Littérature scientifique sur le sujet « Pharmaceutical arithmetic – Problems, exercises, etc »

This article proposes the results of performed work, which aims are to prepare junior schoolchildren with severe speech disorders to solve arithmetic problems in speech therapy classes. Our previous research has found that children with severe speech disorders had difficulty solving arithmetic problems. In the process of preparing junior schoolchildren with severe speech disorders to solve arithmetic problems in speech therapy classes, we observed specific errors at the level of: pronunciation of sounds, words; sentence construction; text translation. To overcome them, we used correction tasks. They were offered to children to perform only when they saw in them a mistake of a certain type, and therefore did not include these tasks in the text of the lesson, and offered them as tips in the working mode. The duration of these correction tasks is 1-2 minutes. The purpose of their use is the awareness of children with severe speech disorders of mistakes and formation of their skills of independent control over their own speech. In order to overcome errors, we offered different tasks based on analytical systems: visual, auditory, tactile-kinesthetic, changing them each time. The final analysis of the features of speech therapy classes has shown that in order to overcome specific errors in oral and written speech among pupils with severe speech disorders during speech therapy classes was effective to use not only tasks for speech development, but also corrective exercises that were involved in different situations depending on the manifestation. In particular, to correct the phonetic side of speech, pupils with severe speech disorders were taught to focus on analytical systems: auditory – associating speech sounds with different sounds of the environment; tactile-kinesthetic – feeling vibration; visual – imagining the articulatory image and associating the sound of speech with visual support. In the future, based on the concise tips of a speech therapist (figurative, gestural, facial expressions, etc.) children were offered to correct mistakes. And when the tips were taken away, they were applied only when needed to individual pupils with severe speech disorders.

The article is devoted to the investigation of criminal legal norm, namely, to one of its parts – sanction. In this aspect, a brief overview of general theoretical problems is made, their importance and prospects in further study for science and practice are shown. The aim of the article: to analyze the general concept of criminal legal sanction, to investigate the sanctions of norms provided by Art. 321 of the CC of Ukraine, to identify the shortcomings of their design and to suggest ways of their improvement. The research methodology: historical-legal, comparative-legal, logical ones, the method of analysis and synthesis. The definition of the concept of sanction is described, as well as what types of sanctions exist, which prevail in the norms of the law of Ukraine on criminal liability, etc. In addition, the peculiarities of the sanction design, in particular in comparison with foreign criminal legislation, and the existing shortcomings in the domestic criminal law are provided. In total, this provided an opportunity to analyze Art. 321 of the Criminal Code of Ukraine (hereinafter – the CC of Ukraine), and to formulate ways to improve it. The main results: to apply the experience of foreign criminal law, which provides the gradation of even each type of punishment, the use of arithmetic rules to increase and decrease the amount of punishment in case of existence of mitigating or aggravating circumstances, etc., at least for the most common crimes.

This study is based on a qualitative investigation framed within an interpretive paradigm, and aims to investigate the extent to which question design affects the solution strategies adopted by children when solving linear number pattern generalisation tasks presented in pictorial and numeric contexts. The research tool comprised a series of 22 pencil and paper exercises based on linear generalisation tasks set in both numeric and 2-dimensional pictorial contexts. The responses to these linear generalisation questions were classified by means of stage descriptors as well as stage modifiers. The method or strategy adopted was carefully analysed and classified into one of seven categories. A meta-analysis focused on the formula derived for the nth term in conjunction with its justification. The process of justification proved to be a critical factor in being able to accurately interpret the origin of the sub-structure evident in many of these responses. From a theoretical perspective, the central role of justification/proof within the context of this study is seen as communication of mathematical understanding, and the process of justification/proof proved to be highly successful in providing a window of understanding into each pupil’s cognitive reasoning. The results of this study strongly support the notion that question design can play a critical role in influencing pupils’ choice of strategy and level of attainment when solving pattern generalisation tasks. Furthermore, this study identified a diverse range of visually motivated strategies and mechanisms of visualisation. An awareness and appreciation for such a diversity of visualisation strategies, as well as an understanding of the importance of appropriate question design, has direct pedagogical application within the context of the mathematics classroom.

Como indicam os Parâmetros Curriculares Nacionais, um dos objetivos do Ensino Fundamental no Brasil é o de que os alunos sejam capazes de questionar a realidade formulando problemas e tratando de resolvê-los (PCN, 1998, p. 27). Na mesma perspectiva, um dos propósitos do terceiro ciclo, que corresponde ao sexto ano do Ensino Fundamental, em Matemática, é o de que os alunos sejam capazes de resolver situações-problema envolvendo números naturais, inteiros, racionais e a partir delas ampliar e construir novos significados para as operações aritméticas (op. cit., p. 64). Assim, a Matemática pode dar sua contribuição à formação do cidadão ao proporcionar a construção de estratégias, a comprovação e a justificativa de resultados (op. cit., p. 27) no desenvolvimento da capacidade para resolver problemas, sejam eles dessa ou de qualquer outra área do conhecimento. O ensino de Matemática não tem só a função evidente de propiciar o desenvolvimento de competências referentes ao manuseio das mais diversas habilidades matemáticas, mas deve ter também a preocupação de promover o desenvolvimento de capacidades como comunicação, argumentação e validação de processos (PCN, 1998, p. 56). Essas, por sua vez, necessitam das habilidades de interpretação e expressão escrita e/ou falada. Aprender a resolver problemas matemáticos na escola é deparar-se com um mundo de conceitos que envolvem leitura e compreensão, tanto da língua materna como da linguagem matemática. A resolução de problemas exige compreensão leitora. Para essa compreensão, o aluno precisa de um referencial linguístico e, para expressar os dados em sentenças matemáticas, de um referencial de linguagem matemática, ambos adequados a cada situação-problema a que for exposto. Oferecer ao aprendiz oportunidades de compreensão do enunciado de problemas, por certo o auxiliarão não só a resolvê-los como também a ampliar e aperfeiçoar o estabelecimento de inferências e de conexões lógicas. Há vários estudos sobre as dificuldades em leitura e sobre as dificuldades na resolução de problemas, separadamente, mas poucos aproximam essas duas áreas do conhecimento. O objetivo desta pesquisa é o de verificar como os mecanismos coesivos, presentes em enunciados de problemas de aritmética, podem se constituir fatores intervenientes na compreensão leitora desses enunciados. Pensa-se ser possível, a partir daí, vislumbrar aproximações entre os estudos sobre língua materna e linguagem matemática, no que tange à compreensão de enunciados de problemas aritméticos. Parte-se do pressuposto de que a não compreensão do enunciado de problemas aritméticos compromete a conversão dos dados apresentados em linguagem matemática e, por conseguinte, a resolução desses problemas.
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As the Parâmetros Curriculares Nacionais indicate, one of the purposes of Elementary Schools in Brazil is that students should be able to question reality by formulating problems and trying to solve them (PCN, 1998, p. 27). In that same perspective, one of the purposes in Mathematics for the third cycle, which corresponds to the 6th grade in Elementary School, is that students should be able to solve problem-situations involving, natural numbers, whole numbers, and rational numbers and from those situations be able to enhance and build new meanings for arithmetic operations (op. cit., p. 64). Thus, Mathematics can give its contribution to citizens, by providing the construction of strategies, the evidence and justification of results (op. cit., p. 27) towards the development of the capacity of solving problems, whether they belong to this or any other area of knowledge. Teaching Mathematics does not only have the obvious function of providing the development of competences related to handling with the most varied mathematical abilities, but it must also be concerned with the promotion of the development of abilities such as communication, argumentation, and process validation (PCN, 1998, p. 56). These abilities, on their turn, require abilities of written and/or spoken expression and interpretation. Learning to solve mathematical problems at school means facing a world of concepts that involves reading and comprehension both of one‟s native language and of mathematical language. Solving problems requires reading comprehension. For that comprehension, students need to have some linguistic references and to express data in mathematical sentences they need to have some mathematical references, which should be appropriate according to each problem-situation they are exposed to. Offering learners opportunities to understand the problem utterances should certainly help them not only solve the problems but also to widen and improve their ability to establish inferences and logical connections. Many studies have been carried out about reading and about difficulties in solving problems, although very few have put these two areas of knowledge together. The purpose of this study is to verify how cohesive mechanisms, which are present in the utterances of arithmetic problems, can become intervenient factors in the reading comprehension of those utterances. The author believes it is possible from that point of view to catch a glimpse of ways of making studies of native language get closer to studies of mathematical language in what concerns the comprehension of arithmetical problem utterances. The study starts from the assumption that if the arithmetic utterance is not understood, that compromises the conversion of the data presented in mathematical language and, hence, compromises solving those problems.