Primary school teacher’s noticing of students’ mathematical thinking in problem solving

Professional noticing of students’ mathematical thinking in problem solving involves the identification of noteworthy mathematical ideas of students’ mathematical thinking and its interpretation to make decisions in the teaching of mathematics. The goal of this study is to begin to characterize pre-service primary school teachers’ noticing of students’ mathematical thinking when students solve tasks that involve proportional and non-proportional reasoning. From the analysis of how pre-service primary school teachers notice students’ mathematical thinking, we have identified an initial framework with four levels of development. This framework indicates a possible trajectory in the development of primary teachers’ professional noticing.

Brazilian Portuguese idiom list, selected on the basis of range and frequency of occurrence;

"Issued under the auspices of the Committee on Foreign Language Teaching of the American Council on Education in conjunction with the Institute for Brazilian Studies in Vanderbilt University."

[Culinary ephemera : gelatin and tapioca].

Corporate contributors include: Genesee Pure Food Company; Jell-O-Co. Inc.

Symposium on mathematics for engineering students being the proceedings of the joint sessions of the Chicago section of the American mathematical society and Section A, Mathematics, and Section D, Mechanical science and engineering of the American Association for the Advancement of Science held at the University of Chicago December 30 and 31, 1907.

Caption title: The American Association for the Advancement of Science. Section D--Mechanical science and engineering. Engineering Mathematics symposium.

Syllabus of mathematics: a symposium

Mode of access: Internet.

Bibliography of Franco-Spanish literary relations (until the XIXth century)

Printed in France.

I. Spanish spoliations, 1795. II. French indemnity, 1803. III. French indemnity, 1831.

"Notes on some of the questions decided by the Board of Commissioners under the convention with France, of 4th July 1831" [by John Kane]: p. [377]-442.

French & Italian alumni newsletter /

Latest issue consulted: Vol. 15 [i.e. v. 18] (summer 2004).

The municipalities of the Roman empire,

"The present volume is the outcome of a course of lectures on the Municipalities of the Roman Empire, originally delivered in the University of London, as part of a scheme for the 'higher teaching' of students. The lectures, with some changes, were given afterwards to American audiences, first as 'Lowell lectures' in Boston, then in the Columbia University, New York."--Pref.

To the people of the United States.

A statement of the transactions of the Board of commissioners appointed in 1803 for the adjustment of claims of American citizens against the French government. Introductory note signed: A member of the late board [William Maclure] cf. Sabin, Bibl. amer.

The works of Théophile Gautier ...

"Printed for members only."

Porcupine's works : containing various writings and selections, exhibiting a faithful picture of the United States of America; of their governments, laws, politics and resources; of the characters of their presidents, governors, legislators, magistrates, and military men; and of the customs, manners, morals, religion, virtues and vices of the people : comprising also a complete series of historical documents and remarks, from the end of the war, in 1783, to the election of the President, in March, 1801 /

continued: ... XII. Historical documents and remarks (from December, 1799 to March, 1801) ; Trial of Cooper ; Emigration Society ; Washington's death ; Proceedings in Congress during the session which began December, 1799 ; Board of Commissioners ; Defence of the Quakers of Pennsylvania ; Farewell advertisement ; Prison eclogue ; Republican morality ; Jefferson's election ; Adam's public conduct ; Jefferson's character ; Convention concluded between America and France, in 1800 ; Proceedings in Congress during the session which ended in March, 1801 ; Index.

On the principles of English university education ;

Of the subjects of university teaching.--Of direct and indirect teaching.--Of discipline.--Thoughts on the study of mathematics as a part of a liberal education.

Digital Classics Outside the Echo-Chamber : Teaching, Knowledge Exchange and Public Engagement /

The international perspectives on these issues are especially valuable in an increasingly connected, but still institutionally and administratively diverse world. The research addressed in several chapters in this volume includes issues around technical standards bodies like EpiDoc and the TEI, engaging with ways these standards are implemented, documented, taught, used in the process of transcribing and annotating texts, and used to generate publications and as the basis for advanced textual or corpus research. Other chapters focus on various aspects of philological research and content creation, including collaborative or community driven efforts, and the issues surrounding editorial oversight, curation, maintenance and sustainability of these resources. Research into the ancient languages and linguistics, in particular Greek, and the language teaching that is a staple of our discipline, are also discussed in several chapters, in particular for ways in which advanced research methods can lead into language technologies and vice versa and ways in which the skills around teaching can be used for public engagement, and vice versa. A common thread through much of the volume is the importance of open access publication or open source development and distribution of texts, materials, tools and standards, both because of the public good provided by such models (circulating materials often already paid for out of the public purse), and the ability to reach non-standard audiences, those who cannot access rich university libraries or afford expensive print volumes. Linked Open Data is another technology that results in wide and free distribution of structured information both within and outside academic circles, and several chapters present academic work that includes ontologies and RDF, either as a direct research output or as essential part of the communication and knowledge representation. Several chapters focus not on the literary and philological side of classics, but on the study of cultural heritage, archaeology, and the material supports on which original textual and artistic material are engraved or otherwise inscribed, addressing both the capture and analysis of artefacts in both 2D and 3D, the representation of data through archaeological standards, and the importance of sharing information and expertise between the several domains both within and without academia that study, record and conserve ancient objects. Almost without exception, the authors reflect on the issues of interdisciplinarity and collaboration, the relationship between their research practice and teaching and/or communication with a wider public, and the importance of the role of the academic researcher in contemporary society and in the context of cutting edge technologies. How research is communicated in a world of instant- access blogging and 140-character micromessaging, and how our expectations of the media affect not only how we publish but how we conduct our research, are questions about which all scholars need to be aware and self-critical.

French furniture and decoration in the XVIIIth century,

Appendix: List of artists and workmen leaving Paris for St. Petersburg in 1716.--Spaendonck, G. van. Salons.--Oudry, J. B. Salons.--List of officials at the Gobelins.--Caffieri, J. Chronological list of his work for the crown.--Oeben and Reisener. Detailed agreement for the Bureau du roi.--Gouthière. Entries in the sale catalogue of the duke d'Aumont.--Duplessis. Entries in the livre-journal of Lazare Duvaux.--List of French cabinet-makers.