Demonstração de fórmulas matemáticas no ensino médio

The objective of this study is to analyze the validity of working with proofs in the classroom and to present a partial list of proofs of mathematical formulae of the Brazilian secondary/high school curriculum. The adaptation of the proofs into the knowledge and abilities of a secondary school student should also be considered. How the teaching of proofs is treated in official publications in Brazil and other countries is also described. Working with proofs provides a number of benefits to the students, including: the development of logical reasoning, argumentative capacity, analytical skills on a daily basis, as well as motivation and a better understanding of mathematics as a science. The convenience of including the teaching of proofs in Brazilian secondary school curriculum and the need of a balance between the abstraction of proofs and contextualization of the school programmes is discussed. The approach of the proof teaching in the classroom can become a motivating factor or, conversely, a discouraging one. The conclusion is that it would be very useful to create a reference list covering the mathematical expressions of school programmes with their respective proofs that can be understood by secondary school students.

A case study of teachers' mathematics content knowledge and attitudes toward mathematics and teaching

This study intended to measure teacher mathematical content knowledge both before and after the first year of teaching and taking graduate teacher education courses in the Teach for America (TFA) program, as well as measure attitudes toward mathematics and teaching both before and after TFA teachers’ first year. There was a significant increase in both mathematical content knowledge and attitudes toward mathematics over the TFA teachers’ first year teaching. Additionally, several significant correlations were found between attitudes toward mathematics and content knowledge. Finally, after a year of teaching, TFA teachers had significantly better attitudes toward mathematics and teaching than neutral.

Integrating concrete and virtual materials in an elementary mathematics classroom : a case study of success with fractions

This paper describes an approach to introducing fraction concepts using generic software tools such as Microsoft Office's PowerPoint to create "virtual" materials for mathematics teaching and learning. This approach replicates existing concrete materials and integrates virtual materials with current non-computer methods of teaching primary students about fractions. The paper reports a case study of a 12-year-old student, Frank, who had an extremely limited understanding of fractions. Frank also lacked motivation for learning mathematics in general and interacted with his peers in a negative way during mathematics lessons. In just one classroom session involving the seamless integration of off-computer and on-computer activities, Frank acquired a basic understanding of simple common equivalent fractions. Further, he was observed as the session progressed to be an enthusiastic learner who offered to share his learning with his peers. The study's "virtual replication" approach for fractions involves the manipulation of concrete materials (folding paper regions) alongside the manipulation of their virtual equivalent (shading screen regions). As researchers have pointed out, the emergence of new technologies does not mean old technologies become redundant. Learning technologies have not replaced print and oral language or basic mathematical understanding. Instead, they are modifying, reshaping, and blending the ways in which humankind speaks, reads, writes, and works mathematically. Constructivist theories of learning and teaching argue that mathematics understanding is developed from concrete to pictorial to abstract and that, ultimately, mathematics learning and teaching is about refinement and expression of ideas and concepts. Therefore, by seamlessly integrating the use of concrete materials and virtual materials generated by computer software applications, an opportunity arises to enhance the teaching and learning value of both materials.

Mathematics knowledge for teaching and the classroom environment

This study investigated the classroom environment in an underperforming mathematics classroom. The objectives were: (1) to investigate the classroom environment and identify influences upon it, and (2) to further explore those influences (i.e., teacher knowledge). This was completed using a diachronic case study approach in which data were gathered during lesson observations and coaching sessions. These data were analysed to describe and exemplify the classroom environment, then further described against forms of teacher knowledge. Conjectures regarding the importance of teacher knowledge of content were made which formed a base for developing a model of teacher planning and pedagogy.

Developing mathematics understanding and abstraction : the case of equivalence in the elementary years

Generalising arithmetic structures is seen as a key to developing algebraic understanding. Many adolescent students begin secondary school with a poor understanding of the structure of arithmetic. This paper presents a theory for a teaching/learning trajectory designed to build mathematical understanding and abstraction in the elementary school context. The particular focus is on the use of models and representations to construct an understanding of equivalence. The results of a longitudinal intervention study with five elementary schools, following 220 students as they progressed from Year 2 to Year 6, informed the development of this theory. Data were gathered from multiple sources including interviews, videos of classroom teaching, and pre-and post-tests. Data reduction resulted in the development of nine conjectures representing a growth in integration of models and representations. These conjectures formed the basis of the theory.

It really is black and white when you look at it like this : reporting on a study into Australian professors' research and teaching priorities

Despite optimistic claims about the research-teaching nexus, Australian academics still face tension between research and teaching. The teaching and research priorities, beliefs and behaviours of 70 Professorial and Associate Professorial academics in Science, Information Technology and Engineering were examined in this study. The academics from 4 faculties in 3 Australian universities, were asked to rank 16 research activities and 16 matched learning and teaching (L&T) activities from each of three perspectives: job satisfaction, leadership behaviour, and perceptions of professional importance. The findings, which were remarkably consistent across the three universities, were unequivocally in favour of Research. The only L&T activity that was ranked consistently well was “Improving student satisfaction ratings for Teaching”. The data demonstrates that Australian government and university initiatives to raise the status of L&T activity are not impacting significantly on Australia’s future leaders of university learning.

Research and/or learning and teaching : a study of Australian professors' priorities, beliefs and behaviours

This paper presents findings from an empirical study of key aspects of the teaching and research priorities, beliefs and behaviours of 72 professorial and associate professorial academics in Science, Information Technology and Engineering across four faculties in three Australian universities. The academics ranked 16 research activities and 16 matched learning and teaching (L&T) activities from three perspectives: job satisfaction, role model behaviour and perceptions of professional importance. The findings were unequivocally in favour of research in all three areas and remarkably consistent across the universities. The only L&T activity that was ranked consistently well was 'improving student satisfaction ratings for teaching', an area in which academics are increasingly held accountable. Respondents also indicated that their seniors encourage research efforts more than L&T efforts. Recommendations include that higher education rewards for quality L&T are maintained or improved and that recognition of L&T research domains is further strengthened.

The WIL (Work Integrated Learning) Report : A national scoping study [Australian Learning and Teaching Council (ALTC) Final report]

This report provides an account of the first large-scale scoping study of work integrated learning (WIL) in contemporary Australian higher education. The explicit aim of the project was to identify issues and map a broad and growing picture of WIL across Australia and to identify ways of improving the student learning experience in relation to WIL. The project was undertaken in response to high levels of interest in WIL, which is seen by universities both as a valid pedagogy and as a means to respond to demands by employers for work-ready graduates, and demands by students for employable knowledge and skills. Over a period of eight months of rapid data collection, 35 universities and almost 600 participants contributed to the project. Participants consistently reported the positive benefits of WIL and provided evidence of commitment and innovative practice in relation to enhancing student learning experiences. Participants provided evidence of strong partnerships between stakeholders and highlighted the importance of these relationships in facilitating effective learning outcomes for students. They also identified a range of issues and challenges that face the sector in growing WIL opportunities; these issues and challenges will shape the quality of WIL experiences. While the majority of comments focused on issues involved in ensuring quality placements, it was recognised that placements are just one way to ensure the integration of work with learning. Also, the WIL experience is highly contextualised and impacted by the expectations of students, employers, the professions, the university and government policy.

A case study of teaching English and multimodality with ICTs: Constraints and possibilities

Current Australian policies and curricular frameworks demand that teachers and students use technology creatively and meaningfully in classrooms to develop students into 21C technological citizens. English teachers and students also have to learn new metalanguage around visual grammar since multimodal tasks often combine creative with critical General Capabilities (GC) with that of the of ICTs and literacy in the Australian Curriculum: English (AC:E). Both teachers and learners come to these tasks with varying degrees of techno-literacy, skills and access to technologies. This paper reports on case-study research following a technology based collaborative professional development (PD) program between a university Lecturer facilitator and English Teachers in a secondary Catholic school. The study found that the possibilities for creative and critical engagement are rich, but there are real grounded constraints such as lack of time, impeding teachers’ ability to master and teach new technologies in classrooms. Furthermore, pedagogical approaches are affected by technical skill levels and school infrastructure concerns which can militate against effective use of ICTs in school settings. The research project was funded by the Brisbane Catholic Education Office and focused on how teachers can be supported in these endeavours in educational contexts as they prepare students of English to be creative global citizens who use technology creatively.

Linking Research and Teaching: an Applied Soft Systems Methodology Case Study

This paper links research and teaching through an applied Soft Systems Methodology case study. The case study focuses on the redevelopment of a Research and Professional Skills module to provide support for international postgraduate students through the use of formative feedback with the aim of increasing academic research skills and confidence. The stages of the Soft Systems Methodology were used as a structure for the redevelopment of module content and assessment. It proved to be a valuable tool for identifying complex issues, a basis for discussion and debate from which an enhanced understanding was gained and a successful solution implemented together with a case study that could be utilised for teaching Soft Systems Methodology concepts. Changes to the module were very successful and resulted in significantly higher grades and a higher pass rate.

Introduction to engineering : a case study of an interdisciplinary course in Mathematics, Science and Technology

This thesis research was a qualitative case study of a single class of Interdisciplinary Studies: Introduction to Engineering taught in a secondary school. The study endeavoured to explore students' experiences in and perceptions of the course, and to investigate the viability of engineering as an interdisciplinary theme at the secondary school level. Data were collected in the form of student questionnaires, the researcher's observations and reflections, and artefacts representative of students' work. Data analysis was performed by coding textual data and classifying text segments into common themes. The themes that emerged from the data were aligned with facets of interdisciplinary study, including making connections, project-based learning, and student engagement and affective outcomes. The findings of the study showed that students were positive about their experiences in the course, and enjoyed its project-driven nature. Content from mathematics, physics, and technological design was easily integrated under the umbrella of engineering. Students felt that the opportunity to develop problem solving and teamwork skills were two of the most important aspects of the course and could be relevant not only for engineering, but for other disciplines or their day-to-day lives after secondary school. The study concluded that engineering education in secondary school can be a worthwhile experience for a variety of students and not just those intending postsecondary study in engineering. This has implications for the inclusion of engineering in the secondary school curriculum and can inform the practice of curriculum planners at the school, school board, and provincial levels. Suggested directions for further research include classroom-based action research in the areas of technological education, engineering education in secondary school, and interdisciplinary education.