Publications under the project
In this section the project AREA's publications.
Each reference is accompanied by a summary and by keywords.
Some texts are available for download.
Bondoso, T.; Pinto, J. (2009) Portfolio and curricular management in Kindergarten Actas do X Congresso Internacional GalegoPortuguês de Psicopedagogia (pp. 38973909). Braga: CIEd, Universidade do Minho. (download)
A group of teachers has been conducting research about the
assessment of learning while regulating device, under the AREA project. Bondoso, T. & Santos, L. (2009) Portfólios... and other discoveries. Educação e Matemática, 101, 3  9 (download) In the
context of the project AREA a set of teachers has been carrying out several
studies in order to construct of knowing about the assessment as a learning
device regulator of learning. This project is developed in a group of work in
which they are shared and study experiences developed in several levels of
teaching. In individual, the experience that we will be going to board develops
in a kid garden room with 5yearold children. Dias, C. & Santos, L. (2009) Regulated assessment, written feedback, mathematics concepts: a difficult construction triangle. XX SIEM (Seminário de Investigação em Educação Matemática). Viana do Castelo. (download) In this communication we intend
to let know part of a study carried out in order to understand how the written
feedback given to the written productions of the pupils contributes to
theirs learning. The written feedback as a tool for teacherpupil
communications, assumes a central paper in a context of formative assessment. In
this study a qualitative / interpretative methodology was used, with the case
study design. Participants were 4 pupils of the 8th grade. In this
communication we are going to analyse the feedback written type that it
intends to supply traces with mathematical concepts that the pupils must
mobilize and identify difficulties that exist in the writing of this feedback
type. These results allow us to affirm that very often this feedback is
not efficient. The maths symbols supplied in the feedback, still which
present in the expressed one of the task, it seems difficult to see the comment.
Already a similar feedback to the supplied one in classroom, during the
oral questioning, proves to be effective. Dias, C. & Santos, L. (2009) Reflective portfolio in Mathematics. ProfMAT 2009. Lisboa: APM. (download) From than
more a score of years that the guidance curriculum in mathematics for the
assessment for learning advocate the use of different assessment tools. On the
one hand, it is true that there is no assessment tool that can replace all
others, on the other hand, the choice of instrument to use at any given time
depends, first, the proposals that you want to achieve. Seeking to address the
lack of a reflective practice by pupils and the desire to create environments
that favor the development of mathematical communication skills, there was
offered to pupils in 10th grade, first year of Professional Technical
Management, the holding a portfolio that accompany the different modules to be
worked along a year in mathematics. Dias, P. (2009) Assessment and Learning. XX SIEM. Viana do Castelo. (download)
When using the term assessment, you can do it with different meanings and
intentions. When was considered as an integral part of the teaching and
learning, the assessment should be more than one classification, should inform
and guide teachers and students in their decisions.
Dias, P. & Santos, L. (2010) Assessment practices and selfregulated learning mathematics by pupils. I ENJIE (Encontro Nacional de Jovens Investigadores em Educação) Aveiro. (download)
This communication presents a research project that aims to examine assessment
practices of mathematics teachers' in secondary education which encourage the
development of pupil selfregulation , given their mathematical learning. It
fits the theme on management and curriculum development, contributing to the
knowledge of assessment practices. Dias, P. & Santos, L. (2010) The intent of a teacher in the development of selfregulation of learning mathematics. Actas do XXI SIEM pp. 109125 Aveiro (download) As part of a broader interpretive nature research, for the obtainment of a PhD degree, included in the AREA project, we present the assessment practice of a mathematics teacher in a secondary school, Maria. On a collaborative work context, seeks to understand the nature and characteristics of the assessment practices of mathematics teachers that promote selfregulated learning mathematics by students; the constraints that are found and how to overcome them, and how assessment practices are integrated into everyday classroom. Initial results show that assessment practices that promote selfregulation are likely intentional, interactive and have implications for the teaching and learning process. However, they are difficult to achieve and require the teachers’ involvement in additional work: preparation and provision of written feedback and pupils involvement.
Keywords: Assessment
practices; mathematic learning; self regulation. Dias, P. & Semana, S. (2009) Assessment, Teaching and Learning: different pedagogic dimensions of mathematics classroom. X Congresso Internacional GalegoPortuguês de Psicopedagogia. Braga. (download) The project
AREA, researchers and teachers have been developing, implementing and evaluating
assessment for learning practices, both in preschool education and 1st. cycle,
in general, but also in other cycles of Basic Education and 10th, 11th and 12th
grade of Mathematics. In this study, we analyze how to realize an effective
integration of teaching, learning and assessment in the context of written
mathematics reports production, and try to understand how a teaching practice
with these characteristics promotes the learning regulation by pupils. In
particular, we bring an interpretive research case which involved four students
from the 8th grade in the development of four written reports carried out in two
phases and supported by intentionally regulatory strategies. The study shows
that with the support of regulatory strategies implemented, namely investment in
ownership of the assessment criteria by the students and the provision of
written and oral feedback, pupils present quality productions progressively
higher and walk towards the ownership of the assessment criteria and the
regulation of their thought processes and learning, through a course provided
with difficulties, not linear and development. Dias, P. & Santos, L. "Reflect before you act"  Regulatory practice assessment for learning, ICME 11. International Congress on Mathematical Education. Monterrey, Mexico (6 to 13 July of 2008). Available in http://tsg.icme11.org/document/get/681 (download) In this text, we tried to show the
application of a regulated assessment strategy for learning. It is a process applied to a
secondary school in Portugal, which involves students from sixteen and seventeen
years old. The described experience happened in the extent of the work
developed. A group of investigators from project AREA. In the teaching and
learning task as procedure for regulated assessment was tried, this procedure was
called "Reflect before you act". The teacher proposes the task to the students'
discussion and they describe, in writing, the resolution process. After the
teacher resolution feedback, the task is in agreement with the described
strategy. After the analysis of the written results by the students, it is
requested the confrontation among foreseen and accomplished. Collect data is
empiric, it evidences that differences exist between the description for
resolutions strategies and the correct result. Reflect before you act is a
modality of regulated assessment, that can lead to the change of some stages, a
resolution and the overcome of mistakes and difficulties. It is the regulated in
the moment for a premature reflection. Dias, P. & Santos, L. (2008). Reflect before you act. The assessment regulated in Mathematics B. In L. Menezes; L. Santos; H. Gomes & C. Rodrigues (Eds.), Avaliação em Matemática: Problemas e desafios (pp. 163171). Viseu: Secção de Educação Matemática da Sociedade Portuguesa de Ciências de Educação. (download) In the study sought we tried to
understand if the pupils answer to a task can be helped by the understanding and
anticipation of their resolution. In other words, if you think before acting
will be able to contribute to a good performance and consequently to remove
mistakes and difficulties. We were ended what this kind of regulatory assessment
may: develop the written understanding capacity; allow overrunning of mistakes
and difficulties; help solve the task successfully. The deep reflection about
the task can help the pupil to exceed mistakes and difficulties, Dias, S. (2008). The written feedback role in the teaching and leanrning regulated assessment  case study with mathematics pupils of 8th grade. (Tese de mestrado, Universidade de Lisboa). (download)
This study studied how the written feedback given to the written pupils
productions contributes to their learning, for a regulated assessment for
learning. In individual, we tried to study which kind pupil that more they
benefit of feedback and as their position, what the feedback characteristics and
what the pedagogic contexts, tasks and the forms of work, which provide feedback
with regulated effects on the learning. Dias, S. & Santos, L. (2010) Feedback and different mathematics tasks, PME 34. International Group for the Psychology of Mathematics Education. Belo Horizonte, Brazil. (18 a 23 de Julho de 2010). Keywords: Dias, S. & Santos, L. (2010) O feedback e os diferente tipos de tarefas matemáticas. Actas do XX SIEM pp. 126 136 Aveiro. (download)
This article
intends to release a study done within the AREA project, on the relationship
between the feedback and the different kinds of mathematical tasks. Following an
interpretative methodology, were offered to pupils in grade 8, two research
tasks, two library research, two problems and two tests. All these tasks were
conducted in two phases, the first received feedback from the teacher. We define
three dimensions of analysis of feedback: the focus, intent and scope. Tasks
seem more open to give rise to a feedback focused on content and whose intention
is to draw pupils’ attention to specific work aspects. The feedback given the
task seems more closed to focus on encouragement and positive reinforcement or
the mathematical aspects underlying case are more or less challenging,
respectively. The tasks with high challenge degree lead teacher to write longer
comments. Dias, S. & Santos, L. (2009) Regulated assessment, written feedback, mathematics concepts: a difficult construction triangle. XX SIEM (Seminário de Investigação em Educação Matemática). Viana do Castelo. (download) In this communication we
intend to let know part of a study carried out in order to understand how the
written feedback given to the written productions of the pupils
contributes to theirs learning. The written feedback as a tool for
teacherpupil communications, assumes a central paper in a context of formative
assessment. In this study a qualitative / interpretative methodology was used,
with the case study design. Participants were 4 pupils of the 8th grade.
In this communication we are going to analyse the feedback written type
that it intends to supply traces with mathematical concepts that the pupils must
mobilize and identify difficulties that exist in the writing of this feedback
type. These results allow us to affirm that very often this feedback is
not efficient. The maths symbols supplied in the feedback, still which
present in the expressed one of the task, it seems difficult to see the comment.
Already a similar feedback to the supplied one in classroom, during the
oral questioning, proves to be effective. Dias, S. & Santos, L. (2009). Feedback in different mathematics tasks. Proceedings of the 33rd Conference of International Group for the Psychology of Mathematics Education, 2, 409416. (download) The present article aims to
show a research carried out in the context of Project AREA, on the influence
that written feedback has in pupil’s learning, when given to diversified tasks
in the type and in the method of work. The design research was the case study,
the participants in the study were four pupils from the 8th year (aged
thirteen). The feedback given to tasks of problematic, exploratory or
investigative nature seems to be more efficient than in tasks which appeal to
the strict knowledge of mathematical concepts. The feedback given to tasks
solved in small groups seems to enhance learning in a more significant way when
compared to tasks solved individually. Dias, S. & Santos, L. (2008). Why is it important to identify and analyze the pupils mistakes and difficulties? The feedback regulator. In L. Menezes; L. Santos; H. Gomes & C. Rodrigues (Eds.), Avaliação em Matemática: Problemas e desafios (pp. 133143). Viseu: Secção de Educação Matemática da Sociedade Portuguesa de Ciências de Educação. (download) This paper presents the results
of a study in the feedback (Mathematics) area done with a group of 7th grade.
The study main question was “what do the pupils understand of the comments /
annotations that the teachers of Mathematics write when they assess the works
first version?” The results showed that the pupils are not got used to an
assessment in two parts and they tend to suspicions the teacher real
intentions. Additionally, most of pupils involved in the study to reveal little
importance to the comments written by a teacher. Finally, this study
demonstrated the teacher difficulty to give the right feedback in order the
pupil to identify his mistake, to correct it and, ideally, do not correct it
again. Pinto. F. & Santos, L. Definition of assessment criteria / Selfassessment, ICME 11. International Congress on Mathematical Education. Monterrey, Mexico (6 to 13 July of 2008). Available in http://tsg.icme11.org/document/get/687 (download) This article studies the
development of the selfassessment of a group of eleven to thirteen yearold
pupils, through the definition, interpretation and use of assessment criteria in
a group work context on the resolution of an inquiry activity on properties of
the quadrilaterals. The results obtained evidence that the pupils had exceeded
the expectations of the teacher, identifying criteria approaches next to the
teacher ones. The appropriation of the assessment criteria in parallel with the
development of a critical capacity had contributed to a better performance of
the realization of the tasks and of the capacity of communicating mathematically. Pinto, J. &
Santos, L. (2010) Oral feedback in mathematics classroom: patterns and
characteristics.
Keywords:
assessment, assessment for learning, feedback, mathematics classroom. Pinto, J. & Santos, L. The teacher's oral feedback and learning ICME 11. International Congress on Mathematical Education. Monterrey, Mexico (6 to 13 July of 2008). Available in http://tsg.icme11.org/document/get/688 (download)
This article presents an exploratory study that seeks to build an analysis grid
that helps teachers to reflect on its assessment regulatory
practice with regard to oral feedback. Three episodes of the mathematics
classroom were selected, that constituted different activities and outcomes of
learning. The developed analysis allows us to say that the grid could be
applicable in different classroom situations. Additionally this analysis
highlights several feedback patterns explaining the different contributions to
the learning process. Pinto, J. & Santos, L. (2006). Modelos de avaliação das aprendizagens. Lisboa: Universidade Aberta. This book discusses the pupils'
assessment for learning, taking it as a social relationship whose main purpose is
to help the teachers and the pupils to build a formative interaction in terms of
teaching / learning. Besides doing a short review this on the evolution of the
concepts and of the functions in assessment, the book focuses mainly on the
problems that emerge from a framework of formative assessment, namely: the
importance of the work around the criteria of evaluation, the rule paper
leaning process, and still the potentialities and limits of some tools of
assessment. Pinto, J. & Santos, L. (2006). Is a regulation possible even in the daily life of the work of the teacher and of the pupil? Actas do ProfMat 2006. (CDROM). Lisboa: APM. (download)
In this paper,
at first, is analysed the evolution of formative assessment concept, the
importance that is even given it in the different prescriptive Portuguese from
the law still in force to the present and the recommendations definite in
several Mathematics programs during the abovementioned time period. In a second
part they are discussed on basis of situations reports, some possible ways of
implementation of formative assessment, allowed to identify obstacles and
limits, as well as to build a new assessment culture. ___________________________
Since the late 80's that several
learning assessment standards and many curriculum documents give special
emphasis to the training component of the assessment. But one thing is to
prescribe, another is to put it into practice. Developing an assessment practice
with regulatory intent isn’t always easy. This process involves several types of
changes in the classroom work, such as the nature of proposed tasks, the work
method, and rethinking the role of teacher and pupils. Increasingly, teachers
are confronted with pupils' diversity who have not only diversity in the
learning place, but also in the think and learn forms, not to mention the
different cultures, values and Portuguese language, in presence. Thus, the
creation of pedagogical differentiation situations becomes increasingly a
teaching imperative. In this paper we discuss the concept of pedagogical
differentiation and it’s different achievement levels.
Will be presented
and discussed concrete examples of practices to develop differentiated teaching
in the Mathematics classroom. Santos, L. (2008). Dilemmas and challenges of regulatory assessment. In L. Menezes; L. Santos; H. Gomes & C. Rodrigues (Eds.), Avaliação em Matemática: Problemas e desafios (pp. 1135). Viseu: Secção de Educação Matemática da Sociedade Portuguesa de Ciências de Educação. (download) In this text there shows up the evolution
of the formative assessment conception along the last decades. Then, several
assessment practices of regulated nature possible of being developed in the
daily life of the work of the classroom are described and discussed, in
Mathematics individual. For last, there are discussed some of the dilemmas and
obstacles with which the teachers are confronted about this assessment kind.
This discussion is supported in research carried out in this area and, very much
in individual, in some first results obtained in the work developed in the
context of the Project AREA.
In this paper we
reported part of an ongoing investigation to the PhD at the Institute of
Education, University of Lisbon. We wanted understand mathematics
teachers’ assessment practices, in secondary education, contributing to
the promotion of pupils’ selfregulation in Mathematics. The research project
unfolds within the context of collaborative work between the first author and
two teachers. We planup and evaluate the implementation of practices
teaching that promote selfregulation in mathematical tasks by pupils. In this
paper, we describe the teacher’s practice, Jose, one of the tasks performed by
pupils from 11^{th} grade of mathematics, professional course in the 1st
period of 2009/2010. In particular, we study the oral and written feedback while
the privileged communication processes between teacher and pupils. Data
collection occurred through the direct observation of lessons, audio taped and
the collection of written produced for the completion of the experiment
including the pupils’ productions (1st and 2nd versions). The results show that,
in the classroom, the teacher focuses aspects of communication and promotes
understanding of the statement of the task. In written form, the teacher seeks
students approaching their production to a set of assessment levels, discussed
and adapted in collaborative work between teachers, and discussed with pupils.
These strategies associated with task in two phases, and in pairs, were
promoters of mathematics learning selfregulation of by students. Santos. L. & Dias, S. (2006). How do the pupils understand whom the teachers tell them? The complexity of the feedback. Actas do ProfMat 2006 (CDROM). Lisboa. APM. (download) This article reports a study developed within the AREA project which aimed to
know how the pupils understand the written feedback that teachers give to the
theirs activities. Following a methodology of qualitative and interpretative
nature there were studied four pupils' groups of 9th grade two classroom. This
study seems to show up that the same written feedback does not serve likewise
all the pupils. It is important to know the pupils and to give a feedback
appropriate to the academic needed of each one. Pupils with middle Mathematics
performance need a more descriptive and less symbolic feedback. This direction
is so more important as for the fact of these pupils also they do not resort to
a teacher to explain any feedback that they do not understand, whereas pupils
with a good Mathematics performance, besides they use more sources than you
begin, they also seek for the teacher for any clarification.
Santos, L. & Pinto, L. (2009). Lights and shadows of feedback in mathematics learning. Proceedings of the 33rd Conference of International Group for the Psychology of Mathematics Education, 5, 4956. (download).
This article reports on a study involving secondary students in mathematics, where formative assessment was introduced throughout the school year. In this teaching strategy students had to interpret a task, write the resolution strategy and then solve it. The teacher gave feedback to the pupils on their outcomes, changing on the feedback over the year. An interpretive methodology was chosen, using observation, with audio recording and document analysis of students' work, logbooks and teacher reflections. The study pointed out that this strategy contributes to the learning process, helps students to reformulate incorrect reasoning and presents persistent errors and misunderstandings. It is the opposite of standard practice, in that it raises difficulties for the students and challenges the teacher to reflect and interact with others. Keywords: Mathematics education; selfregulated assessment; mathematics learning; assessment interaction; formative assessment.
Semana, S. (2008). The written report while regulated assessment for learning tool of 8th grade pupils in Mathematics. (Tese de mestrado, Universidade de Lisboa). (download) This study aims to understand
the key role of written report as a tool for regulatory assessment of 8th grade
pupils in mathematics. In particular, it try to understand what the difficulties
inherent in drafting the written report, their potential for students' learning
and what the contribution of strategies that are attached to their development.
Semana, S. & Santos, L. (2010). Selfassessment in
written reports
This article studies the development of students’ selfassessment skill in the
context of written reports in Mathematics. In particular, we present an
interpretative case study, which involved two thirteen year old students from
the 8th schooling year and six reports, written in two different stages and
supported by assessment strategies at the teacher´s responsibility. The study
suggests that, in each case, the student´ selfassessment skill evolves
gradually but differentially. The study also suggests that the student´s
appropriation of the assessment criteria is still under development and that
selfassessment is, mostly, operated by students as a process that includes
monitoring and excludes action.
This study
aims to characterize the feedback provided under six written reports in
mathematics 8^{th} grade, over a school year. Following an interpretive
methodology, the data collected primarily through data collection, were analyzed
based on a system of categories supported by theoretical framework. The results
suggest a feedback standard provided: the feedback is focused on the process of
task solving or selfregulation by the pupils does not include value judgments
or corrects the mistakes, but further reflection and encourages pupils to
complete / improve their work by providing clues or not, placed often questions.
Although the standard tends regulator, some of the feedback consisted of simple
calls and pointed out the mistakes. This highlights the complexity of giving
feedback and suggests the need for the teacher to incorporate into their
practice the theoretical orientations, while reflecting on the feedback it
provides and its effects on learning of their pupils. Semana, S. & Santos, L. (2009). Assessment strategies in the regulation of learning in mathematics. XIX SIEM (CDROM). Lisboa: APM. (download) In this
communication we analyze how to provide feedback on ownership and investment
assessment criteria by the pupils in the context of the production of written
reports, contribute to the regulation of pupils learning in mathematics. In
particular, we present the results of an interpretive research which involved
four 8th grade pupils in the development of three written reports in two phases
and supported by regulation strategies. The study suggests that use of the
report script, the assessment criteria and feedback, whether oral or written, in
a combined action, promotes mathematics learning. However, the permanence of
some difficulties and some selfimposed standards on pupils suggests the need to
continue the work. Semana, S. & Santos, L. (2009). Written report in learning geometry: explanation and argumentation CERME6. Lyon. (download)
In this article, we examine how the written report, within
the context of assessment for learning, helps students in learning geometry and
in developing their explanation and argumentation skills. We present the results
of a qualitative case study involving Portuguese 8th graders. This study
suggests that using written reports improves those capabilities and, therefore,
the comprehension of geometric concepts and processes. These benefits for
learning are enhanced through the implementation of some assessment strategies,
namely oral and written feedback.
Within the AREA
project was developed a study aimed at understanding the role of the written
report as a tool for regulatory assessment of the pupils mathematics learning
in the 10th, 11th and 12th grade, in particular with regard to mathematical
reasoning. The development of the written report was supported with a report
script with the negotiation of assessment criteria and written feedback,
supplemented when necessary by oral feedback. The results of this study indicate
that use of the Reporting Guidelines and assessment criteria to allow a growing
realization, by pupils, of the objectives. The two types of feedback provided, a
combined action, help build the mathematical reasoning' s ability. Semana, S. & Santos, L. (2008). Why is it important to explain how I thought: the written report in regulation of learning in Mathematics. ProfMat2008 (CDROM). Lisboa: Associação de Professores de Matemática. (download)
