Susana Carreira

• Doctor of Education
• University of Algarve

7 Educação e Matemática 172 2.º Trimestre 2024 As tarefas são uma parte fundamental nas aulas de matemática e, deste modo, desempenham posição central na educação matemática. As tarefas são geradoras de atividade dos alunos, criando oportunidades para a aprendizagem de conceitos, ideias e estratégias, assumindo diversas formas e graus de dificuldad...

In the field of applications and mathematical modelling there is intensive research. Within the TSG, we have thematically addressed the teaching of mathematical modelling, teacher education, and modelling processes and competencies of school and university students. Future research directions are expected to consider theory building, empirical stud...

The difficulties that modelling tasks pose to students can be explained by the cognitive complexity of these tasks, as they require a diverse range of mathematical and extra-mathematical competencies. However, despite the demands placed on students, mathematical modelling skills can be effectively promoted if the teacher’s actions meet quality crit...

Understanding the mathematics education values held by both teachers and students is essential for fostering effective teaching and learning experiences. This study aims to investigate the alignment between the priorities identified by mathematics teachers and the perspectives of their students, in the Lisbon metropolitan area. A qualitative analys...

Este artigo apresenta o primeiro estudo alargado realizado em Portugal onde se identificam e discutem aspetos que os professores de matemática mais valorizam no ensino e na aprendizagem desta disciplina. O estudo seguiu uma metodologia qualitativa e recorreu a uma análise de conteúdo para categorizar as respostas dos participantes, obtidas através...

The importance of technology for mathematical modelling and problem solving is emphasised and connections between these areas are elaborated, which arise in particular through technology. For this purpose, a teacher's technology-based processing of a modelling and problem-solving task is analysed in detail and conclusions are drawn for the theoreti...

This special issue introduces recent research on mathematics in interdisciplinary STEM education. STEM education is widely promoted by governments around the world as a way of boosting students’ interest and achievement in science, technology, engineering, and mathematics and preparing STEM-qualified workers for twenty-first century careers. Howeve...

In the field of applications and mathematical modelling there is intensive research. Within the TSG, we have thematically addressed the teaching of mathematical modelling, teacher education, and modelling processes and competencies of school and university students. Future research directions are expected to consider theory building, empirical stud...

This edited volume presents applications and modelling as a world-renowned sub-field of research in mathematics education. It includes the discussion on students’ development of modelling competency through the teaching of applications and modelling. The teaching of mathematical modelling is considered from different perspectives, such as mathemati...

This chapter reports part of an ongoing study based on a linear algebra course taking place at a Costa Rican university, which aims i) to support understanding of linear algebra concepts through introducing modelling tasks, ii) to promote students’ modelling competencies, and iii) to highlight potential difficulties. The current qualitative study f...

This volume provides a snapshot of the current state-of-the-art in theory, research, and practice in the area of mathematical modelling in education. Recognising at the outset the important development of the subfield of mathematical modelling in mathematics education in the last decades, this chapter presents the main themes of a set of contributi...

This paper presents the results of an exploratory case study that examined a veteran secondary teacher’s knowledge for teaching non-routine mathematical problem-solving with digital technologies. Data was collected through the observation of a veteran mathematics teacher, in real time, solving a mathematical problem with the digital tools of his ch...

Nesta comunicação apresenta-se um estudo que identifica e discute o que os professores de matemática valorizam no seu ensino, a partir das respostas dadas por 113 professores a lecionar no 7.º e 10.º anos de escolaridade, em escolas públicas, que responderam a um questionário eletrónico. Foi utilizada uma metodologia qualitativa e usada a análise d...

The thematic working group TWG6 takes on the importance of exploring the role of mathematics when it is used and applied in the study of real-world phenomena in educational contexts. TWG6 considers the interplay between empirical research results and theoretical approaches to the teaching and learning of applications and mathematical modelling, in...

Este artigo reporta um estudo em que se pretendeu identificar e discutir os aspetos que os professores de matemática valorizam na aprendizagem desta disciplina. Foram inquiridos, por meio de um questionário eletrónico, 113 professores a lecionar no 7.º e/ou no 10.º ano de escolaridade em escolas públicas de todo o país. O estudo seguiu uma metodolo...

This paper aims to characterize the processes in which mathematics teachers engage while solving non-routine mathematical problems and express their reasoning with technology. The descriptive model Mathematical Problem Solving with Technology was used to analyse an experienced teacher's utterances and actions while solving a mathematical problem wi...

Available at: https://quadrante.apm.pt/article/view/26132/19252

The aim of this study is to understand how students’ mathematical thinking is activated and nurtured in solving a modeling problem, where the problem situation involves the design of a system. From a STEM integrated perspective, 9th grade students worked on a modeling task aiming to create an identification system based on hand biometrics. The theo...

This study addresses the use of digital technologies by mathematics teachers when solving and expressing non-routine mathematical problems that elicit the development of conceptual models of the solutions. A theory-driven descriptive model of Mathematical Problem-Solving with Technology (MPST model) has been developed, proving to be a robust analyt...

Available at: https://quadrante.apm.pt/article/view/24926

Mathematical modelling is a significant and productive context for teaching linear algebra, favoring students’ learning of concepts and modelling competencies, often neglected in undergraduate mathematics. This study aims to characterize the modelling routes performed and the competencies put into practice by Costa Rican undergraduate students in a...

Mathematical modelling has acquired relevance at all educational levels in the last decades since integrating this activity in instruction provides significant contexts for improving students’ learning, including in linear algebra courses that have a notable presence in many undergraduate courses from different fields, including engineering and sci...

This study aims at understanding the role of the tools chosen throughout the processes of solving a non-routine mathematical problem and communicating its solution. In assuming that problem-solving is a synchronous activity of mathematization and expression of mathematical thinking we take our proposed Mathematical Problem Solving with Technology (...

The research on deductive reasoning in mathematics education has been predominantly associated with the study of proof; consequently, there is a lack of studies on logical reasoning per se, especially with young children. Analytical reasoning problems are adequate tasks to engage the solver in deductive reasoning, as they require rule checking and...

This study involves two classes from different educational levels, namely 9th grade and university. Students in both contexts were given a modelling task that required the development of a hand biometrics recognition system, during which they performed experimentation and simulation. As aims of the study, we look for distinctions and commonalities...

A modelação matemática e as aplicações são uma componente da educação matemática cuja presença nos currículos e práticas escolares ainda está aquém do que é desejado e recomendado. No entanto, no domínio da investigação em educação matemática, são hoje evidentes, no contexto internacional, diferentes perspetivas e referenciais teóricos que enquadra...

Neste artigo apresentamos a temática da avaliação, a partir da análise de um processo investigativo junto a estudantes de economia, de uma universidade pública, em que se reflete sobre a percepção que estes graduandos têm sobre avaliação e aprendizagem. O estudo caracteriza-se como uma pesquisa qualitativa, a investigação foi desenvolvida com trint...

RESUMO Este artigo oferece uma reflexão, a partir da elaboração de um projeto de pesquisa de doutorado que envolve os alunos matriculados no primeiro ano dos Cursos Técnicos Integrados ao Nível Médio, no Instituto Federal de Educação, Ciência e Tecnologia do Mato Grosso (IFMT). Com o objetivo de ilustrar o principal trabalho de pesquisa em curso, a...

Research has long been using analytical tools to describe the processes students engage in when solving non-routine mathematical problems. In this chapter we describe and discuss our progress on devising and implementing an analytical tool that aims to account for the use of technological tools by combining a mathematical problem solving model with...

This chapter focuses on the affordances of the spreadsheet in solving a complex word problem in light of the multiple conceptual models that students produce in their approaches to the solution with the digital medium. The empirical study carried out examines, through a qualitative analysis, a set of resolutions produced by a class of 8th grade stu...

Across the world, problem-solving remains a key element of the mathematics curriculum and a central aim of mathematics teaching and learning. In order to embrace innovative ways of thinking and working, mathematical problem-solving in school classrooms is being challenged by the increasingly widespread use of digital technologies, the promotion of...

The innovative volume seeks to broaden the scope of research on mathematical problem solving in different educational environments. It brings together contributions not only from leading researchers, but also highlights collaborations with younger researchers to broadly explore mathematical problem-solving across many fields: mathematics education,...

The mathematical competitions SUB12 and SUB14 are web-based inclusive competitions where multiple affective dimensions come to the fore in relation to mathematics and problem solving. The moderate mathematical challenges proposed to participants, independent of the official curriculum and intended to be mathematically rich problems, allow young stu...

The study that is partially reported in this chapter has been developed, in theoretical and empirical terms, within the Problem@Web Project. The overall goal of the project was to study mathematical problem solving in a context outside the classroom, namely, web-based mathematical problem-solving competitions. One of the research foci of this proje...

Las emociones aún son insuficientemente investigadas cuando se estudia la experiencia de los jóvenes estudiantes, principalmente en el que concierne a las emociones positivas que implican en la actividad de resolución de problemas. Por otro lado, hay muchos estudios que se relacionan con las dificultades, la ansiedad, la resistencia y la pasividad,...

Based on a brief episode of a modeling activity involving experimentation, performed by 9th graders, the goal is to reflect on criteria of authenticity for school modeling tasks. The study shows that students adhered to the experimental work and materials; still their understanding of the real event and their proposed solution to the problem seems...

Based on a teaching intervention with modelling activities involving experimental work in 9th grade classes, the goal of this study is to find out how students estimate the credibility a modelling task setting when it integrates a hands-on experimental approach. The theoretical background is based on the concept of authenticity and its long traditi...

Resumo Assumindo a criatividade como um potencial que pode ser desenvolvido em todos os indivíduos, o objetivo deste estudo consiste em descrever, caracterizar e compreender a criatividade matemática manifestada nas respostas produzidas por alunos do Ensino Básico (10 a 12 anos) num campeonato de resolução de problemas de carácter inclusivo realiza...

Neste artigo discutimos a atividade de resolução de problemas de matemática com um ambiente de geometria dinâmica, o GeoGebra, no âmbito de uma Competição de Matemática, online, o SUB14. É nosso propósito compreender os aspetos do pensamento geométrico envolvido no desenvolvimento de modelos conceptuais aquando da atividade de resolver e exprimir a...

Technology has created an expectation in all phases of education that requires us to understand how we can harness its potential for improving the depth and quality of mathematical learning. It is highly unlikely that there is a universal recipe or formula for how technology should be used that would satisfy every context or culture, but there have...

Este artigo discute a atividade de resolução de problemas de Matemática com tecnologias no âmbito de um campeonato extraescolar a distância. O estudo visa descrever os aspetos subjacentes à utilização simultânea de conhecimento matemático e tecnológico nessa atividade, com foco no desenvolvimento de modelos conceptuais que conduzem às soluções dos...

This study offers a view on students’ technology-based problem solving activity through the lens of a theoretical model which accounts for the relationship between mathematical and technological knowledge in successful problem solving. This study takes a qualitative approach building on the work of a 13-year-old girl as an exemplary case of the nat...

The contributions that formed the working basis of the Thematic Working Group on Applications and modelling were characterized by a strong diversity in the topics and issues that were addressed. The group’s research field has thus shown to be both active and fruitful whilst maintaining its distinctive facet of being inclusive in terms of the differ...

In this study, we look at the use of experimental activities for developing mathematical modelling, considering those as consistent with the Models and Modelling Perspective and Realistic Mathematics Education. The experimentation with several staircases elicited a central model based on linearization. Such model stems from the key idea of average...

O presente estudo buscou aprofundar os conhecimentos sobre avaliação da aprendizagem e conhecer as percepções dos alunos sobre este processo. Procurou-se identificar e analisar as possíveis relações entre as práticas de avaliação e os seus efeitos na vida escolar dos alunos, e também refletir sobre os diversos instrumentos avaliativos que possibili...

This paper addresses mathematical problem solving with technologies in a beyond school web-based competition. We aim to disclose the ways mathematical and technological knowledge are used and combined for solving the given problems. A specific conceptual framework for accounting both these components was developed. By means of the Mathematical Prob...

Research has long been using analytic tools to describe the cognitive processes students engage in when solving non-routine mathematical problems. In this paper we describe and discuss our progress on devising and implementing an analytical tool that aims to account for the use of technological tools by combining a mathematical problem solving mode...

This book brings together the development of a theoretical argument and its translation into an extensive empirical context as a result of the research work carried out by the Problem@Web project. Through the 3 years of the project, we studied youngsters engaged in mathematical problem-solving using digital technologies of their choice and to which...

Today’s youngsters are growing up in an era of rapidly advancing digital technologies. While young people in this generation are undoubtedly active users of digital technologies, the issue of whether their digital competency levels are necessarily well developed is a topic of debate. This chapter provides an introduction to, and an overview of, the...

Over several years of the SUB12 and SUB14 online mathematical competitions, we became aware of the technological fluency of many of the young participants. We draw on quantitative data from a survey that was administered online by inviting all participants to respond. The data show how the participants describe themselves in terms of their experien...

This chapter develops around two fundamental ideas, namely, that (1) the perception of the affordances of a certain digital tool is essential to solving mathematical problems with that particular technology and that (2) the activity thus undertaken stimulates different mathematising processes which, in turn, result in different conceptual models. L...

The final chapter summarises the overall findings of the Problem@Web project and considers the implications of the findings in terms of how the youngsters of today tackle mathematical problems and communicate their mathematical problem-solving. With data from the youngsters’ participation in two online mathematical problem-solving competitions that...

Given that solving mathematical problems entails developing ways of thinking and expressing thoughts about challenging situations where a mathematical approach is appropriate, this chapter unveils a theoretical framework that aims to guide a better interpretation of students’ capability to solve mathematical problems with digital technologies, in t...

This chapter offers the perspectives of teachers on youngsters solving mathematical problems with technology during the SUB12 and SUB14 mathematics competitions. Drawing on a series of interviews with teachers who have supported the participation of their students over several editions of the competitions, we identified what they see as the competi...

In this chapter, we describe and analyse a number of examples of 7th and 8th graders showing diverse ways of expressing their mathematical thinking in solving algebraic word problems with a spreadsheet. Different youngsters’ approaches to situations where quantity variation is involved are characterised. The problems require finding an unknown valu...

Co-variational reasoning has received particular attention from researchers and mathematics educators because it is considered of paramount importance for the understanding of concepts such as variable, function, rate of change, derivative, etc. Some of the critical issues that have been identified in several studies consist of the difficulty in in...

O presente trabalho é embasado em estudos sobre formação continuada de professores para a utilização das tecnologias. A investigação desenvolveu-se com uma professora integrante de um curso de formação continuada para a utilização de tablets nas aulas de Matemática. A proposta do curso, de uma formação ancorada na prática, incluiu não apenas as ses...

O presente trabalho é embasado em estudos sobre formação continuada de professores para a utilização das tecnologias. A investigação desenvolveu-se com uma professora integrante de um curso de formação continuada para a utilização de tablets nas aulas de Matemática. A proposta do curso, de uma formação ancorada na prática, incluiu não apenas as ses...

Resumo O presente estudo buscou aprofundar os conhecimentos sobre avaliação da aprendizagem e conhecer as percepções dos alunos sobre este processo. Procurou-se identificar e analisar as possíveis relações entre as práticas de avaliação e os seus efeitos na vida escolar dos alunos, e também refletir sobre os diversos instrumentos avaliativos que po...

De acordo com um estudo de 2010 do Departamento de Educação dos Estados Unidos, os alunos que frequentam aulas em regime de blended-learning, que combina aulas presenciais com ensino a distância, estatisticamente têm alcançado melhores resultados do que aqueles que apenas frequentam aulas presenciais. Há também um número crescente de estudantes que...

By looking at the global context of two inclusive mathematical problem solving competitions, the Problem@Web Project intends to study young students’ beyond-school problem solving activity. The theoretical framework is aiming to integrate a perspective on problem solving that emphasises understanding and expressing thinking with a view on the repre...

The main goal of this research is to understand the problem solving activity with everyday digital technologies, within the context of a beyond school mathematical competition, SUB14. Following a qualitative approach, we observed the activity of a young student, Marco, when solving a geometrical problem, aiming at describing and analysing his activ...

This study seeks to characterize the mathematical problem solving activity with digital tools that emerges from students’ participation in an online mathematics competition. Using a qualitative approach, we elected the case of a 13-year-old participant aiming to understand the ways in which she interweaves her mathematical competence and her techno...

Nas últimas décadas do século XX ganhou vida um amplo debate sobre a resolução de problemas de matemática reconhecendo-se a utilidade dessa capacidade básica para fazer face aos desafios do dia a dia e, em paralelo, a sua importância no desenvolvimento de aprendizagens matemáticas significativas. A par desse debate, escolas e professores começaram...

The Problem@Web International Conference is an opportunity to gather together participants from the research community in mathematics education as well as from related research areas such as the psychology of education, technology education, mathematics and other relevant fields that converge to the study of mathematical problem solving in differen...

This short opening note introduces the proceedings of the Problem@Web International Conference that was structured to address the themes of technology, creativity, and affect in mathematical problem solving held in May 2014. The conference proceedings incorporate all the research presented in the form of plenary sessions, research papers and e-post...

This paper addresses mathematical problem solving activity within the context of a web-based beyond-school competition – SUB14. Using a qualitative approach, we aim at finding evidences of the contestants' mathematical competence and technological fluency by analysing four solutions to a particular geometry problem from participants who decided to...

Being aware that school is just one of many places where youngsters learn, the research community has been stressing the need to deepen knowledge about the role and relevance of beyond school mathematical learning contexts. In this paper we are focusing on the mathematical problem solving activity that occurs at Sub14 -a beyond school web-based com...

Mathematics educators have been stressing the need to deepen knowledge about the role and relevance of beyond school mathematical learning contexts (Barbeau & Taylor, 2009). Hence, our study(1) focuses on the mathematical problem solving processes that 13-14 year old students engage in a beyond school competition, named Sub14. Our theoretical frame...

Keywords: web-based mathematical competitions; digital technologies; mathematical problem solving; mediational tools.

Résumé. La résolution de problèmes continue à être considérée comme une activité privilégiée pour l’apprentissage des Mathématiques par de nombreux chercheurs nationaux et internationaux, et cette perspective a conduit à plusieurs reformulations du curriculum portugais. Cet article adresse les données recueillies et analysées dans le cadre d'une re...

In this paper we analyze and discuss the mathematical activity of a participant in a web-­‐based problem solving competition – the Sub14. Our purpose is to contribute to the knowledge on the learning processes that occur outside the classroom, constantly and necessarily entangling technologically rich environments. The theoretical framework support...

In our research, we aim to look at the notion of knowledge as it is elicited through mathematical modelling of daily life situations, within the context of adult education. In the school scenario of adult education, notions from situated cognition will be brought into play to examine the meaning of mathematisation and of mathematical modelling comp...

As pointed out by Galbraith and Stillman (2001), the issue of the role played by extra-mathematical knowledge in modelling and applications activities is part of an agenda shared by researchers and educators who are interested in the specific nature and characteristics of modelling activities within educational settings. An important aspect of such...

This paper describes and discusses the activity of grade 8studentson two word problems, using a spreadsheet.We look at particular uses of the spreadsheet, namely at the students’ representations, as ways of eliciting forms of algebraic thinking involved in solving the problems ,which entailed dealing with inequalities .We aim to see how the spreads...

The present study is a classroom-based research where students develop mathematical modelling tasks that involve manipulating and experimenting with real objects. The research was developed in two 9th grade classes of students aged 14/15 years old. These students never had this kind of modelling activities in their mathematics classes before. Our p...

In this article we report and discuss a contextual problem solving task that was proposed to a class of 8th grade (13–14-year-old) students. These students had been developing a reasonable experience in the use of the spreadsheet to model relations within contextual problems and chose to use this tool to solve the mentioned problem, engaging in the...

Este artigo incide sobre um campeonato de resolução de problemas online, o Sub14, e visa obter uma perspectiva da actividade de resolução de problemas dos participantes, tendo em conta duas preocupações fundamentais: reconhecer um conjunto de aspectos significativos no contexto em análise, ao ser encarado como um sistema de actividade, e entender o...

Este estudo incidiu sobre as relações entre competência matemática e utilização das TIC no contexto do Campeonato de Resolução de Problemas Sub14, promovido pelo Departamento de Matemática da Faculdade de Ciências e Tecnologia – Universidade do Algarve. Pretendia-se identificar e compreender as percepções dos participantes no Sub14 relativamente à...

Our purpose is to present some results from a research on students involved in Sub14 1 , a web-based and e-mail interchanging mathematical problem solving competition, addressed to 7 th and 8 th graders. We seek to understand the participants' views regarding their mathematical activity and the role of the technology they have used along the compet...

Este artigo analisa a comunicação matemática ocorrida na resolução de um problema lançado no Campeonato de Resolução de Problemas Sub 14, onde se observa a conjugação do uso da folha de cálculo com a comunicação do raciocínio algébrico. Os dados analisados são provenientes de duas fontes distintas: (i) as resoluções de um conjunto de alunos aos qua...

In this paper we analyze and discuss the use of ICT, particularly the Internet, in the context of a mathematical problem-solving competition named "Sub14", promoted by the University of Algarve, Portugal. Our purpose is to understand the participants' views regarding the mathematical activity and the role of the technology they've used along the co...

Resumo: Pretendemos na presente comunicação analisar até que ponto os alunos utilizam a álgebra e o pensamento algébrico como estratégia na resolução de um problema, para além da tentativa e erro. Este problema foi lançado num Campeonato de Matemática -Sub14, promovido pela Faculdade de Ciências e Tecnologia da Universidade do Algarve. A metodologi...

Resumo. O ponto de partida deste artigo reside na análise e discussão de um conjunto de características presentes nos jovens que actualmente frequentam a escola: os chamados Nativos Digitais. Entre os muitos sinais que lhes é possível apontar, destaca-se aquilo que se apresenta como uma nova forma de pensar, de agir e, sobretudo, de aprender. Tendo...