Teaching and Learning of Calculus

This survey focuses on the main trends in the field of calculus education. Despite their variety, the findings reveal a cornerstone issue that is strongly linked to the formalism of calculus concepts and to the difficulties it generates in the learning and teaching process. As a complement to the main text, an extended bibliography with some of the most important references on this topic is included. Since the diversity of the research in the field makes it difficult to produce an exhaustive state-of-the-art summary, the authors discuss recent developments that go beyond this survey and put forward new research questions

Research on Teaching and Learning Mathematics at the Tertiary Level:State-of-the-art and Looking Ahead

This topical survey focuses on research in tertiary mathematics education, a field that has experienced considerable growth over the last 10 years. Drawing on the most recent journal publication as well as the latest advances from recent high quality conference proceedings, our review culls out the following five emergent areas of interest: mathematics teaching at the tertiary level; the role of mathematics in other disciplines; textbooks, assessment and students’ studying practices; transition to the tertiary level; and theoretical-methodological advances. We conclude the survey with a discussion of some potential ways forward for future research in this new and rapidly developing domain of inquiry

Leadership, staffing and quality of care in nursing homes

<p>Abstract</p> <p>Background</p> <p>Leadership and staffing are recognised as important factors for quality of care. This study examines the effects of ward leaders' task- and relationship-oriented leadership styles, staffing levels, ratio of registered nurses and ratio of unlicensed staff on three independent measures of quality of care.</p> <p>Methods</p> <p>A cross-sectional survey of forty nursing home wards throughout Norway was used to collect the data. Five sources of data were utilised: self-report questionnaires to 444 employees, interviews with and questionnaires to 13 nursing home directors and 40 ward managers, telephone interviews with 378 relatives and 900 hours of field observations. Separate multi-level analyses were conducted for quality of care assessed by relatives, staff and field observations respectively.</p> <p>Results</p> <p>Task-oriented leadership style had a significant positive relationship with two of the three quality of care indexes. In contrast, relationship-oriented leadership style was not significantly related to any of the indexes. The lack of significant effect for relationship-oriented leadership style was due to a strong correlation between the two leadership styles (<it>r </it>= 0.78). Staffing levels and ratio of registered nurses were not significantly related to any of the quality of care indexes. The ratio of unlicensed staff, however, showed a significant negative relationship to quality as assessed by relatives and field observations, but not to quality as assessed by staff.</p> <p>Conclusions</p> <p>Leaders in nursing homes should focus on active leadership and particularly task-oriented behaviour like structure, coordination, clarifying of staff roles and monitoring of operations to increase quality of care. Furthermore, nursing homes should minimize use of unlicensed staff and address factors related to high ratios of unlicensed staff, like low staff stability. The study indicates, however, that the relationship between staffing levels, ratio of registered nurses and quality of care is complex. Increasing staffing levels or the ratio of registered nurses alone is not likely sufficient for increasing quality of care.</p

Lesson study in mathematics with TDS and RME as theoretical support: two cases from the European TIME project

Purpose: The authors investigate the use and potential of a theoretical combination of Realistic Mathematics Education (RME) and the Theory of Didactic Situation (TDS) to support Lesson Study (LS) in upper secondary mathematics. Design/methodology/approach: Case study performed by university researchers, based on theoretical analysis and case studies based on documents and observation from lesson studies. Findings: Even within a project lasting just about three years, teachers (with no preliminary experience of lesson study) engaged in lesson design based on the combination of theoretical perspectives from TDS and RME in ways that confirm the potential of that combination to enrich and focus teachers' professional development within the framework of LS. It is not clear to what extent the intensive and continued engagement of university researchers has been or would be essential for similar and longitudinal realizations of these potentials. Practical implications: As current European frameworks seek to engage researchers and teachers in collaboration and exchange across countries, networking of major paradigms of research (like TDS and RME) and uses of them as supports for teachers' inquiry (like demonstrated in this paper) is of considerable institutional interest and potential impact on schools. Social implications: Teachers' Inquiry in Mathematics Education (TIME) is a prerequisite for the development of Inquiry Based Mathematics Education, which in turn is required in many countries across the world, with the aim of fostering critical and competent citizens. Originality/value: This combination of (major) mathematics education theories to support and enrich LS has not previously been investigated. While several aspects of adapting to LS Western contexts have been investigated in the past, including the inclusion of perspectives and tools from academic research, the role of university researchers is also quite open. While authors do not offer a systematic study of this role, authors examine how this role may involve development of new practical combinations of different, complementary theoretical tools, which indeed hold potential to support lesson study in a European context