Justifications-on-demand as a device to promote shifts of attention associated with relational thinking in elementary arithmetic

Student responses to arithmetical questions that can be solved by using arithmetical structure can serve to reveal the extent and nature of relational, as opposed to computational thinking. Here, student responses to probes which require them to justify-on-demand are analysed using a conceptual framework which highlights distinctions between different forms of attention. We analyse a number of actions observed in students in terms of forms of attention and shifts between them: in the short-term (in the moment), medium-term (over several tasks), and long-term (over a year). The main factors conditioning students´ attention and its movement are identified and some didactical consequences are proposed

Quantitative imaging of concentrated suspensions under flow

We review recent advances in imaging the flow of concentrated suspensions, focussing on the use of confocal microscopy to obtain time-resolved information on the single-particle level in these systems. After motivating the need for quantitative (confocal) imaging in suspension rheology, we briefly describe the particles, sample environments, microscopy tools and analysis algorithms needed to perform this kind of experiments. The second part of the review focusses on microscopic aspects of the flow of concentrated model hard-sphere-like suspensions, and the relation to non-linear rheological phenomena such as yielding, shear localization, wall slip and shear-induced ordering. Both Brownian and non-Brownian systems will be described. We show how quantitative imaging can improve our understanding of the connection between microscopic dynamics and bulk flow.Comment: Review on imaging hard-sphere suspensions, incl summary of methodology. Submitted for special volume 'High Solid Dispersions' ed. M. Cloitre, Vol. xx of 'Advances and Polymer Science' (Springer, Berlin, 2009); 22 pages, 16 fig

Mathematical talent in Braille code pattern finding and invention

The recognition of patterns and creativity are two characteristics associated with mathematical talent. In this study, we analyzed these characteristics in a group of 37 mathematically talented students. The students were asked to find the pattern the Braille code had been built upon and reinvent it with the aim of making its mathematical language become more functional. Initially, the students were unable to identify the formation pattern of Braille, but after experiencing the difficulties that blind people face when reading it, they recognized the generating element and the regularity. The results were in contrast with those of a control group, and it is noted that the students with mathematical talent were more effective in using visualization to identify the regularity of the pattern and their invention proposals were more sophisticated and used less conventional mathematical content.This research is part of the R+D+I project EDU2015- 69,731-R (Spanish Government/MinEco and ERDF)

Teachers and didacticians: key stakeholders in the processes of developing mathematics teaching

This paper sets the scene for a special issue of ZDM-The International Journal on Mathematics Education-by tracing key elements of the fields of teacher and didactician/teacher-educator learning related to the development of opportunities for learners of mathematics in classrooms. It starts from the perspective that joint activity of these two groups (teachers and didacticians), in creation of classroom mathematics, leads to learning for both. We trace development through key areas of research, looking at forms of knowledge of teachers and didacticians in mathematics; ways in which teachers or didacticians in mathematics develop their professional knowledge and skill; and the use of theoretical perspectives relating to studying these areas of development. Reflective practice emerges as a principal goal for effective development and is linked to teachers' and didacticians' engagement with inquiry and research. While neither reflection nor inquiry are developmental panaceas, we see collaborative critical inquiry between teachers and didacticians emerging as a significant force for teaching development. We include a summary of the papers of the special issue which offer a state of the art perspective on developmental practice. © 2014 FIZ Karlsruhe

Reflexões sobre Relações entre Currículo, Avaliação e Formação de Professores na Área de Educação Matemática

ResumoNo presente texto, o objetivo é trazer algumas reflexões voltadas para a articulação das pesquisas sobre currículo, avaliação e formação de professores na área de Educação Matemática, particularmente voltadas para o modo como se articulam os projetos/ações que constituem políticas públicas no Brasil, considerando-se essa tríade. Essas reflexões baseiam-se em experiências vivenciadas em nosso grupo de pesquisa e em projetos/ações governamentais de reorganização curricular e formação de professores. Destacamos a necessidade de desenvolver de forma articulada pesquisas sobre currículo, avaliação e formação de professores e que seus resultados sejam mais bem divulgados, com vistas a contribuir efetivamente na formulação de políticas públicas. Ainda no âmbito de projetos/ações que constituem políticas públicas no Brasil, observa-se que as propostas de discussão curricular, de avaliação e de formação de professores conversam pouco entre si e são implementadas como se fossem autossuficientes, com desarticulação visível

Relationships between students' conceptions of constructivist learning and their regulation and processing strategies

The present study investigated relationships between students' conceptions of constructivist learning on the one hand, and their regulation and processing strategies on the other hand. Students in a constructivist, problem-based learning curriculum were questioned about their conceptions of knowledge construction and self-regulated learning, as well as their beliefs regarding their own (in)ability to learn and motivation to learn. Two hypothesized models were tested within 98 psychology students, using a structural equation modelling approach: The first model implemented regulation and processing variables of the Inventory of Learning Styles [ILS, Vermunt (Learning styles and regulation of learning in higher education - towards process-oriented instruction in autonomous thinking, 1992)], the second model of the Motivated Strategies for Learning Questionnaire [MSLQ, Pintrich and de Groot (Journal of Educational Psychology, 82, 33-40, 1990)]. Results showed that structural relations exist between conceptions of constructivist learning and regulation and processing strategies. Furthermore, students who express doubt with regard to their own learning capacities are at risk for adopting an inadequate regulation strategy. A three-tiered structure of conceptual, controlling, and operational level appeared valid for the MSLQ variables, but not entirely for those of the ILS

Avaliação de argamassas colantes por reometria rotacional

As argamassas colantes são produtos constituídos por areia natural ou artificial, ligantes (cimento) e aditivos químicos que cumprem uma função de adesivo para assentamento de revestimentos em pisos e paredes. Atualmente, a avaliação em campo sobre a mistura do produto é efetuada de forma empírica. O aplicador (pedreiro) determina, por meios de aspectos sensoriais, a facilidade ou a dificuldade de mistura, classificando a argamassa em pesada, leve, macia, de fácil ou de difícil mistura, etc. Porém, essas descrições são subjetivas e é difícil de mensurar quantitativamente a aplicabilidade do produto, além do que induzem a erros de avaliação, pois cada aplicador pode ter uma percepção diferente. O propósito deste trabalho foi medir, através da reometria rotacional, duas composições para avaliar o comportamento de mistura e reológico de forma quantitativa. Foram utilizadas duas argamassas colantes de mercado do tipo ACI (Argamassa Colante do Tipo I) e ACIII (Argamassa Colante do Tipo III), as quais foram submetidas a ensaios de reometria rotacional, variando-se o teor de água. Os resultados desta pesquisa demonstram que o tempo de mistura de 150 s é eficiente e suficiente para homogeneizar e estabilizar as argamassas testadas, e que a argamassa do tipo ACI apresenta maior dificuldade de mistura e resulta em uma suspensão com maior viscosidade e tensão de escoamento do que a argamassa ACIII. Este estudo mostra a aplicação e os resultados inéditos de reometria rotacional para avaliação do comportamento reológico de argamassas colantes. Essa transferência do conhecimento visa ampliar os horizontes sobre os comportamentos dos materiais de construção civil para melhorar o desempenho de aplicação e avaliação da argamassa no estado fresco

Empowering Qualitative Research Methods in Education with Artificial Intelligence

Artificial Intelligence is one of the fastest growing disciplines, disrupting many sectors. Originally mainly for computer scientists and engineers, it has been expanding its horizons and empowering many other disciplines contributing to the development of many novel applications in many sectors. These include medicine and health care, business and finance, psychology and neuroscience, physics and biology to mention a few. However, one of the disciplines in which artificial intelligence has not been fully explored and exploited yet is education. In this discipline, many research methods are employed by scholars, lecturers and practitioners to investigate the impact of different instructional approaches on learning and to understand the ways skills and knowledge are acquired by learners. One of these is qualitative research, a scientific method grounded in observations that manipulates and analyses non-numerical data. It focuses on seeking answers to why and how a particular observed phenomenon occurs rather than on its occurrences. This study aims to explore and discuss the impact of artificial intelligence on qualitative research methods. In particular, it focuses on how artificial intelligence have empowered qualitative research methods so far, and how it can be used in education for enhancing teaching and learning

Creating and knowing mathematics through language and experience

The radical constructivist assertion that the student constructs his or her own knowledge as opposed to receiving it ldquoready maderdquo echoes the classical debate as to whether the human subject constitutes the world or is constituted by it. This paper shows how the philosophical traditions of post-structuralism and hermeneutic phenomenology offer approaches to effacing this dichotomy and how this forces a re-assertion of the teacher's role in the student's constructing of mathematical knowledge. It is also shown how hermeneutic phenomenology provides an opportunity to ground constructivist mathematical thinking in the material qualities of the world