Malmö University

Numeracy or mathematics?

Preparatory Adult Education in Denmark

Tine Wedege

School of Teacher Education

Malmö University

Sweden

In 2001, a new curriculum in adult mathematics education was introduced in Denmark. The aim was that the students further developed their numeracy.

The development of education and teacher education was research based and an operational model of Numeracy was the pivotal point in this work.

A new curriculum

Three years later, in 2004, the Danish Evaluation Institute evaluated this educational programme, Preparatory Adult Education (PAE).

In the light of my experience from development and evaluation of this mathematics programme, I question if the concept of Numeracy is implemented in the teaching and learning practices of PAE-mathematics.

A new curriculum: PAE mathematics

The aim of PAE is that students further develop their numeracy (da: numeralitet) understood as functional mathematical skills and understanding that in principle all people in society need to have.

According to this definition, numeracy changes in time and space along with social change and technological development.

(Lindenskov & Wedege, 2001)

Preparatory Adult Education (PAE)

in Mathematics

My question is this

Is the concept of Numeracy adopted in the teaching and learning practices of Preparatory Adult Education mathematics?

Numeracy or mathematics?

Publicly financed adult education can be roughly divided into three main categories:

• Adult liberal education (e.g. basic mathematics courses at evening schools)

• General adult education (e.g. numeracy and mathematics at primary and secondary level)

• Vocationally oriented adult education and training from VET level (e.g. mathematics-containing truck course) to the highest academic level (e.g. master in mathematics).

Only the education in the last two sectors is formally qualifying.

Mathematics in the Danish Adult Educational System

Adult Education and Continuing Vocational Training

Liberal Adult

Education

General Adult

Education

Adult Vocationally Oriented Education

Basic Education

System

Years of Education

Master Level

Long-cycle

Higher Education

Diploma

Level

Further Adult

Education

Short-cycle

Higher Education

KVU

Medium-

cycle Higher

Education MVU

Bachelor

13th-17th

13th-15th

13th-14th

Higher

Preparatory Education

HF

Adult

Vocational Education

VEUD

Basic Adult

Education GVU

Vocational Education

& Training

Advanced Upper Secondary School

Continuing Vocational Training

CVT &

Adult Vocational Training

AMU

General Adult

Education AVU

Folk High Schools

&

Day Folk High Schools

&

Evening Schools

Preparatory

Adult Education

FVU

Primary and Lower Secondary School

10th-12th

9th-10th

At the Third Nordic Conference on Mathematics Education (NORMA01) in 2001, I presented our concept of numeracy and some of the basic ideas of PAE-mathematics in a lecture with the title “Mathematics that’s what I cannot do” (Wedege, 2005).

After my lecture, Australian Bill Barton asked if it was really necessary to introduce numeracy in Denmark?

Apart from being the research base of the new curriculum, I regarded the new term, numeracy, as important to avoid a usual teacher reaction when presented for a new curriculum:

“This is what we have always done”.

Why the term ”numeracy”?

Media (a) written information and communication (b) oral information and communication, c) concrete materials, d) time and e) processes.

Context (a) working life, (b) family life, (c) educational context, (d) social life, and (e) leisure.

Personal intention (a) to inform/be informed, (b) to construe, (c) to evaluate, (d) to understand, (e) to practice, etc.

Skills & Understanding - Dealing with and sense of (a) quantity and numbers, (b) dimension and form, (c) patterns and relations, (d) data and chance, (e) change, (f) models.

NumeracyAn operative model for the study of adult numeracy with four interrelated dimensions (Lindenskov & Wedege, 2001)

Four analytical dimensions of NumeracyAn operational model

Where? Why?

Situation context Personal intention

Numeracy

What? How? Media & data Mathematical knowledge and activity

(Wedege, 2004:113)

This model has been used and further developed as an analytical tool in adult mathematics and research.

During the development of PAE-mathematics, we found inspiration in Bishop's (1988) cross-cultural studies of mathematical components in everyday activity and added mathematical activities such as

• Counting Measuring Locating• Designing Playing Explaining

to the fourth dimension (skills and understanding)

Mathematical activities

In Copenhagen airport

A building site

Quality control

The content of PAE-mathematics is described as a dynamic interplay:

Mathematical Concepts and Operations*

Activities

Data & Media

• (level 1) figures and quantity and

• (level 2) patterns and relations, • which in addition include the area of form and dimension,

as well as data and chance.

PAE mathematics has two levels

• From a survey on the teachers’ beliefs and attitudes towards mathematics before the start in August 2001 of PAE we know that the majority of the teachers described mathematics as a tool in everyday life according with the rhetoric of Danish basic adult education in mathematics.

(Wedege & Henningsen, 2002)

The teachers’ views of mathematics before …

The Ministry of Education offered the task of evaluating PAE to the Danish Evaluation Institute (EVA) in 2003.

Mertens refers arguments of what distinguishes evaluation from other forms of social inquiry. It is its political inherency:

• Evaluations are conducted on the merit and worth of programs in the public domain, which are themselves responses to prioritized individual and community needs that resulted from political decisions. Program evaluation “is thus intertwined with political power and decision making about societal priorities and directions”.

(Mertens, 2005:49-50)

Evaluation of an educational programme

• merit : the excellence of an object as assessed by its intrinsic qualities or performance

• worth : the value of an object in relation to a purpose.

Evaluation of an educational programme

project team (EVA)

• preliminary study

• terms of reference

• self evaluation (educational institutions)

evaluation group (experts)

supplementary surve

site visit

report

follow-up (Ministry of Education & educational institutions)

(see www.EVA.dk)

The evalution method

Many students benefit greatly, both personally and socially, and a number of them use PAE as a springboard for further education.

• A general example was adults now being able to help their children with the home work.

• And happy people telling that, after all, they were able to learn mathematics.

Although the word numeracy was not mentioned by the teachers I am sure that many students further developed their numeracy as a result of PAE-mathematics.

Worth: Is what PAE does important?

Some of the mathematics teaching practice that we met during the visit didn’t have anything to do with PAE.

• We saw for example ordinary mathematics education compensating for young students’ poor mathematical skills in vocational educational.

• In this institution – like in others – we saw and heard of the use of standard mathematics text books.

Merit: How well does PAE perform?

Like in an adult education institution where a student said:

• “He gave us a book and then we worked individually. We didn’t use the material from the workplace although we asked about it. The teacher took material from grade 2 to 3. When we told him that we wanted to learn to calculate area, he said that we would meet this problem later in the book.”

Merit: How well does PAE perform?

In general, PAE is characterised by dedicated teachers and managers capable of creating a successful environment for adult education in which the students feel safe and with teaching based on the students’ needs and qualifications.

However:• In a locker marked with the words “concrete material” in

a well equipped classroom, I found only gadgets in plastic normally used in the children’s mathematics classroom.

Merit: How well does PAE perform?

When students spoke in general about mathematics they often used the terms “equation”, “x” and “y”.

An example of no change in the adults’ views of mathematics and their self-conceptions in relation to mathematics: A woman who was fired after 32 years in the same job, said:

"For the last 32 years I have only worked in LEGO’s design department. I cannot do any mathematics."

Merit: How well does PAE perform?

Playing and designing

LEGO/Logo: Learning Through and About Design

Mitchel Resnick and Stephen Ocko

Epistemology and Learning Group

MIT Media Laboratory - Cambridge, MA 02139

Abstract

Most classroom problem-solving activities focus on analytic thinking: decomposing problems into subproblems. Students rarely get the opportunity to design and invent things. In this paper, (…) we examine how students using LEGO/Logo can learn important mathematical and scientific ideas through their design activities (…).

Designing and learning from googling on www:

Listen to the PAE teacher:

“We go to this meeting; we listen and we go home doing what we are used to do.”

• The matter meant was numeracy• The matter taught in many “classrooms” is mathematics

The matter meant versus

The matter taught

Israelian Anna Sfard (2003):“Success of educational ideas, however, is never a simple function of the ideas themselves. There is no direct route from general curricular principles to successful instruction.” (p. 354)

….. And there is no direct route from instruction to students’ learning.

The matter meant versus

The matter taught

Adult students develop their numeracy in school mathematics and in everyday life.

…………………..

There are no competencies in and of themselves; there are only competent people. (Fragnière, 1996)

… versus The matter learned

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.

References on the EMMA site:http://www.statvoks.no/emma/