Presentaci

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Teaching mathematics with adults using a
dialogical teaching and learning approach
Javier Díez-Palomar María Padrós CREA - Center
of Research in Theories and Practices that
Overcome Inequalities crea_at_ub.edu
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Teaching mathematics with adults using a
dialogical teaching and learning approach
CONTENTS

• Introduction
• Overview of adult learning in Spain
• Overview of adult learning in Catalonia
• Adult learning mathematics in Spain
• Some features of adult learning mathematics
• What type of mathematics
• The dialogic learning approach
• Some examples in adult learning mathematics
• Next steps

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Teaching mathematics with adults using a
dialogical teaching and learning approach
INTRODUCTION
Information Age
People who dont have educational credentials are
excluded of our society.
APEL Policies in Europe
Recognition of non-scholar knowledge Discussion
about curriculums contents in mathematics
(impact of last PISA)
What is the impact of this situation on Adult
Educational Systems? What about Mathematics?
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Teaching mathematics with adults using a
dialogical teaching and learning approach
INTRODUCTION
Participation in any learning activities (formal,
non-formal, informal), by educational attainment,
2003 ( of population aged 25 to 64)
Source Eurostat yearbook, 2006-2007.
(1) At most lower secondary education (ISCED 0 to
2). (2) Upper secondary and post-secondary
non-tertiary education (ISCED 3 and 4). (3)
Tertiary education (ISCED 5 and 6). (4) Informal
learning is excluded
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Teaching mathematics with adults using a
dialogical teaching and learning approach
INTRODUCTION
Mathematics is embedded in our lives (Niss, 1995)
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Teaching mathematics with adults using a
dialogical teaching and learning approach
OVERVIEW OF ADULT LEARNING IN SPAIN
In Spain adult education is grounded on popular
initiatives from the end of the XVIII Century.
The ideas of emancipation and critical
transformation are still embedded in adult
education practices in Spain.
Transformation
Education
Agency
Labor Market
Confidence
Freedom practices
Flecha, López, Saco (1988) Tellado (2007)
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Teaching mathematics with adults using a
dialogical teaching and learning approach
OVERVIEW OF ADULT LEARNING IN SPAIN
Article 52. Objective. Permanent education
offers lifelong learning to all members of the
public in order to acquire, update, complete and
extend their abilities and skills for their
professional and personal development. To do
this, the administration of education will
collaborate with the civil service departments
with competencies in terms of adult education,
and especially in employment management.
(...) Public administrations prioritizes all
these people who have not completed their basic
education, for various reasons. Also people
over the age of 16 would be able to participate
in adult education if they cannot attend a
standard educational centre because of their job
or other circumstances. (...) The
administration of education will promote specific
programs for the Spanish language, culture and
other co-official languages in order to integrate
the immigrant population. (Source LOGSE
General Arrangement of the Educational System
Law).
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Teaching mathematics with adults using a
dialogical teaching and learning approach
OVERVIEW OF ADULT LEARNING IN SPAIN
SCHOOL MODEL
SOCIAL MODEL
Meaningful education Teachers as
facilitators Adults as participants
Formal education Teacher conducted Adults as
students
Medina (1997)
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Teaching mathematics with adults using a
dialogical teaching and learning approach
OVERVIEW OF ADULT LEARNING IN SPAIN

• Basic Adult Education
• Professional training
• Courses to prepare for exams in order to access
  other levels of education
• Spanish classes for the immigrant population
• Non-regular courses

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Teaching mathematics with adults using a
dialogical teaching and learning approach
OVERVIEW OF ADULT LEARNING IN SPAIN
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Teaching mathematics with adults using a
dialogical teaching and learning approach
OVERVIEW OF ADULT LEARNING IN SPAIN
In Spain every region (comunidad autónoma) is
responsible about its educational system. The
main government establishes the general features
that every level of education have to reach.
Then, each region manages its own educational
system.
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Teaching mathematics with adults using a
dialogical teaching and learning approach
OVERVIEW OF ADULT LEARNING IN CATALONIA
Main levels
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Teaching mathematics with adults using a
dialogical teaching and learning approach
ADULT LEARNING MATHEMATICS IN SPAIN
Main objectives of adult learning mathematics in
Spain

• To update the educational background and to
  facilitate access to different educational
  levels to each person who may require it.
• To develop programs and courses related to
  specific educational needs from excluded
  groups.
• To improve professional qualifications and/or to
  acquire training in order to develop other
  professions.
• To develop people's capacity to participate in
  social, cultural and political events.

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Teaching mathematics with adults using a
dialogical teaching and learning approach
ADULT LEARNING MATHEMATICS IN SPAIN
To
Incorporate the language and arguments typical of
mathematical reasoning (numerical, graphical,
geometrical, logical, algebraic, probabilistic)
in order to be able to communicate in a precise
and rigorous way. Use logical ways of thinking,
to formulate and verify conjectures, to make
inferences and deductions, and to organize and
link information related to daily life and
problem solving. Quantify real situations by
virtue of data, measures and numbers while making
the appropriate computations. (Alsina, 2001 3-4).
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Teaching mathematics with adults using a
dialogical teaching and learning approach
ADULT LEARNING MATHEMATICS IN SPAIN
To
Elaborate personal strategies for analyzing
concrete situations and for problem solving using
various resources and instruments, analyzing the
final results obtained. Use elementary
techniques for collecting data to obtain
information about phenomena and situations and to
represent this information by means of numerical
or graphical forms in order to evaluate it.
Recognize the diversity of different situations
and to see how different points of view can be
used to explain it (deterministic / random,
finite / infinite, exact / approximate). (Alsina,
2001 3-4).
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Teaching mathematics with adults using a
dialogical teaching and learning approach
ADULT LEARNING MATHEMATICS IN SPAIN
To
Identify shapes and spatial relations present in
reality, analyzing geometrical properties and
relationships. Identify the mathematical
elements (statistical data, graphics, maps,
computations, etc.), which are present in news,
pools, commercials, etc., critically analyzing
their functions and possibilities for a better
understanding of messages. Approach day-to-day
situations and problem solving in a mathematical
way (exploring alternatives, using a precise
language, etc.). Know and value personal
mathematical skills in order to deal with
situations that require their use or in which one
can enjoy the creative, manipulative, aesthetic
or useful aspects of mathematics (Alsina, 2001
3-4).
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Teaching mathematics with adults using a
dialogical teaching and learning approach
ADULT LEARNING MATHEMATICS IN SPAIN
Target in adult learning mathematics courses

• They go to the adult school because they want
• They feel interested / excited in doing /
  studying mathematics
• They already have prior experiences with
  mathematical ideas

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Teaching mathematics with adults using a
dialogical teaching and learning approach
SOME FEATURES OF ADULT LEARNING MATHEMATICS
Difference between their prior experience with
mathematics and current mathematics in the adult
school
Gloria of problems We were dividing all day
long! If the topic was division, then the whole
year we did divisions if it were division by
decimal numbers, then the whole year we did
divisions by decimal numbers I mean, I remember
it was very monotonous, burdensome very, I
dont know. Now I find them (mathematics) more
pleasant, because they are more
varied. Rosario ...more varied Gloria yes,
difficult well, to do the operations and so,
but they are more enjoyable with the computer,
with, well, it is also a competition with your
children who also know how to do that, and you
too, and you still take things with more
enthusiasm, and you really like them you learn
them. Now if you say how hard mathematics is,
well
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Teaching mathematics with adults using a
dialogical teaching and learning approach
SOME FEATURES OF ADULT LEARNING MATHEMATICS
Social image about mathematics
Mathematics are so difficult!
Mathematics is not for me.
I like Mathematics, but it is very difficult to
me.
Im not able to learn Mathematics
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Teaching mathematics with adults using a
dialogical teaching and learning approach
SOME FEATURES OF ADULT LEARNING MATHEMATICS
They feel more comfortable and safe using
algorithms rather than solving problems.
They are influenced by their memories from their
previous schooling.
For them mathematics make a lot of
calculations / hacer muchas cuentas.
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Teaching mathematics with adults using a
dialogical teaching and learning approach
SOME FEATURES OF ADULT LEARNING MATHEMATICS
They feel more comfortable with visual and
concrete procedures to solve problems, rather
than abstract procedures.
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Teaching mathematics with adults using a
dialogical teaching and learning approach
SOME FEATURES OF ADULT LEARNING MATHEMATICS
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Teaching mathematics with adults using a
dialogical teaching and learning approach
SOME FEATURES OF ADULT LEARNING MATHEMATICS
They prefer exact answers rather than
estimations, nor rounding.
For them mathematics exactitude
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Teaching mathematics with adults using a
dialogical teaching and learning approach
SOME FEATURES OF ADULT LEARNING MATHEMATICS
There is no correspondence between level of
literacy and level of mathematical literacy /
numeracy.
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Teaching mathematics with adults using a
dialogical teaching and learning approach
SOME FEATURES OF ADULT LEARNING MATHEMATICS
There is a gap between scholar Mathematics and
real Mathematics.
Gloria The kind of mathematics that we women do
is not like the kind of mathematics that you do,
as mathematicians. Because in order to solve each
problem, we have to make huge jumps, I mean, that
is... You, a woman who already knows how to use a
computer, well, you do wonders, because...
because it is a better mathematics than that one
you know, the one that you use when you pay the
bus, and you always pay the same amount, so you
check if this month is the same fare as the last
one, I mean, you check the bills, those bills
that you have to pay when you run a house the
phone, the school for the kids, the...
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Teaching mathematics with adults using a
dialogical teaching and learning approach
SOME FEATURES OF ADULT LEARNING MATHEMATICS
There is no identification of the everyday life
knowledge as being mathematics
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Teaching mathematics with adults using a
dialogical teaching and learning approach
WHAT TYPE OF MATHEMATICS?
So, what is Mathematics in terms of adult
education and what kind of Mathematics should be
included in the curriculum for Adults?
How can we validate / legitimate adults
knowledges (grounded on their experiences), that
they bring in the classroom?
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Teaching mathematics with adults using a
dialogical teaching and learning approach
THE DIALOGIC LEARNING APPROACH
Egalitarian dialogue
Cultural intelligence
Instrumental learning
Transformation
Solidarity
Creation of meaning
Equality of differences
Flecha (2000)
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Teaching mathematics with adults using a
dialogical teaching and learning approach
SOME EXAMPLES IN ADULT LEARNING MATHEMATICS
Valorization of different types of mathematics
Mari Luz- Or by giving examples that touch what
we are doing, because that way you get it more
easily. If you give examples, well, as you do it
sometimes, examples, then of course, it gives you
a better idea. You understand better. To me, the
most important point is that you get motivated.
Thats me.
Egalitarian dialogue Equality of differences
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Teaching mathematics with adults using a
dialogical teaching and learning approach
SOME EXAMPLES IN ADULT LEARNING MATHEMATICS
Contextualization / Mathematization
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Creation of meaning Instrumental learning
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Teaching mathematics with adults using a
dialogical teaching and learning approach
SOME EXAMPLES IN ADULT LEARNING MATHEMATICS
Contextualization / Mathematization
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Creation of meaning Instrumental learning
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Teaching mathematics with adults using a
dialogical teaching and learning approach
SOME EXAMPLES IN ADULT LEARNING MATHEMATICS
Previous experience grounded on everyday practices
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Creation of meaning Instrumental learning
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Teaching mathematics with adults using a
dialogical teaching and learning approach
SOME EXAMPLES IN ADULT LEARNING MATHEMATICS
Correlation between emotions and learning
Alejandra When I came to get the certificate,
the first afternoon, I told Rosa Look, I will
sit here at a table, alone, because if the other
women look at me, I will not write. And well, two
days later I started working and now, now I have
overcome that.
Solidarity and transformation
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Teaching mathematics with adults using a
dialogical teaching and learning approach
SOME EXAMPLES IN ADULT LEARNING MATHEMATICS
Correlation between emotions and learning
Mari Luz Thats it, and being a strongpoint, and
being with everyone, because some of us are
clumsier, for example, as you said already, that
I should keep trying, and so Gloria It is not
that there are clumsier (people) what happens is
that that person, specifically the one from
yesterday, she got nervous because she thought
that he was going to smack her, because, because
he had done it before. Well, no. I, look, I
understood it this way Lourdes explained it to
me, and we try and I solved the problem
correctly (...) Gloria.- Then, it happens
exactly the same with older people. We understood
it by hammering it down There were two or three
ladies that did not understand it, so I
completely ignored the teacher and I explained it
to that lady
Solidarity and transformation
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Teaching mathematics with adults using a
dialogical teaching and learning approach
SOME EXAMPLES IN ADULT LEARNING MATHEMATICS
Mathematics as a critical practice
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Transformation
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Teaching mathematics with adults using a
dialogical teaching and learning approach
NEXT STEPS
In Spain a new line of research in adult learning
mathematics is going to be open at the Autonoma
University of Barcelona

• PhD Graduate Program - UAB line in adults
  learning mathematics
• European Master in Mathematics Education line in
  adult learning mathematics and dialogic learning

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Teaching mathematics with adults using a
dialogical teaching and learning approach
NEXT STEPS
We need more research
to understand how the interactions work as
bridges that mediate the learning process in a
classroom with adults. We need to include adults
voices from a non-deficit point of view.
Some possible research questions could be
How do personal features impact on aspects such
as participation?
Do different types of participation promote
learning?
How to create challenging situations to
problematize adults experiences (Freire, 1970,
1977, 1987) without provoking discouragement
among them?
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Teaching mathematics with adults using a
dialogical teaching and learning approach
THANK YOU!