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- Undergraduate Students' Learning of Linear Algebra Through Mathematical Modelling RoutesPublication . Ramirez-Montes, Guillermo; Henriques, Ana; Carreira, SusanaMathematical 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 sciences. This paper reports a study aiming to characterise the distinct modelling routes performed by Costa Rican undergraduate students when solving a mathematical modelling task involving the concept of system of linear equations (SLE). In analysing those modelling routes, it was possible to identify their learning of linear algebra concepts and their modelling competencies as well as the associated difficulties that students faced. Data collection included participant observation, with audio recording of the students' discussions, their written work on the task, and digital files of their work with technology. The results show that non-linear routes are associated with a greater mobilisation of students' knowledge on SLE concepts and with their development of modelling competencies. The results also highlight the need to improve the students' competency of validating results, an important step that they did not take, and suggest the need to make technology relevant to the students' work on modelling tasks.
- Mathematical models and meanings by school and university students in a modelling taskPublication . Carreira, Susana; Baioa, Ana Margarida; Werle de Almeida, Lourdes MariaThis 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 between the models developed in the two classes and seek to know how simulation and experimentation influence students' production of meaning. The theoretical framework comprises the relationship between the modelling process and the prototyping process and adopts Peirce's pragmatic perspective on meaning. The research is of a qualitative nature, assuming the characteristics of a case study. The results reveal many commonalities between the modelling in the two contexts. Moreover, experimentation and simulation were relevant elements for the production of meaning by the students, which is endorsed by a pragmatic perspective on meaning.
- Mathematics and interdisciplinary STEM education: recent developments and future directionsPublication . Goos, Merrilyn; Carreira, Susana; Namukasa, Immaculate KizitoThis 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. However, the role of mathematics in STEM education often appears to be marginal, and we do not understand well enough how mathematics contributes to STEM-based problem-solving or how STEM education experiences enhance students' learning of mathematics. In this survey paper, we present a narrative review of empirical and conceptual research literature, published between 2017 and 2022. These literature sources are organised by a framework comprising five thematic clusters: (1) interdisciplinary curriculum models and approaches; (2) student outcomes and experiences; (3) teacher preparation and professional development; (4) classroom implementation and task design; and (5) policy, structures, and leadership. We use the framework to provide an overview of the papers in this issue and to propose directions for future research. These include: investigating methods and rationales for connecting the constituent STEM disciplines so as to preserve the disciplinary integrity of mathematics; clarifying what is meant by student "success" in interdisciplinary STEM programs, projects, and other educational approaches; moving beyond classroom practices that position mathematics as just a tool for solving problems in other disciplines; understanding what makes a STEM task mathematically rich; and asking how STEM education research can productively shape STEM education policy.
- Venues for analytical reasoning problems: how children produce deductive reasoningPublication . Carreira, Susana; Amado, Nélia; Jacinto, HéliaThe 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 option elimination, for which chains of inferences based on premises and rules are accomplished. Focusing on the solutions of children aged 10–12 to an analytical reasoning problem proposed in two separate settings—a web-based problem-solving competition and mathematics classes—this study aims to find out what forms of deductive reasoning they undertake and how they express that reasoning. This was done through a qualitative content analysis encompassing 384 solutions by children participating in a beyond-school competition and 102 solutions given by students in their mathematics classes. The results showed that four di erent types of deductive reasoning models were produced in the two venues. Moreover, several representational resources were found in the children’s solutions. Overall, it may be concluded that moderately complex analytical reasoning tasks can be taken into regular mathematics classes to support and nurture young children’s diverse deductive reasoning models.
- Mathematical thinking about systems – students modeling a biometrics identity verification systemPublication . Baioa, Ana Margarida; Carreira, SusanaThe 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, 9(th) grade students worked on a modeling task aiming to create an identification system based on hand biometrics. The theoretical framework proposes a conceptualization of the interplay between the mathematical modeling process, from a cognitive perspective, and the engineering design process. Central ideas refer to the cyclical nature of both processes and to the sub-processes involved in them. The empirical data were collected in two design-based research cycles with different 9(th) grade classes. The data from the groups' audio and video recording and the students' productions were analyzed under a directed qualitative content analysis informed by theory. The results showed a global pattern in the students' thinking in solving a design system problem. The overlapping and interplay between the mathematical modeling and the design process was a prominent characteristic of students' thinking. The modeling cycle was mirrored by a design cycle, with both running in parallel. System thinking pushed and drove students' mathematical thinking, from the system requirements to the prototype validation.