Introduction to geodesics in sub-Riemannian geometry

International audience

"Am I Korean American?": beliefs and practices of parents and children living in two languages and two cultures

The purpose of this study is to explore attitudes and practices regarding their heritage language and the dominant English language among Korean American immigrant families. Using the framework of Language Ideology (Silverstein, 1979), I had three research questions: a) why do parents send their children to a Korean language school, b) what attitudes do immigrant parents and their children show toward Korean and English, and c) how are the parents and children involved in the practices of these two languages? I conducted a survey of parents whose children attended a Korean language school in Urbana-Champaign, Illinois, where the number of Korean sojourners (temporary residents) exceeds that of Korean immigrants. Forty participant parents provided demographic information. They described their children's language-use patterns depending on interlocutors as well as their language proficiency in both Korean and English. The reasons for sending their children to the Korean language school were significantly different depending on the respondents' residential status. In comparison to the sojourners, immigrants tended to give more priority to their children's oral language development and Korean identity construction. I also conducted case studies of three Korean immigrant families with 3- to 5-year-old children, using interviews, observations, and photographs of children's work. The collected data were analyzed according to themes such as daily life, parental beliefs about two languages, practices in two languages, children's attitudes toward two languages, and challenges and needs. Despite individual families' different immigration histories, the three families faced some common challenges. Because of their busy daily routines and different lifestyles, the immigrant families had limited interactions with other Koreans. The parents wanted their children to benefit from two communities and build a combined ethnic identity as Korean Americans. I argue that a Korean language school should expand its role as a comfort zone for all Koreans and Korean Americans. This study explores the heterogeneity among Korean sojourner and immigrant families and their language use and identity construction.

The background impact in HEI math lectures: an experience in math in the 1st year of Accounting and Management Degree

It is a fact, and far from being a new one, that students have been entering Higher Education courses with many different backgrounds in terms of secondary school programs they attended. The impact of these basic skills is a general and worldwide challenge, fundamentally when facing some specific “constructive” subjects like foreign languages and Mathematics. Working with students with an extensive variety of Math qualifications is an outrageous challenge when they enter an advanced Math course, leading to an almost generalized expectations’ failure - from students enrolled in course and from their teachers, who feel powerless in trying to monitor knowledge construction from completely different “starting points”. If teachers’ "haste" is average, more than half of the students do not “go along” and give up, even before experiencing any kind of evaluation procedure. On the contrary, if the “speed” is too low, others are discouraged (feeling not progressing at all) and the teacher runs the risk of not meeting the minimum objectives (general and specific) of its course, which may have a negative impact on students’ future training development. Failure in Mathematics, despite being a recurrent and global issue, does not have any “magical solution”, however, in general, teachers in this area seem untiring, searching, investigating, trying and implementing new and old “recipes” to tackle and demystify this subject. In this article we describe a project developed in a Math course, with the first year students from an Accounting and Management bachelor degree, and its outcomes since it was brought to practice, revealing its impact in students’ success, from approval to dropout rates, in this course. We will shortly describe students’ differentiated Math backgrounds, their results in a pre-assessment analysis and how we try to deal with these differences and level them up, having in mind the same “finish line”. One should never forget that all these students where officially accepted in higher education institutions, so they are ones’ reality, the reality of institutions whose name one should value and strive to defend.

“Varopoulos paradigm”: Mackey property versus metrizability in topological groups.

The class of all locally quasi-convex (lqc) abelian groups contains all locally convex vector spaces (lcs) considered as topological groups. Therefore it is natural to extend classical properties of locally convex spaces to this larger class of abelian topological groups. In the present paper we consider the following well known property of lcs: “A metrizable locally convex space carries its Mackey topology ”. This claim cannot be extended to lqc-groups in the natural way, as we have recently proved with other coauthors (Außenhofer and de la Barrera Mayoral in J Pure Appl Algebra 216(6):1340–1347, 2012; Díaz Nieto and Martín Peinador in Descriptive Topology and Functional Analysis, Springer Proceedings in Mathematics and Statistics, Vol 80 doi:10.1007/978-3-319-05224-3_7, 2014; Dikranjan et al. in Forum Math 26:723–757, 2014). We say that an abelian group G satisfies the Varopoulos paradigm (VP) if any metrizable locally quasi-convex topology on G is the Mackey topology. In the present paper we prove that in any unbounded group there exists a lqc metrizable topology that is not Mackey. This statement (Theorem C) allows us to show that the class of groups satisfying VP coincides with the class of finite exponent groups. Thus, a property of topological nature characterizes an algebraic feature of abelian groups.

Eleição nas escolas: uma análise do impacto do diretor eleito sobre o desempenho educacional no Estado da Bahia

In Brazil, the selection of school principals is set in a decentralized manner by each state and city, such that processes may vary with time for a specific locality. In the state of Bahia, school principals were appointed by a higher political hierarchy until 2008, when schools under state administration started selecting principals by elections. The main goal of this work is to evaluate whether changing this specific rule affected students proficiency levels. This is achieved by using a panel data and difference-in-differences approachs that compares state schools (treatment group) to city schools (control group) that did not face a selection rule change and thus kept having their principals politically appointed. The databases used are Prova Brasil 2007, 2009 and 2011, the first one prior and the other two former to the policy change. Our results suggest that students attending schools with principals that are selected and elected have slightly lower mean proficiency levels both in mathematics and in portuguese exams than those attending schools with appointed principals. This result, according to the literature, could be related to perverse effects of selecting school administrators by vote, such as corporatism, clientelism and politicization of the school environment

Some misspecfication problems in long-memory time series models

Doctor of Philosophy in Mathematics

Investigating stratification, language diversity and mathematics classroom interaction

Research on the socio-political dimensions of language diversity in mathematics classrooms is under-theorised and largely focuses on language choice. These dimensions are, however, likely to influence mathematics classroom interaction in many other ways than participants’ choice of language. To investigate these influences, I propose that the notions ofheteroglossia, orders of indexicality and scale-jumping, can provide new theoretical tools with which to understand the links between classroom interaction and broader social patterns of marginalisation. To illustrate the utility of these ideas, I include some analysis of an episode observed in a sheltered elementary school second language mathematics classroom in Canada.

Steps to success : family-friendly guide for fourth grade : mathematics

This document is designed to: provide examples of the standards, skills, and knowledge your child will learn in mathematics and should be able to do upon exiting fourth grade ; suggest activities on how you can help your child at home ; offer additional resources for information and help.

Steps to success : family-friendly guide for third grade : mathematics

This document is designed to: provide examples of the standards, skills, and knowledge your child will learn in mathematics and should be able to do upon exiting third grade ; suggest activities on how you can help your child at home ; offer additional resources for information and help.

Steps to success : family-friendly guide for fifth grade : mathematics

This document is designed to: provide examples of the standards, skills, and knowledge your child will learn in mathematics and should be able to do upon exiting fifth grade ; suggest activities on how you can help your child at home ; offer additional resources for information and help.

Orals ain't orals : how instruction and assessment practices affect delivery choices with prepared student oral presentations.

Despite an ostensibly technology-driven society, the ability to communicate orally is still seen as an essential ability for students at school and university, as it is for graduates in the workplace. The need to develop effective oral communication skills is often tied to future work-related tasks. One tangible way that educators have assessed proficiency in this area is through prepared oral presentations. While some use the terms oral communication and oral presentation interchangeably, other writers question the role more formal presentations play in the overall development of oral communication skills. Adding to the discussion, this paper is part of a larger study examining the knowledge and skills students bring into the academy from previous educational experiences. The study examines some of the teaching and assessment methods used in secondary schools to develop oral communication skills through the use of formal oral presentations. Specifically, it will look at assessment models and how these are used as a form of instruction as well as how they contribute to an accurate evaluation of student abilities. The purpose of this paper is to explore key terms and identify tensions between expectations and practice. Placing the emphasis on the ‘oral’ aspect of this form of communication this paper will particularly look at the ‘delivery’ element of the process.

Methodologies for investigating relationships between concept development and the development of problem solving abilities

This paper is the second in a pair that Lesh, English, and Fennewald will be presenting at ICME TSG 19 on Problem Solving in Mathematics Education. The first paper describes three shortcomings of past research on mathematical problem solving. The first shortcoming can be seen in the fact that knowledge has not accumulated – in fact it has atrophied significantly during the past decade. Unsuccessful theories continue to be recycled and embellished. One reason for this is that researchers generally have failed to develop research tools needed to reliably observe, document, and assess the development of concepts and abilities that they claim to be important. The second shortcoming is that existing theories and research have failed to make it clear how concept development (or the development of basic skills) is related to the development of problem solving abilities – especially when attention is shifted beyond word problems found in school to the kind of problems found outside of school, where the requisite skills and even the questions to be asked might not be known in advance. The third shortcoming has to do with inherent weaknesses in observational studies and teaching experiments – and the assumption that a single grand theory should be able to describe all of the conceptual systems, instructional systems, and assessment systems that strongly molded and shaped by the same theoretical perspectives that are being used to develop them. Therefore, this paper will describe theoretical perspectives and methodological tools that are proving to be effective to combat the preceding kinds or shortcomings. We refer to our theoretical framework as models & modeling perspectives (MMP) on problem solving (Lesh & Doerr, 2003), learning, and teaching. One of the main methodologies of MMP is called multi-tier design studies (MTD).

Action research for contexts of change and inequality

Undoubtedly, the past half-century has witnessed an escalation of changes in the social, political, economic and educational structures in many societies around the world. Some have seen change as a challenge and hope while, for many others, it is a source of concern and worry. Some have adopted change with gusto, while for many it is something to be resisted. Some say we live in a world and times with an increasing awareness that “times are changing”, while for some “the more things change, the more they stay the same”.

Year 8, 9 and 10 students’ understanding and access of percent knowledge

This paper reports on Years 8, 9 and 10 students’ knowledge of percent problem types, use of diagrams, and type of solution strategy. Non- and semi-proficient students displayed the expected inflexible formula approach to solution but proficient students used a flexible mixture of estimation, number sense and trial and error instead of expected schema based methods.

Interdisciplinary modelling

This article examines one approach to promoting creative and flexible use of mathematical ideas within an interdisciplinary context in the primary curriculum, namely, through modelling. Three classes of fifth-grade children worked on a modelling problem, The First Fleet (Australia’s settlement), situated within the curriculum domains of science and studies of society and environment. Reported here are the cycles of development displayed by one group of children as they worked the problem, together with the range of models created across the classes. Children developed mathematisation processes that extended beyond their regular curriculum, including identifying and prioritising key problem elements, exploring relationships among elements, quantifying qualitative data, ranking and aggregating data, and creating and working with weighted scores. Aspects of Goldin’s (2000, 2007) affective structures also appeared to play an important role in the children's mathematical developments.