WIDENING AND INCREASING POST-16 MATHEMATICS PARTICIPATION: PATHWAYS, PEDAGOGIES AND POLITICS

This paper explores the potential impact of a national pilot initiative in England aimed at increasing and widening participation in advanced mathematical study through the creation of a new qualification for 16- to 18-year-olds. This proposed qualification pathway—Use of Mathematics—sits in parallel with long-established, traditional advanced level qualifications, what we call ‘traditional Mathematics’ herein. Traditional Mathematics is typically required for entry to mathematically demanding undergraduate programmes. The structure, pedagogy and assessment of Use of Mathematics is designed to better prepare students in the application of mathematics, and its development has surfaced some of the tensions between academic/pure and vocational/applied mathematics. Here, we explore what Use of Mathematics offers, but we also consider some of the objections to its introduction in order to explore aspects of the knowledge politics of mathematics education. Our evaluation of this curriculum innovation raises important issues for the mathematics education community as countries seek to increase the numbers of people that are well prepared to apply mathematics in science and technology-based higher education courses and work places.     

What's in It for Me? Incentives,Learning, and Completion in Massive Open Online Courses

This study investigated the distribution of incentives (e.g., certificates, badges) for massive open online course (MOOC) completion, and relationships between incentives and MOOC outcomes. Participants were 779 MOOC students internationally who participated in at least 303 different MOOCs offered by at least 12 providers. MOOC participants most commonly intended to receive, and in actuality received, free and paid course certificates of completion; other incentives (e.g., digital badges, postsecondary credits) were far less common. In addition, MOOC participants' intentions to receive both free and paid certificates were consistently and positively related to perceived learning and course completion, net other factors. (Keywords: massive open online courses, MOOCs, motivation, incentives, microcredentials, certificates of completion)     

Study-service as a significant factor in career development

The purpose of this paper is to describe the role of the Botswana study-service scheme (Tirelo Setshaba) in the career development of its participants. Study-service is defined as community service used to educate those who participate in contrast to other service programmes where the main objective is to provide manpower e.g. by providing service to the community. First, the existing career development situation in Botswana for senior secondary school students is reviewed and findings from some recent research in this field in the country are presented. Second, the nature of the one year experience gained by Tirelo Setshaba participants is described including the uniqueness of Tirelo Setshaba as compared to other similar schemes in that service takes place before post-secondary education, but with other policies being similar to those developed for university students. Third, the paper presents a rationale for career development assistance for Tirelo Setshaba participants and describes career development material prepared for them. The nature of the scheme, with two or a maximum of four participants assigned to a village, has made it necessary to design a career service for clients who are so widely scattered that the often-used career talks, conventions or one-to-one counselling are impractical. Finally, the paper argues for a proper evaluation of Tirelo Setshaba's impact on career development as the conclusions drawn in the paper are based on limited observations.Senior Research Fellow, National Institute of Development Research and Documentation, University of Botswana. She has served for several years as planning officer with the Ministry of Education in Botswana and as a psychologist (career guidance) in Sweden.Tirelo Setshaba Adviser, Ministry of State President, Botswana. He has long experience from study-service schemes in a number of countries, inter alia Botswana, Nepal and Indonesia.     

A content analysis of the presentation of the mole concept in chemistry textbooks

The goal of this study was to examine the means used by textbook authors to introduce, define, and explain the mole concept in high school and introductory college chemistry textbooks. The analysis was framed by four questions:

• 1 How is the mole defined?
• 2 What concepts about the atom are introduced prior to the mole?
• 3 Is Avogadro's constant presented as an experimentally determined value?
• 4 What is the context for introducing the mole?

Twenty-nine high school and introductory college level chemistry texts were examined. After independent reading of appropriate sections of each text, discussion of differences, second or third readings of texts, and subsequent discussions, both authors reach 100% agreement concerning the results. Major conclusions were

• 1 Two ways of defining the mole dominate the texts. One way defines the mole as Avogadro's number (6.02 × 10²³) particles; the other method defines the mole in terms of carbon-12.
• 2 All texts that present a definition in terms of C-12 introduce and define concepts about the atom prior to introducing the mole.
• 3 Most texts at all levels point out that the value 6.02 × 10²³ is an experimentally determined quantity.
• 4 Nearly all texts discuss the mole in relation to die problem of finding a way to count particles that are too small to be directly weighed. Most texts also use a familiar counting unit, such as the dozen, to introduce the mole by analogy.

Four issues were discussed: (a) the defining attributes of the mole concept itself and the cognitive requirements for comprehending the two most frequently used definitions; (b) the connection between the definition of the mole presented in the text and the concepts about atoms that are introduced before the mole concept is developed; (c) the experimental nature of Avogadro's number; and (d) the context or setting for developing the mole concept.     

A different type of charter school: in prestige charters,a rise in cachet equals a decline in access

This paper seeks to elucidate a specific type of charter school. While much has been written about school choice and the expanding charter school segment, a growing and important number of charter schools do not fit in to the common understanding of these schools. Distinct from many of their counterparts, prestige charter schools have the following two features: elements which foster a reputation similar to that of elite private schools and a student population demographically distinct from local public district schools – whereby the prestige charters serve a disproportionate number of advantaged families. The prestige elements include: founding by advantaged community members; parental involvement; wait lists; popularity with advantaged professionals; high test scores; and niche themes. The authors will show through two in-depth case studies that prestige charter schools work hand-in-hand with gentrification in urban neighborhoods, and result in racial and class segregation and inequality. This paper examines how these charter schools struggle when a rise in prestige coincides with a decline in access for low-income students. The authors recommend that given the current system of school choice, prestige charter schools must use tools and mechanisms to maintain demographic diversity and educational equity which is in the best interest of all children.     

Thinking with certainty or with doubt: a Lacanian theorisation of discursive knowledge in teacher education

ABSTRACT

The paper presents a theorisation of pedagogic knowledge formation, as a continuous attempt to understand the positions in discourse we occupy. The paper documents some participatory practitioner research by teacher educators centred on a course development initiative for student teachers of English, at an English university. Students researched their experiences of becoming a teacher within a course that was largely school-based, whilst their tutors researched their own involvement in the process (the main focus of this paper). Drawing on Lacanian theory, tutors are depicted as learning subjects having more or less certainty or doubt about the knowledge they possess. In attempting to understand this interplay of certainty and doubt, tutors arrive at stronger conceptualisations of learning. Through this approach, the paper provides a theoretically informed conception of professional knowledge, as involving a process of renewing ideas about learning, in meeting or resisting external demands.