|1: Prof Bernt Gustavsson: Folkbildning, bildning, utbildning.|
This lecture takes the point of departure
in the nordic tradition of popular-democratic education.
It can be considered how a german concept of Bildung is transformed in a new context, in the popular movements in the phase of industrialism and democratisation of society.
The next step is to show how this tradition can be transformed into a new view in order to meet the strong reduction of education and knowledge, which has taken place from 1985, a reduction which can be analysed in economic terms, human capital, or technocratic terms. How can the democratic and humanistic dimensions of education and knowledge be reconsidered?
This step takes the point of departure in hermeneutic and pragmatic philosophy, and a concept of Bildung expressed in hegelian thoughts, and is followed by an analysis of knowledge in different forms connected to different activities and actions Man is involved in. Episteme is the scientific form where mathematics is considered to be the ideal acitivity, thechne is the productive or creative form, and practical wisdom connected to the human being as a social and ethical creature. This is an attempt to widen the understanding of education and knowledge with the intention to transcend it´s instrumental development which has taken place in modernity.
|2: Michaela Inglis: “I said I taught the horse how to sing; I didn´t say it learnt “: Issues underlying appropriate training for vocational uses of Mathematics.|
Due to the dominance of work in human
existence (Straesser, 1996; Schrag, 1988),
Those around the world familiar with
the pursuit of research into mathematics in the workplace would also
argue that such a key area is of importance to workers of many other
nationalities. This plenary will attempt to give some insight into the
background of, and issues surrounding,
mathematics education for, and within workplace environments.
|3: Lars Gustafsson, Lars Mouwitz: Adults and Mathematics – a vital subject|
National Center for Mathematics Education (NCM) is a Swedish national
resource center for mathematics education. In October 2001 NCM was
assigned by the Swedish Government to carry out a survey and produce
an analysis of the measures required to improve adult learning of
mathematics. The results of this assignment were presented in the
report Vuxna och matematik – ett livsviktigt ämne (Adults and mathematics
– a vital subject).
the light of this report, and with reference to current ideological
and scientific perspectives and background rationales, adults learning
of mathematics is discussed. A special emphasis is put on the meaning
of ”mathematical proficiency for everyone” and this is contrasted
with a more limited view of mathematics/numeracy as it often is
expressed in national and international policy documents.
|4: Lene Oestergaard Johansen: Bildung: a pseudo-justification or a hidden reason for adult mathematics?|
|The question “Why teach numeracy to adults with lack of basic mathematical skills?” has been the core question in my research for the last four years. I have used the new Danish adult education: Preparatory Adult Education (PAE) and the development of the New National Adult Numeracy Curriculum as a case of today trying to find answers to my question. From the beginning of my work I wondered ‘can Bildung be an answer to the problem of justification?’ knowing that the Concept of Bildung includes both ideals and ways of forming people to reach those ideals. I will present how Active Citizenship is a common ideal of human development in Denmark today shared by both politicians and researchers in adult numeracy education and that formal education also is a common argument as a way to reach this ideal, however how beautiful it seems and how much it looks like a united community of practise I will show and discuss the differences in the political and the researches discourse asking the question “Is Bildung the real reason for offering numeracy education to adults or is it a pseudo-justification?”|
Johansen, L. Ø. (2004b): Functional
skills and understanding what does it mean in Adult Mathematics.
Study Group no. 6 (TSG6).
Johansen, L.Ø (2003a):
“Why teach numeracy to Adults?“
in Kaye, D. et al.(2003): Policies
and Practices for Adults Learning Mathematics: Opportunities and
Risks Proceedings of
the 9th International Conference on Adults Learning
Mathematics. London: Avanti Books. Side 204-213.
L. Ø. (2002d): “Why teach math to the excluded?”
& Skovsmose, O.: Mathematics Education and Society. Centre
for Research in Learning Mathematics. The Danish University of
Education, Roskilde University and Aalborg University. Side 330 –
L. Ø. (2002e): The Concept of Bildung and goals of numeracy
|Paper presentations, workshops, discussion groups|
Ana Lúcia Braz Dias – Central Michigan University
|This is a case study of mathematics teaching in an atypical school in Brasilia, Brazil. The City Park´s School is an open school, with flexible curriculum and diversified activities. It was created to attend the clientele of street children and adolescents or young adults in “assisted parole”. Some of these students are homeless. Others have to reconcile school activities with work to supplement family income or as an only source of support to their families. The adolescents and young adults in this school can join the activities any time at their convenience, from 7:30 am to 6:00 pm. The school functions in an open space, a park in the center of the city close to the city´s major concentrations of formal and informal jobs. The school is also flexible in its reception of new students, accepting new members at any time of year. The program is individualized (although it comprises collaborative activities). Assessment is done on a daily basis and there is no grade retention. This study examines mathematics teaching in this setting, and aims at identifying the role that mathematics learning and the use of technology can play in the re-insertion of these homeless or convicted young adults into society.|
|Gail E. FitzSimons – Monash University|
|During the last 18 months I have had the privilege of visiting several workplaces under the auspices of two research grants. Building on a burgeoning corpus of research into how mathematics/numeracy is used in workplaces around the world, and using activity theory as a research methodology, my goal in the first was to gain further insights in the Australian context. This is in preparation for the next phase of my major research project which is to design an evaluative framework for new learning technologies in adult numeracy. A second, smaller project has involved investigating how mathematics/numeracy is learned on the job in the case of chemical spraying and handling. Activity theory will again play a useful part in the analysis.|
Linda Galligan – University of Southern Queensland
|Today more adults than ever before are studying at university. Preparation and support of these students for the mathematical rigours of university study requires that program designers have knowledge of teaching staff expectations within university courses and a clear picture of the numeracy demands of a variety of courses. Although the numeracy demands of traditional mathematically based courses are considered to be well understood, the demands of courses which are often considered to be non-mathematically based (eg in many arts, nursing, psychology, and business programs) are less well understood by students and teaching staff. Further, changes in curriculum in both universities and schools has created a blurred picture of these demands and the expectations of students and staff appear to have drifted apart. To clarify this picture a numeracy audit of some key non-mathematically based 1st year courses was undertaken along with a survey of all staff teaching first year courses. The results indicate that there was a mismatch between expectation and actuality, and that teaching staff were concerned about the mathematical abilities of entering students, generally in the areas of critical thinking and problem solving, and specifically in areas particular to their courses. The audit of courses and survey of staff identified many academic numeracy concerns not previously considered. The paper details how these concerns have been utilized in the development of preparatory and support programs within an Australian regional multi-mode university.|
|Eigil Peter Hansen – VUC Syd|
|Since 2001 I have been working on a model for flexible learning. In my class room you will meet adults learning Math hoping to finish at the G or E level. To meet the syllabus they have to work with different themes from everyday life and in the themes they will work with the appropriate mathematics. New pupils may start on Tuesdays (continuous enrolment), which means they will quickly have to learn to evaluate their own level, seek means to fill gaps and progress from there. Any pupil can at any given time find additional material either at a lower or a higher level within the various subjects. Because I want an abundance of and great variety in material and because my VUC lack money, much teaching is based on digital material, which they may print according to individual needs.|
|Among other things the possibility for the individual|
|- To spend adequate time on the different subjects|
|- To acquire the necessary skills|
|- To fill knowledge gaps|
|- To work at her / his own pace|
|- To work with the material which suits her / him the best e.g. books, pc, video, internet, theory, exercises|
my presentation I will share my ideas and experiences with you. My plan is
to show you how all this can be coordinated into a teaching programme the
pupils and other teachers can fathom.
|Torkel Haugan Hansen - Vox|
|The main objective in my ph.d.-project is (1) to establish and visualize mathematics as a general competence in the modern labour market in Norway and (2) to analyze and characterize the mathematical competences of adults with significant work experience, in order to better adapt adult education to this group.|
|The paper discusses a qualitative study which has been made as a pilot-study for this research. The study involves one single worker that has been observed at work and interviewed in order to localize the mathematical competences in its job-function.|
|A vital assumption based on earlier empirical studies is that some of their mathematical competence is in form of tacit knowledge. An indication is that “No” is a common answer among workers when they are asked whether they use mathematics in their job. The study design is based on theories on tacit knowledge, and made in order to identify and externalize this into explicit knowledge.|
|The subject of the pilot-study works at a cafeteria in connection with a nursing home. The job consists of buttering buns and sandwiches, making waffles and coffee, receiving payment and giving out change, warming and serving dinner, keeping the premises tidy and washing dishes.|
|The findings show that mathematics/calculations were used in a number of situations in this job-function. Technological appliances were available to help the worker with the majority of these tasks, but not always used. This seems to depend more on the time pressure and the demand for accuracy, than on the difficulty of the mathematical problem. When something had to be done fast and accurate, the technological appliance was used. In situations where these factors of stress were not that present, they were disregarded as “superfluous and bothersome”. This finding will be studied further as a result of this pilot, to investigate whether time pressure and accuracy demand (and possibly other stress factors) are variables that more generally affects how workers use appliances to solve mathematical problems.|
|Lave, Jean (1988). Cognition in practice. Mind, mathematics and culture in everyday life. Now Your: Cambridge University Press|
|Polanyi, Michael (1967). The Tacit Dimension. USA: Anchor Books Edition|
|Wedege, Tine (1999). Matematikviden og teknologiske kompetencer hos kortuddannede voksne. Rekognosceringer og konstruktioner I graenselandet mellem matematikkens didaktik og forskning I voksenuddannelse. Roskilde: IMFUFA, Roskilde Univercitetscenter./2000/|
|Jens Langpaap – Universität Hamburg|
|In the centre of my work are adults who acquired only rudimentary mathematical knowledge, which is not always adequate to manage simple everyday problems. Their innumeracy is described as a consequence of developmental dyscalculia. At the moment I´m teaching ten female students (26 to 51 years old) with little mathematical knowledge, to whom I´m giving single lessons. The aim is an individual access to mathematics and the development of fundamental mathematical competence. In cooperation with the students I create individual instruction sequences, where we start with everyday life situations and subjects of the students life and interest. In the course of the process the students express the meaning of their innumeracy for their own lives. They talk about how they manage their everyday life referring to mathematical demands, about their psychological and mental burden and their attitudes to mathematics. In this report I´d like to draw a first picture of these statements and to introduce to my concept.|
|Terry Maguire and John O Donoghue – University of Limerick|
|A national survey of tutors in Ireland clearly demonstrated that tutors who teach adult numeracy in Ireland are not a homogenous group. Tutors differ both in terms of their conceptualisation of what constitutes numeracy and their beliefs about mathematics. They are working in a wide range of education and training environments and are driven by a diverse array of organisational imperatives. Three categories of numeracy tutor were identified based on the type of mathematics/numeracy that they delivered.|
|Category 1: Non-accredited customised numeracy programme|
|Category 2: Vocational Numeracy (mathematics related programmes)|
|Category 3: Formal Mathematics (nationally accredited adult mathematics programmes)|
|This paper discusses the different profile of tutors and the range of training needs that were identified within each category.|
|Further the paper discusses the use of both “traditional” and “reform” models of professional development (Richardson, 1998) and explores how effective professional development opportunities can be designed to meet the range of training needs identified for each category of tutor whilst taking cognisance of individual tutor motivation and learning style.|
|The paper concludes by considering the potential of “learning communities” which can provide opportunities for continuous learning and reflection, in supporting the professional development of adult numeracy tutors.|
|Essential qualities and
differences in students´ mathematical self-system structures.
The study to be presented relates to the idea of self-systems and self-system processes as the broader theoretical framework for describing the essential structures and dynamical qualities of students´ personal mathematics learning processes and experiences. Self-systems point here to important habitual and structural personal metacognitive, cognitive and affective sets or systems and behavioural patterns constructed through past mathematical experiences. Accordingly, in this study we will construct connections between the kind of students´ mathematical beliefs, affective responses and mathematics learning behaviours that have also in previous
math education research turned out to play a significant role in math learning and problem solving for school students as well as for adult students. Moreover, research results of the variations in these self-system structures along with students´ gender and math achievement level will shed light on the development of individual differences in personal mathematics learning. Special attention is paid to the differences in the qualities and connections of students´ self-perceptions, anxiety responses and self-regulatory behavioural patterns. Quantitative data from the measurement of Finnish secondary school students´ self-system structures are applied to illustrate the essential qualities and divergences in these personal structures.
|Kay Owens – Charles Sturt University|
|Although the majority of our primary school teacher education students enter with a positive attitude to mathematics, their understanding of mathematics is challenged in a problem solving and investigative subject. The subject involves the use of computers. It is a challenge to keep them positive about ICTs and mathematics while challenging their beliefs. The students who are not so positive and have difficulties with either the mathematics or the technology need support. This paper looks at the support that is provided and the outcomes of the subject. One successful focus has been on the links between their understanding of mathematics, its application in a community project and their role as a future primary school teacher. Another has been the nature of the computer laboratory classroom learning experiences.|
|Katherine Safford-Ramus – Saint Peter´s College|
|Over the course of the past two years I have read approximately sixty doctoral dissertations about adult mathematics education research in North America. Several of these dissertations reported research on intervention programs that attempted to enhance the learning experience of the students. In this session I will present descriptions of the intervention strategies that were implemented and report the findings of each researcher on the level of success that their program achieved.|
|Geoff Wake – University of Manchester|
|Mathematics educators often turn to the world of work in an attempt to understand how mathematics in workplace practice might:|
- inform design of future curricula;
- provide contexts for realistic mathematical activities to support learning.
|Some studies aimed at informing the former of these have attempted to identify appropriate mathematical content by recognising its use or required understanding across a range of different workplaces and activities, and have, perhaps by necessity, used frameworks that rely on what might be considered “academic” mathematics to organise findings. Other particularly more recent, studies have used theoretical frameworks such as Cultural Historical Activity Theory to attempt to come to an understanding of how the mathematical activity of workers might be better understood by taking account of how the worker´s activity is culturally and historically situated. Focussing on a particular mathematical activity within such studies often results in researchers pointing to how idiosyncratic tools and artefacts often mediate the activities of workers.|
|This paper will describe one case study based around the work of railway signalling engineers and the attempts of students on a pre-vocational engineering course to make sense of this. The different episodes of activity are analysed using these different frameworks and the resulting findings synthesised in an attempt to draw lessons for future curriculum development. Finally, reflecting on this research from the viewpoint of a curriculum developer, I consider how we might, in future, better inform curriculum design and development from workplace studies.|
Juergen Maasz and Kathy Ramus Safford
strength of our organization Adults Learning Mathematics (ALM) is the
international character of the membership.
each member country, prominent learning theorists shape the research
agenda of the national adult education community.
year participants in topic group A (Day 1) will be invited to articulate
the theories that dominate their national dialogue.
|At the second session, contributors will be invited to discuss the application of the various theories to our work in numeracy and their role in the future of our organization, ALM.|
|Topic Group B: Mathematics Education for the Workplace|
|Lisbeth Lindberg, Michaela Inglis|
|In keeping with the theme of ALM 11, the focus for the topic group this year will be on Teaching and Learning for Mathematics Education in the Workplace. In order to begin the dialogue, there will be a brief look at the content of the Topic Group from previous ALM Conferences, and then to discuss any research that is currently underway in the area of Mathematics Education for the Workplace.|
|At ALM 10, much conversation took place regarding different aspects of learning and knowledge. Specifically, debate centred around the lack of knowledge of any real research ‘out there’ regarding the teaching and learning of mathematics for the workplace. To investigate this dilemma, there will be the following focus questions:|
1. What is mathematical knowledge in workplace contexts?
2. How is such knowledge acquired?
3. How can this process of accrual be identified?
4. What mechanisms/theories may assist in the teaching and learning of
mathematics for the workplace?
5. What are the main issues/hurdles related to the teaching and
learning of mathematics for the workplace?
7: Topic Group started – Beginning conceptions
vocational programs in upper-secondary schools with some people working in
numeracy programs in workplaces.
group acknowledged that more work needed to be done in the area.
8: Focus on vocational aspects with many papers about collecting data in
mathematics versus applied as found in the workplace.
of mathematics versus life-long learning.
9: What is happening in different countries?
skills are required?
possible to deal with numeracy in schools? Workplaces? Both? Neither?
between workplaces and schools:
10: Began to look for “black holes” in research areas.
Work being done in the packaging industry, and hospitals and nurses.
These workplaces asked for help with their mathematics.
project consisted of some wonderful tasks using mathematics, but the
workers were not interested in looking at the mathematics involved. A
question arose asking whether there are workplaces where the workers are
hiding their lack of mathematics?
One project involving lorry drivers and an oil union asked for a literacy
program to supplement the numeracy program.
interest to focus more on competent workers than incompetent workers, to
see how the competent workers are managing.
Some discussion regarding useful methodologies to examine workplace
vocational teachers use a “rule of thumb” rather than to explain the
teachers need to learn to communicate the “big ideas.”
on learning and knowledge. Questions
are we defining learning?
we acquire mathematical knowledge?
we know what learning experiences are important to go to the next level of
to acknowledge and investigate:
|Topic Group C: Affective Factors in Adult Mathematics Learning|
|Convenor: Wolfgang Schloeglmann, University of Linz, Austria|
Topic Group continued its discussions at a well-attended meeting at
ALM-10. At this meeting, there was substantial support for a continuation
of this workshop at future ALM conferences. Topics of interest that were
Categories of affect and research methods
Affect and its influence on cognitive processes
Affective and attitude results from the international surveys
year, the convenor propose for discussion in the Topic Group
Survey of the research in this area (e.g. McLeod, 1992; Evans,
2000; Evans/Hannula/Philippou/Zan, 2004);
J. (2000). Adults´Mathematical Thinking and Emotions: a study of numerate
practices. London: RoutledgeFalmer.
J/Hannula, M./Philippou, G/Zan, R. (2004). Thematic Group 2: Affect and
Mathematical Thinking. Proccedings of CERME3
McLeod, D. (1992). “Research on Affect in Mathematics Education: a Reconceptualisation”. In Grouws, D.A. (ed.) Handbook of Research in Mathematics Education Teaching and Learning (pp. 575-596), New York: Macmillan.
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