Challenging the mathematician’s ‘ultimate substantiator’ role in a low lecture innovation

In this paper we draw on our experiences as member of the International Advisory Board and principal investigator of a research project on undergraduate mathematics teaching and learning to comment on the study of university mathematics as a process of enculturation into new mathematical practices and new ways of constructing and conveying mathematical meaning. We see this enculturation as the adaptation of different ways to act and communicate mathematically. We take a discursive perspective and we treat the changes to the mathematical and pedagogical perspectives of those who act – students and lecturers – as discursive shifts (Sfard, 2008). Our particular focus is on the shifts concerning the ‘ultimate substantiator’ role typically attributed to the lecturer

Creating a Space for Mathematicians and Educators: The philosophical basis for the Klein Project

The Klein Project is unique within contemporary initiatives in mathematics education because it is deliberately designed to use the potential of both mathematicians and mathematics educators to enhance the quality of teaching at the upper levels of secondary school. This means that a "space" must be created where productive discussions can be held, free from the divisions, pre-conceptions, and acrimony that has characterised some interactions between these two groups. It also means that there must be a mechanism for all those interested to make a significant contribution. I discuss how this is achieved

L’enseignement des fractions en France et en Nouvelle- Zélande

International audienceIt might be expected that teaching fractions and decimals in English-speaking countries and in French-speaking countries would be closely similar. This study argues that this is not the case. The most obvious difference concerns mixed numbers, which are neither used nor taught anymore in France. Reasons for these differences seem to be more socio-political than mathematical. We examine the history of fractions and discuss issues of notation. The history of the decimalisation of weights and measures is also relevant. Decimalisation originated in France at the end of the 18 th century and today is still not fully adopted in Anglo-Saxon countries. Using a decimal system for weights and measures makes mixed numbers a mathematical oddity. The mathematical differences, evident in the two groups of countries, are reflected in the everyday language used for numbers and measurement. In English, mixed numbers are expressed as numbers, but in French the whole and fractional parts are separated. The comparison of the French and the New Zealand curricula reveals that in France fractions are taught after decimals, which is the opposite in New Zealand. This difference of order of presentation in the mathematics curricula influences students' conceptions of number and the errors they are prone to make.Ce travail examine les connaissances mathématiques utilisées dans la vie courante et enseignées à l'école en Nouvelle-Zélande et en France en particulier concernant les fractions. Dans les pays anglo-saxons, les fractions sont abondamment utilisées, et les nombres mixtes du type 3 ½ pour 3,5 sont encore manipulés. Alors qu'en France, pionnière en matière de décimalisation, les écritures décimales sont utilisées beaucoup plus volontiers. Ceci révèle une culture mathématique différente qui aboutit à l'utilisation de notations mathématiques différentes, aussi bien dans la vie quotidienne que dans les programmes scolaires. Afin de situer notre propos, nous développons tout d'abord certains aspects historiques concernant les fractions et les nombres décimaux. Nous examinons ensuite les différences entre la culture anglo-saxonne et française : d'une part en étudiant les aspects culturels et langagiers des fractions puis d'autre part en considérant les aspects didactiques de cette notion. Cette étude montre que si a priori les similitudes sont nombreuses entre l'enseignement de fractions en France et en Nouvelle-Zélande, il existe des points divergents, en particulier la programmation des instructions officielles

Is what you see what you get? representations, metaphors and tools in mathematics didactics

This paper is exploratory in character. The aim is to investigate ways in which it is possible to use the theoretical concepts of representations, tools and metaphors to try to understand what learners of mathematics ‘see’ during classroom interactions (in their widest sense) and what they might get from such interactions. Through an analysis of a brief classroom episode, the suggestion is made that what learners see may not be the same as what they get. From each of several theoretical perspectives utilised in this paper, what learners ‘get’ appears to be something extra. According to our analysis, this something ‘extra’ is likely to depend on the form of technology being used and the representations and metaphors that are available to both teacher and learner

Mathematical Foresight: Thinking In The Future To Work In The Present

Originating from interviews with mathematics colleagues, written accounts of mathematicians engaging with mathematics, and Wes\u27s reflections on his own mathematical work, we describe a process that we call mathematical foresight: the imagining of a resolution to a mathematical situation and a path to that resolution. In a sense, mathematical foresight is the process of imagining a not-yet-experienced mathematical event—the solution to a problem solving scenario, or the creation of a mathematical model for a biological system, for examples that could occur in the future. This future thinking process guides the mathematician\u27s present mathematical activity, motivates them, and bolsters persistence

O Desenvolvimento de um Registro Matemático Maori

O trabalho relatado aqui é uma versão resumida de vários documentos escritos em parceria com Uenuku Fairhall, Escola Secundária de Westem Heights, e Tony Trinick, Faculdade de Educação de Auckland (Barton & Fairhall, 1995,; Barton, Fairhall & Trinick, 1995a, 1995b, 1998,; Fairhall, 1993,; Trinick 1997). Durante os últimos vinte anos, a Nova Zelândia possibilitou e promoveu um debate para o ensino de Matemática em idioma indígena. Houve, em pequeno período de tempo, um grande desenvolvimento de vocabulário e de sintaxe, de construção de currículo e de escrita de texto. Embora cada contexto cultural seja diferente, uma análise dessa situação pode ser instrutiva tanto para outras situações que se assemelhem ao contemplar o ensino de qualquer ciência no idioma indígena, como também para aqueles interessados na relação entre Matemática e idioma. Esta palestra explica alguns dos processos de base e algumas das conseqüências da produção de um discurso matemático forçado. Tradução: Ana Maria Petraitis Libli

Supporting newly qualified nurses in the UK: a systematic literature review

Aim: This is a systematic literature review of the existing published research related to the development of preceptorship to support newly qualified nurses in the United Kingdom (UK). Background: It has been known for some time that newly qualified nurses experience a period of unsettling transition at the point of registration. In the UK, preceptorship has been the professional body’s recommended solution to this for over 20 years. Data Sources: Searches were made of the CINAHL Plus and MEDLINE databases. Review Methods: A systematic review was carried out in August 2011. Twelve separate searches were conducted generating 167 articles, of which 24 were finally reviewed. Papers were critically reviewed and relevant data were extracted and synthesised using an approach based on Preferred Reporting Items for Systematic Reviews and Meta-Analysis ( PRISMA). Results and Discussion: A results table is presented of the twenty-four sources generated by the systematic search. Three themes were identified from the empirical evidence base: ‘Managerial Support Framework’; ‘Recruitment and Retention’; and ‘Reflection and Critical Thinking in Action’;. Conclusion: There is strong evidence that the newly qualified nurse benefits from a period of supported and structured preceptorship, which translates to improved recruitment and retention for the employing organisations. Recommendations for Further Research and Practice: The existing literature provides an evidence base upon which to construct a preceptorship programme and a means by which to measure its efficacy and monitor its future development. Case study research projects should be considered for future preceptorship programmes in order to find the most effective methods of delivery.Research funded by Chesterfield Royal Hospital NHS Trus

The Impact of Prior Authorization on Buprenorphine Dose, Relapse and Cost of Opioid Addiction Treatment

This presentation discusses the impact of prior authorization on Buprenorphine dose, relapse, and cost for opioid addiction treatment for Massachusetts Medicaid members. Presented at the AcademyHealth Annual Research Meeting 2013