Graeme Hutcheson

Inclusion and achievement in mainstream schools

This paper considers the key findings of a DfES‐funded study that explored the relationship between achievement and inclusion in mainstream schools in England. The methodology involved a statistical analysis of nationally held data on all pupils at the end of key stages 1–4, together with a series of site visits to ‘inclusive’ mainstream schools. These were carried out in order to explore school processes that might explain how some schools can manage to be both highly achieving and inclusive. Findings indicate that there is a small, but for all practical purposes, insubstantial relationship between inclusion and academic achievement at the school level although there is also a large degree of variation suggesting strongly there are other factors within a schools make up, rather than its degree of inclusivity, that impact on the average academic achievements of its pupils. This was confirmed from the analysis of the school site visits. The overall conclusion, therefore, is that mainstream schools need not be concerned about the potentially negative impact on the overall academic achievements of their pupils of including pupils with SEN in their schools.

The association between mathematics pedagogy and learners' dispositions for university study

We address the current concerns about teaching‐to‐the‐test and its association with declining dispositions towards further study of mathematics and the consequences for choice of STEM subjects at university. In particular, through a mixed study including a large survey sample of over 1000 students and their teachers, and focussed qualitative case studies, we explored the impact of ‘transmissionist’ pedagogic practices on learning outcomes. We report on the construction and validation of a scale to measure teachers’ self‐reported pedagogy. We then use this measure in combination with the students’ survey data and through regression modelling we illustrate significant associations between the pedagogic measure and students’ mathematics dispositions. Finally, we discuss the potential implications of these results for mathematics education and the STEM agenda.

Measuring students’ transition into university and its association with learning outcomes

Previously we showed how we measured pedagogy and revealed its association with learning outcomes of sixth-form college mathematics students. In this project we followed a similar approach to the study of university transition. We particularly sought to identify the students’ perceptions of the transitional experience, and measure the association with learning outcomes. We drew on longitudinal surveys of students entering different programmes in five universities. Following them into their first year or so, allowed us to track their ‘disposition to complete the course’ and their ‘disposition to study more mathematics’, inter alia. We developed and validated two ‘fit-for-purpose’ measures of students’ perception of their transition, one we call ‘perception of the transitional gap/jump’ and one we call ‘degree of positive feeling about the transition’. We report some statistically and educationally significant associations between these and the students’ developing dispositions, and discuss the prospects fo...

The relationship between inclusion and academic achievement in English mainstream schools

This article presents the key findings and discusses the implications of a major study that explored the relationship between academic achievement and the inclusion of pupils with special educational needs (SEN) in mainstream schools in England. It is based on a statistical analysis of nationally held data on all pupils in England that is collected at the end of each of the 4 key stages, when pupils are aged 7, 11, 14, and 16. The analysis considered the relationship between academic achievement and inclusivity having controlled for a range of other variables. Findings indicate that there is no relationship between academic achievement and inclusion at the local authority (LA) level while there is a small but, for all practical purposes, insubstantial relationship at the school level. In addition, there is also a large degree of variation at the school level, suggesting strongly that there are other factors within a schools make up, rather than its degree of inclusivity, that impact on the average academic achievements of its pupils. The overall conclusion, therefore, is that mainstream schools need not be concerned about the potentially negative impact on the overall academic achievements of their pupils of including pupils with SEN in their schools.

Confidence Intervals for the Predictions of Logistic Regression in the Presence and Absence of a Variance- Covariance Matrix

Confidence intervals for fitted values provide valuable information about the usefulness of regression models. Although such intervals can be easily calculated using standard statistical software for response variables that have normally distributed errors (e.g., in ordinary least-squares regression), it is more difficult to calculate them for response variables that have binomially distributed errors (e.g., logistic regression). Although a number of statistical packages provide confidence intervals for fitted values directly for logistic regression models, some commonly used packages do not (e.g., SPSS). In this article we outline a method of calculating these intervals simply by fitting a model after transforming variables. This technique is evaluated by comparing results with those obtained using a method that utilizes the variance-covariance matrix. Both techniques are described in detail and applied to simple and multiple logistic regression along with step by step instructions and software commands ...

Statistical modeling for management

Measurement Scales Modeling Continuous Data Modeling Dichotomous Data Modeling Ordered Data Modeling Unordered Data Neural Networks Approximate Algorithms for Management Problems Other Statistical, Mathematical and Co-pattern Modeling Techniques

Handling missing data: analysis of a challenging data set using multiple imputation

Missing data is endemic in much educational research. However, practices such as step-wise regression common in the educational research literature have been shown to be dangerous when significant data are missing, and multiple imputation (MI) is generally recommended by statisticians. In this paper, we provide a review of these advances and their implications for educational research. We illustrate the issues with an educational, longitudinal survey in which missing data was significant, but for which we were able to collect much of these missing data through subsequent data collection. We thus compare methods, that is, step-wise regression (basically ignoring the missing data) and MI models, with the model from the actual enhanced sample. The value of MI is discussed and the risks involved in ignoring missing data are considered. Implications for research practice are discussed.

Enrolment, achievement and retention on ‘traditional’ and ‘Use of Mathematics’ pre-university courses

This paper investigates enrolment, attainment and drop-out rates for two different English pre-university advanced mathematics, AS-level, courses, a ‘traditional’ and an innovative ‘Use of Mathematics’ pre-university course. Very different student profiles were found for those enrolled on each course, and a model of attainment at the pre-university level showed a relatively complex relationship with prior achievement at the end of compulsory schooling. Although those pupils who had relatively high prior achievement tended also to achieve relatively highly on the pre-university courses, this relationship was not evident for lower scores. Those pupils with ‘mid-range’ prior attainment tended to make the smallest gains. Taking prior attainment into account, the difference in attainment outcomes between the two courses is small. However, these courses do differ with respect to the number of students retained, with the ‘Use of Mathematics’ course retaining a significantly higher proportion of the students. Contextual factors are discussed, suggesting implications for policy and practice in mathematics education.

Exploring Key Neo-Marketing Directions through the use of an Academic Think Tank: A Methodological Framework

This paper is designed to set the scene in terms of introducing the methodological framework used in the academic “think tank” in marketing held at Lake of Menteith in Scotland in 1999. Some important academic insights and considerations are discussed at the outset with regard to the evaluation of future impacts on the multiple facets of the marketing discipline, although the amount and quality of dedicated academic research in this area has been limited. The new role of the marketing function and new customer market structures are debated, followed by a discussion of the intrinsic capabilities of scenario planning, as an environmental forecasting technique. Furthermore, we analyse the contribution of knowledge based systems to scenario planning and describe the design/development of an expert system at the Lake of Menteith gathering.

Constructing a Knowledge-Based System to Aid Scenario-Based Strategic Planning: An Application to the European Airline Industry

SUMMARY This paper explores the use of scenario planning and the design of a knowledge-based system in strategic decision making, in the context of the European airline industry. Several innovative strategies were derived, as well as other key recommendations based on sound strategic reasoning, and participants testified to the effectiveness of the approach in stretching their thinking. The requirement to draft strategies as expert system rules, with reasons, was useful in clarifying thinking and achieving group consensus. This methodology, therefore, aids effectiveness of the scenario planning process itself, while providing a dynamic, accessible means of storing the resulting strategic thinking. Copyright