Zeitschriftenartikel zum Thema „Nursing – Mathematics – Problems, exercises, etc“

The article discusses various types of digital math tasks to be performed on computers or tablets. The experience of creating digital tasks in mathematics with complex answers from the point of view of automatic verifcation: algebraic expressions, geometric constructions, graphs of functions, etc. is discussed. As an example of the use of digital tasks, the use of digital materials for preparing schoolchildren for the Unifed State Exam in mathematics of a profle level is considered. The article also discusses various forms of using simulators and tests in the educational process: supporting the independent activities of students in the full-time educational process, supporting online learning with a teacher in the context of the coronavirus pandemic, independent online learning without a teacher based on specially prepared and structured training courses. In the latter case, in addition to simulators, it is proposed to use other digital educational resources to increase the visibility of the educational material and organize self-control of learning outcomes: videos, slides, dynamic models, training exercises for problems with a detailed answer to the options for the USE control and measuring materials.

Abstract Introduction. Nursing, midwifery ethics education has been changing over the years. The necessity to reduce the knowledge-practice gap has been highlighted, consequently, modern training methods - based on experience - have been introduced. Aim. To present the importance of empirical teaching methods in the formation of ethical competence of nursing and midwifery students and and the objectives of the project implemented under the ERASMUS + program, KA220-HED entitled “Strengthening the ethical competence of future nurses and midwives: An inter-professional action-learning project on experiential training methods (ETHCOM)”. Material and methods. A non-systematic literature review was performed using databases (PubMed, CINAHL Complete). The analysis included 38 articles published between 2010 and 2023 in Polish and English. Results. In traditional methods of ethical education, the teacher plays the main role, while in those based on experience – the student. Among the experiential methods of learning ethics by nursing and midwifery students that are eff ective in acquiring and development of ethical competence can be distinguished, e.g. learning through games, storytelling, simulation etc. The selection of an educational method in the process of training ethical competence among nursing and midwifery students is important so that future students are able to face contemporary ethical problems.

On the basis of modern approaches, the article substantiates the problems of learning the vocabulary of German social discourse in classes at higher education institutions. The definition of discourse has been clarified according to various theories and approaches. The main aspects of studying the vocabulary of social discourse are highlighted. Based on the systematization and generalization of the theoretical assets of domestic and foreign researchers, as well as through comparative analysis, the main methods of learning social vocabulary were established: 1) use of factual material with a sufficient number of texts on social topics; 2) study of stable phrases and clichés; 3) the possibility of forming language competence with a set of exercises; 4) creation of conditions for independent work of students; 5) use of dictionaries and reference books. The method of working with the book Handbuch Knigge by Birgit Althaus, which is devoted to the rules of behavior and etiquette in various situations of everyday communication, is described. Based on the text, the choice of vocabulary of social discourse for students is substantiated (compound words, established clichés, non-equivalent vocabulary, idiomatic expressions, etc.). It was determined that vocabulary of social discourse has recently become one of the most studied spheres in modern linguistics. A comprehensive approach to the problem of learning social vocabulary stimulates the formation of language competence, which in turn leads to the formation of a holistic view of the culture and language of the German people. According to this, the research of social vocabulary for students with the aim of its further use in some day-to-day situations is promising. Keywords: social discourse; compound noun; stable expression; correct use; background knowledge; language competence; speech situation; mentality.

Studies have shown that the physical, psychological, and social problems of liver cancer patients are more serious than those of other cancer patients and their quality of life is significantly reduced. This may be related to the poor treatment effect of patients with advanced liver cancer. Patients often have adverse symptoms such as cancer pain, pleural effusion, and ascites, etc., which have a great impact on patients’ psychology and recovery from illness. With the change of the medical model, it has become history to rely solely on drugs to care for patients with advanced liver cancer and comprehensive nursing intervention has become very important. Continuous nursing intervention focuses on individualized and full-hearted care, effectively alleviating patients’ anxiety and fear and improving patients’ environmental adaptability and psychological defense mechanisms. However, in the field of liver cancer, there is no detailed comparison between the efficacy of continuous nursing and traditional conventional nursing. This article applies the hidden Markov model, starts with medical data mining, and describes the process achieved by the application of this article and the analysis of the results obtained by the two nursing methods, which reflect the difference in curative effect evaluation, and it proves that continuous nursing has more advantages in the curative effect of patients with liver tumors.

The article examines the constitutional and legal regulation of freedom of reproductive choice, as one of the fundamental reproductive rights of a person. It has been established that the formation of one’s own concept of reproductive rights within the framework of the Constitution of Ukraine and industry legislation is significant in connection with the general demographic situation in Ukraine and the development of legal relations that arise when a person exercises their reproductive rights. Attention is focused on the fact that in ensuring the realization of reproductive rights, it is urgent to recognize public organizations as active subjects of political, social and economic life, their right to participate in the formation of policy in the field of reproduction, health care, and family planning. It is noted that the content of freedom of reproductive choice is embodied not only in respect for the reproductive autonomy of a person, but also in effective directions of state regulation. It is emphasized that the legislation of Ukraine on the regulation of legal relations in the reproductive sphere requires improvement in connection with the absence of a law that would regulate the grounds and procedure for the use of reproductive technologies, the principles that should be guided by their application, the specifics of the implementation of state policy in the sphere of population, etc. The authors conclude that the main directions of state regulation in the aspect of ensuring freedom of reproductive choice should be: development and improvement of legislation in the field of health care; development of the reproductive health care system; formation and improvement of legislation in the field of reproductive health; involvement of public organizations in informational and educational activities aimed at solving problems of reproductive health protection; support for families with children; provision of psychological and legal assistance to individuals in exercising their reproductive rights; state support for scientific research in the field of reproductive health; training of personnel in the field of reproductive health protection and protection of the rights of individuals to reproduction in accordance with international standards; formation of a self-conscious attitude towards the birth of a child; support for families with children; ensuring the availability of family planning services and the provision of medical services, including the use of assisted reproduction.

As Benjamin Franklin quoted, “Tell me and I forget,Show me and I remember, Involve me and I learn.” This statement is true as it forms the essence of Blended Learning. Blended learning methods leads to continuous understanding and learning. It provides methods of teaching which leads to sharpen the skills and attitude furtherto seek resolutions to problems and to create new knowledge and awareness. This research intends to introduce blended learning to its readers and to analyze the trends and issues specially related to mathematics and nursing field.Theresearch focuses on different components of blended learning with emphasis on flexibility as the core component. This is a secondary research analyzing different journals, research articles, thesis, books etc. Lastly, it will highlight the comparison of blended learning with traditional methods. The results of the analysis were interpreted using descriptive analysis, percentages, and frequencies. This analysis found that various fields were practiced in the flipped classroom approach, and some technology tools were used as the online platform for its practice

Introduction: the article deals with one of psychocorrective work direction with younger schoolchildren who have developmental delay and inclusively taught at comprehensive schools. Because of psychological and pedagogical features these children are in the majority of pupils who don’t cope with traditional school curriculum requirements. For systematic and successful education any child needs potential neurobiological readiness of brain systems and subsystems that provides the development of higher mental functions necessary for schooling. The results of neuropsychological investigations demonstrate that children with developmental delay are characterized by partiality of brain systems damage with failing of separate cortical and subcortical functions and larger integrity of higher regulatory processes. The most vulnerable subcortical brain system of physically disabled children is thalamo-hypothalamic complex. Its dysfunction appears both in neurological symptoms (neurometabolic endocrine syndrome, thermoregulatory and vegetovascular dysfunction, carbohydrate metabolism disorder) and psychological problems (developmental delay, absence of orientation to adult speaking as a behavior regulator, retardation in eye-mindedness and visual active thinking formation). It is recognized that hypothalamic structures mature rhythmically. Rhythmical stimulus, coming from environment are very important for them. Understanding the laws of brain process formation we can help develop child’s brain, using external rhythms in the psychocorrective support program for younger schoolchildren with developmental delay. The method of rhythms can be used in motor sphere correction of younger schoolchildren with developmental delay. Within the context of our investigation rhythm, using in folklore is considered as a condition of motor functions development of younger schoolchildren with developmental delay. Motor correction creates a necessary basis for normal higher mental functions operation, increases total power of verbal and nonverbal thinking processes, contributes to overcoming of behavior stereotypes, produces a base for motor providing of speech and language mechanism, form skills to control own behavior, assists in coping with muscle and body tension. In such a way motor correction creates a prerequisite for full psychical processes participating in reading, writing and mathematics acquisition. Results: the article deals with the results of investigation of motor functions of younger schoolchildren with developmental delay that inclusively taught at comprehensive schools. The supplied results are before and after psychocorrective work with the using of rhythm. The measurements for result comparison are kinesthetic and dynamic praxis investigation, reciprocal movements coordination. Diagnostic tasks combined traditional psychological techniques and neuropsychological tests. After sets of samples an own system of scoring was given. Each system took into account character, degree of severity and amount of introduced mistakes. Ball scoring was determined at the base of a scale: three balls – high level of samples making (motions are carrying out correctly, fast, clear), two balls – middle level (motions are carrying out correctly, consequentially, but reaction is delayed, specularity is existed), one ball – low level (needed hands position is choosing on the basis of samples, movements are very slow, specularity, echopraxia and perseveration are existed). As a result of investigation it was found that before psychocorrective work an average ball of all samples of motion block carrying out by schoolchildren with developmental delay was 1,41 point. While examining the position of reciprocal movements coordination (slow rate, disrupted evenness, modeling of both hands) very low characteristics (1,28 point) were found. After the corrective education an average ball of all samples of motion block carrying out by schoolchildren with developmental delay was 2,33. Discussion and Conclusions: the article deals with the structure of psychocorrective work on the development of motion sphere of younger schoolchildren with developmental delay. It includes numerous motion exercises on the development of general and articulate movements, finger exercises, exercises with eponymous and heteronymous cooperation of hands, legs, eye and tong. All the exercises contribute greatly to the reciprocal coordination formation. Every exercise is carried out under the clear rhythm of folklore texts. Folklore texts kept external rhythm to constantly repeated children motions and contributed to the general rhythm of brain structure. Poetical material with clear rhythmical structure had good influence on the children’s feeling. It generated poignant interest and positive emotions, didn’t stress during plural repetition, formed motivation for lessons, decreased emotional tension, contributed to the general activity. Rhythm and switching permitted children to learn how to simultaneously listen, remember and perform motions. These skills were successfully used by children during educational activity, when it was necessary to perform some actions simultaneously, for example, to write, to reflect rules, to remember sentences and etc. So rhythm of motions contributes to the development of subcortical structures of children’s brain, help adapt younger schoolchildren to the learning environment according to the curriculum.

PAGTANAW 2050 unraveled Science, Technology, and Innovation (STI) Talent Development and Retention (TDR) decision-making challenges and implementing them for its four clusters to contribute to the end goal of an archipelagic marine nation within evolving national and global systems. The goals of the proposed Foresight Institute (FI) are viewed through two management science frameworks, input-process-output-outcome (IPOO) and Kotter’s Leading Change model, with illustrative summary cases following six STI TDR steps. The approaches reflect the practical aspects of operationalizing efficiency, using experts, and empathy for people as the science itself adjusts to changing organizational environments. (i) Beginning with the end in mind, foresight-capable people for various roles must be lifelong learners (Outputs). Decision challenges of training (who, why, etc.) are analyzed with a data science use case on regional STI TDR supply-demand imbalance for high-skills future needs and a prospective information technology-business process management (IT/BPM) expansion into data-intensive markets to meet new challenges in climate change or information systems (Outcomes). (ii) The leadership and guiding coalitions (Inputs) need intangible ideas with science, technology, engineering, and mathematics (STEM) tools of emerging technologies like (AI) to transform people, e.g., the sense of urgency but patience for long-term foresight skills awareness, and the phronetic use of translational research for knowledge generation with multidisciplinary team for the overall good. (iii) Business Processes must consider where value is added highest in the IPOO, adjusting STI TDR activities to changing SWOT conditions - as shown in cases on process-induced learning in basic education, STEM retention through innovative first-year course design, and morphing problems in nursing STI. Foresight Institute failure may come from inputs/processes.

<div>Resumen:</div><div><br /></div><div>Una de las ramas en la que la enfermera puede</div><div>desarrollarse profesionalmente es la Enfermer&iacute;a</div><div>Industrial, esta se encarga de la prevenci&oacute;n y control</div><div>de la salud de los trabajadores en las empresas, e</div><div>identifica factores de riesgos que puedan ocasionar</div><div>accidentes fatales dentro de la misma.</div><div><br /></div><div>Dentro de la empresa Kromalabs S.A. de C.V. se</div><div>realizaron practicas de enfermer&iacute;a industrial en la</div><div>que se identificaron ciertas deficiencias y problemas</div><div>que nos parecieron importantes para la realizaci&oacute;n y</div><div>desarrollo de los programas preventivos, tales como</div><div>la elevada incidencia de trabajadores que asist&iacute;an</div><div>al consultorio por lumbalgias, se observaron malas</div><div>posturas y la rutina de trabajo implica movimientos</div><div>repetitivos; as&iacute; como las deficiencias con respecto</div><div>a se&ntilde;alizaciones de evacuaci&oacute;n, alarmas contra</div><div>incendios, ausencia de puntos de reuni&oacute;n, etc. Por esas</div><div>razones creamos los programas: &ldquo;Espalda saludable,</div><div>tranquilidad invaluable&rdquo; y &ldquo;Que no te hagan temblar</div><div>los sismos&rdquo;.</div><div><br /></div><div>Para el desarrollo de los programas, se planearon</div><div>diferentes actividades, como charlas para los</div><div>trabajadores en las que se informaban ejercicios</div><div>para la espalda, posturas correctas, etc. En caso del</div><div>programa de sismo se organizo un simulacro para</div><div>evaluar los conocimientos de los trabajadores acerca</div><div>de las acciones durante y despu&eacute;s de un sismo.</div><div><br /></div><div>Los resultados fueron favorables para ambos</div><div>programas, pues el personal se mostro interesado y</div><div>cooperativo en las actividades que se desarrollaron a</div><div>lo largo de la pr&aacute;ctica.</div><div><br /></div><div>Palabras clave:</div><div>Enfermer&iacute;a Industrial, Lumbalgia, Higiene de</div><div>Columna, Sismo, Simulacro.</div><div><br /></div><div><br /></div><div>Abstract:</div><div><br /></div><div>One of the branches in which the nurse can develop</div><div>professionally is the Industrial, this is responsible for</div><div>the prevention and control of the health of workers in</div><div>an enterprise, in addition to notice and identify risks</div><div>that can cause fatal accidents within the same.</div><div>Within the company Kromalabs S.A. de C.V. were</div><div>performed industrial nursing practices which</div><div>identified certain deficiencies and problems that</div><div>seemed important for the creation and development</div><div>of preventive programs, such as the high incidence</div><div>of workers attending the clinic for back pain, poor</div><div>posture were observed and routine moves work</div><div>involves repetitive and gaps regarding evacuation</div><div>signs, fire alarms, lack of meeting points, etc. for</div><div>these reasons we believe the programs: &ldquo;Healthy back,</div><div>invaluable peace of mind&rdquo; and &ldquo;Do not let earthquakes make you tremble".</div><div><br /></div><div>For program development will be planned activities,</div><div>including lectures for workers which reported back</div><div>exercises, correct posture, etc. If the program was</div><div>organized a mock earthquake to assess the skills and</div><div>knowledge gaps about the workers about the actions</div><div>during and after an earthquake.</div><div><br /></div><div>The results were favorable for both programs, as the</div><div>staff was interested and cooperative activities to be</div><div>developed over the practice.</div><div><br /></div><div>Key words:</div><div>Industrial Nursing, Backache, Column Hygiene,</div><div>Earthquakes, Mock.</div>

Background: Possibility of healthcare personnel to encounter occupational risks varies according to their profession, job and the department in which they work. Nursing is accepted as a stressful profession with work overload due to several negative factors (overwork, overtime and long working hours, role conict and ambiguity, problems with shift work etc.) arising from work circumstances. Healthcare workers are at a higher risk of developing low back pain due to a variety of factors. This problem is associated with major consequences in terms of disability and frequent absence. LBP might lead to activity limitation and sick leaves for more than 50 % of the nurses. This study aims to assess the prevalence and risk factors of LBP among nurses in a tertiary care center. 1. To determine the fre Objectives: quency of low back pain and associated factors among nurses working in a tertiary care hospital 2. To assess the level of functional disability due to low back pain. A cross-sectional study Methodology: was conducted on 125 nurses, aged between 25 and 60 years, who had been working for at least 1 year at CPR Hospital Kolhapur (Maharashtra). Both male and female staff nurses were included in the study. Those who were pregnant and who were not willing to participate were excluded from the study. A self-administered Oswestry Low Back Pain Disability questionnaire which was applied to obtain data from the respondents. Both descriptive and inferential statistics was used. The baseline characteristics were presented as mean with standard deviation or frequencies and percentages whichever appropriate. The determinants of low back pain and knowledge on body mechanics were found using Chi-square. P value <0.05 is considered signicant at 95% condence interval. In the present study, out Results: of 125 participants, 56% were aged 31 to 40 years. Mean age was 32.68±7.32 years. There was female preponderance with 82.4. 71.2% had LBP. Based on Oswestry LBP Disability (OLBPD) Score, 28.8% were found to be free from any disability, 50.4% had minimal, 18.4%) had moderate and only 3 nurses had severe disability. Association was signicant between higher age groups, history of caesarian (44.9%), no history of exercise (53.9%), designation of staff nurse (91.0%), physical exertion during work (92.1%), > 10 years of work experience (43.8%), attending >50 patients per day (22.5%), standing time > 5 hours in duty hours (82.0%) were found to be signicantly associated with LBP (all p values <0.05).

Introduction: Stroke rehabilitation and caregivers training is central to improve post stroke care and reduce caregivers’ burden. Mobile applications(app) may provide a patient and caregiver centric modality to improve stroke care Aim: To develop and evaluate feasibility of a medical application for delivering post stroke care. Methods: A mobile app was developed on an android operating system following a preliminary assessment of post stroke complications to train caregivers. App consists of videos of home based care strategies for bedsore prevention, feeding, mouth care, ROM exercises, catheter care, psychological support to patients etc. App includes awareness videos on stroke, problems faced after stroke, follow up schedule, feedback option. App feasibility was assessed among 25 bedridden stroke survivors and their caregivers selected purposely. App validation was done by 16 stroke experts including neurologists, nurses, psychologists, physiotherapists using semi-structured-questionnaire for data collection. Following this, final "Stroke Home Care" app was developed. Results Feasibility: Mean age of patients and caregivers was 52.6±14.8 and 32.4±8.9years, respectively. 64% patients females, 75% caregivers males. 56% lived in rural. Median NIHSS 14 (IQR: 12-17). Complications were 56% Ryle’s tube, 72% Foley’s catheter, 12% bedsore. 64% caregivers were graduates. 52% sons. All caregivers responded that app contents, videos and language was understandable and appropriate. 92% preferred ‘Hindi’ language. All agreed to App enhancing their stroke knowledge. All were satisfied. Validation: Mean age of experts was 33.2±4years. 75% females. 56% nursing experts and postgraduates,19% MDs. 50% Nursing teachers, 19% Neurology fellows. None faced any app installation problem. 81.3% experts highly satisfied with app functions, its contents, voice clarity, video clarity and duration, contents’ sequence, understandability. Discussion/Conclusion: “Stroke Home Care” App is feasible, pragmatic and user-friendly for use by caregivers of stroke survivors in a resource limited setting/developing country. It should be tested by an RCT to evaluate its efficacy in reducing post stroke complications and reducing caregivers’ burden.

Introduction The Micronesian and Pacific Islander community experiences adverse childhood experiences (ACEs) at rates higher than other ethnic groups. Exposure to ACEs increases the risk of negative outcomes, including heart disease, cancer, and psychosocial problems into adulthood. Early childhood learning (ECL) provides resilience against ACEs. However, Micronesian and Pacific Islander children reportedly have 53.8% not enrolled in ECL. Approach The purpose is to describe a creative community and academic collaboration approach, including culturally responsive partnership building exercises with inspirational reflections as a communication process between partners in the Micronesian Islander Community non-profit organization and Washington State University College of Nursing that led to the development of a culturally responsive, web-based, Micronesian Early Education Toolkit with Micronesian Islander Parent Leader Champions. We engaged a local school district to participate. Tenets of Popular Education guided partnership building. The Early Childhood Education Access Framework guided toolkit development and experiential improvement process. The toolkit includes both text and videos on what is ECL and importance, ECL program types, and navigation of the application process. We used a Plus/Delta evaluation. Findings Nine Parent Leader Champions representing Chamarro, Chuukese, Kapingamarangi, Marshallese, and Pohnpeian communities reported that the toolkit respects cultural values; easy to comprehend and navigate; the process makes it feasible to help enroll Micronesian Islander preschool students; and will be helpful at expanding access to ECL programs. Discussion The toolkit development and experiential improvement process centered the voice of Micronesian Islander Parent Leader Champions. This helped the toolkit to be interactive, clear with specific utility for diverse English-speaking levels, respectful language, and creativity on how families can start. Conclusion This creative community and academic collaboration approach, including Micronesian Islander Parent Leader Champions and engaging a local school district achieved development of a culturally responsive ECL toolkit that was a helpful foundation to begin ECL enrollment.

The relevance of the study is conditioned by many historical and modern aspects. In particular, by revealing the issues of creating an international organisation, it is possible to understand what functions the organisation had, and the purpose of the organisation's existence against the background of historical events and modernity. The purpose of the study is to highlight the prerequisites and history of the creation of the International organisation Group of Seven (also known as G7), to investigate the influence and significance of this organisation, both in the past and in the context of modern international relations. The scientific approach is based on methods of systematic analysis of other studies and publications, and analysis of documents, in particular, international treaties, memoranda, etc. In addition, historical and comparative, historical and system methods were used, which allowed determining the place of the organisation in the general historical process. The main results of scientific research should be considered the definition of both the prerequisites for the establishment of the Group of Seven and its results, namely: the activities and significance of the organisation, and the definition of the role of an international organisation in historical and modern contexts. Practical application of the results obtained in the course of research is possible as a tool for solving a number of both historiographical and political science problems. In particular, the study can help solve the problem of interstate relations between developed countries and developing countries, the problem of the political and economic unity of developed countries, the problem of relevance and loss of influence of Western countries, and the growth of influence of developing countries, the problem of the relevance of the G7 format and its replacement with the G20 format, etc.

Оқу-әдістемелік және ғылыми әдебиеттерді талдай отырып, зерттеушілер графикалық әдісті қолдана отырып, теңдеулер мен теңсіздіктерді шешудің әртүрлі әдістерін бөліп қарастырады, оларға сәйкес әрекеттерді тізімдейді, оларды қалыптастыру үшін жаттығулардың мысалдарын келтіреді деген қорытынды жасауға болады. Бірақ осы әдістің әрбір әрекетін үйрету үшін міндеттер жиынтығын әзірлеу және осы материалды зерттеу үшін ақпараттық технологияларды қолдану қазіргі мектеп біліміндегі өзекті мәселелердің бірі болып қала береді. Мақалада ғылыми және әдістемелік құралдарды талдау нәтижесінде теңдеулер мен теңсіздіктерді шешуде функциялардың қасиеттері қолданылатын жағдайлар анықталды. Мысал ретінде, графикалық әдісті қолдана отырып, теңдеулер мен теңсіздіктерді шешу әдістері білімнен дағдыларға ауысуға мүмкіндік береді, іс-әрекет тәсілдерін көрсетеді, бұл өз кезегінде талдау, синтез, жалпылау және т. б. сияқты ойлау әдістерін ашады деп есептейміз. «Теңсіздік» тақырыбы мектеп алгебрасы курсында маңызды орын алады. Ол мазмұны, теңсіздіктерді шешудің әдістері және алгебраның бірқатар басқа тақырыптарын зерттеуде қолдану мүмкіндіктері бойынша бай. Теңдеулер мен теңсіздіктер математиканың әртүрлі салаларында, маңызды қолданбалы есептерді шешуде кеңінен қолданылатындығы анықталған. Әр түрлі және күрделі теңсіздіктердің жауабын табу математикалық есептерді шеше білудің жоғары деңгейін көрсетеді. Теңсіздіктерді шешудің графикалық әдісі - тапсырмаларды орындаудың оңтайлы әдісі теңдеулер мен теңсіздіктерді шешу әдістерін меңгеру білімнен дағдыларға ауысуға мүмкіндік беретіні мысалдармен көрсетілген. Түйінсөздер: теңдеулер, теңсіздіктер, шешімдер, есептер, оқушылар, графикалық әдіс, алгоритм. Анализируя методическую и научную литературу, можно сделать вывод, что исследователи с помощью графического метода выделяют и рассматривают различные способы решения уравнений и неравенств, перечисляют соответствующие им действия, приводят примеры упражнений на их формирование. Но разработка комплекса заданий для обучения каждому виду деятельности метода и использование информационных технологий для изучения материала остаётся одним из наиболее актуальных вопросов в современном школьном образовании. В результате анализа научно-методического инструментария в статье выявлены ситуации, когда свойства функций используются при решении уравнений и неравенств. Считаем, что методы решения уравнений и неравенств графическим методом позволяют перейти от знаний к умениям, показывают способы действий, которые, в свою очередь, открывают такие способы мышления, как анализ, синтез, обобщение и т. д. Тема «Неравенство» занимает важное место в школьном курсе алгебры. Она богата содержанием, методами решения неравенств и приложениями при изучении ряда других разделов алгебры. Установлено, что уравнения и неравенства широко используются в различных областях математики, при решении важных прикладных задач. Нахождение ответа на разнообразные и сложные неравенства показывает высокий уровень решения математических задач. Графический метод решения неравенств является оптимальным способом выполнения заданий. На примерах показано, что овладение методами решения уравнений и неравенств позволяет перейти от знаний к навыкам. Ключевые слова: равенство, неравенства, решения, задачи, учащиеся, графический метод, алгоритм. Analyzing the methodological and scientific literature, we can conclude that researchers, using the graphical method, identify and consider various methods for solving equations and inequalities, list the actions corresponding to them, and give examples of exercises for their formation. But the development of a set of tasks for teaching each type of activity of the method and the use of information technology to study the material remains one of the most pressing issues in modern school education. As a result of the analysis of scientific and methodological tools, the article revealed situations when the properties of functions are used in solving equations and inequalities. We believe that the methods for solving equations and inequalities using a graphical method allow us to move from knowledge to skills, show ways of action, which, in turn, open up such ways of thinking as analysis, synthesis, generalization, etc. The topic "Inequality" occupies an important place in the school course of algebra. It is rich in content, methods for solving inequalities, and applications in the study of a number of other branches of algebra. It has been established that equations and inequalities are widely used in various areas of mathematics, in solving important applied problems. Finding the answer to various and complex inequalities shows a high level of solving mathematical problems. The graphical method for solving inequalities is the best way to complete tasks. The examples show that mastering the methods for solving equations and inequalities allows you to move from knowledge to skills. Keywords: equality, inequalities, solutions, tasks, students, graphical method, algorithm.

IntroductionThis article addresses the experience of designing and conducting life-writing workshops for a group of clients with severe mental illness; the aim of this pilot study was to begin to determine whether such writing about the self can aid in individual ‘recovery’, as that term is understood by contemporary health professionals. A considerable amount has been written about the potential of creative writing in mental health therapy; the authors of this article provide a brief summary of that literature, then of the concept of ‘recovery’ in a psychology and arts therapy context. There follows a first-hand account by one of the authors of being an arts therapy workshop facilitator in the role of a creative practitioner. This occurred in consultation with, and monitored by, experienced mental health professionals. Life-Writing as ‘Therapeutic’ Life-story or life-writing can be understood in this context as involving more than disclosure or oral expression of a subject’s ‘story’ as in psycho-therapy – life-story is understood as a written, structured narrative. In 2001, Wright and Chung published a review of the literature in which they claimed that writing therapy had been “restimulated by the development of narrative approaches” (278). Pennebaker argues that “catharsis or the venting of emotions” without “cognitive processing” has little therapeutic value and people need to “build a coherent narrative that explains some past experience” in order to benefit from writing” (Pennebaker, Telling Stories 10–11). It is claimed in the Clinical Psychology Review that life-writing has the therapeutic benefits of, for example, “striking physical health and behaviour change” (Esterling et al. 84). The reasons are still unclear, but it is possible that the cognitive and linguistic processing of problematic life-events through narrative writing may help the subject assimilate such problems (Alschuler 113–17). As Pennebaker and Seagal argue in the Journal of Clinical Psychology, the life-writing processallows one to organise and remember events in a coherent fashion while integrating thoughts and feelings ... This gives individuals a sense of predictability and control over their lives. Once an experience has structure and meaning, it would follow that the emotional effects of that experience are more manageable. (1243)It would seem reasonable to suggest that life-writing which constructs a positive recovery narrative can have a positive therapeutic effect, providing a sense of agency, connectedness and creativity, in a similar, integrating manner. Humans typically see their lives as stories. Paul Eakin stresses the link between narrative and identity in both this internal life-story and in outwardly constructed autobiography:narrative is not merely a literary form but a mode of phenomenological and cognitive self-experience, while self – the self of autobiographical discourse - does not necessarily precede its constitution in narrative. (Making Selves 100)So both a self-in-time and a socially viable identity may depend on such narrative. The term ‘dysnarrativia’ has been coined to describe the documented inability to construct self-narrative by those suffering amnesia, autism, severe child abuse or brain damage. The lack of ability to achieve narrative construction seems to be correlated with identity disorders (Eakin, Fictions in Autobiography 124). (For an overview of the current literature on creative and life-writing as therapy see Murphy & Neilsen). What is of particular relevance to university creative writing practitioners/teachers is that there is evidence, for example from Harvard psychiatrist Judith Herman and creative writing academic Vicki Linder, that life-narratives are more therapeutically effective if guided to be written according to fundamental ‘effective writing’ aesthetic conventions – such as having a regard to coherent structure in the narrative, the avoidance of cliché, practising the ‘demonstrate don’t state’ dictum, and writing in one’s own voice, for example. Defining ‘Recovery’There remains debate as to the meaning of recovery in the context of mental health service delivery, but there is agreement that recovery entails significantly more than symptom remission or functional improvement (Liberman & Kopelowicz). In a National Consensus Statement, the Substance Abuse and Mental Health Services Administration (SAMHSA) unit of the US Department of Health and Human Services in 2005 described recovery (in general terms) as being achieved by the enabling of a person with a mental illness to live meaningfully in a chosen community, while also attempting to realize individual potential. ‘Recovery’ as a central concept behind rehabilitation can be understood both as objective recovery – that is, in terms of noting a reduction in objective indicators of illness and disability (such as rates of hospital usage or unemployment) and a greater degree of social functioning – and also as subjective recovery. Subjective recovery can be ascertained by listening closely to what clients themselves have said about their own experiences. It has been pointed out (King, Lloyd & Meehan 2) that there is not always a correspondence between objective indicators of recovery and the subjective, lived experience of recovery. The experience of mental illness is not just one of symptoms and disability but equally importantly one of major challenge to sense of self. Equally, recovery from mental illness is experienced not just in terms of symptoms and disability but also as a recovery of sense of self … Recovery of sense of self and recovery with respect to symptoms and disability may not correspond. (King, Lloyd & Meehan; see also Davidson & Strauss)Symptoms of disability can persist, but a person can have a much stronger sense of self or empowerment – that is still recovery. Illness dislocates the sense of self as part of a community and of a self with skills and abilities. Restoring this sense of empowerment is an aim of arts therapy. To put it another way, recovery is a complex process by which a client with a mental illness develops a sense of identity and agency as a citizen, as distinct from identification with illness and disability and passivity as a ‘patient’. The creative arts have gone well beyond being seen as a diversion for the mentally ill. In a comprehensive UK study of creative arts projects for clients with mental illness, Helen Spandler et al. discovered strong evidence that participation in creative activity promoted a sense of purpose and meaning, and assisted in “rediscovering or rebuilding an identity within and beyond that of someone with mental health difficulties” (795). Recovery is aided by people being motivated to achieve self-confidence through mastery and competence; by learning and achieving goals. Clearly this is where arts therapy could be expected or hoped to be effective. The aim of the pilot study was not to measure ‘creativity’, but whether involvement in what is commonly understood as a creative process (life-writing) can have flow-on benefits in terms of the illness of the workshop participant. The psychologists involved, though more familiar with visual arts therapy (reasonably well-established in Australia – in 2006, the ANZAT began publishing the Australian and New Zealand Journal of Art Therapy), thought creative writing could also be valuable. Preparation for and Delivery of the Workshops I was acutely aware that I had no formal training in delivering a program to clients with mental health illness. I was counselled during several meetings with experienced psychologists and a social worker that the participants in the three workshops over two weeks would largely be people who had degrees of difficulty in living independently, and could well have perceptual problems, could misjudge signals from outside and inside the group, and be on medication that could affect their degree of engagement. Some clients could have impaired concentration and cognition, and a deficit in volition. Participants needed to be free to leave and rejoin the workshops during the afternoon sessions. Attendance might well fall as the workshops progressed. Full ethical clearance was attained though the University of Queensland medical faculty (after detailed description of the content and conduct of the proposed workshops) and consent forms prepared for participants. My original workshop ‘kit’ to be distributed to participants underwent some significant changes as I was counselled and prepared for the workshops. The major adjustment to my usual choice of material and approach was made in view of the advice that recounting traumatic events can have a negative effect on some patients – at least in the short term. For the sake of both the individuals and the group as a whole this was to be avoided. I changed my initial emphasis on encouraging participants to recount their traumatic experiences in a cathartic way (as suggested by the narrative psychology literature), to encouraging them to recount positive narratives from their lives – narratives of ‘recovery’ – as I explain in more detail below. I was also counselled that clients with mental health problems might dwell on retelling their story – their case history – rather than reflecting upon it or using their creative and imaginative ability to shape a life-story that was not a catalogue of their medical history. Some participants did demonstrate a desire to retell their medical history or narrative – including a recurring theme of the difficulty in gaining continuity with one trusted medical professional. I gently guided these participants back to fashioning a different and more creative narrative, with elements of scene creation, description and so on, by my first listening intently to and acknowledging their medical narrative for a few minutes and then suggesting we try to move beyond that. This simple strategy was largely successful; several participants commented explicitly that they were tired of having to retell their medical history to each new health professional they encountered in the hospital system, for example. My principal uncertainty was whether I should conduct the workshops at the same level of complexity that I had in the past with groups of university students or community groups. While in both of those cohorts there will often be some participants with mental health issues, for the most part this possibility does not affect the level or kind of content of material discussed in workshops. However, within this pilot group all had been diagnosed with moderate to severe mental illness, mostly schizophrenia, but also bipolar disorder and acute depression and anxiety disorders. The fact that my credentials were only as a published writer and teacher of creative writing, not as a health professional, was also a strong concern to me. But the clients readily accepted me as someone who knew the difficulty of writing well and getting published. I stressed to them that my primary aim was to teach effective creative writing as an end in itself. That it might be beneficial in health terms was secondary. It was a health professional who introduced me and briefly outlined the research aims of the workshop – including some attempt to measure qualitatively any possible benefits. It was my impression that the participants did not have a diminished sense of my usefulness because I was not a health professional. Their focus was on having the opportunity to practice creative writing and/or participate in a creative group activity. As mentioned above, I had prepared a workshop ‘kit’ for the participants of 15 pages. It contained the usual guidelines for effective writing – extracts from professional writers’ published work (including an extract from my own published work – a matter of equity, since they were allowing me to read their work), and a number of writing exercises (using description, concrete and abstract words, narrative point of view, writing in scenes, show don’t tell). The kit contained extracts from memoirs by Hugh Lunn and Bill Bryson, as well as a descriptive passage from Charles Dickens. An extract from Inga Clendinnen’s 2006 account in Agamemnon’s Kiss: selected essays of her positive interaction with fellow cancer patients (a narrative with the underlying theme of recovery) was also valuable for the participants. I stressed to the group that this material was very similar to that used with beginning writers among university students. I described the importance of life-writing as follows: Life-writing is simply telling a story from your life and perhaps musing or commenting on it at the same time. When you write a short account of something chosen from your life, you are making a pattern, using your memory, using your powers of description – you are being creative. You are being a story-teller. And story-telling is one very important thing that makes us humans different from all other animals – and it is a way in which we find a lot of meaning in our lives.My central advice in the kit was: “Just try to be as honest as you can – and to remember as well as you can … being honest and direct is both the best and the easiest way to write memoir”. The only major difference between my approach with these clients and that with a university class was in the selection of possible topics offered. In keeping with the advice of the psychologists who were experts in the theory of ‘recovery’, the topics were predominantly positive, though one or two topics gave the opportunity to recount and/or explore a negative experience if the participant wanted to do so: A time when I was able to help another personA time when I realised what really mattered in lifeA time when I overcame a major difficultyA time when I felt part of a group or teamA time when I knew what I wanted to do with my lifeA time when someone recognised a talent or quality of mineA time I did something that I was proud of A time when I learned something important to meA memorable time when I lived in a certain house or suburbA story that begins: “Looking back, I now understand that …”The group expressed satisfaction with these topics, though they had the usual writing students’ difficulty in choosing the one that best suited them. In the first two workshops we worked our way through the kit; in the third workshop, two weeks later, each participant read their own work to the group and received feedback from their peers and me. The feedback was encouraged to be positive and constructive, and the group spontaneously adopted a positive reinforcement approach, applauding each piece of writing. Workshop DynamicsThe venue for the workshops was a suburban house in the Logan area of Brisbane used as a drop-in centre for those with mental illness, and the majority of the participants would be familiar with it. It had a large, breezy deck on which a round-table configuration of seating was arranged. This veranda-type setting was sheltered enough to enable all to be heard easily and formal enough to emphasise a learning event was taking place; but it was also open enough to encourage a relaxed atmosphere. The week before the first workshop I visited the house to have lunch with a number of the participants. This gave me a sense of some of the participants’ personalities and degree of engagement, the way they related to each other, and in turn enabled them to begin to have some familiarity with me and ask questions. As a novice at working with this kind of client, I found this experience extremely valuable, especially as it suggested that a relatively high degree of communication and cognition would be possible, and it reduced the anxiety I had about pitching the workshops at an appropriate level. In the course of the first workshop, the most initially sceptical workshop participant ended up being the most engaged contributor. A highly intelligent woman, she felt it would be too upsetting to write about negative events, but ultimately wrote a very effective piece about the empowerment she gained from caring for a stray cat and locating the owner. Her narrative also expressed her realisation that the pet was partly a replacement for spending time with her son, who lived interstate. Another strong participant previously had written a book-length narrative of her years of misdiagnoses and trauma in the hospital system before coming under the care of her present health professionals. The participant who had the least literacy skills was accepted by the group as an equal and after a while contributed enthusiastically. Though he refused to sign the consent form at the outset, he asked to do so at the close of the first afternoon. The workshop was comprised of clients from two health provider organisations; at first the two groups tended to speak with those they already knew (as in any such situation in the broader community), but by the third workshop a sense of larger group identity was being manifested in their comments, as they spoke of what ‘the group’ would like in the future – such as their work being published in some form. It was clear that, as in a university setting, part of the beneficial effect of the workshops came from group and face to face interaction. It would be more difficult to have this dimension of benefit achieved via a web-based version of the workshops, though a chat room scenario would presumably go some way towards establishing a group feeling. Web-based delivery would certainly suit participants who lacked mobility or who lived in the regions. Clearly the Internet is a vital social networking tool, and an Internet-based version of the workshops could well be attempted in the future. My own previous experience of community digital storytelling workshops (Neilsen, Digital Storytelling as Life-writing) suggests that a high degree of technical proficiency can not be expected across such a cohort; but with adequate technical support, a program (the usual short, self-written script, recorded voice-over and still images scanned from the participants’ photo albums, etc) could make digital storytelling a further dimension of therapeutic life-writing for clients with mental illness. One of the most useful teaching techniques in a class room setting is the judicious use of humour – to create a sense of sharing a perspective, and simply to make material more entertaining. I tested the waters at the outset by referring to the mental health worker sitting in the background, and declaring (with some comic exaggeration) my concern that if I didn’t run the workshop well he would report adversely on me. There was general laughter and this expression of my vulnerability seemed to defuse anxiety on the part of some participants. As the workshop progressed I found I could use both humorous extracts of life-writing and ad hoc comic comments (never at the expense of a participant) as freely as in a university class. Participants made some droll comments in the overall context of encouraging one another in their contributions, both oral and written. Only one participant exhibited some temporary distress during one of the workshops. I was allowing another participant the freedom to digress from the main topic and the participant beside me displayed agitation and sharply demanded we get back to the point. I apologised and acknowledged I had not stayed as focused as I should and returned to the topic. I suspect I had a fortunate first experience of such arts therapy workshops – and that this was largely due to the voluntary nature of the study and that most of the participants brought a prior positive experience of the workshop scenario, and prior interest in creative writing, to the workshops. Outcomes A significantly positive outcome was that only one of the nine participants missed a session (through ill-health) and none left during workshops. The workshops tended to proceed longer than the three hours allotted on each occasion. Post-workshop interviews were conducted by a psychologist with the participants. Detailed data is not available yet – but there was a clear indication by almost all participants that they felt the workshops were beneficial and that they would like to participate in further workshops. All but one agreed to have their life-writing included in a newsletter produced by one of the sponsors of the workshops. The positive reception of the workshops by the participants has encouraged planning to be undertaken for a wide-ranging longitudinal study by means of a significant number of workshops in both life-writing and visual arts in more than one city, conducted by a team of health professionals and creative practitioners – this time with sophisticated measurement instruments to gauge the effectiveness of art therapy in aiding ‘recovery’. Small as the workshop group was, the pilot study seems to validate previous research in the UK and US as we have summarised above. The indications are that significant elements of recovery (in particular, feelings of enhanced agency and creativity), can be achieved by life-writing workshops that are guided by creative practitioners; and that it is the process of narrative construction within life-writing that engages with or enhances a sense of self and identity. NoteWe are indebted, in making the summary of the concept of ‘recovery’ in health science terms, to work in progress by the following research team: Robert King, Tom O'Brien and Claire Edwards (School of Medicine, University of Queensland), Margot Schofield and Patricia Fenner (School of Public Health, Latrobe University). We are also grateful for the generous assistance of both this group and Seiji Humphries from the Richmond Queensland Fellowship, in providing preparation for the workshops. ReferencesAlschuler, Mari. “Lifestories – Biography and Autobiography as Healing Tools for Adults with Mental Illness.” Journal of Poetry Therapy 11.2 (1997): 113–17.Davidson, Larry and John Strauss. “Sense of Self in Recovery from Severe Mental Illness.” British Journal of Medical Psychology 65 (1992): 31–45.Eakin, Paul. Fictions in Autobiography: Studies of the Art of Self-Invention. Princeton: Princeton UP, 1985.———. How Our Lives Become Stories: Making Selves. Ithaca: Cornell UP, 1999.Esterling, B.A., L. L’Abate., E.J. Murray, and J.W. Pennebaker. “Empirical Foundations for Writing in Prevention and Psychotherapy: Mental and Physical Health Outcomes.” Clinical Psychology Review 19.1 (1999): 79–96.Herman, Judith. Trauma and Recovery: The Aftermath of Violence - from Domestic Abuse to Political Terror. New York: Basic Books, 1992.King, Robert, Chris Lloyd, and Tom Meehan. Handbook of Psychosocial Rehabilitation. Oxford: Blackwell Publishing, 2007.Liberman, Robert, and Alex Kopelowicz. “Recovery from Schizophrenia: A Criterion-Based Definition.” In Ralph, R., and P. Corrigan (eds). Recovery in Mental Illness: Broadening Our Understanding of Wellness. 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