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Let $F_n$ be a free group of rank $n$, with free generating set $X$. A subset $D$ of $F_n$ is a \emph{Distinct Difference Configuration} if the differences $g^{-1}h$ are distinct, where $g$ and $h$ range over all (ordered) pairs of distinct elements of $D$. The subset $D$ has diameter at most $d$ if these differences all have length at most $d$. When $n$ is fixed and $d$ is large, the paper shows that the largest distinct difference configuration in $F_n$ of diameter at most $d$ has size approximately $(2n-1)^{d/3}$., Comment: 14 pages

We report photometric follow-up observations of thirteen exoplanets (HATS-1 b, HATS2 b, HATS-3 b, HAT-P-18 b, HAT-P-27 b, HAT-P-30 b, HAT-P-55 b, KELT-4A b, WASP-25 b, WASP-42 b, WASP-57 b, WASP-61 b and WASP-123 b), as part of the Original Research By Young Twinkle Students (ORBYTS) programme. All these planets are potentially viable targets for atmospheric characterisation and our data, which were taken using the LCOGT network of ground-based telescopes, will be combined with observations from other users of ExoClock to ensure that the transit times of these planets continue to be well-known, far into the future., Comment: Accepted for publication in the Astronomy Theory, Observations and Methods Journal. Secondary school students (16-17 y/o) performed the majority of the analysis, as well as writing much of the paper, as part of the ORBYTS programme

Children's University (CU) aims to improve the aspirations, attainment, and skills of pupils aged 5-14 by providing learning activities beyond the normal school day. This trial focused on pupils in Years 5 and 6 (aged 9-11), and activities included after-school clubs, visits to universities, museums, and libraries, and 'social action' opportunities such as volunteering in the community. Local CU teams worked with schools to identify opportunities, and organise and monitor the activities. Children volunteered to take part and selected the activities they wished to attend, with the target of completing at least 30 hours of activity per year. Participation in activities was rewarded through credits, certificates, and a 'graduation' event attended by parents. 68 primary schools participated in this efficacy trial from March 2014 until July 2016. 2,603 pupils reported in an initial survey that they would like to take part in the kinds of activities offered, and these 'volunteer' pupils formed the main comparison groups. 1,452 of these pupils were in the 36 schools randomly allocated to receive the CU intervention, and 1,151 were in the 32 schools randomised to the control group. This project evaluated the impact of CU on pupils' reading and maths in Key Stage 2 tests, and on non-cognitive outcomes such as 'teamwork' and 'social responsibility' measured through an attitude survey. Results were obtained for Year 6 pupils after one year and for Year 5 pupils after two years. The headline findings below are based on the results for the 1,258 Year 5 pupils after two years. Surveys and interviews were conducted to explore other aspects of the intervention such as: participants' feedback, challenges of implementation, and control group activity. This trial was jointly funded by the Cabinet Office. Key Conclusions include: (1) Children in the CU schools made 2 additional months' progress in reading and maths compared to children in the other schools. The finding for maths has moderate security, and the finding for reading has low to moderate security; (2) Children in the CU schools made 2 additional months' progress in reading and maths compared to children in the other schools. The finding for maths has moderate security, and the finding for reading has low to moderate security; (3) Children ever eligible for Free School Meals (FSM) made 1 additional month's progress in maths, no additional progress in reading, and small gains in 'teamwork' and 'social responsibility' compared to ever FSM children in the other schools. The smaller number of ever FSM pupils means these results are less secure than the results for all pupils; (4) Compared to pupils in the control group, those in the treatment group were more likely to select professional occupations as their future aspiration, and to report higher levels of communication, empathy, self-confidence, resilience, and happiness, after the intervention, and (5) The intervention was feasible to run with support from school leaders. However, 7 schools decided not to implement the intervention despite receiving the training because of pressures to meet performance targets, and limited time. CU activities were reported as attractive to pupils. Children receiving CU for one year (those in Year 6) made a small gain in maths, but less progress in reading, compared to children in control schools. The smaller size of these effects compared to the results for the Year 5 cohort (that received CU for two years) suggests that children may benefit from longer involvement in CU. Further analyses suggested that all Year 5 children in schools doing CU made better average progress than children in control schools, regardless of their actual level of participation in CU activities. This could be seen as adding further caution to the headline results as to the extent to which gains were due to direct involvement in CU activities. However, one of the original research questions was whether the availability of CU activities could affect the whole cohort. For the non-participating group this may be evidence of such a cohort 'effect'.

The intervention evaluated here is one of two "youth social action" projects jointly funded by the Education Endowment Foundation, the U.K. Cabinet Office, the Pears Foundation and the Stone Family Foundation. It was delivered by the Youth United Foundation (YUF) and involved uniformed youth organisations being established in schools in six areas in the north of England. YUF helped to set up new units of The Scout Association, Fire Cadets, Sea Cadets or St John Ambulance in participating schools. The number, duration, and frequency of sessions varied: most groups met weekly, sessions lasted two hours on average, and the average number of sessions in the academic year was 24. Activities were delivered by trained staff from the uniformed youth organisations and in some cases also involved adult volunteers, including teachers. This project assessed the impact of participation on pupils' academic attainment, and on wider outcomes such as self-confidence and teamwork, using a randomized controlled trial design. The wider outcomes are of particular relevance because the participating organisations share core aims of inspiring young people to do community work and volunteer, to learn new skills, and to be active citizens. Seventy-one schools were randomly allocated to either receive the intervention or not. Of 7,781 Year 9 students, 3,377 reported in the initial survey that they would like to take part in the kinds of activities offered, and 663 took part in uniformed youth group activities during the 2014/2015 academic year. A process evaluation was also conducted to collect information about the mode of delivery and programme implementation, and feedback from teachers, pupils and parents. Key conclusions include: (1) There is no evidence that the intervention had any benefit in terms of pupils' academic performance. Although the attainment data suggests a small negative impact, the quality of this data is too low to draw this conclusion with confidence. The data quality was compromised due to changes in national testing; (2) Participation in the intervention is associated with a small improvement in self-reported nonattainment outcomes including self-confidence and teamwork. It is possible that these small effects are an underestimate due to technical issues regarding the groups of children that were compared in the analysis; (3) For pupils eligible for free schools meals, there is no evidence that the intervention had a positive impact on academic attainment or self-reported character attributes. Again, the attainment data suggests a negative impact, but the quality of this data is too low to draw this conclusion with confidence; (4) Almost a quarter of schools did not deliver the intervention due to issues such as lack of teacher volunteers, and other schools did not deliver a full programme of activity. Support from senior leaders, dedicated space, school staff time, and a dedicated slot in the school day or after school were all identified as necessary conditions for successful implementation; and (5) Study participants were extremely positive about the intervention and many felt it had a positive effect on the behaviour and skills of participating pupils. [This project is one of two "youth social action" projects jointly funded by the Education Endowment Foundation, the U.K. Cabinet Office, the Pears Foundation and the Stone Family Foundation.]

Consumer foraging behaviors are dynamic, changing in response to prey availability, seasonality, competition, and even the consumer's physiological state. The isotopic composition of a consumer is a product of these factors as well as the isotopic 'landscape' of its prey, i.e. the isotopic mixing space. Here we build a mechanistic framework that links the ecological and physiological processes of an individual consumer to the isotopic distribution that describes its diet, and ultimately to the isotopic composition of its own tissues, defined as its 'isotopic niche'. By coupling these processes, we systematically investigate under what conditions the isotopic niche of a consumer changes as a function of both the geometric properties of its mixing space and foraging strategies that may be static or dynamic over time. Results of our derivations reveal general insight into the conditions impacting isotopic niche width as a function of consumer specialization on prey, as well as the consumer's ability to transition between diets over time. We show analytically that moderate specialization on isotopically unique prey can serve to maximize a consumer's isotopic niche width, while temporally dynamic diets will tend to result in peak isotopic variance during dietary transitions. We demonstrate the relevance of our theoretical findings by examining a marine system composed of nine invertebrate species commonly consumed by sea otters. In general, our analytical framework highlights the complex interplay of mixing space geometry and consumer dietary behavior in driving expansion and contraction of the isotopic niche. Because this approach is established on ecological mechanism, it is well-suited for enhancing the ecological interpretation, and uncovering the root causes, of observed isotopic data., Comment: 27 pages, 9 figures

The National Science Education Standards (NRC, 1996) have been one of the leading reformed documents in the U.S. since its release. It has served as a foundation for all state standards and has supported the development of the newest standards documents recently released in the U.S. (i.e., Achieve Inc., 2013; NRC 2012). One of the most important contributions this document has made is in the area of teaching, as it puts forth explicit standards for teaching science grounded framed by constructivism. These standards are quite different than what has traditionally been found in U.S. schools. This article examines each of the teaching standards outlined in the NSES, 1) to better explain the bases and importance of the teaching standard and specific less/more emphasis indicators found in the Changing Emphasis table in the teaching standards, before 2) current science education research that is forming the foundations of each of the standards moving forward is shared. Finally, examination of each teaching standard in the article concludes with exemplar vignettes to provide a vision for the enactment of each standard in the context of teachers' and students' everyday classroom and school experiences.

This paper examines underachievement, a widely used term in education policy and practice often used to refer to nations, home nations, and regions; types and sectors of schooling; physiological, ethnic, and social groups; and individuals. It has been used to mean simply low achievement, also lower achievement relative to another of these groups, and lower achievement than would be expected by an observer. This paper presents examples of each. These multiple uses lead to considerable confusion which, coupled with common errors in assessing the proportionate difference between groups, mean that significant public money has been spent attempting to overcome problems that may not exist. When underachievement is understood to mean a lower achievement level by an individual (or group) than would be expected using a model based on the best available predictors, there is nothing that can be known about underachieving individuals (or groups) that they have in common. They cannot be disproportionately working class males, for example, because class and sex would then be part of the best available predictors. Even if some predictors were reserved from the best model, there is no evidence that underachievers have much in common. In raw score terms, it can be said that a particular social group exhibits lower achievement than another. It can also be said that there is a differential attainment between groups. However, this is not saying that the lower attaining group could and should do better on that assessment, or that the surface dissimilarity is the cause of differences in attainment. Making explicit what is meant by underachievement is essential. (Contains 67 references.) (SM)

The validity of public examinations as measures of academic achievement is not perfect, and the generalizability of paper-and-pencil tests to real-life tasks is rather low. In the United Kingdom, small differences between levels of attainment on public examinations cannot be attributed to real differences in achievement. The comparability of achievement tests is reduced by changes over time, place, examination board, mode of examining, subject, and syllabus. A major thrust of this paper is to suggest that a consideration of standards or effectiveness is not a simple matter of counting and comparing. In fact, there is no real evidence of failing educational standards over time in Britain and no convincing evidence of underperformance relative to the educational systems of other developed nations. International comparisons and those based on local education agencies do suggest that comprehensive systems of schools based on parental choice tend to produce narrower social differences in intake and outcomes. Systems with more differentiation have greater gaps in attainment between social groups. The United Kingdom is in a reasonable comparative position. There are problems related to education, certainly, but the current examination system was designed to differentiate between candidates. This differentiation cannot be used, logically, as evidence of underattainment. (Contains 54 references.) (SLD)

While traditional radio stations are subject to extensive government regulations, Internet radio stations remain largely unregulated. As Internet radio usage has increased certain stakeholders have begun to argue that these Internet radio broadcasters are providing significant and diverse programming to American audiences and that government regulation of spectrum-using radio station ownership may be further relaxed. One of the primary justifications for regulation of ownership has been to protect diversity in broadcasting. This study hypothesizes that Internet radio broadcasting does add diversity to the radio broadcasting industry and that it should be considered as relevant by regulators. This study evaluates the role of Internet radio broadcasters according to five criteria intended to gauge the level of diversity being delivered to listeners online. By measuring the levels of format, channel, ownership, location and language diversity among Internet radio stations, it is possible to draw benchmark lessons about the new medium's ability to provide Americans with diverse broadcasting options. The study finds that Internet radio broadcasters are in fact adding measurable diversity to the radio broadcasting industry. Internet broadcasters are providing audiences with access to an increasing number of stations, owners, formats, and language choices, and it is likely that technologies aiding in the mobility of access as well as broadband evolution will reinforce these findings., Comment: 29th TPRC Conference, 2001