ALM4 Conference

(last update December 10, 2001)

Abstracts

KEYNOTE ADDRESS

MATHEMATICS IS FOR LIVING

 Dr. CON POWER

Business Consultancy, Nemesis Ltd., Dublin

 1.   Mathematics is an academic discipline in its own right and is also a tool-kit for use in a wide variety of life situations, for work, for leisure and for quality of life activities.

 2.   The importance of mathematics has been growing as an integral part of technology and commercial advances particularly over the past century and a half.

 3.   Mathematics plays a vital part in the life of the individual citizen as a member of the workforce, employed, self-employed, or unemployed, and also in the life of the citizen who is outside the workforce. Equally, mathematical competencies have a broadly-based relevance for the citizen as a consumer.

 4.   The largest single expenditure by many individuals throughout their lifetime is the purchase of a home, normally with the aid of a mortgage. This brings mathematical issues relative to interest rates, inflation, and exchange rates within the mainstream consideration of the average citizen.

 5.   The centrality of the role of mathematics in society suggests that it should also have a central role in the educational curriculum by providing an operational link with related subjects through a "team teaching" approach to delivering a student-centred integrated curriculum.  

Technology Transfer - A Useful Metaphor for University Level

Mathematics Courses for Engineers and Scientists

 Juergen Maass, University of Linz, Austria

In Exeter (ALM 2, 1995) Wolfgang Schloeglmann and I presented some results of our research. One of these results is a useful metaphor: Teaching mathematics to engineers and scientists that have finished their university studies and work, for example in industry for many years is structurally similar to the technology transfer from a highly industrialized country in Europe to a so called third world or developing country in Africa. if this metaphor is correct it is useful: we are able to learn something about chances, problems and mistakes. In Exeter we had not enough time to discuss this idea - therefore I will concentrate on this point in Limerick.

·     What we can learn from transfer problems

·     Transfer of technology: A theoretical outline of the problem

·     Technology transfer: Four ways

·     Mathematics as technology?

·     The contribution of mathematics education departments at the university to the transfer of technology.

New tasks for university mathematics education departments in research and training.

 Bibliography

 [1] J. Maass: Mathematik als soziales System, Weinheim 1988

[2] 3. Maass, M. Schulz-Reese: Wissenschaftliche mathematische Weiterbildung als Technologietransfer, in: [5]

[3] 3. Maass, W. Schloeglmann: The mathematical world in the black box - significance of the black as a medium of mathematizing, in: Gybernetics and Systems, An International Journal 19/1988, p.295-309

[4] 3. Beckman: Anleitung zur Technologie, Gottingen 1777, reprint Franzbecker, Hildesheim 1984.

[5] 3. Maass, W. Schloeglmann (Hrsg.): Mathematik als Technologie? Wechselwirkungen zwischen Mathematik, Neuen Technologien, Aus-und Weiterbildung, Weinheim 1989. [6] H. Huelsmann: Die technologische Formation, Berlin 1985

[7] 3. Maass, G. Rahmann: Polyvalenz und Flexibilitaet - Neue Perspektiven fuer die Lehrerausbildung?, in: R. Schaper (Hrsg): Hochschuldidaktik der Mathematik, Alsbach 1985.

[8] N. Havers, K. Parmentier, F. Stooss: Alternative Einsatzfelder fuer Lehrer? Eme Bestandsaufnahme zur aktuellen diskussion. Beitraege zur Arbeitsmarkt - und Berufsforschung 73, Institut fuer Arbeitsmarkt - und Berufsforschung der Bundesanstalt fuer Arbeit, Nuerberg 1983.  

The Adult-Worker-Student and Mathematics Education - a reality in Brazilian society

 Eliana Maria Guedes, University of Taubate-Est. Sao Paulo, Brazil

In the third world countries, the massive expansion of access to education occurred by 1960's having as a result the deterioration of teaching and learning as a whole, which was before, offered to very few people.

It is known by everybody that in these countries the main question is to have a minimum qualified labour work and that the massive access to education attenuates the illiteracy, one of the causes of poverty, but, at the same time, it makes impractical the education's quality, nowadays, one of the main slogans in the world.

How to offer opportunities to those who wishes to continue studying? They are adults, employed in factories and industries, trying to get the proper knowledge to fortify their condition as citizens inserted in the society and, consequently, have an improvement in their professional life.

In most of the cases, the reasons for giving up studies were because they failed in Mathematics examinations, what makes them feel very uncomfortable, needing help. This presentation is about an Education Program called "Rediscovering Math" developed by the University of Taubate (South East of Brazil - Sao Paulo State), where one of its main projects is called "The adult-worker-student and Mathematics Education".

This project, based in Jean Piaget and Paulo Freire, is formed by a group of professors, teachers, volunteers and monitors giving special attention to the adult-worker-student having as the main goal to guide students to re-acquire confidence and ability in their conditions to learn Maths, making them understand that the most difficulties happen due to the idea that Math is a complex science and very difficult to be understood, what is not real, at all.

Teaching Adult Students Mathemafical Investigations -2

 R 0 Angiama, Goldsmiths College Centre for Continuing & Community Education

University of London, UK

 The theme of this paper is Teaching Adult Students Mathematical Investigation' (TASMI-2). It is based on the on-going research work and teaching carried out for the last 7 years of the Mathematics Foundations Course (MFC), at Goldsmiths College University of London (Angiama, R.0., 1992, 1994, 1995, 1996).

I have argued that Teaching Adult Students Mathematical Investigation', is given an insight into the way they learnt mathematics better and removes the barriers of mathematics phobia. It should be a tool in its own right which adult students can associate with and clarify, think, predict, survey, research and should enable them to solve problems in a variety of ways including other related subjects like science, economics, geography, technology and art.

Furthermore mathematical investigation encourages adult students to read, understand and respond to questions better and explanations. It makes them become confident when talking about mathematics. It involves using processes which will lead to the understanding of mathematical concepts, rules and generates mathematical discussions. This paper invites from participants attending the fourth Adults Learning Mathematics - A Research Forum (ALM-4) conference, their views of what they consider Mathematical Investigation' to be, as well as other issues concerning research on all aspects of adult mathematics learning and teaching - vital to increase our understanding and enhance the status of adult mathematics education.

The Cockcroft Report (1982), stated ‘the idea of investigation is fundamental both to the study of mathematics itself and also to an understanding of the ways in which mathematics can be used to extend knowledge and to solve problems in very many fields'. The paper concludes, Mathematical investigation' provides a basis for improving the quality of teaching and learning mathematics which will lead to an achievement in mathematics education and therefore, leads to an improvement on standards. It calls for a critical mathematics curriculum.

Paulo Freire's Legacy for Adults Learning Maths

Diana Coben, Goldsmith's College, University of London, U.K

The death of Paulo Freire in May 1997 is a momentous event for educators everywhere, especially adult educators, and a sad one for those who knew and loved him. I have been thinking and writing about Freire's work for many years, exploring his contribution to a radical politics of adult education. While Freire's work features strongly in debates about adult education generally, and about adult literacy in particular, his significance for adult numeracy/mathematics educators has been less discussed. In this session, I shall try to redress the balance by considering the legacy of Paulo Freire's work for adults learning maths - and for teachers of adults learning maths.

Independent Learning: Numeracy developments in ABE practice.

 Mieke de Laat, Franck Haacke, Simone van Duin

Regional Institute for Adult Education and Vocational Training,

Eindhoven, The Netherlands.

In the framework of creating Independent Learning in Adult Education in The Netherlands, the Regional Institute for Adult Education and Vocational Training in Eindhoven has recently started an Open Learning Centre on Numeracy Education for Adult Basic Education. 45 ABE students from different levels and with different perspectives are mixed in the OLC once a week on Friday morning.

We, three ABE teachers have been guiding this project since the start in January 1997. We developed a prograrrune on study-skills, organized the numeracy activities in the OLC and have started tutorial groups. Students are supposed to study interactively and independently. For that they need to learn to plan their activities, to analyse numeracy problems, to discuss problem solving strategies with other students, to ask for help if needed and how to help each other. This all means quite a change, almost a revolution in the Dutch ABE, for most students and teachers are not used to such an education system.

In this presentation we, the three teachers, will give an account of our experiences. At the end we would like to exchange experiences with other (ABE) teachers.

NCVQ Key Skills and NVQ - Integrated or Bolted-on?

Caz Randall, Lewisham College, London, U.K.

NCVQ Key Skills will form an increasingly important part of NVQ programmes, particularly for Modem Apprentices. lead bodies and employers require the Key Skills delivery and assessment to be relevant to the workplace and the training programme.

This would suggest that Key Skills should be delivered and assessed through the main vocational programme in an integrated fashion. However, this is not as straightforward as it would seem, as anyone who has tried to find Application of Number in an NVQ programme will know.

So how do we integrate something that does not naturally occur?

The only way to ensure relevance of Application of Number in an NVQ programme is to identify it beforehand and be prepared to assess it where it does naturally occur, and then design a "top-up” programme for the gaps, ensuring that the delivery style and any materials and assessment activities are relevant to the vocational programme.

It is unlikely that there will be materials available to use straight “off-the-shelf". Assignments and activities will have to be adapted or designed specifically for each programme. This will take time and should be done co-operatively by key skills specialists and vocational specialists.

I am presently involved in "mapping" Application of Number onto the maths in Engineering NVQ programmes, identifying the gaps and developing "top-up" assignments which will provide assessment opportunities for the missing skills.

Independent versus Autonomous Adult Learning in Mathematics?

Sylvia Johnson and Sue Elliott, Sheffield Hallam University, U.K.

Information and communications technology is being promoted in the UK as a mechanism by which adults may become independent learners ( and an expansion of higher education can be achieved within a reduced budget). An associated development is the increased use of diagnostic packages in mathematics at entry level to higher education. A new orthodoxy is emerging in which a diagnostic tool tells learners what they can and can't do and points them to one of several packages to learn those bits of mathematics they could not do on diagnosis. This process can be completed with no tutor intervention (though maybe tutor monitoring) and is being labelled as 'students engaging in independent learning'.

This interpretation of 'independent learning' concerns us as educators within the HE environment.

What does independent learning actually mean ? How can we articulate what we want adult learners to demonstrate in mathematics? Why are we sceptical that this can be achieved in the way described above?

Using data from adult students and writings by various authors we will examine the meaning of independent learning within a mathematical context and argue that 'autonomous learning' is a better descriptor.

University Pedagogy - How Social Scientists Make Mathematical Meanings

Sybil Cock, University of North London, UK

Our Social Science degree scheme attracts a very wide range of students, nearly all of them mature, mostly women and members of many minority ethnic groups. The degree has a number of pathways and vocational routes including social policy, politics, health studies, information studies, cultural studies. Many students enter the prograrnme with non-standard qualifications and few are prepared for the shock of a compulsory statistics course, which large numbers fail! I have recently helped redesign the course to make it more accessible to the students, of which there are around 350 per year. The pedagogy has shifted from teacher - to student-centred, but institutional constraints did not allow a shift in assessment methods away from a conventional exam.

I have both interviewed and surveyed students and staff over the year and will address some of these issues

·     The best ways of shifting students attitudes towards their maths practices, particularly in relation to confidence

The effects of students maths backgrounds on study habits and attitudes

 ·     The extent to which social statistics or numeracy can ever be effectively taught or learned outside the situations in which it is used

These issues seem to me to be important ones to many teachers who try to change their practice in an institutional context which has to value measurable outcomes as an indicator of the quality of learning.

Developing guidance material to uncover a mathematics profile of adult

participants on a crane course.

 Lena Lindenskov, IMFUFA, Roskilde University, Denmark

'Education', 'Life-long-learning', 'In service-training' are important mantras in the current political and economical discussions. Also adults with not more than limited school experiences are the target for the governmental educational efforts in Denmark. Adult Vocational Training is set up by the Ministry of Labour in order to make it possible for semi-skilled workers, skilled workers and middle management to improve their general and specific qualifications. Mathematics are ingredients among others in the courses. In most courses mathematics are integrated in other subjects, in fewer courses mathematics are separate elements. Mathematics whether integrated or separated bring about a great many difficulties for the students and it seems that the teachers are short of tools to help the students. The extreme short duration of the courses - often only one or two weeks - puts severe challenges onto the teachers. It's very difficult for the teachers to get to know the students enough for being able to understand the students' learning problems and to guide the students.

There is an ongoing attempt to develop a tool that should enable the teachers - and the students themselves - to get a better understanding of the students' difficulties, beliefs and attitudes. The tool shall not only reveal what the student can't do and lacks, but also what (s)he can and what her/his potentials are to take actively part in future learning processes. The tool shall consist of a packet of different test items and questions to reflect upon.

The idea is that the tool should be used for three purposes:

a) - as a pre-test in an individual screening of a student's competences.

b) - for making a diagnosis  in order to get to know some background when the students in an ongoing course experience difficulties which (s)he cannot handle

c) - as an evaluation after a course.

I would like to discuss three main issues at the ALM-4:

1.How to create conditions that ensure the tools are used in order to empower the student (him)herself.

2.Which context/practices are adequate to reveal eventually hidden potentials.

3.Mathematics in context/in practice always involve aims and intentions. How could it be possible to reveal relevant aims, intentions, beliefs and attitudes.

Managing Change: Working with Adults

Janet Duffin, University of Hull, U.K.

The session will build on my contributions to ALM 1, 2 and 3 to look at the whole issue of managing change in terms of student expectations and attitudes and the need for change from teacher dependency to self-autonomy in number matters. Initially the session will be a short introductory talk followed by workshop type questions and opportunities for discussion presented at six tables in the room but I hope that there will also be the time and opportunity for general discussion of the issues involved.

Getting Unstuck in Maths: Building Mathematical Memory

with Rapid Reconstruction

Jeff Simpson, Mastery Learning System, Ukiah, California, USA

Old-fashioned instruction builds memory, but not understanding. Modem methods stimulate understanding, but not memory. Even with a combination of approaches, many learners still can’t remember number facts, and haven’t mastered basic multiplication, division, and fractions. That's because understanding and remembering are not the same thing; and because traditional memory strategies deal with language, rather than mathematical perceptions.

This workshop introduces the Count, Notice, & Remember method of guided discovery and rapid reconstruction, which enables and requires mastery of the basics. It teaches computation through problem-solving, and builds fast, accurate, context­ - derived memory, while giving students ownership of their learning. It succeeds where wordy explanations and language-oriented mnemonic devices fail. It extends constructivist activities in practical ways, enabling students to remember what they have done, rather than forcing them to recall what they have tried to memorize. It is a simple, effective, mathematical way of building applicable mathematical memory.

Assessing mathematical skills

Harrie Sormani

Centre for Innovation of Education & Training, Eindhoven, The Netherlands

In Holland there are many assessment centres. The CINOP has made material for this centre to assess the potential of a candidate. Part of the method is to assess the exact capacities of a candidate. The material exists from situations, that the candidate had to solve at six domains; arithmetic, measure, geometry, tables and graphs, relations and logic problem. At the workshop, after a short introduction, the audience can do a geometry problem and after that we can discuss if this is a way to work at assessment and mathematics.

 Alternative Assessment Methods

in the National Training & Development Institute

Patricia Ward, National Training & Development Institute, Dundalk

The National Training and Development Institute is a vocational training organisation for people with special needs. To deliver effective training programmes it is essential to identify the learning potential of individuals early in their programmes.

A system of assessment has been used for the past four years which was developed for N.T.D.I. While this system was devised for the institute, it has been found to be less than effective. The difficulties inherent in this system and the reasons for its demise are discussed in this session.

Working as a remedial teacher with N.T.D.I. I have undertaken research into the development of alternative assessment methods that would identify learning potential. My particular interest is the area of mathematical assessment. The other aspect of this session is the discussion of this research.

An Introduction to Adults Count Too

Roseanne Benn, University of Exeter, U.K.

The aim of all education, including mathematics education, is to enable learners to satisfy goals such as vocational and personal development but also to facilitate and encourage learners to participate fully as citizens. In a democratic society, this implies curricula that serve everyone in that society, with alms and objectives located in human and social good and which are not just consumer-driven, corporate or reproductive. By this criterion, mathematics education at all levels alienates and fails a large proportion of the population. Nevertheless it is possible to start to change this situation by locating all mathematics education for adults in a philosophical, political, historical and social framework with a curriculum and pedagogy informed by this conceptualisation.

This paper will examine the powerful forces operating on the three main actors in the learning and teaching process - the learner, the tutor and the curriculum. These forces will be represented as a matrix whose elements are vectors ie. variable in both direction and magnitude. Each is acting on the learner, tutor or curriculum with a push or pull factor of varying strength towards either an emancipatory, empowering education or a banking, reproductive one. No variable is intrinsically more important than any other: each has an impact. The strength and direction will vary over individuals, institutions and societies and over time. The paper aims to reconceptualise the process of adults learning maths in terms of this matrix.

Student Nurses and Mathematics

B. Meriel Hutton

University of Central England in Birmingham

For the safety of the public, it is essential that nurses are competent at least in the mathematics that enables them to calculate medications accurately. From a survey by Hek (1994) it is apparent that mathematics is not universally included in the nursing curricula, nor asked for as a pre-requisite to entry. Changes in the profile of the typical student nurse from a school leaver with 5 '0' levels to a more mature woman with often fewer school qualifications have been one of the triggers for this study into student nurses and mathematics.

In this paper, students' feelings about mathematics are explored and related to age, time elapsed since leaving school and performance in a test of nursing mathematics. Provision for revision and mathematics support is described and the results of a post­test analysed. The results indicated that pre-registration nursing courses should include an element of mathematics to alert students to their own shortcomings and provide a means to improve their computational skills before working in the clinical areas.

Reference:

Hek G. (1994) Adding up the cost of teaching mathematics Nursing Standard 8:22, 25-29.  

An exploration of situated cognition in two professional crafts:

upholstery and gardening.

 Dhamma Colwell, King's College, University of London

A report on my progress so far into the following questions:

How do people set about solving the mathematical problems they encounter in everyday life? What strategies do they employ, and how did they develop or acquire them? Are they learnt from working and living with other competent people? Or how much is 'school maths' utilised?

Do the strategies people adopt depend on different styles of remembering and thinking, for example visual-spatial, verbal, kinaesthetic, holistic, linear? Are these innate or learnt? How can they be investigated?

What kinds of language are used in this problem-solving, and to describe it?

Could there be a specific problematique for research in adults mathematics education?

 Tine Wedege, IMFUFA, Roskilde University, Denmark

'Heterogeneity' is the very term for description of the field of research in adults teaching and learning mathematics. This is the authors' message in the chapter, Adults and Mathematics (Adults Numeracy), of the new handbook in mathematics education (FitzSimons et al, 1996). Indeed, as a field of practice 'adults mathematics education' is very complex, and the ways of constructing the object of study are innumerable. The two different points of view, the demand of society for mathematical knowledge vs. the need of the individuals, give rise to several subfields of research.

Nevertheless I think it is possible to locate a ~eitmotif' that crosses the different fields. The issue I want to discuss in this session is the following:

Could there be a specific 'problematique' for research in adults mathematics education (teaching and learning) that is qualitatively different from a 'problematique' concerning children's education?

Starting from the theory of the French philosopher Louis AIthusser, fli try to construct an epistemological concept problematique which is used as a tool in my analysis of five papers from the first two conferences of ALM (Evans & Thorstad, 94; Benn, 95; Coben & Thompson, 95; Maass Schloeglmann, 95; Wedege, 95). In this way I hope to contribute to creating a starting point for a theoretical discussion at ALM-4.

Reference

FitzSimons, G; Jungwith, H; Maasz, J; Schloeglmann, W.(1996). Adults and Mathematics (Adult Numeracy). In Bishop, A.J. (ed) Handbook in Mathematics Education. Dordrecht: Kiuwer Academic.

Cooperative Learning in the Adult Mathematics Classroom: 

Students Helping Students or Stumbling through the Dark Together?

 Katherine Safford, Saint Peter's College, Jersey City, New Jersey, USA

A major theme in mathematics education today is that of collaborative learning. A growing body of research supports the idea that students can learn effectively from each other and that working in groups is beneficial for both the proficient and less skilled students in a class. Much of this research has been conducted in kindergarten through secondary school settings but studies do exist which report on cooperative work at the undergraduate collegiate level and in adult education classes.

This session will summarise the findings contained in those reports and their suggestions for successful implementation of collaborative learning in adult mathematics education. The presenter will discuss the results of her own research in this area. In addition, she will describe her plans for future research to incorporate collaborative learning in college algebra and elementary caculus classes art her home institution.

Constructive Numeracy Teaching as a Gateway to Independent Learning

Mieke van Groenestijn,

Hogeschool van Utrecht, The Netherlands

There is a new wave going on in the Dutch Adult Education, similar to the ideas of Open learning Centres in Further Education in Great Britain. The intention of this movement is to structure adult education in a way that it fits everyone. That means:

more flexible programs, focused on more individual education, teacher independent and graded by certificates at different levels. People must be able to study in their own way and in their own time and pace. The basic idea of the new system is ‘Independent Learning'.

Some starting points of Constructivism can be a base for independent learning. In that way we may wonder how Constructivism, as applied in Realistic Mathematics Education or Numeracy Teaching can be a gateway to independent learning in adult education. if we are able to develop a numeracy programme for Adult (Basic) Education, based on the learning principles of Constructivism, then the students can also be trained in learning to work more independently at the same time.

In this session an account is given of a research project in The Netherlands on this issue in Adult Basic Education.

Adult Return to Mathematics - A Proposed Project in Uganda

(By the Uganda Mathematical Society)

 Janet Kaahwa

Makerere University, Kampala, Uganda

The Uganda Mathematical Society (UM S), (of which I am the current chairperson) is planning to start a project entitled "Adults Return To Mathematics". The project proposal write-up has been completed and funds are being sought to provide initial capital. The project is now in its second phase - that of conducting a baseline study. I hope, by the time of the ALM4 conference, this phase will have been completed. In my presentation I intend to talk about this project. In my paper I will describe the project giving it's aims and how the society intends to implement it. In addition, I will give the details of what will have been achieved by the time of the conference. This project is meant to contribute towards UMS' main aim - that of popularising mathematics to the Ugandan community.