James J. Kaput (1942–2005) imagineer and futurologist of mathematics education

Jim Kaput lived a full life in mathematics education and we have many reasons to be grateful to him, not only for his vision of the use of technology in mathematics, but also for his fundamental humanity. This paper considers the origins of his ‘big ideas’ as he lived through the most amazing innovations in technology that have changed our lives more in a generation than in many centuries before. His vision continues as is exemplified by the collected papers in this tribute to his life and work

Computer algebra systems for the 21st century: new kind of dynamic representations

La idea central de la presentación es la extensión de las representaciones, heredadas de los medios dinámicos en el siglo 21, y cómo estas van más allá de lo que anteriormente era posible en términos de construir las grandes ideas de la Matemática del Cambio y la Variación, incluyendo las ideas subyacentes al Cálculo, en formas más accesibles para nuevas poblaciones de estudiantes

Modelling is for reasoning

In a broad sense, computing is an area of knowledge from which a popular and effective technology emerged long before a solid, specific, scientific methodology, let alone formal foundations, had been put forward. This might explain some of the weaknesses in the software industry, on the one hand, as well as an excessively technology-oriented view which dominates computer science training at pre-university and even undergraduate teaching, on the other. Modelling, understood as the ability to choose the right abstractions for a problem domain, is consensually recognised as essential for the development of true engineering skills in this area, as it is in all other engineering disciplines. But, how can the basic problem-solving strategy, one gets used to from school physics: understand the problem, build a mathematical model, reason within the model, calculate a solution, be taken (and taught) as the standard way of dealing with software design problems? This paper addresses this question, illustrating and discussing the interplay between modelling and reasoning.(undefined

Representing addition and subtraction : learning the formal conventions

The study was designed to test the effects of a structured intervention in teaching children to represent addition and subtraction. In a post-test only control group design, 90 five-year-olds experienced the intervention entitled Bi-directional Translation whilst 90 control subjects experienced typical teaching. Post-intervention testing showed some significant differences between the two groups both in terms of being able to effect the addition and subtraction operations and in being able to determine which operation was appropriate. The results suggest that, contrary to historical practices, children's exploration of real world situations should precede practice in arithmetical symbol manipulation

Students’ Evolving Meaning About Tangent Line with the Mediation of a Dynamic Geometry Environment and an Instructional Example Space

In this paper I report a lengthy episode from a teaching experiment in which fifteen Year 12 Greek students negotiated their definitions of tangent line to a function graph. The experiment was designed for the purpose of introducing students to the notion of derivative and to the general case of tangent to a function graph. Its design was based on previous research results on students’ perspectives on tangency, especially in their transition from Geometry to Analysis. In this experiment an instructional example space of functions was used in an electronic environment utilising Dynamic Geometry software with Function Grapher tools. Following the Vygotskian approach according to which students’ knowledge develops in specific social and cultural contexts, students’ construction of the meaning of tangent line was observed in the classroom throughout the experiment. The analysis of the classroom data collected during the experiment focused on the evolution of students’ personal meanings about tangent line of function graph in relation to: the electronic environment; the pre-prepared as well as spontaneous examples; students’ engagement in classroom discussion; and, the role of researcher as a teacher. The analysis indicated that the evolution of students’ meanings towards a more sophisticated understanding of tangency was not linear. Also it was interrelated with the evolution of the meaning they had about the inscriptions in the electronic environment; the instructional example space; the classroom discussion; and, the role of the teacher

A network analysis of cofactor-protein interactions for analyzing associations between human nutrition and diseases

The involvement of vitamins and other micronutrients in intermediary metabolism was elucidated in the mid 1900's at the level of individual biochemical reactions. Biochemical pathways remain the foundational knowledgebase for understanding how micronutrient adequacy modulates health in all life stages. Current daily recommended intakes were usually established on the basis of the association of a single nutrient to a single, most sensitive adverse effect and thus neglect interdependent and pleiotropic effects of micronutrients on biological systems. Hence, the understanding of the impact of overt or sub-clinical nutrient deficiencies on biological processes remains incomplete. Developing a more complete view of the role of micronutrients and their metabolic products in protein-mediated reactions is of importance. We thus integrated and represented cofactor-protein interaction data from multiple and diverse sources into a multi-layer network representation that links cofactors, cofactor-interacting proteins, biological processes, and diseases. Network representation of this information is a key feature of the present analysis and enables the integration of data from individual biochemical reactions and protein-protein interactions into a systems view, which may guide strategies for targeted nutritional interventions aimed at improving health and preventing diseases

Successive translocation into and out of the mitochondrial matrix

We investigated the import and sorting pathways of cytochrome b2 and cytochrome c1, which are functionally located in the intermembrane space of mitochondria. Both proteins are synthesized on cytoplasmic ribosomes as larger precursors and are processed in mitochondria in two steps upon import. The precursors are first translocated across both mitochondrial membranes via contact sites into the matrix. Processing by the matrix peptidase leads to intermediate-sized forms, which are subsequently redirected across the inner membrane. The second proteolytic processing occurs in the intermembrane space. We conclude that the hydrophobic stretches in the presequences of the intermediate-sized forms do not stop transfer across the inner membrane, but rather act as transport signals to direct export from the matrix into the intermembrane space

Mitochondrial precursor proteins are imported through a hydrophilic membrane environment

We have analyzed how translocation intermediates of imported mitochondrial precursor proteins, which span contact sites, interact with the mitochondrial membranes. F1-ATPase subunit β(F1β) was trapped at contact sites by importing it into Neurospora mitochondria in the presence of low levels of nucleoside triphosphates. This F1β translocation intermediate could be extracted from the membranes by treatment with protein denaturants such as alkaline pH or urea. By performing import at low temperatures, the ADP/ATP carrier was accumulated in contact sites of Neurospora mitochondria and cytochrome b2 in contact sites of yeast mitochondria. These translocation intermediates were also extractable from the membranes at alkaline pH. Thus, translocation of precursor proteins across mitochondrial membranes seems to occur through an environment which is accessible to aqueous perturbants. We propose that proteinaceous structures are essential components of a translocation apparatus present in contact sites

Interactive and multimedia contents associated with a system for computer-aided assessment

This paper presents a research study addressing the development, implementation, evaluation and use of Interactive Modules for Online Training (MITO) of mathematics in higher education. This work was carried out in the context of the MITO project, which combined several features of the learning and management system Moodle, the computer-aided assessment for mathematics STACK, the mathematical software GeoGebra, several packages from the type-setting program LaTeX, and tutorial videos. A total of 1962 students participated in this study. Two groups of students taking a Calculus course were selected for a deeper analysis. In regard to usability and functionality, the results indicate that MITO scored well in almost all aspects, which is fundamental for their introduction into formal university courses. The analysis of the data reveals that the use of MITO educational contents by students mainly occurs about one week and a half prior the evaluations. Moreover, there is a strong correlation between the results of online assessments on MITO in a continuous assessment model and the final grade on the course

Transport into mitochondria and intramitochondrial sorting of the Fe/S protein of ubiquinol-cytochrome c reductase

The Fe/S protein of complex III is encoded by a nuclear gene, synthesized in the cytoplasm as a precursor with a 32 residue amino-terminal extension, and transported to the outer surface of the inner mitochondrial membrane. Our data suggest the following transport pathway. First, the precursor is translocated via translocation contact sites into the matrix. There, cleavage to an intermediate containing an eight residue extension occurs. The intermediate is then redirected across the inner membrane, processed to the mature subunit, and assembled into complex III. We suggest that the folding and membrane-translocation pathway in the endosymbiotic ancestor of mitochondria has been conserved during evolution of eukaryotic cells; transfer of the gene for Fe/S protein to the nucleus has led to addition of the presequence, which routes the precursor back to its “ancestral” assembly pathway