This qualitative case study describes how two teachers translate communication messages from curriculum statements into classroom practice. These illuminative cases illustrate the perspectives and practices of two teachers who support the spirit of the Ontario Mathematics Curriculum by working to implement communication in the Foundations of Mathematics (MFM1P), Grade 9, Applied course (Ontario Ministry of Education, 2005). Data for this study were collected from individual interviews with teachers, classroom observations, and document analysis. Grade 9 Applied mathematics teachers across Ontario indicate on surveys that they support communication in the mathematics classroom (Education Quality and Accountability Office, 2007; Suurtamm & Graves, in press). Despite evidence of support for this aspect of the curriculum, findings from this study point to a need for finer analysis of teachers’ perspectives and practices when it comes to communication in mathematics. The cases presented in this thesis illustrate different images, or meanings, associated with communication in mathematics. Furthermore, even in unique cases where the gap between curriculum developers and teachers images is minimal, the idealized vision of communication may not be realized in classroom practice since teachers may face challenges in implementation. The teachers report that despite additional challenges involved with implementing communication in Grade 9 Applied mathematics, teaching in this context can be a rewarding experience. To minimize the gap between images of communication that are translated from curriculum statements into classroom practice, findings from this study indicate that curriculum developers must find ways to help teachers understand the rationale behind curriculum initiatives. Future research might explore ways to help familiarize teachers with the theory and research underlying communication in mathematics. Research might also examine the impact that these initiatives have on teachers’ perspectives and practices. / Thesis (Master, Education) -- Queen's University, 2008-08-27 16:18:13.815

Chen, Gaowei. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 149-171). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

The purpose of this research is to explore the aspects of abilities of mathematics communication of grade two students in the elementary school, including spoken understanding and as well as written and figural understanding. This researcher adopted action research, having the investigator implemented two months teaching. After referring to mathematics teaching materials grade two, the researcher designed four units. During the period of research, the teacher utilized a variety ways to collect data, such as; video recording, audio recording, questionnaires, reflective notes, observation records and student activities sheets. Eventually, the teacher made qualitative analyzes and explored methods of improvement on her ways of teaching. The results of this research illustrated seven aspects of spoken language expression of understanding. The students were weak in listening; dare to express their opinions; put forward queries regarding teacher's or schoolmates¡¦ questions; some were unable to raise conceptual related questions; when students made exchanges they needed help from the teacher, students spoke with low or vague voice; and, finally, students replied intermittently or silently. Besides the above seven findings on spoken language, there are four findings of phenomena in written and figural understanding. First, students were able to examine mistakes or others¡¦ mistakes according to the record on blackboard. Moreover, the students even can put forward the queries on others¡¦ problem solving records. Yet, they were capable of understanding others¡¦ mathematics records and explained others¡¦ ideas.

The increasing demand for high-mobility and high data rate in wireless communications results in constraints and problems in the limited radio spectrum, multipath fading, and delay spread. The multiple-input multiple-output (MIMO) system has been generally considered as one of the key technologies for the next generation wireless communication systems. MIMO systems which utilize multiple antennas in both the transmit side and the receive side can overcome the abovementioned challenges since they are able to increase the channel capacity and the spectrum usage efficiency without the need for additional channel bandwidth. The detection algorithm is a big bottleneck in MIMO systems. Generally, it is expected to fulfill two main goals simultaneously: low computational complexity and good error rate performance. However, the existing detection algorithms are either too complicated or suffering from very bad error-rate performance. The purpose of this thesis is to comprehensively investigate the detection algorithms of MIMO systems, and based on that, to develop new methods which can reduce the computational complexity while retain good system performance. Firstly, the background and the principle of MIMO systems and the previous work on the MIMO decoding algorithms conducted by other researchers are thoroughly reviewed. Secondly, the geometrical analysis of the signal detection is investigated, and a geometric decoding algorithm which can offer the optimum BLER performance is proposed. Thirdly, the semidefinite relaxation (SDR) detection algorithms are extended to high-order modulation MIMO systems, and a novel SDR detector for 256-QAM constellations is proposed. The theoretical analysis on the tightness and the complexity are conducted. It demonstrates that the proposed SDR detector can offer better BLER performance, while its complexity is in between those of its two counterparts. Fourthly, we combine the SDR detection algorithms with the sphere decoding. This is helpful for reducing the computational complexity of the traditional sphere decoding since shorter initial radius of the hyper sphere can be obtained. Finally, the novel lattice-reduction-aided SDR detectors are proposed. They can provide near-optimum error rate performance and achieve the full diversity gain with very little computational complexity added compared with the stand-alone SDR detectors. / published_or_final_version / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

With more and more focus on accountability, algebra achievement has become a major focus of math curriculum developers. In many states, students are expected to pass standardized Algebra achievement tests in order to satisfy graduation requirements. The purpose of this study was to identify teacher qualities and teaching qualities linked to teacher effectiveness in 7th-grade Algebra I Honors. This study examined two aspects of teachers, teacher quality and teaching quality. Teacher quality refers to the characteristics that teachers possess and teaching quality refers to what teachers do in the classroom to foster student learning. For this study, teacher quality included teacher professional preparation characteristics and teacher knowledge. Also, aspects of teaching quality that promote conceptual understanding in Algebra were examined. The difference between more and less effective teachers in this study lies in teaching quality, what teachers do in the classroom, as opposed to teacher quality, what those teachers bring with them to the classroom. The findings of this study indicate that elements of teaching quality are more indicative of teacher effectiveness than elements of teacher quality among teachers in the study. Although there was some evidence of a relationship between elements of teacher quality and teacher effectiveness, there were clear differences in teaching quality among more effective and less effective teachers in this study. / by Barbara Perez. / Thesis (Ph.D.)--Florida Atlantic University, 2013. / Includes bibliography. / Mode of access: World Wide Web. / System requirements: Adobe Reader.

Thesis (PhD)--Macquarie University, Australian Centre for Educational Studies, Institute of Higher Education Research and Development, 2007. / "2006" Bibliography: p. 167-173.

Estimation of the fetal heart rate (FHR) has gained interest in the last century; low heart rate variability has been studied to identify intrauterine growth restricted fetuses (prepartum), and abnormal FHR patterns have been associated with fetal distress during delivery (intrapartum). Several monitoring techniques have been proposed for FHR estimation, including auscultation and Doppler ultrasound. This thesis focuses on the extraction of the non-invasive fetal electrocardiogram (NI-FECG) recorded from a limited set of abdominal sensors. The main challenge with NI-FECG extraction techniques is the low signal-to-noise ratio of the FECG signal on the abdominal mixture signal which consists of a dominant maternal ECG component, FECG and noise. However the NI-FECG offers many advantages over the alternative fetal monitoring techniques, the most important one being the opportunity to enable morphological analysis of the FECG which is vital for determining whether an observed FHR event is normal or pathological. In order to advance the field of NI-FECG signal processing, the development of standardised public databases and benchmarking of a number of published and novel algorithms was necessary. Databases were created depending on the application: FHR estimation with or without maternal chest lead reference or directed toward FECG morphology analysis. Moreover, a FECG simulator was developed in order to account for pathological cases or rare events which are often under-represented (or completely missing) in the existing databases. This simulator also serves as a tool for studying NI-FECG signal processing algorithms aimed at morphological analysis (which require underlying ground truth annotations). An accurate technique for the automatic estimation of the signal quality level was also developed, optimised and thoroughly tested on pathological cases. Such a technique is mandatory for any clinical applications of FECG analysis as an external confidence index of both the input signals and the analysis outputs. Finally, a Bayesian filtering approach was implemented in order to address the NI-FECG morphology analysis problem. It was shown, for the first time, that the NI-FECG can allow accurate estimation of the fetal QT interval, which opens the way for new clinical studies on the development of the fetus during the pregnancy.

"2006" / Thesis (PhD)--Macquarie University, Australian Centre for Educational Studies, Institute of Higher Education Research and Development, 2007. / Bibliography: p. 167-173. / Introduction -- Experience and expression -- Becoming a professional -- Study design -- Graduates' experiences: a narrative -- Reflections on communication -- Examples of texts -- Reflections on learning and teaching -- Reflections and implications. / The aim of this study is to inform curriculum change in the mathematical sciences at university level. This study examines the transition to professional work after gaining a degree in the mathematical sciences. Communication is used as the basis for the analysis of the transition because of the importance of language choices in work situations. These experiences form part of the capabilities that become part of a person's potential to work as a professional. I found a subtle form of power and, of the opposite, lack of power due to communication skills. It is not as obvious as in, say, politics but it is just as critical to graduates and to the mathematical sciences. -- There were 18 participants in the study who were graduates within five years of graduation with majors in the mathematical sciences. In-depth interviews were analysed using phenomenography and examples of text from the workplace were analysed using discourse analysis. Descriptions of the process of gaining employment and the use of mathematical discourse have been reported in the thesis using narrative style with extensive quotes from the participants. -- The research shows that graduates had three qualitatively different conceptions of mathematical discourse when communicating with a non-mathematical audience: jargon, concepts/thinking and strength. All participants modified their use of technical terms when communicating with non-mathematicians. Those who held the jargon conception tried to simplify the language in order to explain the mathematics to their audience. Those who held the concepts/thinking conception believed that the way of thinking or the ideas were too difficult to communicate and instead their intention with mathematical discourse was to inspire or sell their ability to work with the mathematics. The strength conception considers the ethical responsibility to communicate the consequences of mathematical decisions. Not one of the participants believed that they had been taught communication skills as part of their degree. -- Participants gained a 'mathematical identity' from their studies and acquiring a degree gave them confidence and a range of problem-solving skills. Recommendations are made about changes in university curriculum to ensure that graduates are empowered to make a high-quality transition to the workplace and be in a position to use their mathematical skills. Mathematical skills are necessary but not sufficient for a successful transition to the workplace. Without the ability to communicate, graduates are unable to release the strength of their knowledge. / Mode of access: World Wide Web. / xi, 195 p. ill

Krivelevich and Patkós conjectured in 2009 that χ(G(n, p)) ∼ χ=(G(n, p)) ∼ χ∗=(G(n, p)) for C/n < p < 1 − ε, where ε > 0. We prove this conjecture for n−1+ε1 < p < 1 − ε2 where ε1, ε2 > 0. We investigate several measures that have been proposed to indicate centrality of nodes in networks, and find examples of networks where they fail to distinguish any of the vertices nodes from one another. We develop a new method to investigate core-periphery structure, which entails identifying densely-connected core nodes and sparsely-connected periphery nodes. Finally, we present an experiment and an analysis of empirical networks, functional human brain networks. We found that reconfiguration patterns of dynamic communities can be used to classify nodes into a stiff core, a flexible periphery, and a bulk. The separation between this stiff core and flexible periphery changes as a person learns a simple motor skill and, importantly, it is a good predictor of how successful the person is at learning the skill. This temporally defined core-periphery organisation corresponds well with the core- periphery detected by the method that we proposed earlier the static networks created by averaging over the subjects dynamic functional brain networks.