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Numerical algorithms for personalized search in self-organizing information networks
This book lays out the theoretical groundwork for personalized search and reputation management, both on the Web and in peer-to-peer and social networks. Representing much of the foundational research in this field, the book develops scalable algorithms that exploit the graphlike properties underlying personalized search and reputation management, and delves into realistic scenarios regarding Web-scale data.
Sep Kamvar focuses on eigenvector-based techniques in Web search, introducing a personalized variant of Google's PageRank algorithm, and he outlines algorithms--such as the now-famous quadratic extrapolation technique--that speed up computation, making personalized PageRank feasible. Kamvar suggests that Power Method-related techniques ultimately should be the basis for improving the PageRank algorithm, and he presents algorithms that exploit the convergence behavior of individual components of the PageRank vector. Kamvar then extends the ideas of reputation management and personalized search to distributed networks like peer-to-peer and social networks. He highlights locality and computational considerations related to the structure of the network, and considers such unique issues as malicious peers. He describes the EigenTrust algorithm and applies various PageRank concepts to P2P settings. Discussion chapters summarizing results conclude the book's two main sections.
Clear and thorough, this book provides an authoritative look at central innovations in search for all of those interested in the subject.
eBook
Numerical algorithms for personalized search in self-organizing information networks
\"This book lays out the theoretical groundwork for personalized search and reputation management, both on the Web and in peer-to-peer and social networks.\" The book develops scalable algorithms that exploit the graphlike properties underlying personalized search and reputation management, and delves into realistic scenarios regarding web-scale data.--[book cover]
Book
Mathematics teachers’ levels of technological pedagogical content knowledge and information and communication technology integration barriers
Many mathematics teachers struggle to effectively integrate information and communication technology (ICT) in their teaching and need continuous professional development programmes to improve their technological pedagogical content knowledge (TPACK). This article aims to identify mathematics teachers’ levels of TPACK and barriers to integrating ICT as a means to inform their continuous professional development needs. The TPACK framework of Mishra and Koehler was used as a lens for this the study. Both quantitative and qualitative research methods were utilised. Ninety-three mathematics teachers, who completed a quantitative questionnaire, reported higher levels of content, pedagogical, and pedagogical content knowledge, with comparatively lower levels of technology, technological pedagogical, and technological content knowledge. Ten of these participants also participated in semi-structured interviews and revealed six primary barriers to integrating ICT in the classroom, namely curriculum-related time constraints, technological infrastructure, impact of ICT use on the learning process, ineffective professional development, teachers’ pedagogical beliefs and poor leadership. Continuous professional development programmes addressing specific ICTintegration barriers can effect significant changes in teachers’ TPACK, which may promote better teaching and learning of mathematics.
Journal Article
How specific can language as resource become for the teaching of algebraic concepts?
Classroom research into mathematics and language has studied issues of context specificity such as cultures of explanation or the impact of language policies on practice. More recently, researchers in the domain have started to study issues of content specificity aimed at performing language-responsive mathematics teaching for the learning of precise mathematical content. Progress in the conceptualization of language as resource for mathematics teaching and learning makes it necessary to strengthen the discussion of the contexts of culture and interaction along with the linguistic demands given by the specificity of the mathematical content at play. In this paper, I introduce a sociocultural framing for a mathematical-linguistic view of grammar as resource with the focus on explicitness in communication. I then report developmental work with two teachers on their teaching of algebraic concepts, and address the question of how to learn to communicate explicit meanings for these concepts in classroom mathematical talk. The structuring principle adopted for this work was to critically distinguish and choose or produce instances of teacher talk that overtly communicated conceptual meaning within the algebra of equations. I conclude with preliminary evidence of the effectiveness of the work with the teachers.
Journal Article
Evaluation of 6th Grade Students' Mathematical Communication Levels within the Framework of Realistic Mathematics Education Approach 1
The purpose of this study 1s to investigate the levels of mathematical communication demonstrated by sixth-grade students in the context of instructional activities grounded in the principles of Realistic Mathematics Education (RME). There are several skills that mathematics education aims to develop in students. Mathematical communication skills are among these essential skills. Among the aims of realistic mathematics education is to encourage students to actively participate in the learning process and to make sense of mathematical knowledge in real-life situations. In this study, the case study method, one of the qualitative research methods, was used. The study was carried out during the 2022-2023 academic year at a public middle school located in the Southeastern Anatolia Region, involving 12 students who were selected through convenience sampling. Data were collected through RME problems, interviews, audio recordings, and observations, and were subjected to descriptive analysis and content analysis in line with the problems of the study. In individual applications, students mathematical communication levels were found to be below zero, inadequate, and partially adequate, while in group work, mathematical communication levels were found to be partially adequate, adequate, and constructive. As a result of the study, it was seen that students mathematical communication levels were at lower levels in realistic mathematics education problems in which they worked individually, while students mathematical communication levels were at higher levels in group work. In individual tasks, students levels of mathematical communication were observed to range from below zero to partially adequate, whereas in collaborative group activities, their communication levels ranged from partially adequate to constructive. The findings indicate that students demonstrated lower levels of mathematical communication when engaging with RME tasks individually, while their communication skills improved notably during group-based problem-solving processes. Based on these results, suggestions were made to increase mathematical communication levels.
Journal Article
Designing an instrument to measure the development of techno-mathematical literacies in an innovative mathematics course for future engineers in STEM education
Techno-mathematical Literacies (TmL), which are defined as a combination of mathematical, workplace and ICT knowledge, and communicative skills, are acknowledged as important learning goals in STEM education. Still, much remains unknown about ways to address them in teaching and to assess their development. To investigate this, we designed and implemented an innovative course in applied mathematics with a focus on Techno-mathematical Literacies for 1st-year engineering students, and we set out to measure the learning effect of the course. Because measuring TmL is an uncharted terrain, we designed tests that could serve as pre- or posttests. To prevent a test learning effect, we aimed to design two different but equally difficult tests A and B. These were assigned randomly to 68 chemistry students, as a pretest, with the other one serving as posttest after the course. A significant development in TmL was found in the B-pre group, but not in the A-pre group. Therefore, as a follow-up analysis we investigated whether the two tests were equally difficult and searched for possible explanations. We found that test B was indeed perceived as more difficult than test A, but also that students who were assigned B (pre) were previously higher achieving than A (pre), and a sound mastery level of basic skills that ground the higher-order TmL seemed necessary. Furthermore, as TmL are very heterogenous by nature, some of them are easier learned and measured than others. Based on the results, we propose ways of testing TmL, which should be validated in future research.
Journal Article
Leader noticing of facilitation in videocases of mathematics professional development
In this article, we report on
Researching Mathematics Leader Learning (RMLL)
, a project designed to support leaders in learning how to facilitate robust opportunities for teachers’ mathematical learning. Our two-phase research design allowed us to construct a set of videocase seminars, enact the seminar design with leaders, analyze these data, refine our seminar design, and implement a second set of seminars with a new group of leaders. We drew on the noticing literature to examine leaders’ pedagogical reasoning as they discussed videocases of professional development. In this article, we demonstrate how changes in our framework for leader development and the resulting changes in the prompts and tasks shaped leader noticing in three ways: (a) accounting for the mathematical work of the facilitator and teachers in the videocase; (b) linking the mathematical work to goals for teacher learning; and (c) reasoning around the facilitator’s work in advancing those learning goals. Analysis indicates that in Phase II, leader discussions were more focused on the mathematical and pedagogical work needed to advance teacher learning. Based on our research and development work with over 70 leaders, we offer a set of design principles for leader professional development.
Journal Article
The preparation experiences of elementary mathematics specialists: examining influences on beliefs, content knowledge, and teaching practices
Many in the field of mathematics education call for elementary schools to have elementary mathematics specialists (EMSs) who provide needed mathematical expertise and support for children and teachers. EMSs serve as a reasonable, immediate alternative to the challenges generated by elementary teachers needing improved mathematical knowledge for teaching in the classroom. However, limited inquiry has explored how to best prepare EMSs and how program features and learning activities influence their development. This mixed-method study identifies some of the interrelated benefits from a K-5 Mathematics Endorsement Program designed to prepare EMSs through examining changes in mathematical beliefs, specialized content knowledge (SCK), and classroom teaching practices during the program. Data (
n
= 32) were collected over the 2-semester program via belief surveys, a content knowledge assessment, observations of teaching practices, and individual interviews from elementary teachers participating in the program. The findings show some changes in beliefs can be made relatively quickly, other shifts in beliefs take more time and continued support, and changes in SCK and adoption of various aspects of standard-based pedagogy require considerably greater opportunities to learn. The described program features and learning experiences provided a context for these changes and offer considerations for EMS preparation programs.
Journal Article
“This is the First Time I’ve Done This”: Exploring secondary prospective mathematics teachers’ noticing of students’ mathematical thinking
This mixed methods study investigates the ways in which secondary mathematics prospective teachers acquire skills needed to attend to, interpret, and respond to students’ mathematical thinking and the ways in which their perceived strengths and weaknesses influence their skills when this type of formalized training is not part of their program. These skills (attending, interpreting, and responding) are defined as teachers’ professional noticing of students’ thinking. Results indicate that seniors respond to students’ thinking in significantly different ways from juniors and sophomores. Converging the data highlighted inconsistencies in how participants’ were making sense of students’ mathematical thinking, as well as in participants’ self-identified strengths and weaknesses.
Journal Article