Family Mathematics
Education: Building
Dialogic Spaces for Adult
Learning Mathematics
Díez-Palomar, J.; Molina Roldan, S.
[email protected] ; [email protected]
Universitat Autònoma de Barcelona
Teacher training for a family mathematics education in
multicultural contexts, 2007/ARIE/00026 (AGAUR)
THEORETICAL BACKGROUND
RESEARCH QUESTION
METHODOLOGY
THE WORKSHOPS
DISCUSSION
CONCLUSIONS
Díez-Palomar & Molina; ALM 16; London
THEORETICAL BACKGROUND
How does adults learn?
Merriam (2004) argues that we have no single theory
or model of adult learning. What we have instead is
what she calls “knowledge base of adult learning”,
that is “a colorful mosaic of theories, models, sets of
principles, and explanations.” (Merriam, 2004, page
199).
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THEORETICAL BACKGROUND
How does adults learn?
Adults learn...
Making meaningful connections to their previous
experiences (Flecha, 2000; Freire, 1977, 1997;
Knowles, 1984, Lave & Wenger, 1991; Mezirow, 1997;
Rogers, 1969).
Adults as agents of their own learning process.
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THEORETICAL BACKGROUND
Active learning methodologies
- Freire (1977; 1997): Read and write the
World critically; “el método de la palabra”
- Knowles (1984): Andragogy (learning selfdirected)
- Mezirow (1991, 2000): trasformational
learning
- Flecha (2000): Dialogic Learning
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THEORETICAL BACKGROUND
“Social turn” to explain how adults learn
People from disadvantaged environments are
penalised at schools (Abreu & Cline, 1998; Abreu,
2005; Secada, 1992; Gallimore Goldenerg, 1993; Tate,
1997; Civil & Andrade, 2002)
Theoretical concepts from Bourdieu & Bernstein
- Cultural capital
- The distinction - habitus
- Classification / Frames / codes
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THEORETICAL BACKGROUND
“Predicated on the assumption that classroom
cultural and linguistic patterns should be congruent
with cultural and linguistic community patterns,
researchers and practitioners sought to bridge what
came to be regarded as the discontinuity or
mismatch gap” (González, Andrade, Civil, Moll, 2001,
p. 116).
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THEORETICAL BACKGROUND
Transfer knowledge
transferability
(Evans)
-
Thesis
of
Situated practice (Lave & Wenger, 1991)
Culturally transmitted (Scribner & Cole, 1981; Lave,
1988)
Dialogical practices (Flecha, 2000; Freire, 1997;
Aubert, Flecha, Garcia, Flecha, Racionero, 2008;
Bakhtin, 1981; Wells, 2001)
Funds of knowledge (Moll et al., 2005)
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THEORETICAL BACKGROUND
(1) adults learn in context, and
(2) adults are more likely
autonomous and self-directed in
their own process of learning.
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THEORETICAL BACKGROUND
What are the contributions from the
previous researches and theories?
Social and cultural contexts are relevant variables
that have an important impact on how adults learn
Our proposal
We want to go further: building spaces where adults
feel free to participate is a crucial fact to promote
this “transfer” of knowledge.
Díez-Palomar & Molina; ALM 16; London
RESEARCH QUESTION
How dialogic spaces impacts on adults’
learning mathematics?
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RESEARCH QUESTION
What does it mean “dialogic spaces”?
A dialogic space is a “place” (a classroom, a meeting
point, a situation, etc.) created by the persons
involved in a particular activity, according to nonpower criteria, but dialogical principles.
Dialogical principles include (1) the same opportunity for all
participants involved in the activity to make contributions,
drawing on their own background, experience, etc.; (2) to
reach agreements drawing on validity claims, not to impose
statements based on a particular power-position; (3) to
recognize everybody’s knowledge, not just the academic
knowledge.
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METHODOLOGY
Teacher training for a family mathematics education in
multicultural contexts, 2007/ARIE/00026 (AGAUR) //
Family training for school inclusion, 2008/ARIE/00011
(AGAUR)
MAIN AIM
To improve the quality of the teaching practices
carried out in Catalonia, through the intervention
on family training
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METHODOLOGY
Teacher training for a family mathematics
education in multicultural contexts, 2007/
ARIE/00026 (AGAUR) // Family training for school
inclusion, 2008/ARIE/00011 (AGAUR)
MAIN AIM
To improve the quality of the teaching practices
carried out in Catalonia, through the intervention
on family training
Díez-Palomar & Molina; ALM 16; London
METHODOLOGY
Teacher training for a family mathematics education in
multicultural contexts, 2007/ARIE/00026 (AGAUR)
SPECIFIC AIMS
(1) to identify the elements and educational strategies in the
work with adult people in the field of mathematics
education, from a multicultural lens; (2) to create training
resources addressed to teachers of mathematics in adult
education, in order to promote equity and opportunities for
everyone to learn mathematics; and (3) to offer resources
for a teacher training of quality, connected to real
classroom-situations, in order to promote a inclusive family
training in mathematics education
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METHODOLOGY
2 CASE STUDIES
(Stake, 1995)
1 elementary school: CEIP Las flores --> Learning
Community
1 middle and high school: IES Las manzanas
4 workshops of mathematics addressed to the families
(drawing on CEMELA’s work)
25 families involved
Different nationalities: Catalonia, Morocco, Colombia,
Ecuador, Romania, Czech Republic, Armenia
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METHODOLOGY
CRITICAL COMMUNICATIVE METHODOLOGY
Universality of language and action
People as transformative social agents
Communicative rationality
Common sense
The disappearance of the premise of an interpretative
hierarchy
Equal epistemological level
Dialogic knowledge
Gómez, J., Latorre, A., Sanchez, M., Flecha, R. (2006). Metodología
comunicativa crítica. Barcelona: El Roure.
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METHODOLOGY
DATA COLLECTION
Qualitative techniques: videotape, field notes, discussion
groups and in-depth interviews.
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METHODOLOGY
DATA ANALYSIS
Children’s perceptions of
parent’s involvement
Home-based
involvement
Encouragement
FAMILY
INVOLVEMENT
School-based
involvement
Modeling
Reinforcement
Family
perceptions
Instruction
Hoover-Dempsey
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METHODOLOGY
Adult Education
TEACHING AND
LEARNING OF
MATHEMATICS
Prior
experience
Creation of meaning
Interaction
Social Process
Dialogic Learning
Egalitarian dialogue
(or not)
Family Training
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Social
Representations
Attitudes towards
mathematics
Expectations
towards
mathematics
METHODOLOGY
DATA ANALYSIS
A posteriori
Grounded Theory (Glasser & Strauss, 1967)
Categories
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THE WORKSHOPS
Some examples of activities
Elementary school
- The Catalan Giant’s Tale
- The Candy Jar
Secondary school
- Meeting through statistics
- Algebra: equations (systems), algebraic language, etc.
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THE WORKSHOPS
The Catalan Giant’s Tale: El gegant del pi
How tall is the giant?
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THE WORKSHOPS
The Catalan Giant’s Tale: El gegant del pi
A food measures 1/7 parts of a person’s height.
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THE WORKSHOPS
The Catalan Giant’s Tale: El gegant del pi
A food measures 1/7 parts of a person’s height.
The golden ratio
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THE WORKSHOPS
The Candy Jar
Doing estimations
The jar was full of candies. How many candies are there
in the jar?
Working groups (mothers and children) to propose
possible answers.
Strategies: grounded on “volume”, or “counting”.
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THE WORKSHOPS
The Candy Jar
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THE WORKSHOPS
Meeting through statistics
To introduce basic statistics
concepts using personal and
everyday elements.
•How
have?
many children do you
•What is your favorite color?
•How
many brothers
sisters do you have?
and
•Etc.
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THE WORKSHOPS
Algebra
Solving equations (systems)
•From
natural language
to algebraic one
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DISCUSSION
Building a “dialogic space”: the ice-breaking activities
(Díez-Palomar & Prat, 2009)
to (a) break the gap between
“home-based practices” and the
school ones, and (b) create this
environment of safety
We did it using the dialogic learning principles (Flecha,
2000; Aubert, Flecha, Garcia, Flecha, Racionero, 2008)
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DISCUSSION
What we mean by “dialogic learning principles”?
Díez-Palomar & Molina; ALM 16; London
DISCUSSION
What we mean by “dialogic learning principles”?
Egalitarian dialogue
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DISCUSSION
What we mean by “dialogic learning principles”?
Egalitarian dialogue
Solidarity
Díez-Palomar & Molina; ALM 16; London
DISCUSSION
What we mean by “dialogic learning principles”?
Egalitarian dialogue
Solidarity
Transformation
Díez-Palomar & Molina; ALM 16; London
DISCUSSION
What we mean by “dialogic learning principles”?
Egalitarian dialogue
Solidarity
Transformation
Creation of meaning
Díez-Palomar & Molina; ALM 16; London
DISCUSSION
What we mean by “dialogic learning principles”?
Egalitarian dialogue
Solidarity
Transformation
Creation of meaning
Equality of differences
Díez-Palomar & Molina; ALM 16; London
DISCUSSION
What we mean by “dialogic learning principles”?
Egalitarian dialogue
Solidarity
Transformation
Creation of meaning
Equality of differences
Instrumental learning
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DISCUSSION
What we mean by “dialogic learning principles”?
Egalitarian dialogue
Solidarity
Transformation
Creation of meaning
Equality of differences
Instrumental learning
Multicultural intelligence
Díez-Palomar & Molina; ALM 16; London
DISCUSSION
What we mean by “dialogic learning principles”?
Egalitarian dialogue
Solidarity
Transformation
Creation of meaning
Equality of differences
Instrumental learning
Multicultural intelligence
Flecha, R. (2000). Sharing words. Rowman Littlefield.
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DISCUSSION
Making a safe environment for adult learners
Javier (facilitator): So... eh... as I was telling you... The first activity... Can be to
introduce ourselves to each other and we can meet each other... is to draw a
graph using our own personal data. So, for instance, the first question could
be “how many children do you have?” So that way...
Joan: We write down... Do we need to write down our name?
Javier:Yes. If you want, I can write it down for you...
Maria: Ah, ok. So he can start... the “gentlemen”...
Joan: Me? I have no children.
Maria: Three.
Celia: One.
Hadiya: Three.
Kristina: Two, two boys.
Javier (facilitator): And Javi... by the moment zero.
Participants: - laughing- (Source: Fieldwork, CEIP Las Flores. First session;
2007/ARIE/00026; AGAUR, Agència Catalana de Gestió d’Ajuts Universitaris
per a la Recerca).
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DISCUSSION
Sharing different ways to solve a situation
The Catalan Giant Tale
Díez-Palomar & Molina; ALM 16; London
DISCUSSION
Sharing different ways to solve a situation
The Catalan Giant Tale
Javier (facilitator): It seems that there are more
groups solving the problem in this way: that is,
they call the height of the giant as “x”. Then they
established the relationship: if my length is this, and
my foot measures that, then the giant should be...
if we know the height of the foot, then “x” would
be that. So they used the “rule of three”. (Source:
Fieldwork, CEIP Las Flores. First session; 2007/
ARIE/00026; AGAUR, Agència Catalana de Gestió
d’Ajuts Universitaris per a la Recerca).
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DISCUSSION
Javier (facilitator): Ah... Over there, I think that you also
were doing something in relation to statistical average of
several feet...
Many people:Yes, yes...
Will: ... This is a way to explain that too...
Maria:You explain!
Will: Well, we took several samples to calculate it more
precisely, more exactly... So we did it by statistics. This is
statistics sampling. Then you calculate the average. That’s
why I was asking you. Because to me... I already knew that,
as average. To me the rate does not make any sense.
Javier (facilitator): Aha, aha... ok. This is another way to solve
it. (Source: Fieldwork, CEIP Las Flores. First session; 2007/
ARIE/00026; AGAUR, Agència Catalana de Gestió d’Ajuts
Universitaris per a la Recerca).
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DISCUSSION
Solving “conflicts” about mathematics
Context: We are in a classroom placed in a centre
with Middle and High School. First row of chairs
was empty. Five mothers were sitting in the
second one. In the third, three mothers. Behind
them, three more mothers are present in the
classroom. We know that there is a man also in
the audience: a father. They are working on lineal
equations. They are translating sentences from
regular language to algebraic language. Tona (the
facilitator) is solving a equation on the
chalkboard. Some noise is in the room. It seems
that some mothers do not understand the
strategy that Tona is using to solve the equation.
Díez-Palomar & Molina; ALM 16; London
DISCUSSION
Solving “conflicts” about mathematics
Díez-Palomar & Molina; ALM 16; London
DISCUSSION
Solving “conflicts” about mathematics
Tona (facilitator): Every equation such as has one unique solution.
Mother 1: But... but...
Tona (facilitator):Yes... (At the same time).
Mother 1: I always did it like this, and I understand it that way... But
teachers now they teach children to simplify, to let the “x” like...
to have all numbers simplified. Then if I get three “x” here, and
two more “x” over there, to make them “disappear” I need to
take away these two “x” in this side and I also need to take away
the same 2 “x” in this other side...
Tona (facilitator): They [the children] do the same...
Mother 1:Yes, but this is more complicated...
Tona (facilitator): Let me explain you.
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DISCUSSION
Solving “conflicts” about mathematics
Mother 1: Because she [the teacher] wants [the homework]
like this... and to me is, is...
Tona (facilitator): Let me explain you.
Mother 1: It is more complicated.
Tona (facilitator): Yes, it is more complicated, but the teacher
may considerer that this is more clear in terms of concepts.
Mother 1:Yes...
(Some noise can be heard in the background. Tona starts to
write down something in the board –see the figure-). Javier
(facilitator): Aha, aha... ok. This is another way to solve it.
(Source: Fieldwork, IES Las manzanas. Third session; 2007/ARIE/
00026; AGAUR, Agència Catalana de Gestió d’Ajuts
Universitaris per a la Recerca).
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DISCUSSION
Solving “conflicts” about mathematics
Díez-Palomar & Molina; ALM 16; London
DISCUSSION
Building knowledge towards dialogue and interactions
Context: Parents are working to solve this problem: “If
is 3/4 parts of a ribbon, draw the ribbon corresponding to 1/2, 2/4, 4/3
and 3/2.You may justify your answer.
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DISCUSSION
Building knowledge towards dialogue and interactions
Agustín: To four... three fourths... since they are the
same, this bit would be the whole ribbon. That means...
(Some noise in the background)
Pilar: The total... the ribbon would be that...
Alberto: The unit is four fourths. You need to divide the
bits, so you get four fourths.
Pilar (at the same time): ... we need for the whole
unit...
Agustín: I don’t remember the percentages...
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DISCUSSION
Somebody: The half.
Agustín: ... so if we have five sixths, then... here we can
add as much bits as we need, and this would be the
parts that correspond.
Javier (facilitator) –He stands up and goes to the
boardSomebody: There are two.
Javier (facilitator): Do you understand? (Source:
Fieldwork, IES Las manzanas. Fourth session; 2007/
ARIE/00026; AGAUR, Agència Catalana de Gestió
d’Ajuts Universitaris per a la Recerca).
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CONCLUSIONS
- Dialogic spaces are spaces where people interact to each other.
- Adult learners share their own ways to solve the different
activities, which provides a plethora of different mathematical
strategies to consider and discuss among all the participants.
- Adult learners bring home-based examples to solve the
activities.
- These home-based examples usually are grounded on “funds of
knowledge” referents.
- Dialogue becomes a “tool” to connect school-based knowledge
and non-school-based types of knowledge (everyday live
experiences).
- Adults come with all these experiences when they feel safe and
comfortable in the learning space (classroom, etc.).
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Díez-Palomar & Molina; ALM 16; London
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