A brief survey of symmetry in mathematics

This paper presents a brief survey of the idea of symmetry in mathematics, as exemplified by some particular developments in algebra, differential equations, topology, and number theory.

Earth’s Rotation: A Challenging Problem in Mathematics and Physics

A suitable knowledge of the orientation and motion of the Earth in space is a common need in various fields. That knowledge has been ever necessary to carry out astronomical observations, but with the advent of the space age, it became essential for making observations of satellites and predicting and determining their orbits, and for observing the Earth from space as well. Given the relevant role it plays in Space Geodesy, Earth rotation is considered as one of the three pillars of Geodesy, the other two being geometry and gravity. Besides, research on Earth rotation has fostered advances in many fields, such as Mathematics, Astronomy and Geophysics, for centuries. One remarkable feature of the problem is in the extreme requirements of accuracy that must be fulfilled in the near future, about a millimetre on the tangent plane to the planet surface, roughly speaking. That challenges all of the theories that have been devised and used to-date; the paper makes a short review of some of the most relevant methods, which can be envisaged as milestones in Earth rotation research, emphasizing the Hamiltonian approach developed by the authors. Some contemporary problems are presented, as well as the main lines of future research prospected by the International Astronomical Union/International Association of Geodesy Joint Working Group on Theory of Earth Rotation, created in 2013.

The use of films and television in mathematics education, December 1957.

Mode of access: Internet.

University of California publications in mathematics

Mode of access: Internet.

Studies in mathematics education, a brief survey of improvement programs for school mathematics.

Bibliography: p. 70-71.

Studies in mathematics education, a brief survey of improvement programs for school mathematics.

"An extension and revision of 'Summaries of current studies on improving school mathematics' prepared ... in November, 1958."

Scientific serials; characteristics and lists of most cited publications in mathematics, physics, chemistry, geology, physiology, botany, zoology, and entomology.

Mode of access: Internet.

Supervised study in mathematics and science,

Bibliography: p. 229-231.

A course in mathematics, for students of engineering and applied science.

Mode of access: Internet.

Syntactic complexity measures and their relation to oral proficiency in Japanese as a foreign language

The study reported in this article is a part of a large-scale study investigating syntactic complexity in second language (L2) oral data in commonly taught foreign languages (English, German, Japanese, and Spanish; Ortega, Iwashita, Rabie, & Norris, in preparation). In this article, preliminary findings of the analysis of the Japanese data are reported. Syntactic complexity, which is referred to as syntactic maturity or the use of a range of forms with degrees of sophistication (Ortega, 2003), has long been of interest to researchers in L2 writing. In L2 speaking, researchers have examined syntactic complexity in learner speech in the context of pedagogic intervention (e.g., task type, planning time) and the validation of rating scales. In these studies complexity is examined using measures commonly employed in L2 writing studies. It is assumed that these measures are valid and reliable, but few studies explain what syntactic complexity measures actually examine. The language studied is predominantly English, and little is known about whether the findings of such studies can be applied to languages that are typologically different from English. This study examines how syntactic complexity measures relate to oral proficiency in Japanese as a foreign language. An in-depth analysis of speech samples from 33 learners of Japanese is presented. The results of the analysis are compared across proficiency levels and cross-referenced with 3 other proficiency measures used in the study. As in past studies, the length of T-units and the number of clauses per T-unit is found to be the best way to predict learner proficiency; the measure also had a significant linear relation with independent oral proficiency measures. These results are discussed in light of the notion of syntactic complexity and the interfaces between second language acquisition and language testing. Adapted from the source document

An iterative-style approach to constructing intelligent tutoring systems in mathematics

Mathematics is highly structured and also underpins most of science and engineering. For this reason, it has proved a very suitable domain for Intelligent Tutoring System (ITS) research, with the result that probably more tutoring systems have been constructed for the domain than any other. However, the literature reveals that there still exists no consensus on a credible approach or approaches for the design of such systems, despite numerous documented efforts. Current approaches to the construction of ITSs leave much to be desired. Consequently, existing ITSs in the domain suffer from a considerable number of shortcomings which render them 'unintelligent'. The thesis examines some of the reasons why this is the case. Following a critical review of existing ITSs in the domain, and some pilot studies, an alternative approach to their construction is proposed (the 'iterative-style' approach); this supports an iterative style, and also improves on at least some of the shortcomings of existing approaches. The thesis also presents an ITS for fractions which has been developed using this approach, and which has been evaluated in various ways. It has, demonstrably, improved on many of the limitations of existing ITSs; furthermore, it has been shown to be largely 'intelligent', at least more so than current tutors for the domain. Perhaps more significantly, the tutor has also been evaluated against real students with, so far, very encouraging results. The thesis thus concludes that the novel iterative-style approach is a more credible approach to the construction of ITSs in mathematics than existing techniques.

The Initial Stage of Teaching Proof in Mathematics Course

This article discusses techniques for organization of propaedeutic stage of teaching proof in mathematics course. It identifies types of tasks that allow students of 5–6 classes to form the ability to carry out simple proofs. This article describes each type of tasks features, it gives some examples.