¿Para qué sirven los problemas en la clase de matemáticas? = What is the use of problems in Mathematics lessons?

The results obtained in several yield tests, at an international level (mainly the famous PISA 2003 report, by the OCDE), have raised a multiplicity of performances in order to improve the students' yield regarding problem solving. In this article we set a clear guideline on how problems should be used in Mathematics lessons, not for obtaining better scores in the yield tests but for improving the development of Mathematical thinking in students. From this perspective, the author analyses, through eight reflections, how the concept of problem, transmitted both in the school and from society, influences the students

Una visión actualizada de la didáctica de la matemática en educación infantil = An up-to-date vision of pre-school mathematics teaching

This article aims to investigate pre-school mathematics teaching from an uptodate perspective. To pursue this contemporary vision we focus on four key questions: what kind of maths is being worked on, who is doing it, how it is being done, and why it is being done

Evaluation of antiradical assays used in determining the antioxidant capacity of pure compounds and plant extracts

The efficiency of the chemiluminescence luminol method and colorimetric DPPH and ABTS methods in evaluating the antiradical capacity of pure compounds and plant extracts with antioxidant potential is compared. In case of pure compounds, the values of parameter 'n' (number of radicals quenched per molecule of antiradical) for ascorbic acid, p-hydroquinone, catechol, quercetin, and rutin are similar when measured by colorimetric assays; however, considerably lower values of n are obtained with the luminol assay. The antiradical activity of extracts from male and female individuals of Baccharis burchelli and Baccharis crispa were determined by the luminol assay and expressed using the new Trolox® percentage (%Trolox®) parameter.

Spectrophotometric determination of mosapride in pure and pharmaceutical preparations

Two simple and sensitive spectrophotometric methods (M1 and M2) for the determination of mosapride in pure and in pharmaceutical preparations are described. These methods are based on the interaction of diazotized mosapride (MSP) couples with chromotropic acid (CTA) [M1] in alkaline medium and diphenylamine (DPA) [M2] in acidic medium. The resulting azo-dyes exhibit maximum absorption at 560 nm and at 540 nm for methods M1 and M2, respectively. All variables were studied in order to optimize the reaction conditions. No interferences were observed from excipients, and the validity of the each method was tested against reference method.

Teaching mathematics and programming : new approaches with empirical evaluation

Programming and mathematics are core areas of computer science (CS) and consequently also important parts of CS education. Introductory instruction in these two topics is, however, not without problems. Studies show that CS students find programming difficult to learn and that teaching mathematical topics to CS novices is challenging. One reason for the latter is the disconnection between mathematics and programming found in many CS curricula, which results in students not seeing the relevance of the subject for their studies. In addition, reports indicate that students' mathematical capability and maturity levels are dropping. The challenges faced when teaching mathematics and programming at CS departments can also be traced back to gaps in students' prior education. In Finland the high school curriculum does not include CS as a subject; instead, focus is on learning to use the computer and its applications as tools. Similarly, many of the mathematics courses emphasize application of formulas, while logic, formalisms and proofs, which are important in CS, are avoided. Consequently, high school graduates are not well prepared for studies in CS. Motivated by these challenges, the goal of the present work is to describe new approaches to teaching mathematics and programming aimed at addressing these issues: Structured derivations is a logic-based approach to teaching mathematics, where formalisms and justifications are made explicit. The aim is to help students become better at communicating their reasoning using mathematical language and logical notation at the same time as they become more confident with formalisms. The Python programming language was originally designed with education in mind, and has a simple syntax compared to many other popular languages. The aim of using it in instruction is to address algorithms and their implementation in a way that allows focus to be put on learning algorithmic thinking and programming instead of on learning a complex syntax. Invariant based programming is a diagrammatic approach to developing programs that are correct by construction. The approach is based on elementary propositional and predicate logic, and makes explicit the underlying mathematical foundations of programming. The aim is also to show how mathematics in general, and logic in particular, can be used to create better programs.

The mathematics of McTaggart's paradox

Mc Taggart's celebrated proof of the unreality of time is a chain of implications whose final step asserts that the A-series (i.e. the classification of events as past, present or future) is intrinsically contradictory. This is widely believed to be the heart of the argument, and it is where most attempted refutations have been addressed; yet, it is also the only part of the proof which may be generalised to other contexts, since none of the notions involved in it is specifically temporal. In fact, as I show in the first part of the paper, McTaggart's refutation of the A-series can be easily interpreted in mathematical terms; subsequently, in order to strengthen my claim, I apply the same framework by analogy to the cases of space, modality, and personal identity. Therefore, either McTaggart's proof as a whole may be extended to each of these notions, or it must embed some distinctly temporal element in one of the steps leading up to the contradiction of the A-series. I conclude by suggesting where this element might lay, and by hinting at what I believe to be the true logical fallacy of the proof.

HILBERT BETWEEN THE FORMAL AND THE INFORMAL SIDE OF MATHEMATICS

Abstract: In this article we analyze the key concept of Hilbert's axiomatic method, namely that of axiom. We will find two different concepts: the first one from the period of Hilbert's foundation of geometry and the second one at the time of the development of his proof theory. Both conceptions are linked to two different notions of intuition and show how Hilbert's ideas are far from a purely formalist conception of mathematics. The principal thesis of this article is that one of the main problems that Hilbert encountered in his foundational studies consisted in securing a link between formalization and intuition. We will also analyze a related problem, that we will call "Frege's Problem", form the time of the foundation of geometry and investigate the role of the Axiom of Completeness in its solution.

Evaluation of the throughfall and stemflow nutrient contents in mixed and pure plantations of Acacia mangium, Pseudosamenea guachapele and Eucalyptus grandis

The interception of the rainfall by the forest canopy has great relevance to the nutrient geochemistry cycle in low fertility tropical soils under native or cultivated forests. However, little is known about the modification of the rainfall water quality and hydrological balance after interception by the canopies of eucalyptus under pure and mixed plantations with leguminous species, in Brazil. Samples of rainfall (RF), throughfall (TF) and stemflow (SF) were collected and analyzed in pure plantations of mangium (nitrogen fixing tree -NFT), guachapele (NFT) and eucalyptus (non-nitrogen fixing tree -NNFT) and in a mixed stand of guachapele and eucalyptus in Seropédica, State of Rio de Janeiro, Brazil. Nine stemflow collectors (in selected trees) and nine pluviometers were randomly disposed under each stand and three pluviometers were used to measure the incident rainfall during 5.5 months. Mangium conveyed 33.4% of the total rainfall for its stem. An estimative based on corrections for the average annual precipitation (1213 mm) indicated that the rainfall's contribution to the nutrient input (kg ha-1) was about 8.42; 0.95; 19.04; 6.74; 4.72 and 8.71 kg ha-1 of N-NH4+, P, K+, Ca+2, Mg+2 and Na+, respectively. Throughfall provided the largest contributions compared to the stemflow nutrient input. The largest inputs of N-NH4+ (15.03 kg ha-1) and K+ (179.43 kg ha-1) were observed under the guachapele crown. Large amounts of Na+ denote a high influence of the sea. Mangium was the most adapted species to water competitiveness. Comparatively to pure stand of eucalyptus, the mixed plantation intensifies the N, Ca and Mg leaching by the canopy, while the inputs of K and P were lower under these plantations.

Conceptions of mathematics teacher education : thoughts among teacher educators in Tanzania

This study addresses the question of teacher educators’ conceptions of mathematics teacher education (MTE) in teacher colleges in Tanzania, and their thoughts on how to further develop it. The tension between exponents of content as opposed to pedagogy has continued to cause challenging conceptual differences, which also influences what teacher educators conceive as desirable in the development of this domain. This tension is connected to the dissatisfaction of parents and teachers with the failure of school mathematics. From this point of view, the overall aim was to identify and describe teacher educators’ various conceptions of MTE. Inspired by the debate among teacher educators about what the balance should be between subject matter and pedagogical knowledge, it was important to look at the theoretical faces of MTE. The theoretical background involved the review of what is visible in MTE, what is yet to be known and the challenges within the practice. This task revealed meanings, perspectives in MTE, professional development and assessment. To do this, two questions were asked, to which no clear solutions satisfactorily existed. The questions to guide the investigation were, firstly, what are teacher educators’ conceptions of MTE, and secondly, what are teacher educators’ thoughts on the development of MTE? The two questions led to the choice of phenomenography as the methodological approach. Against the guiding questions, 27 mathematics teacher educators were interviewed in relation to the first question, while 32 responded to an open-ended questionnaire regarding question two. The interview statements as well as the questionnaire responses were coded and analysed (classified). The process of classification generated patterns of qualitatively different ways of seeing MTE. The results indicate that MTE is conceived as a process of learning through investigation, fostering inspiration, an approach to learning with an emphasis on problem solving, and a focus on pedagogical knowledge and skills in the process of teaching and learning. In addition, the teaching and learning of mathematics is seen as subject didactics with a focus on subject matter and as an organized integration of subject matter, pedagogical knowledge and some school practice; and also as academic content knowledge in which assessment is inherent. The respondents also saw the need to build learner-educator relationships. Finally, they emphasized taking advantage of teacher educators’ neighbourhood learning groups, networking and collaboration as sustainable knowledge and skills sharing strategies in professional development. Regarding desirable development, teacher educators’ thoughts emphasised enhancing pedagogical knowledge and subject matter, and to be determined by them as opposed to conventional top-down seminars and workshops. This study has revealed various conceptions and thoughts about MTE based on teacher educators´ diverse history of professional development in mathematics. It has been reasonably substantiated that some teacher educators teach school mathematics in the name of MTE, hardly distinguishing between the role and purpose of the two in developing a mathematics teacher. What teacher educators conceive as MTE and what they do regarding the education of teachers of mathematics revealed variations in terms of seeing the phenomenon of interest. Within limits, desirable thoughts shed light on solutions to phobias, and in the same way low self-esteem and stigmatization call for the building of teacher educator-student teacher relationships.

Mathematics inspired by Darwin. Adaptive dynamics of dispersal and cooperation

In 1859, Charles Darwin published his theory of evolution by natural selection, the process occurring based on fitness benefits and fitness costs at the individual level. Traditionally, evolution has been investigated by biologists, but it has induced mathematical approaches, too. For example, adaptive dynamics has proven to be a very applicable framework to the purpose. Its core concept is the invasion fitness, the sign of which tells whether a mutant phenotype can invade the prevalent phenotype. In this thesis, four real-world applications on evolutionary questions are provided. Inspiration for the first two studies arose from a cold-adapted species, American pika. First, it is studied how the global climate change may affect the evolution of dispersal and viability of pika metapopulations. Based on the results gained here, it is shown that the evolution of dispersal can result in extinction and indeed, evolution of dispersalshould be incorporated into the viability analysis of species living in fragmented habitats. The second study is focused on the evolution of densitydependent dispersal in metapopulations with small habitat patches. It resulted a very surprising unintuitive evolutionary phenomenon, how a non-monotone density-dependent dispersal may evolve. Cooperation is surprisingly common in many levels of life, despite of its obvious vulnerability to selfish cheating. This motivated two applications. First, it is shown that density-dependent cooperative investment can evolve to have a qualitatively different, monotone or non-monotone, form depending on modelling details. The last study investigates the evolution of investing into two public-goods resources. The results suggest one general path by which labour division can arise via evolutionary branching. In addition to applications, two novel methodological derivations of fitness measures in structured metapopulations are given.

Effects of oil-water mixed frying and pure-oil frying on the quality characteristics of soybean oil and chicken chop

Abstract The effects of oil-water mixed frying (OWF) and pure-oil frying (POF) on changes in quality characteristics of soybean oil and chicken chop during six days of frying were comparatively investigated. The results showed that the changes in specific extinction coefficients, p-anisidine value, carbonyl value, viscosity and color of soybean oil were more pronounced in the case of POF, indicating that oil oxidative and polymeric degradation was retarded by OWF. Concerning fat content of chicken chop, lower (p<0.05) values were observed in the last three days in the case of OWF than POF. Meanwhile, OWF led to lower acrylamide formation in chops during the six days. Sensory evaluation showed that OWF provided chops with five attributes similar to those of chops fried by POF on the first day. As frying days increased, the decreases in scores for color, odor, flavor and overall acceptability were less in the case of OWF. In conclusion, OWF could be a worthwhile alternative for retarding oil deterioration and producing healthier and higher quality fried meat products.

Utilising student profiles in mathematics course arrangements

This thesis develops a method for identifying students struggling in their mathematical studies at an early stage. It helps in directing support to students needing and benefiting from it the most. Thus, frustration felt by weaker students may decrease and therefore, hopefully, also drop outs of potential engineering students. The research concentrates on a combination of personality and intelligence aspects. Personality aspects gave information on conation and motivation for learning. This part was studied from the perspective of motivation and self-regulation. Intelligence aspects gave information on declarative and procedural knowledge: what had been taught and what was actually mastered. Students answered surveys on motivation and self-regulation in 2010 and 2011. Based on their answers, background information, results in the proficiency test, and grades in the first mathematics course, profiles describing the students were formed. In the following years, the profiles were updated with new information obtained each year. The profiles used to identify struggling students combine personality (motivation, selfregulation, and self-efficacy) and intelligence (declarative and procedural knowledge) aspects at the beginning of their studies. Identifying students in need of extra support is a good start, but methods for providing support must be found. This thesis also studies how this support could be taken into account in course arrangements. The methods used include, for example, languaging and scaffolding, and continuous feedback. The analysis revealed that allocating resources based on the predicted progress does not increase costs or lower the results of better students. Instead, it will help weaker students obtain passing grades.