Preparatory adult education in denmark some basic ideas and some dilemmas
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Preparatory Adult Education in Denmark: Some basic ideas and some dilemmas. EMMA Study Visit Copenhagen 9 – 12 May 2007 Lena Lindenskov 10 May 2007, DPU. The study visit shows stories and voices at three levels.

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Preparatory adult education in denmark some basic ideas and some dilemmas

Preparatory Adult Education in Denmark: Some basic ideas and some dilemmas

EMMA Study Visit Copenhagen 9 – 12 May 2007

Lena Lindenskov

10 May 2007, DPU


The study visit shows stories and voices at three levels
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
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
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
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
The two levels on a row course for adults

  • level 1 : figuresand quantity

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


Basic ideas a
Basic ideas - A course for adults

  • 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
Basic ideas - B course for adults

  • Oblige adult participants as co-citizens

  • 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

  • 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. course for adultsLet 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

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


Ll tw s inspiration for curriculum development which countermeasures the invisibilities

Anthropological studies (Alan Bishop and others) course for adults

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)

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


Official intented aims for preparatory adult education
Official intented aims for course for adultsPreparatory 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 education1
Official intented aims for course for adultsPreparatory Adult Education

  • 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
Mathematical awareness course for adults

  • 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
SPC-modellen course for adults



Bishop s six activities
Bishop’s six activities course for adults

  • Counting

  • Measuring

  • Locating

  • Designing

  • Playing

  • Explaining


Fvu mathematics level 1 activities
FVU-mathematics level 1 activities course for adults

  • 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
FVU-mathematics level 2 activities course for adults

  • Counting

  • Measuring

  • Locating

  • Designing

  • Playing

  • Explaining


Fvu mathematics level 1 goals
FVU-mathematics level 1 goals course for adults

  • 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
FVU-mathematics level 1 goals (continued) course for adults

  • 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 continued1
FVU-mathematics level 1 goals (continued) course for adults

  • 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
Level 1 Data and media course for adults

  • 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
Level 2 Data and media course for adults

  • 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
Level 1: Math concepts/operations course for adults

  • 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
Level 1: Math concepts/operations (continued) course for adults

  • 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
Level 2: Math concepts/operations course for adults

  • 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
Level 2: Math concepts/operations (continued) course for adults

  • 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
References course for adults

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 guidelines from Ministry course for adults

  • 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.”


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