The impact of virtual fractional flow reserve and virtual coronary intervention upon treatment decisions in the cardiac catheter laboratory

Background Using fractional flow reserve (FFR) to guide percutaneous coronary intervention for patients with coronary artery disease (CAD) improves clinical decision making but remains under-used. Virtual FFR (vFFR, computed from angiographic images) permits physiological assessment without a pressure wire and can be extended to virtual coronary intervention (VCI) facilitating treatment planning. This study investigated the effect of adding vFFR and VCI to angiography in patient assessment and management. Methods Two cardiologists independently reviewed clinical data and angiograms of 50 patients undergoing invasive management of coronary syndromes, and their management plans were recorded. The vFFRs were computed and disclosed, and the cardiologists submitted revised plans. Then, using VCI, the physiological results of various interventional strategies were shown, and further revision was invited. Results Disclosure of vFFR led to a change in strategy in 27%. VCI led to a change in stent size in 48%. Disclosure of vFFR and VCI resulted in an increase in operator confidence in their decision. Twelve cases were reviewed by six additional cardiologists. There was limited agreement in the management plans between cardiologists based upon either angiography (kappa=0.31) or vFFR (kappa=0.39). Conclusions vFFR has the potential to alter decision making, and VCI can guide stent sizing. However, variability in management strategy remains considerable between operators, even when presented with the same anatomical and physiological data

Understanding and Enriching Problem-Solving in Primary Mathematics Classrooms.

This up to date book is essential reading for all those teaching or training to teach primary mathematics. Problem solving is a key aspect of teaching and learning mathematics, but also an area where teachers and pupils often struggle. Set within the context of the new primary curriculum and drawing on research and practice, the book identifies the key knowledge and skills required in teaching and learning problem solving in mathematics, and examines how these and can be applied in the classroom. It explores the issues in depth while remaining straightforward and relevant, emphasises the enrichment of maths through problem-solving, and provides opportunities for teachers to reflect on and further develop their classroom practice

A representational approach to developing primary ITT students' confidence in their mathematics

Representations of mathematical concepts play an important role in understanding: both in helping learners understand the to-be-learned material and in facilitating teachers’ understanding of pedagogical processes which, in turn, are involved in developing learners’ understanding. In this paper, we report on work with a cohort of pre-service primary teachers, with the aim of developing their understanding of mathematics, their confidence in their subject knowledge and their confidence in teaching mathematics. This was attempted through the introduction and use of a ‘representational approach’ to the teaching of the mathematical concepts required of teachers training to teach in primary schools in the UK. We present the results of attitude measures and a follow-up qualitative questionnaire in identifying whether and how the use of this representational approach supported pre-service teachers’ understanding and their confidence in teaching mathematics. The results suggest that the representational approach used had a positively significant impact on the attitudes towards studying and teaching mathematics

How Young Children View Mathematical Representations: A study using eye-tracking technology

Background: It has been shown that mathematical representations can aid children’s understanding of mathematical concepts but that children can sometimes have difficulty in interpreting them correctly. New advances in eye-tracking technology can help in this respect because it allows data to be gathered concerning children’s focus of attention and so indicate on what aspects of the representations they are focussing. However, recent eye-tracking technology has not been used to any great degree in investigating the way children view and interpret mathematical representations. Purpose: This research explored the use of new advances in eye-tracking technology in investigating how young children view and interpret mathematical representations of multiplication. Sample: Nine Year 5 children (four boys, five girls, aged 9–10 years of age) from a local primary (elementary) school in the North-East of England were asked to complete the test during school time. The children represented a range of attainment levels across the mathematical domain (three higher-, three middle- and three lower-attaining children) and were selected accordingly by their class teacher. We recognise that this study was only based on a small sample of children, however, this number still allowed us to make meaningful comparisons in particular between the different types of representations presented. Design and methods: The study consisted of each child looking at 18 static slides, one after the other, with each slide presenting a symbolic and a picture representation of multiplication problems. The data that was captured by the eye tracker and recorded was then analysed quantitatively (e.g. time on each slide, time on each area of interest specified within the software) and qualitatively (video recordings of each child’s gaze trajectory during each representation was carried out, thereby allowing a categorisation of the different approaches adopted). Results: The study showed that (a) the particular form of the number line representation used in this study was less successful than the other picture representations used (equal groups, array) in promoting multiplicative thinking in children, and (b) the success of children to think multiplicatively with the ‘groups’ and the array representation was related to their general mathematics attainment levels. Conclusion: These findings have implications for teacher practice in that teachers need to be clear about the possible drawbacks of particular representations. Even in using more successful representations, for lower-attaining children, the progression in their understanding of the representation needs to be taken into account by the teacher. The study also highlighted that the eye-tracking technology does have some limitations but is useful in investigating young children’s focus of attention whilst undertaking a mathematics assessment task