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 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.
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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 5-year-old children.
Keywords: Kindergarten; assessment; learning; portfolio.
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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 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.
Keywords:
Mathematic learning; regulated assessment; feedback; mathematics conceptions.
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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.

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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. 
Keywords:
Assessment; regulated assessment; learning; assessment and regulated learning.
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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.
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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.
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Dias, P. & Semana, S. (2009) Assessment, Teaching and Learning: different pedagogic dimensions of mathematics classroom. X Congresso Internacional Galego-Português de Psicopedagogia. Braga. (download)

The project AREA, researchers and teachers have been developing, implementing and evaluating assessment for learning practices, both in pre-school 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.
Keywords: Assessment; assessment criteria; reports;
feedback; learning.
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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.
Keywords: Regulated assessment; tasks; resolutions strategies; feedback.
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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. 163-171). 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,
as soon as he will develop the necessary mechanisms to assess the  feasibility or not of a resolution strategy.
Keywords: Assessment in Mathematics; reflection; resolutions strategies.
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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.
Keywords: Regulated assessment; mathematic learning; feedback; mathematic tasks; individual work an work in group.
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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:
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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.

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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.
Keywords:
Mathematic learning; regulated assessment; feedback; mathematics conceptions.
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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, 409-416. (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.
Keywords: Mathematics teaching; mathematic tasks; assessment; learning; feedback.
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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. 133-143). 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.
Keywords: Assessment in Mathematics; learning in Mathemathics; feedback.
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Pinto. F. & Santos, L. Definition of assessment criteria / Self-assessment, 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 self-assessment of a group of eleven to thirteen year-old 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.
Keywords
: Assessment criteria; self-assessment; communicating mathematically.
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Pinto, J. & Santos, L. (2010) Oral feedback in mathematics classroom: patterns and characteristics. European Educational Research Association. ECER2010. Helsinquia. (download)

Keywords: assessment, assessment for learning, feedback, mathematics classroom.
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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.
Keywords: Formative assessment; feedback; pupils.

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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.
Keywords: Assessment models; assessment of learning; formative assessment; assessment tools.
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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, 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 above-mentioned 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.
Keywords: formative assessment conceptions; formative assessment practices;  7th, 8th, 9th, 10th, 11th and 12th grade assessment law; the assessment in mathematics programs.

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Santos, L. (2009). Diferenciação pedagógica: Um desafio a enfrentar. Noesis, 79 pp. 52-57(download)

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.
Keywords:
Formative assessment; pedagogical differentiation; Mathematics for all; teaching and learning of Mathematics.
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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. 11-35). 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.
Keywords: Formative assessment; oral questioning; feedback; self-assessment.
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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.
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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 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.
Keywords: Assessment in Mathematic; regulated assessment; assessment practices; feedback.
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Santos, L. & Pinto, L. (2009). Assessment for learning: the use of feedback and portfolio. European Educational Research Association. ECER2009. Viena de Austria (28 to 30 September of 2009). (download)


Keywords:
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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, 49-56.  (download).

Feedback as a practical assessment for learning, especially in mathematics, has been studied in recent decades. Based on the evidence gathered by several previous studies, we had intended to study how the "form" and "dimension" of the feedback influence student learning. Four studies were conducted interpretative over a period of three years. The participants, pupils aged between twelve and fourteen years, show that trends can be studied to find out how crucial it is that feedback is effective in linking student achievement in school and his views on assigned tasks.
Keywords: Assessment; learning; feedback; feedback; characteristics of the feedback.

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Santos, L. & Pinto, L. (2009). Self-regulating assessment in Mathematics: saying before doing. Bolema, 33, 51-68. (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; self-regulated assessment; mathematics learning; assessment interaction; formative assessment.

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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.
Keywords: Regulatory assessment; self-regulation; mathematical learning; written reports; feedback; assessment criteria.
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Semana, S. & Santos, L. (2010). Self-assessment in written reports Proceedings of the 34th Conference of International Group for the Psychology of Mathematics Education. Brazil (download)

This article studies the development of students’ self-assessment 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´ self-assessment skill evolves gradually but differentially. The study also suggests that the student´s appropriation of the assessment criteria is still under development and that self-assessment is, mostly, operated by students as a process that includes monitoring and excludes action.
Keywords
: Self-regulation; written report; assessment criteria; Mathematics.
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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.
Keywords: Feedback; written report; self-regulation; learning.
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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.

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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.
Keywords: Geometric thinking, explanation, argumentation, assessment for learning, written reports.
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Semana, S. & Santos, L. (2008). Assessment and Mathematical reasoning. Educação e Matemática, 100, 51-60. (download)

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.
Keywords: Mathematical reasoning; written report; regulatory assessment.
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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)

This study aimed to understand the written report main role as a tool for regulatory assessment for learning in Mathematics 3rd cycle pupils. It was developed during the academic year 2007/2008, in the AREA project.
We will focus in report on a two-stage by a group of four pupils in the 8th grade, from an math class investigation. We intend to highlight the role of the report script, the assessment criteria and oral and written feedback, demonstrating the work potential of regulation learning pupils, particularly, in its self-evaluation.
Keywords: Assessment in Mathematics; feedback; report in two phases; regulated assessment.
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