Maria Pampaka

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...

Mathematics students’ aspirations for higher education: class, ethnicity, gender and interpretative repertoire styles

This paper reports how students talk about their aspirations in regard to higher education (HE) and their mathematics, what ‘repertoires’ they use to mediate this discourse, and how students’ predominant ‘repertoire style’ relates to their cultural background. Our analyses draw on an interview sample (n=40) of students selected because they are ‘on the cusp’ of participation or non‐participation in mathematically demanding programmes in further and higher education. The interviews explored the students’ aspirations for their future in general and HE in particular, influences on these choices, and the place of mathematics in these. Thematic analysis revealed four interpretative repertoires commonly in use, which we call ‘becoming successful’, ‘personal satisfaction’, ‘vocational’, and ‘idealist’ repertoires. Most of the sample was found to use a single, predominant repertoire, which we call their repertoire ‘style’: what is more, this style is found to be strongly related to background factors independently obtained. The implications for policy and practice are discussed.

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.

Mathematics coursework as facilitator of formative assessment, student-centred activity and understanding

We seek to illuminate reasons why undertaking mathematics coursework assessment as part of an alternative post-compulsory, pre-university scheme led to higher rates of retention and completion than the traditional route. We focus on the students’ experience of mathematical activity during coursework tasks, which we observed to be qualitatively different to most of the other learning activities observed in lessons. Our analysis of interviews found that these activities offered: (i) a perceived greater depth of understanding; (ii) motivation and learning through modelling and use of technology; (iii) changes in pedagogies and learning activities that supported student-centred learning; and (iv) assessment that better suited some students. Teachers’ interviews reinforced these categories and highlighted some motivational aspects of learning that activity during coursework tasks appears to provide. Thus, we suggest that this experience offered some students different learning opportunities, and that this is a plausible factor in the relative success of these students.

Beyond traditional school value-added models: a multilevel analysis of complex school effects in Chile

ABSTRACT School value-added studies have largely demonstrated the effects of socioeconomic and demographic characteristics of the schools and the pupils on performance in standardised tests. Traditionally, these studies have assessed the variation coming only from the schools and the pupils. However, recent studies have shown that the analysis of academic performance could significantly benefit from additional complexity in the model structure, incorporating non-hierarchical and unexplored levels of variation. Using data on secondary students from the Chilean National Pupil Database (2004–2006), this study shows how the traditional value-added models fall short in addressing the complex phenomenon of academic performance, because they largely overestimate school effects. A 4-level contextualised value-added model for progress in Mathematics was implemented and shown to avoid the masking of classroom and locality effects found in the traditional models. We also analyse the effects of important structural factors in Chile such as family income and school type.

Rasch analysis of the Antimicrobial Self-Assessment Toolkit for National Health Service (NHS) Trusts (ASAT v17)

Objectives The Antimicrobial Self-Assessment Toolkit for National Health Service (NHS) Trusts (ASAT) was developed to evaluate hospital-based antimicrobial stewardship programmes. Iterative validity investigations of the ASAT were used to produce a 91-item ASAT v17 utilizing qualitative methodology. Rasch analysis was used to generate question (item) behaviour estimates and to investigate the validity of ASAT v17. Methods In 2012, the partial credit model (PCM) was used to analyse ASAT responses from 33 NHS Trusts within England. WINSTEPS® outputs such as fit statistics and respondent/item maps were examined to determine unidimensionality, item discrimination and item hierarchy. Ordinary least squares regression modelling was used to determine the predictive validity using NHS Trust ability estimates generated from the PCM and corresponding Clostridium difficile rates. Results Each domain contained items that were misfitting the PCM (with INFIT MNSQ <0.7 or >1.3), except Domain 3. Subsequent iterative item removal had a negligible effect on the fit indices within most ASAT domains. Scale analysis demonstrated that most items were productive for measurement (n = 81). Respondent/item maps showed ceiling effects (n = 3) and floor effects (n = 1) within ASAT domains. Ordinary least squares regression modelling identified that there was limited predictive validity due to the small positive correlation between the predictor and outcome variables for participating hospitals (&rgr; = 0.146; P = 0.418). Conclusions Rasch analysis was an effective measurement technique for evaluating the validity of ASAT v17 by providing evidence that each sub-scale and the overall scale demonstrated unidimensionality (construct validity). Improved item targeting may be required to improve item discrimination within the toolkit.

Is the educational ‘what works’ agenda working? Critical methodological developments

We began preparing this special issue with a widely accepted realization: the search of ‘what works’ in educational contexts has been problematic in practice and in theory as well as in the interch...

Differential Correct Attribution Probability for Synthetic Data: An Exploration

Synthetic data generation has been proposed as a flexible alternative to more traditional statistical disclosure control (SDC) methods for limiting disclosure risk. Synthetic data generation is functionally distinct from standard SDC methods in that it breaks the link between the data subjects and the data such that reidentification is no longer meaningful. Therefore orthodox measures of disclosure risk assessment - which are based on reidentification - are not applicable. Research into developing disclosure assessment measures specifically for synthetic data has been relatively limited. In this paper, we develop a method called Differential Correct Attribution Probability (DCAP). Using DCAP, we explore the effect of multiple imputation on the disclosure risk of synthetic data.