isometriesand patterns ~ a creative approach
TRANSCRIPT
University of Aveiro
Dep. of Education
Lúcia Matos
Isabel Cabrita
ISOMETRIES AND PATTERNS
~ A CREATIVE APPROACH ~
University of Aveiro
Dep. of Education
Lúcia Matos
Isabel Cabrita
Sructure of the presentation
Problematic of the research
Objectives of study
Theoretical background
Methodology
key Findings
University of Aveiro
Dep. of Education
Lúcia Matos
Isabel Cabrita
Problematic of the research
AGD
Creative approach, tasks and resolution
Patterns
isometric transformations
Geometry
University of Aveiro
Dep. of Education
Lúcia Matos
Isabel Cabrita
Geometrical Knowledge
- isometries
Skillsgeneral | transversal | specific
Communication
More affectionate relationship
with the geometry
Autonomy
To Assess the impact of a creative approach of isometries
through the study of patterns and using GSP:
Objectives of the study
University of Aveiro
Dep. of Education
Lúcia Matos
Isabel Cabrita
Breda et al., 2011; Cabrita et al., 2008, 2009;
Dodge, 2004; ME, 2010; NCTM, 2007; Ponte et al., 2007;)
GEOMETRIC TRANSFORMATIONS
Isometries
PATTERNS(Devlin, 2003; Orton, 1999;
Vale et al., 2006;
Vale & Barbosa, 2009)
DGS(Breda et al., 2011; Cabrita et al., 2009;
Candeias, 2005; Gorgulho, 2005;
Hoylees, Lagrange, 2010;
Kasten, Sinclair, 2009;
NCTM, 2007; Ponte et al., 2007;
Veloso, 1998
Theoretical background
University of Aveiro
Dep. of Education
Lúcia Matos
Isabel Cabrita
� Essentially qualitative (Bodgan e BilKen, 1994; Huberman & Miles,
2002)
� Multiple case study (Hartley , 2004; Stake, 2007; Yin, 1989, 2005)
� Participants: 21 students of the 9th grade
Half rural
Elementary
school of Aveiro
Class of 9 th
year
•Different school
achievements
•Facility to
communicate
ideas
Methodology
University of Aveiro
Dep. of Education
Lúcia Matos
Isabel Cabrita
Logbook
Students' productions
Informal talks
Test
PEE/PCE/PCT/PAD/Program
October-November
novembro a dezembro
February
February-March
1st Stage
2nd Stage
3rd Stage
4th Stage
January-March
QuestionnaireCharacterization of the target group
Planification
Pre-test
Didactical approach
inquiry
document analysis
document analysis
Direct observation
Document Analysis
research design
University of Aveiro
Dep. of Education
Lúcia Matos
Isabel Cabrita
Questionnaire
Test
march
may
january to december
5th stage
6th stage
7th stage
8th stage
Content
Analysisstatistical
analysis
Post-test
Final Questionnaire
Treatment of data
Presentation of data
document analysis
inquiry
Narrative, transcripts,
tables, images, …
research design
University of Aveiro
Dep. of Education
Lúcia Matos
Isabel Cabrita
� 9 diverse tasks applied during 1 month;
Didactic sequence
� Students solve them in pairs, using GSP;
� Confrontation of the various resolutions;
� A summary of the main mathematician aspects involved to retain
� the test
� a theoretical part;
� a practical one – solved with GSP and another one solved in pairs.
University of Aveiro
Dep. of Education
Lúcia Matos
Isabel Cabrita
Categories of analisys
Isometries
Patterns
Confidence
Enthusiasm
Motivation
Interest
Geometrical
knowledge
Development
of a new
math vision
Autonomy
Interactions –Teacher and
Students
Math comm.
Communica-
tion
treatment of the data
University of Aveiro
Dep. of Education
Lúcia Matos
Isabel Cabrita
Key findings
geometrical knowledge
Students improved its knowledge:
to reproduce, continue, complete, create and identify
repeating sets related with friezes, rosaceas and tilings
University of Aveiro
Dep. of Education
Lúcia Matos
Isabel Cabrita
Key findings
geometrical knowledge
“The work centered in patterns (and the GSP) allowed us to have a better
perception of the geometrical concepts involved” (FQ) - the students
absolutely or partially agreed
University of Aveiro
Dep. of Education
Lúcia Matos
Isabel Cabrita
Key findings
communication
�reciprocal negotiation
“working in groups was very pleasant and I
learned more”
“the use of this software fosters the
interaction between students”
University of Aveiro
Dep. of Education
Lúcia Matos
Isabel Cabrita
Key findings
communication
• difficulty in communicating mathematical ideas, mainly in writing,
“For the first shape we used isometries of rotation. And in the
second one, we used isometries of rotation and reflection. The first
one is cyclic and the second one is dihedral”.
University of Aveiro
Dep. of Education
Lúcia Matos
Isabel Cabrita
Key findings
autonomy
• Gradually, they earned some autonomy,
and recognize their – “it was important
that the students drew their own
conclusions”.
• First, the students would call for help - “Teacher, I don’t
know what to do!”, “What should I answer? We don’t
understand!”
• FQ - they affirmed to have enjoyed to use GSP, which contributes to
an active and dynamical learning of Geometry
University of Aveiro
Dep. of Education
Lúcia Matos
Isabel Cabrita
GSP and patterns motivated the learning and catalyzed their interest
didactic approach contributed “to a more positive view towards
Geometry” as well as “for the development of an affective relation” with
the subject (FQ).
“it made Geometry wonderful”
Key finding
positive view
University of Aveiro
Dep. of Education
Lúcia Matos
Isabel Cabrita
• Adams, D. & Hamm, M. (2010). Demistify Math, Science, and Technology: Creativity, Innovation, and Problem
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básico.Lisboa: DGIDC.
• Cabrita, I. et al. (coord.) (2007 a 2011). Coleção de livros m@c1/2. Aveiro: Universidade de Aveiro, Comissão
Editorial.
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References
University of Aveiro
Dep. of Education
Lúcia Matos
Isabel Cabrita
• McMillan, J. Classroom Assessment. Principles and Practices for Effective Instruction, Pearson, United Kingdom,
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References
University of Aveiro
Dep. of Education
Lúcia Matos
Isabel Cabrita
Lúcia Matos
Elementary School Castro Matoso
Isabel Cabrita
University of Aveiro