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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/