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Almeida, A.; Almeida, C. & Morais, C. (2004). Implementation of the portfolios in Mathemactics learnings: the case study of 10th grade pupils. Actas do XV SIEM (Seminário de Investigação em Educação Matemática) (pp. 193-211). Lisboa: APM.

Este artigo descreve um projecto de acção pedagógico-didáctica que procurou estudar as implicações do recurso ao portfolio de evidências de aprendizagem. Seguindo uma metodologia de natureza interpretativa, desenvolveram-se dois estudos de caso de alunos do 10º ano de escolaridade. Na dimensão cognitiva, este estudo evidencia que o uso do portfolio permitiu desenvolver uma prática de pedagogia diferenciada, favorecendo o processo de metacognição dos alunos e fomentando a capacidade de trabalharem o mais autonomamente possível. No domínio das atitudes e valores, as práticas pedagógicas implementadas orientaram-se por valores de tolerância, respeito, responsabilidade, inter-ajuda, e partilha do poder.
Keywords: Assessment in Mathematics; 10th grade; self-assessment; portfolio.

Bondoso, T.; Pinto, J. (2009) Portfolio and curricular management in Kindergarten Actas do X Congresso Internacional Galego-Português de Psicopedagogia (pp. 3897-3909). 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.
This communication occurs in the context of this work and concerns the progress made on a kindergarten room for three academic years, where the organization and use of Portfolios was undergoing changes and readjustment, eventually ended by being an assessment instrument that also started to be part of the curriculum planning.
The intervention focuses on how to use this instrument, initially as shared assessment; it constituted itself as the focus for children, a process that was becoming, simultaneously, a curriculum management tool for the educator, a mechanism for self organization for children, and a powerful resource for the knowledge learning that supports the skills construction. It can be concluded that this process requires a deliberate intentionality that implies a theoretical act and that can become a way of working in partnership with the students.
Keywords: Regulated assessment, portfolios in kindergarten; curricular management in kindergarten.

Cyrino, M.; Soares, Mª T: & Buriasco, R. (2003). From the evaluation of the school profit to the assessment for learning in Mathematics: a research in Paraná/ Brazil. Actas do XIV SIEM (Seminário de Investigação em Educação Matemática) (pp. 381-412). Lisboa: APM. 

This paper concerns a study that analises the pupils' productions of a sample of 729 exams obtained from the universe of the Mathematics exams carried out by the pupils of 4th and 8th series from the Paraná Education System. In particular, tries to identify if the pupil chooses or not a proceeding that resolves the question, if he tests the alternatives, if he registers the data of the question and finally what type of notation is used .
Keywords: Assessment in Mathematics; pupils works; solving process problems.

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.
Keywords: Learning in Mathematics; portfolio; reflection; metacognition; mathematic communication.

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.
Assessment; regulated assessment; learning; assessment and regulated learning.


Dias, P. (2005). Avaliação reguladora no ensino secundário: Processos usados pelos alunos. Actas do XVI SIEM pp. 233-252. Lisboa. APM. 

This study sought to understand the processes, difficulties and resources that pupils use and face when doing mathematics research in classroom. Through an interpretative methodology developed four pupils' case studies in 10th grade. In the interpretation phase of research pupils develop processes such as translation, initial experience, internalize and anchor. In developing the task, deepen, zigzag, conjecture, experiment, solve and generalize. The errors were used to guide, teach, or deflect. The resources that pupils use are the establishment of interactions with the teacher, with peers and themselves and same teaching materials.
Keywords: Assessment in Mathematics; high school; mathematics research; reflection; self-regulation; mathematics process; resources.


Dias, P. & Santos, L. (2010) Assessment practices and self-regulated 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 self-regulation , given their mathematical learning. It fits the theme on management and curriculum development, contributing to the knowledge of assessment practices.
Keywords: Assessment practices; self-regulation; mathematic learning.

Dias, P. & Santos, L. (2010)  The intent of a teacher in the development of self-regulation of learning mathematics. Actas do XXI SIEM pp. 109-125 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 self-regulated 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 self-regulation 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, 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.
Keywords: Formative assessment; feedback; mathematic tasks


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 teacher-pupil 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.
Mathematic learning; regulated assessment; feedback; mathematics conceptions.

Fernandes, M. (1994). The self-assessment in the primary education as strategy to improve the school performance in Mathematics. Actas do V SIEM. pp. 137-148. Lisboa: APM.

This paper presents part of the research outcomes which assesses the effects of the regular use self-assessment strategies on the school performance (Mathematics) at the 1st cycle. The self-assessment strategies were analysed and tried by a group of 25 teachers, in a course of training. The results show that the children from the involved classes (n=354) disclose significant progress in their school performance when they are compared with a group of control children (n=313) belong to classes where the strategies of self-assessment aren't required.
Keywords: Assessment in Mathematics; Mathematic learning; self-assessment.

Garcia, C. (2004). The errors in mathematics: reasons students in the secondary education. Actas do XV SIEM. pp. 415-431. Lisboa: APM.  

This paper presents a research that tries to lead to the reflection about the school failure in the Mathematics, in the 7th, 8th and 9th grade. There was constituted a diversified sample of 68 pupils who frequent 7th, 8th and 9th grade in two schools, so that the pupils with failure were well represented. The outcomes point to a link between the failure in Mathematics and the lack of pupil's attention and concentration in the classroom and the learning difficulties perception of the subject taught.
Keywords: Assessment in mathematics; failure to mathematic; 7th, 8th and 9th grade.

Inácio, Mª A. & Ramalho, G. (1996). How teachers deal with pupil's mistakes. Actas do VII SIEM (Seminário de Investigação em Educação Matemática) (pp. 89-115). Lisboa: APM.

This paper concerns a research that tries to understand how the teachers deal with the pupil's mistakes, especially when they plan out activities to correct these mistakes. From a test on decimal numbers, applied to two 6th grade classes, the data gathering resorted to a questionnaire applied to 59 teachers of the great Lisbon 2nd cycle of 10 schools and an interview. This study shows up that, in general, the teachers identify the pupils' "standard" mistakes , but it seems that they don't consider important to have them in mind when they plan out activities in order to correct these mistakes. Mostly to reason of the standard existence is the ignorance of the mathematical content.
Keywords: Assessment in Mathematic; 5th and 6th grade; planning; mistakes; mistakes interpretation; teacher's conceptions.

Lopes, P. (1993). Formative assessment – The pupils' time. Actas do IV SIEM (Seminário de Investigação em Educação Matemática) (pp. 101-112). Lisboa: APM. 

This paper shows an experience carried out over school year with 7th grade's pupils in Mathematics. Through the application of formative tests it was looked that the pupils were carrying out a self-assessment work through the filling out of an assessment sheet, completed by teachers also improve then the first output. There was a general development of the class for the line between the evaluation done by the teacher.
Keywords: Assessment in Mathematic; 7th, 8th and 9th grade; formative assessment; formative tests; self-assessment.

Martins, Mª P. (1995). Assessment for learning. The teacher's point of view. Actas do VI SIEM (Seminário de Investigação em Educação Matemática) (pp. 263-278). Lisboa: APM.

This paper tries to know and understand how the Mathematics teachers face the assessment of learning and how they act. Following a interpretative methodology, through the Mathematics teacher case study. It is the results of this study that the teacher: (i) even though she faces the assessment as an integrant part of the learning process, she did not yet find a way of implementing differentiation strategies; and (ii) she uses different assessment techniques, using the classroom observation without feeling necessity of gathering and of registering systematic information.
Keywords: Assessment in Mathematic; 10th, 11th and 12th grade; formative assessment; school practice; assessment tools.

Menino, H. & Santos, L. (2004). Tools for assessment of learning in mathematics. The use of the written report, the test in two phases and the portfolio in the 5th grade and 6th grade. Actas do XV SIEM (Seminário de Investigação em Educação Matemática) (pp. 271-291). Lisboa: APM. (download) 

This paper intends to let know some of the research outcomes that tried to study the potentialities and limitations of the use of three instruments for assessment of learning, in the 2nd cycle, the written report, the test in two phases and the portfolio, in the teachers' perspective.
Keywords: Mathematics; teaching and learning process; assessment of learning; assessment methods;  written report; test with 2 phases; portfolio.

Morgan, C. (1998). Assessment in mathematics education: A critical social research perspective. Actas do IX SIEM (Seminário de Investigação em Educação Matemática) (pp. 5-23). Lisboa. APM.

This paper proposes an alternative perspective to the dominant paradigm in the field of the assessment in mathematical education that takes into account the social nature of the behaviour in mathematics, the speeches and communication theories and of the social analysis papers of the education, the mathematics and the assessment in  society.
Keywords: Mathematic Education; Assessment in Mathematic; social perspective; assessment mathematic research.

Nunes, C. & Ponte, J. (2005). The assessment as regulation of the Mathematics teaching and learning process of the pupils of the 7th, 8th and 9th grade. Actas do XVI SIEM (Seminário de Investigação em Educação Matemática) (pp. 103-123). Lisboa. APM.

This study aims to know what the 3rd cycle pupils think on the assessment about Mathematics and how they react to innovatory practices. This is a qualitative and interpretative investigation on professional practice based on two pupils case study of a group of the 7th grade class, with which an innovatory assessment system was instructed. The pupils are engaged in learning, appreciated the assessment process and recognized that they them helped the feedback given along the year improving their learning.
Keywords: Assessment in Mathematic; 7th, 8th and 9th grade; regulated assessment; assessment practices; assessment alternative tools.

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. (CD-ROM). Lisboa: APM. (download) 

In this paper, at first, there's an analysis of the evolution of formative assessment concept, the importance that is even given it in the different Portuguese prescriptive from the law still in force to the present and the recommendations definite in several Mathematics programs during the above-mentioned time period. In a second part it's 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.
Keywords: formative assessment conceptions; formative assessment practices;  7th, 8th, 9th, 10th, 11th and 12th grade assessment law; the assessment in mathematics programs.

Santos, L. (2005). The assessment for learning in Mathematics: a look at your route. In L. Santos, A. P. Canavarro & J. Brocardo (Orgs.), Educação e matemática: Caminhos e encruzilhadas. Actas do encontro internacional em homenagem a Paulo Abrantes pp. 169-187. Lisboa: APM. (download) 

This article seeks to analyse the assessment directions and practices distance in the last 20 years, in Portugal. This analysis is supported on research developed during this time within mathematical education. Finally present and discuss a possible diary to be developed in the near future.
Keywords: Assessment; Mathematic;  guidelines curricular; assessment practices; assessment ways and tools.

Santos. L. (2003). The research in the pedagogic assessment in Mathematics, in Portugal. Actas do XIV SIEM (Seminário de Investigação em Educação Matemática) (pp. 9-27). Lisboa. APM. (download)

This article takes as a base a comparative analysis of the studies carried out in Portugal about  assessment for learning in Mathematics from 1992 to 2003. These five reviews cover the secondary education. All of they followed a methodological approach of interpretative nature as cases studies. The cases studies are divided in two groups: those who did not try to intervene in wrapped teachers' practice and those who they tried in collaboration with the teachers to develop and to study assessment practices alternative. The outcomes differ between these two types of study, namely as for the conceptions and practices of assessment.
Keywords: Assessment in Mathematic; formative assessment; summative assessment; conceptions of assessment; assessment practices.

Santos, L. & Dias, P. Self-regulation of mathematics learning by students, the teachers' action. (EIEM) Encontro de Investigação em Educação Matemática, Lisboa (17 e 18 de Abril de 2010) (download)

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’ self-regulation in Mathematics. The research project unfolds within the context of collaborative work between the first author and two teachers. We plan-up and evaluate the implementation of practices  teaching that promote self-regulation in mathematical tasks by pupils. In this paper, we describe the teacher’s practice, Jose, one of the tasks performed by pupils from 11th 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 self-regulation of by students.
Keywords: Assessment practices; teacher; auto-regulation; 11th grade; tasks in two phases.

Santos. L. & Dias, S. (2006). How do the pupils understand whom the teachers tell them? The complexity of the feedback. Actas do ProfMat 2006 (CD-ROM). 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 pupil groups of 9th grade in two classrooms. This study seems to show 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.
Keywords: Assessment in Mathematic; regulated assessment; assessment practices; feedback.

Semana, S. & Santos, L. The feedback in written reports in mathematics class. (EIEM) Encontro de Investigação em Educação Matemática, Lisboa (17 e 18 de Abril de 2010) (download)

This study aims to characterize the feedback provided under six written reports in mathematics 8th 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 self-regulation 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.
Feedback; written report; self-regulation; learning.

Semana, S. & Santos, L. (2009). Assessment strategies in the regulation of learning in mathematics. XIX SIEM (CD-ROM). 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 self-imposed standards on pupils suggests the need to continue the work.
Keywords: Regulatory assessment for learning; feedback; assessment criteria.


Semana, S. & Santos, L. (2008). Why is it important to explain how I thought: the written report in regulation of learning in Mathematics. ProfMat2008 (CD-ROM). Lisboa: Associação de Professores de Matemática. (download)

The study had as an aim objective understood the written report role while a regulated assessment tool of the pupils' 7th, 8th and 9th grade learning in Mathematics and it was developed during the academic year 2007/2008, in the context of the project AREA. In this paper we will focus on a report prepared in two phases by 8th grade group from an research carried out in the Mathematics classroom. We intend to highlight the the script to produce report role, of the assessment criteria and of the oral and written feedback, showing up the potential of work developed in the pupils learning regulated and, in individual, in their self-assessment.
Keywords: Assessment in Mathematic; feedback; report in 2 phases; regulated assessment.