Helena Rocha

The present study aims to understand the potentialities and implications,
to the teacher and her practice, of the use of formative assessment with the support
of educational technology.
Regarding the research methodology, this study is part of the research on own
practice. The participants were the teacher, who was simultaneously a researcher,
and the students of a 9th grade class.
In the course of this experience it was found that the use of formative assessment
allows, on the one hand, the student to realize what he manages to understand, and
what he has to do to overcome what are less consolidated parts of the content in
study; and, on the other, the teacher to detect in a timely manner the difficulties of
the student and to change strategies to allow the student to overcome his difficulties.
The lack of time, the difficulties in managing the curriculum and the existence of
national exams are three of the main obstacles mentioned by the teachers for the
non-realization of formative assessment. In this experience it was found that the use
of new technologies turns possible to overcome these limitations.
This type of assessment had a very positive impact on teacher’s practice and in the
learning of the students.
Keywords: assessment; formative assessment; new technologies.

O potencial da tecnologia para o ensino e a aprendizagem é há muito reconhecido. Contudo, cada vez mais surgem estudos que indiciam que a sua utilização fica aquém das expectativas. O acesso à tecnologia, o papel que lhe é atribuído na aprendizagem e as características das tarefas em que é utilizada, encontram-se entre as principais influências identificadas sobre a utilização que é feita da tecnologia e potencialmente responsáveis pelas características dessa utilização. O estudo que aqui se apresenta teve como principal objectivo analisar e compreender a utilização que os professores fazem da tecnologia à luz dos aspectos referidos, procurando identificar de que forma estes definem diferentes tipos de utilização. A abordagem metodológica adoptada foi de natureza qualitativa e interpretativa, com a realização de estudos de caso de duas professoras de Matemática que utilizavam a calculadora gráfica. A recolha de dados foi concretizada através de entrevistas semi-estruturadas, observação de aulas e recolha documental, sendo a análise de dados orientada pelo quadro teórico, conciliado com a interpretação destes. As conclusões do estudo sugerem alguma diversidade tanto nas características das tarefas em que as professoras recorrem à tecnologia (exercícios, explorações, problemas, modelação de situações reais), como no papel que lhe é atribuído (obter informação, efectuar cálculos, experimentar), mas apontam também para uma diversidade com características que se traduzem em perfis de utilização da tecnologia distintos: um mais exploratório e outro mais prescritivo.

The different representations of functions are assumed as central on the development of the concept of function. Being widely recognized the complexity of this concept, the different representations allow the student to understand in a representation what could not be understood in another representation. And the integration of technology into the teaching and learning process provides an easy and quick way to access different representations. This study intends to analyse the understanding of upper secondary students about the information transmitted by each of the representations of functions usually available on technology. Specifically, it intends to understand which transitions between representations are more easily understood by the students and which ones are more difficult to perform. It also intended to identify some aspects that may contribute to this. This study adopts a quantitative methodology in which the answers given by a class to a test focused on the transition from one representation to another are analysed; and a qualitative methodology based on interviews to three of the students in the class, as a way of seeking comprehension about their answers. The results achieved suggest a greater ease of understanding associated to the graphical representation and a greater difficulty associated to the tabular representation. The reasons for this seem to be related to the specific characteristics of each representation, but fundamentally with aspects related to the experiences lived by the students on the mathematics classes, being the integration of technology an influence not to neglect.

The teacher’s knowledge has long been viewed as a strong influence on the students’ learning. Several authors have sought to develop procedures to assess this knowledge, but this has proved to be a complex task. In this paper I present an outline of a conceptualization to analyze the teacher's knowledge, based on the model of the Knowledge for Teaching Mathematics with Technology (KTMT) and a set of tasks. These tasks are chosen by the teacher taking into account the potential of the tasks to take advantage of the technology’s potential. The analysis of the teacher’s KTMT is based on the characteristics of the tasks chosen by the teacher; the balance established between the representations provided by the technology that the tasks advocate; the way how the tasks pay attention to the new issue of seeking for a suitable viewing window; and also the way how the tasks take into account the expectable difficulties of the students in the process of looking for the window.

Teachers’ knowledge plays a central role in technology integration. In this study we analyze situations, where there is some divergence between the mathematical results and the information offered by the graphing calculator (lack of mathematical fidelity), putting the focus in the teachers and in their approaches. The goal of this study is to analyze, in the light of knowledge for teaching mathematics with technology (KTMT) model, the teachers’ professional knowledge, assuming the situations of lack of mathematical fidelity as having the potential to reveal some characteristics of their knowledge. Specifically, considering the teaching of functions at 10th grade (age 16), we intend to analyze: (1) What knowledge do the teachers have of technology and of its mathematical fidelity? (2) What can the teachers’ options related to situations of lack of mathematical fidelity tell us about their knowledge in other KTMT domains? The study adopts a qualitative and interpretative approach based on the case studies of two teachers. Data were collected by interviews and class observation, being the analysis guided by the KTMT model. The main result points to the relevance of the mathematics and technology knowledge. However, there is evidence of some difficulties to integrate the information provided by the technology with the mathematics, and also of some interference of the teaching and learning and technology knowledge, and specifically of the knowledge related to the students. This suggests that the analysis of the teachers’ actions in relation to situations of lack of mathematical fidelity, can be useful to characterize their KTMT.

For most teachers, the use of games is not a common practice. This limited professional experience forces the teacher to reflect on the use of games, on how to integrate them into class work, and on how to enhance the development of learning based on them. Our objective is to analyse a set of game scenarios and study aspects that characterise each of them, relating these characteristics to aspects of the professional knowledge to teach with technology. The study adopts an interpretative and qualitative methodology that seeks to understand the relationship between teachers' choices and their professional knowledge. The main findings suggest that the different characteristics of the game scenarios imply the creation of different working environments in the classroom; enhance the emergence of different student difficulties, requiring different ways to support their work; allowing/promoting different conceptual approaches; and the work with different representations. These differences between the game scenarios point to different emphases on the teaching and learning knowledge and the chemistry knowledge, suggesting different mobilizations of the teacher's professional knowledge.

The influence of mathematical communication over the students’ learning led to this research, whose main goal is to understand the impact on problem solving of the students’ communication difficulties. The study adopts a qualitative and interpretative methodology, undertaking two case studies of 10th grade students. The reached conclusions point to the students’ difficulties at the interpretation of the problem, namely at the interpretation of figures, and at the interpretation of the available data, especially when part of them is irrelevant to the problem. Some difficulties were also identified at the communication level, in relation to the arguments used by the students to support their ideas, where a clear preference to restrict them to mathematic calculations was identified.

Resumo
A importância da comunicação matemática sobre a aprendizagem dos alunos, levou à realização desta investigação que pretendeu compreender o impacto sobre a resolução de problemas das dificuldades de comunicação evidenciadas pelos alunos. Optou-se por uma metodologia de natureza qualitativa e interpretativa e pela realização de estudos de caso envolvendo dois alunos do 10.º ano. As conclusões alcançadas apontam para dificuldades na interpretação do enunciado, nomeadamente relativamente às figuras e a dados em quantidade superior ao necessário. Também ao nível da comunicação da resolução foram identificadas dificuldades em fundamentar ideias, evidenciando uma preferência pelo recurso ao cálculo.