ALM5 Conference
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ALM5 Conference |
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Plenary Sessions
Opening
keynote address:
Empowerment
and Numeracy development: Research challenges
Dr.
Iddo Gal (University
of Haifa, Israel)
Empowerment
is a multi-faceted construct that has emerged in recent years in several
This
talk will discuss key premises, concepts, and dilemmas associated with
empowerment in the context of mathematics education and specifically adult
numeracy education, in light of overarching goals of lifelong learning and the
need to develop autonomy, participation, and effective functioning of citizens.
Among the issues discussed will be the nature of numerate behavior and its
reliance on knowledge bases from mathematics but also literacy, the need to
attend not only to the cognitive but also to the dispositional and affective
aspects of numerate, empowered individuals, as well as the need to broaden the
current thinking about the goals of mathematics education for adults if an
empowerment perspective is adopted. Implications of the empowerment perspective
will be presented for research and evaluation efforts, regarding both the need
to focus on empowerment processes and outcomes among learners (but also among
teachers) as well as the need to employ research approaches or designs that can
foster empowerment of all stakeholders. Implications for instructional
practices, teacher training, and assessment will also be briefly raised.
Second
keynote address:
Everyday
mathematics and Adult Mathematics Education
Prof.
Analucia Schliemann (Tufts
University, Medford, MA, USA)
Research
on everyday cognition shows that, out of schools, through participation in
everyday activities, people come to develop mathematical understanding and
procedures to solve mathematical problems.
Strategies for solving arithmetical operations, use of the properties of
the decimal system, understanding and solution of proportionality problems,
measurement, geometry, and probability concepts are examples of mathematical
knowledge developed in everyday settings by children or adults with restricted
schooling.
Acknowledging
development and use of logico-mathematical reasoning by people with
limited school experience is a crucial step towards promoting opportunities for
progress and learning in schools.
It is by bringing previous knowledge into the process of understanding
new situations and representational systems that students come to develop more
advanced mathematical knowledge. But how can people use previous knowledge and experiences constitute the
basis for learning school mathematics? Should we replicate everyday situations in the classroom?
Can we find everyday tasks that would fit all or most of the contents in
the mathematics curriculum? And, if so, once an everyday task is replicated in the classroom, are we
dealing with the same task?
Can we expect that adult students will be as involved in understanding
school mathematical situations as they are when they search for solutions to
problems in everyday life?
Answering
these questions demands careful analysis of the characteristics of everyday
mathematics, as opposed to school mathematics.
In this presentation the relevance of everyday mathematics for adult
mathematics education will be considered through the review of previous studies
on everyday mathematics, focusing on five main aspects: (a) the question of
meaning, (b) the question of generalization and transfer, (c) the question of
concrete referents for mathematical symbols, (d) the socio-interactive
contexts of mathematical activity, and (e) the relevance of school instruction.
The
available research data shows that, although everyday mathematical understanding
can constitute a solid, meaningful basis for the development of more advanced
mathematical activities in school and to the meaningful learning of new
conventional symbolic systems, it has its own limits. Schools can provide a much
wider range of situations and tools for use and representation of mathematical
concepts and relations, allowing for learners to explicitly focus on these from
different perspectives, establishing links between situations that would
otherwise remain unrelated.
Recognizing
the importance of school does not diminish the importance of the prior knowledge
students bring into mathematics instruction from their everyday experiences. In fact, recent studies show that everyday mathematics constitutes an
even broader and deeper source of knowledge and intuition than was previously
thought. Moreover,
for meaningful learning to take place in the classroom, reflection upon
mathematical relations must be embedded, as it happens in everyday life, in
meaningful socially relevant situations where mathematics becomes a tool to
achieve relevant goals. Such school situations, however, must allow for a wider variety of
concepts and representations and for the discovery of features that are not
usually involved in street situations. They should also be as meaningful, challenging, flexible, and relevant
for adult students as getting the correct change is for the street seller and
his customers.
Numeracy
results of the International Adult Literacy Survey (IALS) and follow up research
into adult numeracy: International Life Skills Survey (ILSS)
Stan
Jones (Statistics Canada, Yarmouth, Novia Scotia, Canada)
Willem
Houtkoop (Max Goote Kenniscentrum, Amsterdam, The Netherlands)
Between
1994 and 1996 a number of countries collected data on the literacy skills of
their adult population as part of the International Adult Literacy Survey (and
others are still in the field collecting data). Part of the survey included a measure of quantitative literacy, the
ability to use numbers found in texts. While the quantitative literacy measure does not include everything one
might include in numeracy, it does provide some insight into the mathematics
skills of adults. In
this presentation we will discuss the nature the quantitative literacy measure,
identify some of the important consequences of differences in quantitative skill
in the different countries. One of the important findings of the survey is that occupations that are
growing are particularly demanding of quantitative skill.
We
will also suggest ways in which the measure might be expanded to cover a broader
range of numeracy skills.
As
a follow-up to the International Adult Literacy Survey (Statistics Canada and
the Organisation for Economic Co-operation and Development, 1994-1998), a number
of countries have expressed an interest in a more extensive study of adult
skills, the International Life Skills Survey (ILSS). One purpose of such a project would be to support the strategic
directions on lifelong learning set out by the OECD Education Committee at the
Ministerial level in January 1996.
One
of the areas to be covered in the study is adult numeracy, understood as the use
of mathematics at work and in everyday life.
This presentation will present the developing framework for the numeracy
assessment so that participants in the conference can contribute to the design
of the study. It is intended that the comments of the participants will be
reported to the advisory committee and used in revising the framework.
It is hoped that the framework will reflect the current understanding of
adult numeracy and that the project will serve to validate and publicise this
understanding.
Key
principles for designing effective South African inset mathematical curricula.
Prof.
Hugh Glover, University of Port Elizabeth, South Africa
Many
South African teachers are products of a former education system, where they
were severely disadvantaged.
Most of them were exposed to pre-service courses which lacked emphasis on
developing teachers own conceptual understandings and competencies in
mathematics and mathematics teaching. Whilst some attempts are currently being made to address these
shortfalls, current South African mathematics education reforms will fail unless
serious attention is given to addressing these needs.
This
paper will briefly describe a mix of mathematics In-service programmes designed
and implemented by a South African project based at the University of Port
Elizabeth’s Centre for Continuing Education (UPE, CENCE). This project is located in the Eastern Cape, one of South Africa’s nine
provinces.
It
will then, as a major focus of the presentation, highlight key principles that
have emerged as important in the development of In-service curricula, offered by
UPE, CENCE.
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the active participation by learners in all learning experiences, in
order to promote reflective practices.
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the development of rich, deep mathematical concepts, through the design
and implementation of appropriate mathematical tasks
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the development of relatively inexpensive, durable and appealing
classroom materials
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the design and implementation of classroom teaching-learning situations
which promote positive, confident pupils with good mathematical understanding
The
manner in which each of these principles has guided curriculum development will
be outlined through the provision of specific examples related to the initial
programme overview.
Workshops
Understanding
graphs in adult mathematical education
Esther
Leonelli (Community
Learning Center, Cambridge, MA)
Research
shows that students learn to use and talk about graphs without previous teaching
about the formal rules involved in graphing.
Rather, they became graph‑users by recognizing how the shape of a
graph can tell stories, by expressing their own kinesthetic experiences with
graphs, and by identifying meaning for the visual attributes of a graph
(Nemirovsky,1994). Thus,
learning graphing requires a rich environment that encourages conversations and
explorations around intuitions rooted in the everyday experience of life with
symbols and events.
This
workshop will demonstrate the activities and results of a pilot classroom study
designed to explore these ideas in an adult education program.
The activities aimed at the creation of interactive environments which
included technological tools and where the teacher and the students engage in
the activity with a playful attitude and with the sense of being
co‑researchers, trying their ideas to achieve certain goals. Students are not asked to show what they know but, instead, they try to
describe and represent events.
There are no previously established correct answers; the sense that they
have achieved a good representation emerges from their discussion and
reflections. Use
of everyday experience comes in different formats.
It enriches the activities, gives a purpose to them, and provides ways to
first attempt to represent events. Previous experiences with numbers, space, directions, turns, all come
into play, allowing the establishment of analogies which enrich students
understanding of representations.
Like in everyday life, they develop mathematical ideas in order to
achieve meaningful goals. Social
interactions provide the opportunity for the development of new
forms of reasoning and representations, as each individual try new
approaches and reasons about the results and the questions and constraints
raised by the others. There
is a progression and enrichment of the representation that results from
conflicting views between the participants and a search for coherence between
and within events and representations.
The
workshop will provide hands-on experience with the activities and opportunities
to analyze selected videotaped classroom interactions. Further, we will discuss
how our results led us to develop emergent perspectives on the nature of
graphing, the use of educational technology to incorporate kinesthetic
experiences in mathematical understanding, and the relationship between everyday
cognition and adult mathematics education. Through the combination of these
perspectives we hope to contribute to the creation of richer environments to
support mathematical understanding as part of lifelong learning.
'ALM'
as a community of practice and research
Roseanne
Benn (University of Exeter, Great Britain),
'Adults
learning mathematics' is a new field of research between adult education and
mathematics education. Some of the research questions are sociological, some
psychological; other questions are educational or didactic.
At
the conference ALM-4 at Limerick in 1997, Tine Wedege started a meta-discussion
about the nature of this new field of research. She formulated the question:
Could there be a specific problematique for research in adults' mathematics
education? (Meaning a systematically linked problem field in which questions and
answers about the subject field are formulated on the basis of a certain
theoretical and/or methodological approach.) The debate showed that this is a
very complex issue.
In
this workshop, we will discuss whether our community of practice and research in
ALM is situated within the didactics of mathematics (meaning the scientific
discipline related to research and development work in mathematics education) or
not?
Do
practice and research in ALM exceed the limits of the didactics of mathematics?
Count
on me
Wim
Matthijsse (National
Center for Research and Development for Adult Education,
The
project ‘Count on me’ aims the development of a series of 10 CD-roms on
mathematics for students in adult education and vocational training who want to
brush up their mathematical knowledge and skills or to fill gaps in this area.
Students
should be able to work independently with these materials. They will be guided
by an adaptive built-in tutor system.
The
first prototype, that will be presented at the conference, is on percents. This module contents a database with in it, amongst other, video-clips with real
life situations, selected video-clips with specific instruction on percents,
assignments with feedback, three interactive mental models. The student may want
to be guided from an adaptive built-in tutor. This tutor’s guidance is based
on ‘student-history’ information in the program. However the student will
also be able to set aside the tutor’s advice and to take decisions how to go
further in the program apart from the tutor’s advice. This is called ‘mixed
control’.
Discussion:
A
question in the field of adaptive CD-roms is in what way and until what point
educational cumputer programs could and should take over the guidance and
instruction of the teacher.
What
functions would be wished to be automatized and based on what didactical point
of view?
What
instruction and guidance functions can be automatized?
In
what way will it be possible to create an interaction between student and
computer program as ‘natural’ as possible?
How should the learning process be guided?
A
main point of discussion is the tense between an open learning environment in
which the student decides as opposed to a tutor-guided learning situation in
which the program decides about the next step in the program.
The
virtual mathematics workplace
Harrie
Sormani (National Center for Research and Development for Adult Education,
The
purpose of this workshop is to introduce the audience in the use of Internet in
a math classroom for Dutch adult students working on so called ‘KSE levels
1-4'. That means: for people with very little mathematics background. The Dutch
National Institute for Research and Development in adult education and
vocational training (Cinop), together with teaching teams of the Regional
Education Center Eindhoven and the Regional Education Center Rijn and IJssel
College, developed a website in past months to which mathematics problems can be
posted every month. These math problems are not only meant to yield an answer
but also to start discussions among students. A student may post hist results to
the electronic bulletin board and by this he will be able to compare these with
the answers of other students from other institutes. They can discuss together
their solving procedures and solutions. The math problems have been constructed
in such a way that they provoke practical application of integrative
mathematical knowledge and skills. Developers and teachers have their own
private meeting page where they can work jointly, apart from the student page. How it works will be demonstrated during the workshop.
Teaching
and Learning Mathematics through art:
Eliana
Maria Guedes, Regina Maria Zandonadi, Diomar Cesar Lobão
The
environment where counseling and support activities in Mathematics take place,
directly helping students and teachers with the Project AArt and Mathematics will
be presented, focusing particularly on how the relationship of shapes and
geometry has been incorporated into art, providing an engaging introduction to
this realm of mathematics. This project,
part of the Educational Programme Rediscovering Mathematics, has been
developed with adult students which attend elementary evening courses.
The
principal aims of the activities are to break the barrier of myths which usually
comes with the teaching and learning of Mathematics and
to develop creativeness through the integration of Art and Mathematics
looking for:
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the development of the visual ability.
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the learning and teaching of Mathematics.
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the integration between Mathematics and Art.
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the social integration.
We
have been doing this work in different regions of Brazil and South America,
bringing together students, teachers and tutors interested in the teaching and
learning of Mathematics through Art, considering that:
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interest is one of the first rules of learning, having the world as a
mediator to a process by which man learns about himself and others.
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the teaching of Mathematics, specially Geometry through Art contributes
to the formative process, improving creativeness and favouring a particular type
of thought, seeking new situations and being sensitive to the visual impact.
Together, Art and Mathematics, form a perfect union of creativeness and
knowledge, the one the instrument for the other, functioning at their highest
and best.
The
teaching and learning of Mathematics, specially Geometry through Art contributes
to the formative process, improving creativeness and favouring a particular type
of thought, seeking new situations and being sensitive to the visual impact.
Adult
Maths and everyday life: building bridges, Facilitating 'Transfer'
Dr.
Jeff Evans, Middlesex University, UK
What
kind of maths should we teach in order to enable adults to function
satisfactorily in their work and everyday lives? A typical adult has a
life/lives based on activities that are relatively fully developed and in which
s/he is relatively fully involved (compared with a typical child).
But
in the usual A.B.E. or college pre‑calculus course, there will be much
variation in the relevant activities that different students are involved in.
And further for each student there will be much variation in their activities
over their lifetime. Thus, in order to empower our students the mathematics
taught must be flexible, powerful, and critical.
In
offering some ideas as to how to proceed I shall describe an approach that
builds on but moves beyond, both traditional learning transfer theories and
situated cognition. For the curriculum, it aims to locate and to describe a
shared discourse such as "ctritical citizenship" (Evans &
Thorstad, 1995/ALM‑1); in pedagogy, it aims to emphasise "transfer of
strategies" over "transfer of algorithms" (Schliemann,
1995/PME.19) and to draw on ideas for "teaching for transfer" from
cognitive psychologists.
Getting
at QAdult Basic Education Students' Sturdy Strategies: a Pilot study.
Mary
Jane Schmitt (Milton, USA)
What
sturdy, workable strategies and algorithms do adults enrolled in adult basic
education programs in the U.S. use in their everyday lives to deal with
quantities? Recently,
I conducted a small‑scale qualitative research project to begin lend
insight to this question. My hypothesis is that adult numeracy students use
strategies that are quite different from those taught in adult basic education
programs, and these strategies often remain hidden from teachers. How can we
identify these strategies? What can we learn from identifying and documenting
these numeracy practices? Are the strategies idiosyncratic, or can we detect
themes? How might this inform the adult mathematics curriculum? My research
draws upon the works of Carraher, Schliemann, Harris, Lave and Scribner, but
also considers Dehaene's theory of the existence of an innate and persistent
"number sense."
Building
the concepts of multiplication and division
Ruth
Polkinghorne (Bath, UK)
Tutors
of basic numeracy students tend to teach the four rules one after the other as
if they follow a logical order directly building on the preiously learned skill.
To some extend this is the case but not totally so. Just because a student can
add and take away does not mean that they have all the skills or understand all
the concepts that are needed to go on to multiply and divide.
To
add follows on from counting. The need to do this on a simple level is all
around. To subtract is also something with which they are familiar. Using money
gives lots of examples of the need in very practical terms to add and take away.
1.
Do they avoid multiply and divide because they cannot handle the
concepts?
2.
If they knew their tables fluently would they be more likely to use them?
3.
Do they not know their tables because there is no incentive to learn?
4.
If the concept is difficult can it be broken down into more basic
concepts to enable them to build up to them?
These
are questions I have been asking myself and which form the basis of ongoing
work.
This
presentation relates to the theme of lifelong learning as it is about the way
students can develop the skills to enable them to carry out the sort of
calculations most of us take for granted.
Who
is an adult? How does our definition affect our practice?
Kathy
Safford (St. Peter’s College, New Jersey, USA)
The
traditional definition of an adult student does not accurately describe the
diverse adult student populations whom we meet in our classrooms. This session
will introduce major psychological and educational theories relevant to adult
mathematics education. The presenter will then give examples of evidence of
their presence or absence from her experiences. Participants will be asked to
share insights based on their own work with adult math students.
The
developmental psychology theory incorporated into this session is particularly
applicable to the theme of lifelong learning. Little is learned by the student
in isolation. All new information or skills require assimilation into the
previous knowledge base of the individual, knowledge acquired during a lifetime
spent in and out of formal schooling. The adult education practitioner
experiences are validated and enhanced by knowledge of the theoretical framework
within which s/he practices.
The role of feelings and logic and their interaction in the solution of everyday problems
Dhamma
Colwell (King’s College, University of London, UK)
In
my ongoing research project investigating what maths adults use in their
everyday lives, I have been recording discussions in a focus group of women and
observing upholsterers and gardeners at work. The results concord with Lave and
Wenger's theory of situated cognition (1991) and with an expanded version of
Saxe's model of culture and cognition (1991).
I
am finding that the participants use logical processes to solve everyday
emergent problems and that their feelings about themselves and other people, and
about maths, strongly influence what they choose to do and how they choose to do
it. After reporting on my work, I would be grateful for colleagues' response to
my analysis.
TWIN -project: Useful mathematics for technical vocational education
Henk
van der Kooij (Freudenthal
Institute, Utrecht, Netherlands)
In
most vocational courses in The Netherlands, mathematics education is a formal,
merely algebraic course in which students learn algorithmic behaviour that
doesn't make any sense outside the mathematics classroom. Skipping mathematics
as a separate course from the educational program was the most logical option
for vocational education. Only a shift towards a more practical program could
save math from fading away.
In
1997 a curriculum project was started with the aim to design a program in which
mathematics is really supportive for vocational practice and in which new tools
from information technology are integrated. Starting point for the design of the
student materials is the theory of Realistic Mathematics Education (RME) as it
is developed by the Freudenthal Institute (Freudenthal, 1973, 1991; Treffers,
1987; de Lange, 1987; Gravemeijer, 1994).
In
the RME approach of mathematics, rich context problems are starting point for
mathematical activities. The concreteness of the contextual problems offers
students the opportunity to develop own strategies to attack and solve problems.
When contexts and problems are chosen carefully, it is possible for students to
experience a kind of guided re-invention of mathematical methods. These personal
strategies of students lead to a formalization of strategies, in which de-contextualization
of the strategies makes strategies applicable to new problems in other contexts
(transfer-principle). Furthermore: technology leads to non‑traditional
methods that often can replace usual strategies.
In
this workshop the ideas behind this approach will be discussed. Of course there
will be hands on activities, just to experience the theory yourself.
Statement:
Mathematics,
class and lifelong learning
Roseanne
Benn (University of Exeter, UK)
The
call for papers for this conference asks what kind of maths should we teach in
order to enable adults to manage their own life and to function optimally in
work and social life. In the session I will suggest that what we teach is
linked to who we teach. Therefore we must always consider the social and
cultural background of our students. I will argue that Britain is still a
class-ridden society, illustrating the importance of this by examining the
strong association between social background and educational performance. The
class-related factors in maths education for adults will be discussed and some
ways suggested of overcoming class differentiation. I hope that the group can
spend some time discussing this subject which is now 'taboo' in our supposedly
'classless' society.
The practice of Independent Learning in Adult Basic Education
Mieke
de Laat, Simone van Duin, Frank Haacke, Riny Beckers, Nettie van Leek
Demands
from society and government make it necessary to have a continuously changing
proces in our adult education system. Students demand an individual approach. In
a flexible society
it is a need for them to reach their goals quickly, without education that
offers them superfluous knowledge.
The
answer from us is independent learning. Teacher and student cooperate to achieve
the planned goals. Students follow their own individual route and work together
in groups.
The
change of our
education stands for a new learning environment, new instruction means,
a different way of teaching and specific appliances to enable the student
to learn more and more independently. These means are a plan board, tutorials
and a special diary.
Individual
routes are necessary in combination with learning in a group. The role of the
teacher has changed from teaching into asking and explaining questions. The
teacher keeps in mind the Plan-Do-Review principle all the time.
In
this workshop we will present our experiences with independent learning and the
specific appliances we developed for that.
Whose
Numeracy?
Dhamma
Colwell (King’s College, University of London, UK)
The
three presenters experience of teaching numeracy varies. Janet and Sue both work
with undergraduates. Janet also works with university employees. Dhamma's
experience is of teaching adults in Adult and Further Education provision (i.e.
not university provision), mainly at the basic level, where many students also
have low levels of written or spoken English. However, although our students are
different our approaches to teaching are not. Our common approach is to discover
and validate students' existing
knowledge, skills, attitudes to maths and current goals, which are very
diverse.
By
considering the attitudes and needs of students at different stages of life
might we not further our work amongst adults learning mathematics by gaining
greater insights into their different needs and attitudes? We invite colleagues
who would like to discuss this issue to join us in a session at ALM 5
A
numeracy curriculum
Dave
Tout, Beth Marr
(Victoria, Australia)
This
new innovative numeracy and mathematics curriculum framework has been developed
for adults and has been widely used across Australia since 1997.The framework
offers a style of competency or outcome statement which is holistic rather than
fragmented, in that it is based upon realistic purposes and uses of mathematics,
and which encompasses a particular perspective on numeracy and its relationship
to mathematics. The paper outlines the rationale and development of the
curriculum, explains how it is constructed, and gives some examples of the
detailed learning outcomes
Foundation
maths and portfolio assessment: an Irish experience
John
O’Donoghue (University
of Limerick, Ireland)
The
National council for Vocational Awards (NCVA) was established in 1991 to set,
monitor and certify stadards for vocation, education and training programmes
provided within the further education sector.
NCVA
awards are intended to provide access to employment, further education and
further training. The Council through its awards and activities serves as an
important facilitating agency in life long learning for Irish citizens. Its
awards are adult‑ focused and programmes leading to NCVA certification are
conducted in a variety of settings including schools, workshops, community and
adult education centres.
The
NCVA has been innovative in its approach to assessment and certification. It has
pioneered the use
of portfolios of evidence for assessment purposes in a wide range of subjects in
Ireland. The authors have been providing support sevices for the Foundation
Level Mathematics for a number of years including the training of tutors. This
paper focuses on the use of portfolio assessment in foundation level
mathematics:the stategy for implementation on a national scale; learners'
portfolios; problems and opportunities; and future directions.
QUESTIONS
1.
How important is assessment in adult mathematics learning?
2.
Should mathematics assessment be tailored for adults? If so, how?
Learning
to learn other people’s knowledge - acquiring self-sufficiency in a math
classroom
Brian
G. Cann (University of Maryland, Heidelberg, Germany)
Mathematics
is viewed by many adults as external to their lives and experience: it is seen
as other people's knowledge. Without a sense of the personal relevance of the
subject matter, mature study habits are frequently abandoned in favor of study
strategies half remembered from school. The result is a feeling of not being in
control that is expressed as math anxiety.
As
more adults as required to take post school mathematics classes for skill
acquisition or further qualification, the need to make learners aware of
specific and successful study strategies for learning mathematics is also a way
of opening access to the subject. This paper discusses the theoretical
background and practical implementation of strategies that are currently being
applied at the University of Maryland Mannheim Campus to raise students'
awareness of how they can be active participants in their study of mathematics.
The acquisition of appropriate study strategies is seen as a prior requisite for
the willingness to embrace rather than avoid mathematics in the context of
lifelong learning.
Can
skills acquired by learning mathematics be used in learning other topics?
Bert
Imandt (Regional Center for Adult Education, Rotterdam, Netherlands)
The
main question of this workshop will be: Can skills acquired by learning mathematics be used in learning other topics?
In
lifelong learning the skill of learning is an essential skill. In societal and
working situations people learn from activities, discussions, cooperation and
success and failure. Most of the time this learning is not intended. It happens
unconsciously: only when you are confronted with earlier experienced problems
you can re-call what you have learned. The ways of learning in such cases are
mostly totally unknown to the learner.
In
learning mathematics one can learn a lot of learning skills as well. The learner
has to explore and investigate problems. He has to try, test and reflect on
solutions and ways of problem solving. He can learn to talk about problem
solving.
Learning
mathematics is a very good way of learning to learn. Teachers can use the
teaching of mathematics to teach learning skills. By provoking discussion on
problem solving he can force his students to think and compare several ways of
problem solving. By stimulating reflection on problem solving he can force
students to think about learning, etc.
In
this workshop I want to discuss the skills used in problem solving and learning
mathematics. I shall compare these skills with more general skills, used in
learning. I want to explore ways of teaching these skills and teaching the use
of these skills in other fields of education and societal activities.
A
democratic classroom
Alison
Tomlin (London, UK)
I
have been working on a research project which started out looking into using
writing in adult basic maths classes, but has developed into looking into how to
strengthen students’ voices in the classes. I will be sharing work including
-
using line graphs as a presentation of personal maths histories
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a conference organised by and for students
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arising from the conference, a magazine of students’ writing about
maths, again produce by students
-
students writing their own maths questions
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negotiating the curriculum and lesson plans
-
students observing and commenting on the discourse of their own
classrooms.
I
don’t want to take up all the time with me talking; some of this material will
be in displays and handouts, and I hope participants will be able to share their
own experiences.
This
work has raised questions around what we mean by a democratic classroom or
negotiating the curriculum, and it presents challenges to some traditional views
of an appropriate curriculum. I hope the workshop will be of use to me in trying
to develop a theoretical framework, and of practical use to people trying to
work in similar directions.
The
conference is about ‘What kind of maths should we teach?’ I would like to
extend that question, so that we ask also ‘and who should decide?’
Application
of Number in Vocational Training
David
Kaye, City of Westminster College, London
During
the last five years the GNVQ (General National Vocational Qualification) has
been developed as the main qualification in England and Wales.
GNVQs
are available for a wide range of vocational studies including Business
This
presentation will look closely at the key skill of Application of Number
which is intended to assess a basic competence in number skills with relevance
to the chosen vocational area.
-
to give an introduction to the contents and assessment methods of
Application of Number;
-
to raise issues and ask questions on the validity and reliability of
Application of Number as a process for teaching and assessing students’
numeracy in a vocational context
- to gather and collate the views of ALM5 attendees to these issues and questions with reference to the relevance of Application of Number in maintaining and improving lifelong learning
The
effect of gender and fluency in English on the mathematical confidence and
achievement in a realistic mathematics course
Barbara
Miller-Reilly (University of Auckland, New Zealand)
This
research project aimed to explore the reactions of students to the style of
teaching and assessment in a year-long mathematics course/paper at the
University of Auckland, New Zealand. This paper was established to attract and
help students returning to mathematics after a break, or to help students who
have not succeeded in previous mathematics study. It aims to build the
confidence of students by providing the opportunity for them to engage in
mathematical modelling in a variety of contexts. A preliminary survey was
undertaken in 1995 to explore students' reactions to the paper and the findings
from this survey are presented.
A
comparison was made of students' mathematical confidence, how relevant they
found the approach, and their achievement in the paper. Results indicate that
for students who are fluent in English, a higher proportion of females than
males indicated a definite increase in mathematical confidence. In comparison,
for students who are not fluent in English, a reasonably high proportion were
negative about the approach in the paper, as well as the effect on their
mathematical confidence, and this group did not achieve as well as those who
were fluent in English.
These
research results link to the 'Lifelong Learning' theme for this conference
because many adults in this course have indicated in their evaluation and in
personal discussions that they found the approach taken in this course to be
relevant to them. They now have a better understanding of the usefulness of
mathematics and more confidence to use mathematics themselves in their everyday
lives. However other students are unable to gain this confidence and insight.
Factors which seem to influence this outcome appear to be the students' fluency
in English or their beliefs about the learning of mathematics.
On
the Relationship between cognitive and affective components of learning
mathematics
Prof.
Wolfgang Schlöglmann (University of Linz, Austria)
If
one considers the research on learning mathematics, one receives the impression
that the learning of mathematics is primary a cognitive problem. However, in
practice, the learning of mathematics is strongly influenced by affective
components, especially in the case of adult education.
In
the first part of my lecture I intend to discuss a general concept of L. Ciompi
An Affect logic, which attempts to connect cognitive and affective aspects of
learning.
In
the second part, I will describe some consequences for the learning situation in
courses of adult education in mathematics.
The
relationship between cognitive and affective components are important for
learning processes, especially in the case of ‘Lifelong Learning’.
Common sense or good sense? Ethnomathematics and the Prospects for a Gramscian Politics of Adults' Mathematics Education.
Dr.
Diana Coben (Goldsmiths College, University of London, UK)
Teaching
Mathematics across the undergradutate curriculu: an
investigation into how specialist and non-specialist teachers of
mathematics explain
successful teaching experiences, and how difficulties in teaching mathematics
are perceived.
Pat
Drake (University of Sussex Institute of Education, Falmer, Brighton BN1 9RG,
England)
Mathematics
as a core subject is permeating the curriculum at undergraduate level, just as
it did in schools and then in vocational further education and training. Thus there is, or shortly will be an even greater demand for teachers of
mathematics to work with the students who need it to be taught.
However, at advanced level in school, and at undergraduate level in
university, fewer people are electing to study mathematics, despite an overall
massification of higher education, suggesting a smaller pool of appropriately
qualified people from which to draw teachers.
Experience
from other sectors of education suggests that as the need arises,
non‑specialist mathematicians are drawn into teaching mathematics, with
varying degrees of enthusiasm. These teachers tend to take a pragmatic rather than an esoteric view of
teaching mathematics, to start with at least being primarily concerned with
their own mastery of the subject knowledge that was required of them.
However I believe that non‑specialist mathematics teachers are
characterised by range of approaches to and beliefs about successful mathematics
teaching. So
far as I know, little attention has been paid to approaches taken by these
teachers in the standard discourse of mathematics educators (through
professional associations etc.).
It
is the intention in this research project broadly to define circumstances
associated with successful mathematics teaching and learning at university
level, and to examine the issues from the perspective of those who are teaching
mathematics, either as specialists or as non-specialists. Research questions are aimed at defining and exploring the relationships
between specific cognitive, contextual and cultural dimensions that teachers of
mathematics recognise in their teaching.
Lifelong
learning question:
Non-specialist
teachers of mathematics are drawn to working in mathematics in spite of as well
as as a result of previous experience.
What can be learned from these lifelong learners of mathematics?
Parents
as Resources for Mathematical Instruction
Marta
Civil and Rosi Andrade (University of Arizona, Tucson, USA)
This
paper will address one component of a research project that aims at the
development of mathematics instructional innovations in classrooms composed of
predominantly minority working‑class students.
Our goal is to develop
teaching innovations in mathematics that capitalize on students' (and their
families') knowledge and experiences from everyday life.
In the paper, we will focus on the work with parents in this project.
This
work takes three different avenues:
a)
teachers make ethnographic household visits of some of their students'
parents. Our
premise is that
the students' households and community can provide strategic resources for
classroom practice;
b)
regular mathematical workshops with a core group of working class,
immigrant, Spanish speaking mothers. Through these workshops, we explore these
women's ideas about and understanding of mathematics as well as their use of
mathematics in their everyday life, while maintaining a two-way dialogue
to better inform our work with their children;
c)
interviews to uncover the uses of mathematics in some typical occupations
in this community (e.g., construction worker, carpenter, seamstress).
Analysis of these interviews should provide us with insight into
curricular connections between in-school and out-of-school
mathematics, as well as into our work with parents as adult learners of
mathematics.
Forum
Discussion
Maths
as part of lifelong learning
At
the end of the conference the theme of the conference ‘Maths as part of
lifelong Learning’ will be discussed during the forum discussion.