely calculate numbers, length, height and distance, as well as weight, materials, time and money.

Convert measurements of length (cm/m), weight (g/kg), time (min/hours and days/weeks) and volume (dl/l).

Formulate arithmetical problems to handle simple quantitative questions

Level 1 Data and media

Amount, time, price, discount, loss, weight, temperature, volume, length, distance, numbers, and dates.

Written information and communication (informative and instructive texts, reference and fill-in texts), oral information and communication, concrete materials. 

Level 2 Data and media

Currency, interest, price, discount, loss, weight, temperature, distance, direction, point, diagrams, figures, set of data, probability, numbers, time, date

Written information and communication (informative and instructive texts, reference and fill-in texts), oral information and communication, as well as concrete materials. 

Level 1: Math concepts/operations

Cardinal numbers, ordinal numbers and codes and numbers.

Less than, more than, equal to, the same as and different from.

Positional system.

Units (metre, litre, kilogram, hours) and conversion.

Level 1: Math concepts/operations (continued)

Addition, subtraction, multiplication, division of whole numbers, and decimals using aids.Special figures and connections usable in mental arithmetic and estimations.Special fractions (¼, ½, ¾,) and percentages (10%, 25%, 50%).Length, height, breadth, and perimeter 

Level 2: Math concepts/operations

Proportions and proportionality

Simple formulas from everyday contexts

Systems of units and scale

Triangle, quadrangle, circle, box, cylinder

Symmetry in patterns

Level 2: Math concepts/operations (continued)

Area and volume of planes and spatial figures in everyday life

System of co-ordinates and simple graphs

Bar and pie charts

Mean and dispersion

Simple combinatorics 

References

Lindenskov, Lena (2004). Aviser i matematikundervisningen – hvorfor og hvordan?: - matematisk opmærksomhed med og mod avisen som medie. I: LAMIS Sommerkurs-rapport 2003 (s. 58-82). Trondheim: Norwegian Centre for Mathematics Education.

Lindenskov, Lena; Wedege, Tine (2001). Numeracy as an Analytical Tool in Adult Education and Research. Centre for Research in Learning Mathematics, Publication no.31, Roskilde University.

Wedege, Tine (2004). Lifelong learning of mathematics, focus on adult education. In Stedøy, Ingvill M. (ed.) Mathematics Education – The Nordic Way. A Pre ICME-10 production (pp.41-50). Trondheim: Norwegian Centre for Mathematics Education.

Wedege, Tine (2006). Numeracy as a tool in adult mathematics education: success or failure? To be published in Bergsten, C. (eds.) Proceedings from the fifth seminar on research in mathematics education. MADIF 5. Linköping: SMDF.

Curriculum and guidelines from Ministry

• Curriculum and teacher requirements : ”Bekendtgørelse om undervisning m.v. inden for forberedende voksenundervisning (FVU-bekendtgørelsen) BEK nr 1374 af 15/12/2005 (Vedrører lovbekendtgørelse Nr.16 af 07/01/2005)”

• See the guidelines at http://us.uvm.dk/voksen/fvu/vejledninger.htm?menuid=350525 by pressing at ”Undervisningsvejledning i FVU-matematik.”