1. Malmö University Numeracy or mathematics? Preparatory Adult Education in Denmark Tine Wedege School of Teacher Education Malmö University Sweden

2. 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

3. 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

4. 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

5. My question is this Is the concept of Numeracy adopted in the teaching and learning practices of Preparatory Adult Education mathematics? Numeracy or mathematics?

6. 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

8. 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”?

9. 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. Numeracy An operative model for the study of adult numeracy with four interrelated dimensions (Lindenskov & Wedege, 2001)

11. Four analytical dimensions of Numeracy An operational model

12. 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

13. In Copenhagen airport

14. A building site

15. Quality control

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

17. (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

18. 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 …

19. 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

20. 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

21. 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)www.EVA.dk The evalution method

22. 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?

23. 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?

24. 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?

25. 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?

26. 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?

27. Playing and designing

28. 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:

29. 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

30. 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

31. 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

32. 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/