Schools’ Strategies for Promoting Girls’ Participation in Mathematics

Fewer girls than boys in England participate in post-compulsory mathematics. Previous studies have shown the significance to girls of their mathematics lessons and teachers, of cultural constructions of gender and mathematics, of career perceptions A multiple case-study project investigated institutions with unusually high participation by girls in mathematics. Focus groups and lesson observations were used to explore school pedagogy and culture. Common factors were: early preparation for demanding mathematics, a departmental ethos which encouraged student-teacher interactions in and out of lessons, teachers who explicitly and repeatedly confirmed that girls would succeed at mathematics A-level, appreciation of mathematics as opening doors to many careers

Variations in duty arrangements to respond to concerns about children's welfare

Historians and philosophers of mathematics share an interest in the nature of mathematics: what it is, what features affect its growth, how it informs other disciplines. But much of the work done in history and philosophy of mathematics suggests that the two groups largely work in isolation. A reconsideration of the history of mathematical analysis in the 19th Century suggests that history and philosophy of mathematics can be done together to the advantage of both, and also how legitimately different enquiries need not drive them apart

Pariah moonshine

Finite simple groups are the building blocks of finite symmetry. The effort to classify them precipitated the discovery of new examples, including the monster, and six pariah groups which do not belong to any of the natural families, and are not involved in the monster. It also precipitated monstrous moonshine, which is an appearance of monster symmetry in number theory that catalysed developments in mathematics and physics. Forty years ago the pioneers of moonshine asked if there is anything similar for pariahs. Here we report on a solution to this problem that reveals the O'Nan pariah group as a source of hidden symmetry in quadratic forms and elliptic curves. Using this we prove congruences for class numbers, and Selmer groups and Tate--Shafarevich groups of elliptic curves. This demonstrates that pariah groups play a role in some of the deepest problems in mathematics, and represents an appearance of pariah groups in nature.Comment: 20 page

Recruiting More Mathematics Teachers Using Collaboration as the Main Ingredient: An Effective Model from Missouri

A National Science Foundation grant was designed to develop a series of courses to connect mathematics concepts taught in middle school classes with actual class materials used at the middle school level; however, a second component of the grant focused on efforts to recruit more teachers into the field of mathematics. By collaborating with several groups across Missouri, several strategies were developed that were shown to have positive results, both in increasing awareness of mathematics teacher shortage issues, and in encouraging attendance in Missouri mathematics education programs. The strategies developed were easy to implement and low in cost. The Missouri team encourages others to duplicate or adapt this recruitment model in their own regions

Curricular orientations to real-world contexts in mathematics

A common claim about mathematics education is that it should equip students to use mathematics in the ‘real world’. In this paper, we examine how relationships between mathematics education and the real world are materialised in the curriculum across a sample of eleven jurisdictions. In particular, we address the orientation of the curriculum towards application of mathematics, the ways that real-world contexts are positioned within the curriculum content, the ways in which different groups of students are expected to engage with real-world contexts, and the extent to which high-stakes assessments include real-world problem solving. The analysis reveals variation across jurisdictions and some lack of coherence between official orientations towards use of mathematics in the real world and the ways that this is materialised in the organisation of the content for students

Mathematical Communication: What And How To Develop It In Mathematics Learning?

Mathematics is the language of symbols so that everyone who studied mathematics required having the ability to communicate using the language of these symbols. Mathematical communication skills will make a person could use mathematics for its own sake as well as others, so that will increase positive attitudes towards mathematics. Mathematical communication skills can support mathematical abilities, such as problem solving skills. With good communication skills then the problem will more quickly be represented correctly and this will support in solving problems. Students' mathematical communication skills can be developed in various ways, one with group discussions. Brenner (1998) found that the formation of small groups facilitate the development of mathematical communication skills. This paper describes the mathematical communication and how to develop the mathematical communication skills in learning mathematics. For further clarify the discussion, given also the example of learning that emphasizes the development of mathematical communication skills. Keywords: Mathematical Communication, Mathematics Learning

Topological Entropy and Algebraic Entropy for group endomorphisms

The notion of entropy appears in many fields and this paper is a survey about entropies in several branches of Mathematics. We are mainly concerned with the topological and the algebraic entropy in the context of continuous endomorphisms of locally compact groups, paying special attention to the case of compact and discrete groups respectively. The basic properties of these entropies, as well as many examples, are recalled. Also new entropy functions are proposed, as well as generalizations of several known definitions and results. Furthermore we give some connections with other topics in Mathematics as Mahler measure and Lehmer Problem from Number Theory, and the growth rate of groups and Milnor Problem from Geometric Group Theory. Most of the results are covered by complete proofs or references to appropriate sources