Apresentação realizada no âmbito do programa Psst em 2014 em Linz/Áustria

1. Dilaila Botas,
Universidade Aberta/CEMRI/ EB1 Nº2 de Queluz
Psst 2014- Personal&Shared Strategies for Teachers in Web 2.0

2. Location: Portugal in Europe

3. Lisbon district

4. • The population is constituted
by 514 students grouped in
• 22 classes (schedule from 9h
to 17h15)
• The school under study is an
elementary school located in
Queluz.
• It is one of the eight schools
that, altogether, constitute a
group of schools

5. In elementary schools how are
didactic materials used in the
teaching of Mathematics?

7.  The use of didactic materials in Mathematics
lessons is constantly highlighted and
recommended as very important to help the
concretization of mathematical ideas and concepts
 There is not much research on didactic materials in
the learning process of mathematics, although
some take into account the interest of these
learning materials.
National Curriculum for Basic
Education;
 Portuguese Elementary school
Curriculum
 Mathematics Report (APM,2001)

8. Overviews of
Mathematics
•The way teachers
view mathematics
can influence their
teaching practices.
All that the teachers
do in the classroom
results of what they
think about
mathematics and
how they feel they
should (Hyde 1989,
Serrazina 1993).
Didactic Material: the
concept
•Curriculum
Material,educational
resource
•Didactic resourse;
•Structured materials
•Manipulable
material
•Virtual
manipulatives
Some examples of
didactic materials
•Abacus
• logic blocks
•Cuisenaire rods
• computer

9. The Importance of
materials
•They must be used as
tools and the
students gain more
knowledge through
their use (Moyer,
2001)
The use of materials
•Advocated by several
mathematics
educators such as
Declory, Montessorri,
Reys.
•Referred to in the
mathematics
curriculum
•National Council of
Teachers of
Mathematics (NCTM
1989, NCTM 1991,
NCTM 1995, NCTM
2000)
•Curriculum/Nacional
Programs( DEB1990,
DEB 2001;DEB 2007)
The teachers and the
materials
•The few studies (APM,
1998, Moyer, 2001)
show that teachers
recognize the
importance of using
materials. However,
this trust does not
result in behavior in
the classroom.
Textbooks
•It corresponds to the
most widely used
medium of instruction
(APM / ERI 1998)
•Digital book

10. What is a manipulative ?
geoplan
Graphics
Vale(2002)
movement
Graphics
draws
Technological progress
Computers Dynamic
Static

11. Emergent category of didactic
materials – Virtual manipulatives
Moyer, Bolyard & Spkiell( 2002)
Visual Static
Representation:
graphics, draws,
spreadsheets
Visual Dynamic
Representation:
manipulatives,
objects
Although both are virtual manipulatives, the
visual dynamic representation constitutes the
“really” virtual manipulatives because they can
be manually manipulated (swipe, rotate ...)
and can also be manipulated by computer

12. Another definition is presented by Vale (2002)
Calculaters
Computers
Shultz(
1989)
Active
manipulatives
Passive
Manipulatives
No
manipulatives
Concrete
models that
students
manipulate
(bars
cuisineire)
Teachers
manipulate to
demonstrate
concepts
Models that are no
handled
manipulated :
Record, manual,
designed Abaco
that are drawn
Calculators, computers: can be used of the three forms

13. Moyer (2001) “objects designed to
represent explicitly and concretely
mathematical ideas that are abstract
(p.176)
Gellert (2004) any
object can be used in
math class provided it is
applied by the teacher
with the intention to
develop mathematical
activities, or as a
mediator between the
intention of teaching
and the results obtained
by students
Computer
calculators,
interactive games
digital textbooks
manipulatives
virtual manipulatives

14.  Quantitative study, beginning with an exploratory
study with descriptive characteristics.
•Techniques of data collection :
List of existing didactic materials in the group of schools
 in order to know what materials exist in the group
 making an inventory
Exploratory semi-directive interviews
 to two teachers belonging to the group under study, in order to
gather opinions
on the use of teaching materials in mathematics classes and get
ideas or clues for elucidating the structure of the questionnaire;
script organized in five thematic sections.
Pre-questionnaire
given to five teachers belonging to the group under study, in order
to obtain information and assess the final questionnaire.

15. Questionnaire
Distributed to 53 teachers of the 1st cycle of the group
under study, with the aim to obtain information on the use of
didactic materials in mathematics classes.
Structured in two parts:
1st part consists of 30 items that characterize the
population involved in the study
2nd part consists of 117 items grouped around the
following dimensions:
Definition of didactic materials
Overview of Mathematics
Role of didactic materials in the class
Mathematics didactic materials and the teacher in the
class
Mathematics didactic materials and the teacher in the
school
Mathematics school manual in the class

16. 0
10
20
30
40
50
60
70
Never+rarely
sometimes
often + always
Materials used by teachers

17. •About half of the teachers (51%) use the computer in their mathematics
classes while the other half is divided by its degrees of "never or rarely"
(28.6%) and "often or always" (20.4 %).
•Over half of the teachers says "never or rarely" use the calculator (69.4%)
in their mathematics classes.
Other findings:
•The calculator was not a material found in the school ;
•There is 26 computers, 13 around the classroom and another 13 in the
media room.

18. Technological Plan 2005
“an agenda for change for the
Portuguese society that seeks
to mobilize businesses,
families and institutions so that
with the combined effort of all,
can be overcome the
challenges of modernization
that Portugal faces "”
http://www.cnel.gov.pt/pt/planotecnolog
ico/o-que-e-o-plano/lista.aspx
competitiva edge
development
tecnology
innovation knowledge
The Technological Plan for Education
“is the greatest program of technological modernization of the educational
system in Portugal” http://www.pte.gov.pt/pte/PT/OPTE/index.htm

19. • “To ensure that teachers have their
ICT competencies
certified”(Ministério da Educação,2008)
Adherence to
new
opportunities
• “To ensure high-speed broadband
Internet connection in all
Schools”(Ministério da Educação,2008)
Internet
connection in
classroom
• “To achieve the ratio of two students
per computer with Internet
connection”(Ministério da Educação,2008)
E-escolas:
mass
distribution
of computers
The Technological Plan for Education

20. The technological Plan for education at elementary School : E-escolinha
“to provide acess to a laptop with learning resources to students of primary
school” http://www.pte.gov.pt/pte/PT/Projectos/Projecto/index.htm?proj=72

21. Laptop:
“Magalhães”
And to promote the use of technology in the teaching
process, the school was provide
Video projectors
Interactive whiteboards

22. A small trial observation was conducted to
understand what kind of issues arises in relation
student-student at the presence of laptop
"Magalhães"
•Note: 3 days
•Non-school time
•Student-student relationships
•Environments: outside the classroom
•Observations of 20 minutes period authorized by
monitors for students to use technology

23. where the observations were made
School
1
2
3
5
4 8
8
8
8
8
8
8
8
8 8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
8
88
8
8
8
1,2- ATL
3- Football Field
4,5-School
8 -students
8 -students with
laptop

24. •The group was composed of all boys
•The ages of the children ranged from 6 up to 9 years old
Students belonging to various classes of different levels of education
(1st to 4th year)
•12 students and 4 "Magalhães-PC"
•They played the "Pokemon" and "Tiger" games available on the laptop
"Magalhães"
•Owner pc and two colleagues, one on each side
•A playing, the others watched and suggested little tricks or procedures
When a lost, went to another pc
•When students go to the toilet: landed the laptop and put the game on
pause; the group met its momentary output colleague; not shuffled on
laptop; awaiting the return of his colleague.
•When played felt difficulties in the game, other colleagues helped
advising or making his move
Some
data
collected

25. The groups were
composed of only boys
in the groups there was an
exchange of experiences
and learning
Respect for time colleague
and kept the laptop without
vandalizing
All playing the same
game
Will promotes the formation of
groups of one sex?
Does the laptop"Magalhães"
enables greater complicity
between children?
Does the excuse of not being able to take
the laptop "Magalhães" to school because of
thefts, is justified?
The integration of laptop promotes uniformity
of behavior? To belong to a group, the student
is taken to mimic the behavior of colleagues?

26. Some conclusions
•The computer is a great aid in
teaching-learning process
because it makes interesting
lessons.
•The computer can also be an
enriching agent in the social
life of students:
-Enabling the sharing of
knowledge;
-Respect for others;
-Approach through common
interests.

27. APM, IIE. (1998). Matemática 2001. Diagnóstico e Recomendações para o
Ensino e Aprendizagem da Matemática. Lisboa: APM.
DEB. (2007).Programa de Matemática do Ensino Básico Lisboa: Ministério da
Educação
DEB. (2001). Currículo nacional do ensino básico: Competências essenciais.
Lisboa: Ministério da Educação
DEB. (1998) Organização Curricular e Programas, ensino Básico – 1º ciclo.
Mem Martins: Ministério de Educação
GELLERT, U. (2004). Didactic Material Confronted with the concept of
mathematical literacy. Educational Studies in Mathematics. Nº55. p.p 163-179.
MOYER, P.S. ( 2001) Are we having fun yet? How teachers use
manipulative to teach mathematics Educational Studies in Mathematics.
Nº47 p.p 175-197

28. HYDE,A(1989).Staff development:Directions and realities.Em New directions
for elementary school mathematics (pp.223-233).Reston, Virgínia:National
Council of Theachers of Mathematics
MOYER .P; BOLYARD.J; SPIKELL.A(2002) What are virtual manipulatives?
Teaching Children .2002
NCTM (1989/1991) Normas para o currículo e avaliação em matemática
escolar. Lisboa: APM& IIE
NCTM (1991/1994).Normas Profissionais para o Ensino da Matemática.
Lisboa: APM&IIE
NCTM(1995).Assessment Standarts for School Mthematics.Reston:NCTM
NCTM (2000).Princípios e Normas para a Matemática Escolar.Lisboa:APM
SERRAZINA, M. L. (1993). Concepções dos professores do 1º Ciclo
relativamente à Matemática e práticas de sala de aula. Em Revista Quadrante
vol. 2 Nº 1. Lisboa: APM