Real-World Modelling to Increase Mathematical Creativity

Modelling could be characterised as one of the core activities in mathematics education. However, when learning and teaching mathematics, mathematical modelling is mostly used to apply and deepen mathematical knowledge and competencies. Our educational study aims to explore how mathematical modelling, using real objects and high-quality mathematical technologies, could be utilised to acquire mathematical knowledge and competencies, and how learners could creatively use their existing knowledge. To discover the potential of mathematical modelling using real objects and high-quality mathematical technologies to acquire mathematical knowledge and competencies, and to stimulate learners\u27 creativity, first, we combined cognitive and creative spirals and mathematical modelling cycles. Then, in a case study, we tested this combination of cognitive and creative spirals and mathematical modelling cycles in a secondary school and teacher education. Applying the combination of cognitive and creative spirals and mathematical modelling cycles, we discovered that it could be collaboration among learners and technological knowledge and skills of learners that determine whether knowledge can be acquired in mathematical modelling

Towards Flipped Learning in Upper Secondary Mathematics Education

Challenges for students in the 21st century, such as acquiring technology, problem-solving, and cooperation skills, also necessitate changes in mathematics education to be able to respond to changing educational needs. One way to respond to these challenges is by utilizing recent educational innovations in schools, for instance, among others are flipped learning (FL) approaches. In this paper, we outline our explorative educational experiment that investigates vital elements of mathematics learning in FL approaches in upper secondary education. We describe the methodologies and findings of our qualitative study based on design-based research to discover key elements of FL approaches in upper secondary education. Analyzing the oral and written data collected over ten months using grounded theory approaches suggested categories (a) confidence when learning; (b) learning by working, and, and (c) flexibility when learning could be essential to understand FL approaches practices in mathematics classrooms. These categories indicate that when using FL approaches in mathematics learning, it could be essential for students to acquire knowledge in a confident and adaptable environment actively

Die Verebnung der Welt

Die folgende Arbeit setzt sich mit dem fächerübergreifenden Unterricht der Unterrichtsgegenstände Mathematik sowie Geographie und Wirtschaftskunde auseinander. Das erste Kapitel soll die Vorteile und Vorzüge des fächerübergreifenden Unterrichts hervor streichen, jedoch auch die Herausforderungen beleuchten, welche damit verbunden sind. Es wird hierin beschrieben, welchen Mehrwert die schulische Behandlung eines konkreten Problems hat, wenn man sich jenem aus unterschiedlichen Richtungen nähert. Das zweite Kapitel soll das Vorurteil brechen, dass Mathematik nur in Verbindung mit Physik oder Chemie fächerübergreifend unterrichtet werden kann. Meines Erachtens ist es möglich, dass man jedes Unterrichtsfach in Verbindung mit Mathematik fächerübergreifend lehrt – was am Beispiel der Geographie und Wirtschaftskunde gezeigt wird. Den Kern dieserArbeit bildet das Kapitel drei. Darin soll gezeigt werden, welche Teile der nichteuklidischen Geometrie mit den Schülerinnen und Schülern behandelt werden könnten und dass diese gewissen Aspekte jenes Teilgebiets der Mathematik auch selbständig erarbeitet werden können. Weiters soll verdeutlicht werden, dass die Möglichkeiten, ein reales Problem mathematisch darzustellen, begrenzt ist und dass man hiervon öfter im Alltag betroffen ist als man unter Umständen glaubt. Die Hauptaufgabe der „Kartographie in Wahlpflichtfach Mathematik“ ist jedoch den Schülerinnen und Schülern das mathematische Argumentieren und Schlussfolgern näher zu bringen und somit die Lernenden in die mathematische Denkweise einzuführen. Der letzte Abschnitt dieser Arbeit soll zeigen, wie einfach man die Geographie und Wirtschaftskunde in den Mathematikunterricht integrieren und jenen dadurch mit noch mehr Leben füllen kann

The Effect of Cabri Express in Geometry Learning on Students' Mathematical Communication Ability

Cabri is characterized by an attractive advantage and provides wide-ranging benefits in the teaching of mathematics. Although today there have been many studies on the edges of Cabri, experiments on Cabri-Express have not been widely explored. For this reason, a quasi-experimental study with a randomized posttest only design involving 80 grade VII junior high school students in Ruteng, Indonesia, was conducted to analyze the effect of Cabri-Express in learning geometry on students' overall mathematical communication ability (MCA) and based on students' initial mathematical abilities. The results of the MCA test are the research data, which consists of 5 questions that are then analyzed by t-test and preceded by conducting an analysis prerequisite test. The Hedges equation describes how much influence the Cabri-Express model has on students' MCA. The results showed that the overall MCA of students who were taught using the help of an Cabri-Express was better than students who were taught using the conventional model. From the Hedges equation, an effect size of 1.23 is obtained, indicating that the use of Cabri-Expresses strongly affects students' MCA. These results interpret that students who are ranked 13th in the experimental class are equivalent to those who are ranked 5th in the control class. By clarifying the effect of Cabri-Express on students' MCA, this study recommends the need to use Cabri-Express in mathematics classes. The analysis results can also help researchers explore other material in a relatable context

Analysis of students' thinking level in solving Pythagoras' theorem problems based on Van hiele's theory

The aims of this analysis are to explain the level of thinking of grade VIII students at SMP Negeri 1 Talang Ubi in solving Pythagorean Theorem questions based on Van Hiele's theory. The research approach used in this analysis is descriptive qualitative case study research. The subjects of this research were three students of grade VIII of SMP Negeri 1 Talang Ubi, South Sumatera Indonesia. The three students were chosen based on their test answers on the Pythagorean Theorem material, with one being a high-ability student, one being a medium-ability student, and one being a low-ability student. The study's data collection techniques included assessments, interviews, and documentation. Techniques for data processing include data reduction, data presentation, and conclusion. The findings revealed that high-ability students could complete all four stages of Van Hiele's thinking: imagination, interpretation, informal deduction, and deduction. Moderate students achieved three levels of Van Hiele's thinking, including visualization, analysis, and informal deduction, while low-ability students achieved only one level of Van Hiele's thinking, visualization

Technology-enhanced Flipped Mathematics Education in Secondary Schools: A Synopsis of Theory and Practice

This article focuses on the technology-supported Flipped Classroom Approach (FCA) in Mathematics education and how this form of teaching and learning can be implemented in secondary schools. In the German-speaking countries in particular, research on the FCA focuses on the individual components of this form of education and how this approach can be used and implemented in tertiary education. Our research contributions to the scholastic and practical application of the FCA in Mathematics still show gaps, which should be reduced with this work. In addition, the new possibilities that can arise in a flipped classroom setting through the targeted use of modern educational technologies will be highlighted. The findings and contents of this article can also be used as a support for teachers who would like to design and conduct their mathematics lessons in the near future according to the Flipped Classroom Approach

Early detection and intervention using neutrophil gelatinase-associated lipocalin (NGAL) may improve renal outcome of acute contrast media induced nephropathy: A randomized controlled trial in patients undergoing intra-arterial angiography (ANTI-CIN Study)

<p>Abstract</p> <p>Background</p> <p>Patients with pre-existing impaired renal function are prone to develop acute contrast media induced nephropathy (CIN). Neutrophil gelatinase-associated lipocalin (NGAL), a new biomarker predictive for acute kidney injury (AKI), has been shown to be useful for earlier diagnosis of CIN; however, urinary NGAL values may be markedly increased in chronic renal failure at baseline. Results from those studies suggested that urinary NGAL values may not be helpful for the clinician. An intravenous volume load is a widely accepted prophylactic measure and possibly a reasonable intervention to prevent deterioration of renal function. The aim of our study is to evaluate NGAL as an early predictor of CIN and to investigate the clinical benefit of early post-procedural i.v. hydration.</p> <p>Methods/Design</p> <p>The study will follow a prospective, open-label, randomized controlled design. Patients requiring intra-arterial contrast media (CM) application will be included and receive standardized, weight-based, intravenous hydration before investigation. Subjects with markedly increased urinary NGAL values after CM application will be randomized into one of two study groups. Group A will receive 3-4 ml/kg BW/h 0.9% saline intravenously for 6 hours. Group B will undergo only standard treatment consisting of unrestricted oral fluid intake. The primary outcome measure will be CIN defined by an increase greater than 25% of baseline serum creatinine. Secondary outcomes will include urinary NGAL values, cystatin C values, contrast media associated changes in cardiac parameters such as NT-pro-BNP/troponin T, changes in urinary cytology, need for renal replacement treatment, length of stay in hospital and death.</p> <p>We assume that 20% of the included patients will show a definite rise in urinary NGAL. Prospective statistical power calculations indicate that the study will have 80% statistical power to detect a clinically significant decrease of CIN of 40% in the treatment arm if 1200 patients are recruited into the study.</p> <p>Discussion</p> <p>A volume expansion strategy showing a benefit from earlier intervention for patients with markedly elevated urinary NGAL values, indicating a CIN, might arise from data from this study.</p> <p>Trial registration</p> <p>ClinicalTrials.gov <a href="http://www.clinicaltrials.gov/ct2/show/NCT01292317">NCT01292317</a></p

Developing and Evaluating Educational Innovations for STEAM Education in Rapidly Changing Digital Technology Environments

In this paper, we offer three examples from our research projects on both technological and pedagogical innovations to illustrate the impact of rapid technology changes on research. Members of our research team both developed and used technology applications in their research projects, utilizing design-based research (DBR). During the experiments, we encountered new challenges by the end of the research cycle due to updates in technologies. Although we had an idea of how to redesign the project for the next cycle based on the analyses of data, we noticed that we needed to not only redesign our approaches based on the research results but the changes in technologies were so rapid that materials and pedagogies needed to be altered as well. In our article, we propose an additional aspect to be considered in DBR while researching technology integration or innovative technologies. Moreover, the rapid change in technology raises further challenges to teachers’ professional development and the integration of those innovative technologies in classrooms. We anticipate our work to contribute to the development of technology resources and related pedagogies as well as the refinement of research methodologies in technology environments. Our contributions for the development of technology resources and refinement of research methods in technology-supported learning environments should, among other things, contribute to a less complex and at the same time more sustainable integration of pedagogical innovations into scientific and school practices

Comparative mortality of hemodialysis patients at for-profit and not-for-profit dialysis facilities in the United States, 1998 to 2003: A retrospective analysis

<p>Abstract</p> <p>Background</p> <p>Concern lingers that dialysis therapy at for-profit (versus not-for-profit) hemodialysis facilities in the United States may be associated with higher mortality, even though 4 of every 5 contemporary dialysis patients receive therapy in such a setting.</p> <p>Methods</p> <p>Our primary objective was to compare the mortality hazards of patients initiating hemodialysis at for-profit and not-for-profit centers in the United States between 1998 and 2003. For-profit status of dialysis facilities was determined after subjects received 6 months of dialysis therapy, and mean follow-up was 1.7 years.</p> <p>Results</p> <p>Of the study population (<it>N </it>= 205,076), 79.9% were dialyzed in for-profit facilities after 6 months of dialysis therapy. Dialysis at for-profit facilities was associated with higher urea reduction ratios, hemoglobin levels (including levels above 12 and 13 g/dL [120 and 130 g/L]), epoetin doses, and use of intravenous iron, and less use of blood transfusions and lower proportions of patients on the transplant waiting-list (<it>P </it>< 0.05). Patients dialyzed at for-profit and at not-for-profit facilities had similar mortality risks (adjusted hazards ratio 1.02, 95% CI 0.99–1.06, <it>P </it>= 0.143).</p> <p>Conclusion</p> <p>While hemodialysis treatment at for-profit and not-for-profit dialysis facilities is associated with different patterns of clinical benchmark achievement, mortality rates are similar.</p

Flipped approaches in secondary mathematics education

New technologies are increasingly influencing everyday life of young people in Western countries. In mathematics education, it is above all the Matura (school leaving examination) which has been influenced in Austria for some years by the mandatory use of technologies. For innovations, such as utilising modern educational technologies, to be integrated into school learning, modern pedagogics and didactics are required in addition to adequate hardware equipment in schools. One of the new educational approaches that could combine school-based learning and using technologies is flipped education. There are a variety of possibilities to disseminate new educational approaches combined with utilising modern technologies in education. In my PhD research, I have dealt with professional mathematics teacher development as well as with teacher pioneers as ways to disseminate new educational approaches and using modern technologies in mathematics education. For this purpose, I collected data from teacher trainers, scientists, teachers, and students for 16 months. The collected data was analysed using a mix of qualitative research methodologies and methods and insights gained in this process were continuously integrated into the research and instructional design of my PhD studies. This qualitative investigation in flipped education indicated that in professional math teacher development for flipped approaches the categories (a) Participants in a PTD course, (b) Administrative requirements and frameworks, (c) Generating take-homes in PTD courses, and (d) Active learning through concrete examples could be vital. With regard to further developing flipped approaches, the qualitative analysis demonstrated that the categories (a) Self-confidence and self-efficacy when learning, (b) A variety of classroom formats of learning, (c) Developing knowledge and competencies, and (d) Students are empowered to make decisions could be central.eingereicht von Robert WeinhandlJohannes Kepler Universität Linz, Dissertation, 2019OeBB(VLID)455519