The effective mathematics department: adding value and increasing participation?

Given the commonly accepted view that having a mathematically well-educated populace is strategically important, there is considerable international interest in raising attainment, and increasing participation, in post-compulsory mathematics education. In this article I develop multi-level models using datasets from the UK Department for Education’s National Pupil Database (NPD) in order to explore 1) school effects upon student progress in mathematics from age 11-16 in England, and 2) student participation in advanced level mathematics over the following two years. These analyses highlight between-school variation in the difference between mathematical and general academic progress. Furthermore, the between–school differences in post-compulsory mathematics participation are large. Importantly, there is no evidence to suggest that schools/departments with higher ‘contextual value added’ from 11-16, a key measure in government accountability processes in England, are also more effective in recruiting and retaining students in post-16 advanced mathematics courses

Reconsidering the rise in A-level mathematics participation

There is growing support for making the study of mathematics to age 18 compulsory for all young people in England. This paper aims to inform this debate through new insights into historic A-level Mathematics participation trends. We analyse full-year cohorts from the Department for Education’s National Pupil Database for age-16 students from 2004-2010, a total of just over 4.5 million young people. Using a cohort-tracking approach we aim to better understand the flow of young people through upper secondary mathematics education. Earlier work identified GCSE attainment as the strongest predictor of A-Level Mathematics participation. In this paper we show that the percentage of students progressing to A-Level by GCSE grade has not changed significantly over the period in question, with some exceptions. This implies that the increase in A-level Mathematics numbers is largely explained by the growing proportion of higher GCSE grades. We discuss the implications for policy that this raises, e.g. the possible impact of making GCSE mathematics more demanding

The effective mathematics department: adding value and increasing participation?

Given the commonly accepted view that having a mathematically well-educated populace is strategically important, there is considerable international interest in raising attainment, and increasing participation, in post-compulsory mathematics education. In this article I develop multi-level models using datasets from the UK Department for Education’s National Pupil Database (NPD) in order to explore 1) school effects upon student progress in mathematics from age 11-16 in England, and 2) student participation in advanced level mathematics over the following two years. These analyses highlight between-school variation in the difference between mathematical and general academic progress. Furthermore, the between–school differences in post-compulsory mathematics participation are large. Importantly, there is no evidence to suggest that schools/departments with higher ‘contextual value added’ from 11-16, a key measure in government accountability processes in England, are also more effective in recruiting and retaining students in post-16 advanced mathematics courses

Toward Synthesis of Network Updates

Updates to network configurations are notoriously difficult to implement correctly. Even if the old and new configurations are correct, the update process can introduce transient errors such as forwarding loops, dropped packets, and access control violations. The key factor that makes updates difficult to implement is that networks are distributed systems with hundreds or even thousands of nodes, but updates must be rolled out one node at a time. In networks today, the task of determining a correct sequence of updates is usually done manually -- a tedious and error-prone process for network operators. This paper presents a new tool for synthesizing network updates automatically. The tool generates efficient updates that are guaranteed to respect invariants specified by the operator. It works by navigating through the (restricted) space of possible solutions, learning from counterexamples to improve scalability and optimize performance. We have implemented our tool in OCaml, and conducted experiments showing that it scales to networks with a thousand switches and tens of switches updating.Comment: In Proceedings SYNT 2013, arXiv:1403.726

Connecting mathematics teaching with vocational learning

For many vocational students in England, mathematics is now a compulsory part of their programme, yet the inclusion of an academic subject within a vocational course presents challenges. In this paper, an analysis of a series of case studies of vocational student groups in Further Education colleges in England shows how contrasting practices in ‘functional mathematics’ and vocational classes reinforce perceptions that mathematics is an isolated and irrelevant subject. Some mathematics teachers made contextual connections by embedding mathematical problems in vocationally-related scenarios but distinctive socio-cultural features of vocational learning situations were often absent from mathematics classes. Addressing this disconnection requires a pedagogical approach and classroom culture that links mathematics learning with vocational values. The findings suggest that adopting mathematics classroom practices that reflect the surrounding vocational culture creates greater coherence for students and has positive effects on their engagement with mathematics learning

Connecting mathematics teaching with vocational learning

For many vocational students in England, mathematics is now a compulsory part of their programme, yet the inclusion of an academic subject within a vocational course presents challenges. In this paper, an analysis of a series of case studies of vocational student groups in Further Education colleges in England shows how contrasting practices in ‘functional mathematics’ and vocational classes reinforce perceptions that mathematics is an isolated and irrelevant subject. Some mathematics teachers made contextual connections by embedding mathematical problems in vocationally-related scenarios but distinctive socio-cultural features of vocational learning situations were often absent from mathematics classes. Addressing this disconnection requires a pedagogical approach and classroom culture that links mathematics learning with vocational values. The findings suggest that adopting mathematics classroom practices that reflect the surrounding vocational culture creates greater coherence for students and has positive effects on their engagement with mathematics learning

Mathematics education policy enactment in England’s Further Education Colleges

England’s Further Education (FE) sector is in permanent flux with policy interpretations and translations taking place at multiple levels within increasingly large and complex multi-site organizations. Devolved responsibility gives managers considerable influence in policy enactment processes which can lead to within-college tensions between vocational and mathematics teachers. This paper examines two within-college policies affecting students’ mathematics learning opportunities: 1) subject choice, and 2) examination entry levels. These policies have produced inequitable opportunities for students on different vocational study programmes. Given the strategic importance of improving mathematics education, this paper explains how multiple actors and structures interact in the enactment of policy in complex FE college settings. Such understandings are needed to inform better policy design and implementation that in turn can improve mathematics education in Further Education colleges in England

Evaluation of the effect of tyrothricin on beta-hemolytic streptococci in salva. Part I: The effect of salvia upon bacteria. Part II: Effect of tyrothricin on the New York 5 strain of Streptococcus pyogenes in saliva

Part II of thesis by Brancato, Noyes, and Swift. Part I of thesis by Swift. Thesis (M.A.)--Boston UniversityThe antibacterial effect of saliva has been known for many years. Still the exact nature of the antagonistic action of saliva upon bacteria is as yet unsettled. Most workers agree, however, that the salivary bacterial inhibitory action is brought about in at least six ways: The first antibacterial effect is changes in pH, which affect the growth of oral organisms. Furthermore, this change in pH is dependent on diet and on the type of organisms in the oral cavity. The second is the mechanical factors involved, for saliva not only flushes bacteria from the mouth, but dilutes the number of organisms as well. The third is the antibacterial action of the cellular components in saliva. The leukocytes in saliva have a phagocytic action, and the non-phagocytic epithelial cells slough off in sheets, carrying with them thousands of organisms which have lodged in the partially turned edges of the necrotic cells . The fourth antibacterial action is ascribed to the presence of immune bodies in the saliva which lyse or agglutinate the oral bacteria. The fifth is the presence of oral bacteria which are antagonistic to new invaders. And the sixth is the presence of enzymes that lyse some oral bacteria or alter their cell membranes thereby inhibiting further growth. In recent years a great deal of investigation has been made to ascribe the enzymatic effect as the chief antibacterial agent in saliva; however, contradictory work has been done to try to attribute the chief antibacterial action of salivary cocci. Indeed the antibacterial effect of saliva is not always present, for the bacteriostatic effect of saliva is variable from day to day and from individual to individual. The only way of reducing the number of oral bacteria is to add to the saliva an antibiotic. Tyrothricin was used. In an attempt to delineate the range of concentration of tyrothricin per ml. effective against the New York 5 strain of Streptococcus pryogenes in saliva, this experiment was carried out. It was molded after the unpublished work of Belding concerning the effect of tyrothricin on the Oxford Strain of Staphylococcus aureus in saliva. The required inoculum of approximately one million organisms per ml was obtained by growing cultures of the streptococci under uniform conditions and setting up a table of the absorbances and viable cell counts, from which dilution factors for further cultures could be estimated. Controls were set up for determining possible inhibition of tyrothricin and/or test organisms by the various diluting fluids including saliva. Final concentrations per ml of 10, 25, 50, 75, and 100 µg of tyrothricin integrated with saliva and an approximated number of streptococci were plated out after 30 and 60 minutes exposure periods and were counted after 24 and 48 hours of incubation at 37°C. Whereas 1 µg per ml of tyrothricin reduced markedly the number of streptococci suspended in water during a 30 minute exposure period and 10 µg per ml, under similar conditions, caused complete inhibition, 10 µg per ml of the antibiotic was ineffective against this test organism suspended in saliva during a 30 minute exposure period but caused about an 80 per cent reduction in viable organisms during 60 minutes exposure. The length of the exposure period necessary for effective inhibition varied inversely with the concentration of tyrothricin per ml, 100 µg per ml causing a 98 per cent reduction of viable organisms during an exposure period of 1 minute. For the 30 minute exposure period, the quantity of tyrothricin effective against this strain of streptococci mixed in saliva would fall in the 10 µg - 25 µg per ml range and for shorter exposure periods, the concentration per ml would have to be greater. Cultures completely negative during 24 hours incubation at 37°C, showed a typical growth during 48 hours. This is considered indicative of the bacteriostatic action of tyrothricin which, prolonged, resulted in the death of large numbers of the streptococci. The results which were obtained in these experiments serve chiefly to point out the way for further work and to form a basis for the general conclusions listed below: 1. The action of tyrothricin on bacteria is inhibited by saliva to a large degree. 2. The minimal amounts of tyrothricin necessary to produce complete inhibition of growth of Streptococcus pyogenes in saliva is between 25 and 50 µg per ml acting for 30 minutes. 3. There is an effective reduction of Streptococcus pyogenes in saliva by concentrations of tyrothricin between 10 and 25 µg per ml acting for 30 minutes. 4. Tyrothricin acts immediately upon contact with Streptococcus pyogenes. 5. The action of tyrothricin on Streptococcus pyogenes in saliva is apparently bacteriostatic and not of a permanent nature as manifested by growth of atypical colonies during 48 hours incubation. 6. Tyrothricin above a concentration of 50 µg per ml had a definite reducing effect on the bacterial population of this saliva. 7. Saliva also has a bactericidal or bacteriostatic (or both) action against Streptococcus pyogenes

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