The Experts below are selected from a list of 133587 Experts worldwide ranked by ideXlab platform
Christoph Lange - One of the best experts on this subject based on the ideXlab platform.
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Mashups Using Mathematical Knowledge
Semantic Mashups, 2013Co-Authors: Christoph Lange, Michael KohlhaseAbstract:Mashups offer new functionality by combining, aggregating and transforming resources and services available on the Web. This chapter deals with Mathematical mashups and focuses on those that process Mathematical Knowledge rather than, e.g., huge amounts of numeric data, as it is the structure of Knowledge that distinguishes mathematics from other application domains.
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SWiM - a semantic wiki for Mathematical Knowledge management
Proceedings of the 5th European semantic web conference on The semantic web: research and applications, 2008Co-Authors: Christoph LangeAbstract:SWiM is a semantic wiki for collaboratively building, editing and browsing Mathematical Knowledge represented in the domain-specific structural semantic markup language OMDoc. It motivates users to contribute to collections of Mathematical Knowledge by instantly sharing the benefits of Knowledge-powered services with them. SWiM is currently being used for authoring content dictionaries, i. e. collections of uniquely identified Mathematical symbols, and prepared for managing a large-scale proof formalisation effort.
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ESWC - SWiM - a semantic wiki for Mathematical Knowledge management
Lecture Notes in Computer Science, 1Co-Authors: Christoph LangeAbstract:SWiM is a semantic wiki for collaboratively building, editing and browsing Mathematical Knowledge represented in the domain-specific structural semantic markup language OMDoc. It motivates users to contribute to collections of Mathematical Knowledge by instantly sharing the benefits of Knowledge-powered services with them. SWiM is currently being used for authoring content dictionaries, i. e. collections of uniquely identified Mathematical symbols, and prepared for managing a large-scale proof formalisation effort.
Michael Kohlhase - One of the best experts on this subject based on the ideXlab platform.
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Mashups Using Mathematical Knowledge
Semantic Mashups, 2013Co-Authors: Christoph Lange, Michael KohlhaseAbstract:Mashups offer new functionality by combining, aggregating and transforming resources and services available on the Web. This chapter deals with Mathematical mashups and focuses on those that process Mathematical Knowledge rather than, e.g., huge amounts of numeric data, as it is the structure of Knowledge that distinguishes mathematics from other application domains.
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Markup for Mathematical Knowledge
OMDoc – An Open Markup Format for Mathematical Documents [version 1.2], 2006Co-Authors: Michael KohlhaseAbstract:Mathematicians make use of various kinds of documents (e.g. e-mails, letters, pre-prints, journal articles, and textbooks) for communicating Mathematical Knowledge. Such documents employ specialized notational conventions and visual representations to convey the Mathematical Knowledge reliably and efficiently. The respective representations are supported by pertinent markup systems like TEX/LATEX.
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MKM - An exploration in the space of Mathematical Knowledge
Lecture Notes in Computer Science, 2006Co-Authors: Andrea Kohlhase, Michael KohlhaseAbstract:Although Knowledge is a central topic for MKM there is little explicit discussion on what ‘Knowledge’ might actually be. There are specific intuitions about form and content of Knowledge, about its structure, and epistemological nature that shape the MKM systems, but a conceptual model is missing. In this paper we try to rationalize this discussion to give MKM a firmer footing, to start a discussion among MKM researchers and help relate the MKM intuitions and discourses to other communities. Starting from the observation that many concrete realizations of Mathematical Knowledge objects are considered equivalent, we propose a conceptual model of the space of (Mathematical) Knowledge objects graded by levels of abstraction and presentational explicitness and draw conclusions for MKM markup formats.
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towards collaborative content management and version control for structured Mathematical Knowledge
Mathematical Knowledge Management, 2003Co-Authors: Michael Kohlhase, Romeo AnghelacheAbstract:We propose an infrastructure for collaborative content management and version control for structured Mathematical Knowledge. This will enable multiple users to work jointly on Mathematical theories with minimal interference.We describe the API and the functionality needed to realize a CVS-like version control and distribution model. This architecture extends the CVS architecture in two ways, motivated by the specific needs of distributed management of structured Mathematical Knowledge on the Internet. On the one hand the one-level client/server model of CVS is generalized to a multi-level graph of client/server relations, and on the other hand the underlying change-detection tools take the math-specific structure of the data into account.
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system description mbase an open Mathematical Knowledge base
Lecture Notes in Computer Science, 2000Co-Authors: Andreas Franke, Michael KohlhaseAbstract:In this paper we describe the MBASE system, a web-based, distributed Mathematical Knowledge base. This system is a Mathematical service in MATHWEB that offers a universal repository of formalized mathematics where the formal representation allows semantics-based retrieval of distributed Mathematical facts.
Heather C Hill - One of the best experts on this subject based on the ideXlab platform.
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the nature and predictors of elementary teachers Mathematical Knowledge for teaching
Journal for Research in Mathematics Education, 2010Co-Authors: Heather C HillAbstract:This article explores elementary school teachers' Mathematical Knowledge for teaching and the relationship between such Knowledge and teacher characteristics. The Learning Mathematics for Teaching project administered a multiple-choice assessment covering topics in number and operation to a nationally representative sample of teachers (n = 625) and at the same time collected information on teacher and student characteristics. Performance did not vary according to Mathematical topic (e.g., whole numbers or rational numbers), and items categorized as requiring specialized Knowledge of mathematics proved more difficult for this sample of teachers. There were few substantively significant relationships between Mathematical Knowledge for teaching and teacher characteristics, including leadership activities and self-reported college-level mathematics preparation. Implications for current policies aimed at improving teacher quality are addressed.
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Mathematical Knowledge for teaching and the Mathematical quality of instruction an exploratory study
Cognition and Instruction, 2008Co-Authors: Heather C Hill, Merrie Blunk, Charalambos Y Charalambous, Jennifer M Lewis, Geoffrey Phelps, Laurie Sleep, Deborah Loewenberg BallAbstract:This study illuminates claims that teachers' Mathematical Knowledge plays an important role in their teaching of this subject matter. In particular, we focus on teachers' Mathematical Knowledge for teaching (MKT), which includes both the Mathematical Knowledge that is common to individuals working in diverse professions and the Mathematical Knowledge that is specialized to teaching. We use a series of five case studies and associated quantitative data to detail how MKT is associated with the Mathematical quality of instruction. Although there is a significant, strong, and positive association between levels of MKT and the Mathematical quality of instruction, we also find that there are a number of important factors that mediate this relationship, either supporting or hindering teachers' use of Knowledge in practice.
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“Mathematical Knowledge for teaching”: adapting U.S. measures for use in Ireland
Journal of Mathematics Teacher Education, 2008Co-Authors: Seán Delaney, Heather C Hill, Deborah Loewenberg Ball, Stephen G. Schilling, Deborah ZopfAbstract:This article describes a study in which measures of Mathematical Knowledge for teaching developed in the United States were adapted to measure Mathematical Knowledge for teaching in Ireland. When adapting the measures it was not assumed that the Mathematical Knowledge used by Irish and U.S. teachers is the same. Instead psychometric and interview-based methods were used to determine a correspondence between the constructs being measured, and ensure the integrity of item performance in the Irish context. The study found overlap between the Knowledge that is used to teach in both Ireland and the United States, and that the items tapped into this Knowledge. However, specific findings confirm the usefulness of conducting extensive checks on the validity of items used in cross-national contexts. The process of adaptation is described to provide guidance for others interested in using the items to measure Mathematical Knowledge for teaching outside the United States. The process also enabled the authors to raise questions about the assumptions that lie behind the practice-based construct of Mathematical Knowledge for teaching.
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Effects of Teachers’ Mathematical Knowledge for Teaching on Student Achievement
American Educational Research Journal, 2005Co-Authors: Heather C Hill, Brian Rowan, Deborah Loewenberg BallAbstract:This study explored whether and how teachers' Mathematical Knowledge for teaching contributes to gains in students' mathematics achievement. The authors used a linear mixed-model methodology in which first and third graders' Mathematical achievement gains over a year were nested within teachers, who in turn were nested within schools. They found that teachers' Mathematical Knowledge was significantly related to student achievement gains in both first and third grades after controlling for key student- and teacher-level covariates. This result, while consonant with findings from the educational production function literature, was obtained via a measure focusing on the specialized Mathematical Knowledge and skills used in teach- ing mathematics. This findingprovides supportforpolicy initiatives designed to improve students' mathematics achievement by improving teachers' math- ematical Knowledge.
Deborah Loewenberg Ball - One of the best experts on this subject based on the ideXlab platform.
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Making Progress on Mathematical Knowledge for Teaching
The Mathematics Enthusiast, 2016Co-Authors: Mark Hoover, Deborah Loewenberg Ball, Reidar Mosvold, Yvonne LaiAbstract:Although the field lacks a theoretically grounded, well-defined, and shared conception of Mathematical Knowledge required for teaching, there appears to be broad agreement that a specialized body of Knowledge is vital to improvement. Further, such a construct serves as the foundation for different kinds of studies with different agendas. This article reviews what is known and needs to be known to advance research on Mathematical Knowledge for teaching. It argues for three priorities: (i) finding common ground for engaging in complementary studies that together advance the field; (ii) innovating and reflecting on method; and (iii) addressing the relationship of such Knowledge to Mathematical fluency in teaching and to issues of equity and diversity in teaching. It concludes by situating the articles in this special issue within this emerging picture.
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Mathematical Knowledge for teaching and the Mathematical quality of instruction an exploratory study
Cognition and Instruction, 2008Co-Authors: Heather C Hill, Merrie Blunk, Charalambos Y Charalambous, Jennifer M Lewis, Geoffrey Phelps, Laurie Sleep, Deborah Loewenberg BallAbstract:This study illuminates claims that teachers' Mathematical Knowledge plays an important role in their teaching of this subject matter. In particular, we focus on teachers' Mathematical Knowledge for teaching (MKT), which includes both the Mathematical Knowledge that is common to individuals working in diverse professions and the Mathematical Knowledge that is specialized to teaching. We use a series of five case studies and associated quantitative data to detail how MKT is associated with the Mathematical quality of instruction. Although there is a significant, strong, and positive association between levels of MKT and the Mathematical quality of instruction, we also find that there are a number of important factors that mediate this relationship, either supporting or hindering teachers' use of Knowledge in practice.
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“Mathematical Knowledge for teaching”: adapting U.S. measures for use in Ireland
Journal of Mathematics Teacher Education, 2008Co-Authors: Seán Delaney, Heather C Hill, Deborah Loewenberg Ball, Stephen G. Schilling, Deborah ZopfAbstract:This article describes a study in which measures of Mathematical Knowledge for teaching developed in the United States were adapted to measure Mathematical Knowledge for teaching in Ireland. When adapting the measures it was not assumed that the Mathematical Knowledge used by Irish and U.S. teachers is the same. Instead psychometric and interview-based methods were used to determine a correspondence between the constructs being measured, and ensure the integrity of item performance in the Irish context. The study found overlap between the Knowledge that is used to teach in both Ireland and the United States, and that the items tapped into this Knowledge. However, specific findings confirm the usefulness of conducting extensive checks on the validity of items used in cross-national contexts. The process of adaptation is described to provide guidance for others interested in using the items to measure Mathematical Knowledge for teaching outside the United States. The process also enabled the authors to raise questions about the assumptions that lie behind the practice-based construct of Mathematical Knowledge for teaching.
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Effects of Teachers’ Mathematical Knowledge for Teaching on Student Achievement
American Educational Research Journal, 2005Co-Authors: Heather C Hill, Brian Rowan, Deborah Loewenberg BallAbstract:This study explored whether and how teachers' Mathematical Knowledge for teaching contributes to gains in students' mathematics achievement. The authors used a linear mixed-model methodology in which first and third graders' Mathematical achievement gains over a year were nested within teachers, who in turn were nested within schools. They found that teachers' Mathematical Knowledge was significantly related to student achievement gains in both first and third grades after controlling for key student- and teacher-level covariates. This result, while consonant with findings from the educational production function literature, was obtained via a measure focusing on the specialized Mathematical Knowledge and skills used in teach- ing mathematics. This findingprovides supportforpolicy initiatives designed to improve students' mathematics achievement by improving teachers' math- ematical Knowledge.
Claudio Sacerdoti Coen - One of the best experts on this subject based on the ideXlab platform.
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CICM - A Survey on Retrieval of Mathematical Knowledge
Lecture Notes in Computer Science, 2015Co-Authors: Ferruccio Guidi, Claudio Sacerdoti CoenAbstract:We present a short survey of the literature on indexing and retrieval of Mathematical Knowledge, with pointers to 72 papers and tentative taxonomies of both retrieval problems and recurring techniques.