Pre service primary teachers’ approaches to mathematical generalisation

In our teaching with primary pre-service teachers (PSTs), each of us includes generalising tasks in the context of mathematical reasoning. We set out to explore the value of such activity from the perspective of PSTs and their approaches to generalisation. In this paper, we focus on one PST’s mathematical reasoning when working on the ‘flower beds’ problem. We analyse the ways in which this PST attends to: looking for a relationship; seeing structure within a single figure in a sequence; and seeing sameness and difference between figures in a sequence. We consider what motivates shifts in attention, we reflect on the significance of students’ prior experience, and of student collaboration in our teaching sessions

Deconstructing ‘good practice’ teaching videos: An analysis of pre-service teachers’ reflections

Video clips of mathematics lessons are used extensively in pre-service teacher education and continuing professional development activities. Given course time constraints, an opportunity to critique these videos is not always possible. Because of this, and because pre-service teachers make extensive use of material found during internet searches, much of it purporting to exemplify ‘good’ practice, we were interested to know what sense they make of such material. By encouraging pre-service teachers to reflect and comment on the practices being promoted in this way, we wanted to hear what they focused on, their initial views of the teaching and learning shown in the video, and how their views were formed and affected by engaging in discussion. Findings indicate that pre-service teachers’ responses to the material were dominated by their beliefs about mathematics, and that engaging in discussion enabled them to appreciate the interpretations of others

Pre-service primary teachers' approaches to mathematical generalisation

In our teaching with primary pre-service teachers (PSTs), each of us includes generalising tasks in the context of mathematical reasoning. We set out to explore the value of such activity from the perspective of PSTs and their approaches to generalisation. In this paper, we focus on one PST’s mathematical reasoning when working on the ‘flower beds’ problem. We analyse the ways in which this PST attends to: looking for a relationship; seeing structure within a single figure in a sequence; and seeing sameness and difference between figures in a sequence. We consider what motivates shifts in attention, we reflect on the significance of students’ prior experience, and of student collaboration in our teaching sessions

Primary pre-service teachers: reasoning and generalisation

Generalising tasks, in the context of mathematical reasoning, have featured in our work with primary pre-service teachers (PSTs). We used two particular problems - 'matchstick squares' and 'flower beds' - to explore the generalisation approaches taken by PSTs. In this paper, we analyse the ways in which one of them, Terry, uses recursive or functional approaches to generalisation, and how he attends to looking for a relationship and seeing sameness and difference between figures in a sequence. We consider what motivates shifts in attention, the significance of the PST's prior experience and of PST-collaboration in our teaching sessions. We conclude with a discussion about the significance of this activity in the PST’s preparation for teaching, with reference to Mason's (2010) notions of pro-spection and retro-spection.https://bsrlm.org.uk/wp-content/uploads/2018/11/BCME9-Research-Proceedings.pd

Comparison of EGFR and K-RAS gene status between primary tumours and corresponding metastases in NSCLC

In non-small-cell lung cancer (NSCLC), epidermal growth factor receptor (EGFR) and K-RAS mutations of the primary tumour are associated with responsiveness and resistance to tyrosine kinase inhibitors (TKIs), respectively. However, the EGFR and K-RAS mutation status in metastases is not well studied. We compared the mutation status of these genes between the primary tumours and the corresponding metastases of 25 patients. Epidermal growth factor receptor and K-RAS mutation status was different between primary tumours and corresponding metastases in 7 (28%) and 6 (24%) of the 25 patients, respectively. Among the 25 primary tumours, three ‘hotspot' and two non-classical EGFR mutations were found; none of the corresponding metastases had the same mutation pattern. Among the five (20%) K-RAS mutations detected in the primary tumours, two were maintained in the corresponding metastasis. Epidermal growth factor receptor and K-RAS mutations were detected in the metastatic tumours of three (12%) and five (20%) patients, respectively. The expressions of EGFR and phosphorylated EGFR showed 10 and 50% discordance, in that order. We conclude that there is substantial discordance in EGFR and K-RAS mutational status between the primary tumours and corresponding metastases in patients with NSCLC and this might have therapeutic implications when treatment with TKIs is considered

‘Classical' but not ‘other' mutations of EGFR kinase domain are associated with clinical outcome in gefitinib-treated patients with non-small cell lung cancer

‘Classical' mutations in the EGFR tyrosine kinase domain (exons 18, 19 and 21) have been associated with sensitivity to tyrosine kinase inhibitors (TKIs) in patients with NSCLC. The aim of the current study was to evaluate whether other than the classical G719X, DEL19 and L858R mutations of EGFR confer sensitivity to TKIs. Genomic DNA was extracted from microdissected formalin-fixed paraffin-embedded tumour tissue from 86 patients treated with gefitinib. Exons 18, 19 and 21 were amplified and subjected to direct sequencing. Eleven (13%) patients harboured the classical exon's 18, 19 and 21 mutations, while 14 (16%) had ‘other' variants. There was a significantly higher percentage of ‘never-smoker' patients with ‘classical' EGFR mutations (P=0.002). Among patients with ‘classical' mutations 3 patients achieved PR and 7 SD, while in the ‘other' mutations group 10 patients had SD as best response. In the wild-type group, there were 3 patients with PR and 25 with SD. Median TTP was 16, 64 (P=0.002) and 21 weeks and median survival was 36, 78 and 67 weeks for patients with wild-type, ‘classical' and ‘other' EGFR mutations, respectively. The clinical relevance of ‘other' EGFR mutation variants remains uncertain and requires further assessment in a prospective study

Child and parental physical activity: Is there an association with young children activity?

Objectives: The aim of the study is to examine the physical activity (PA) of young children and their parents on weekdays and at the weekend, as well as possible associations between them. Methods: Fifty-eight children (29 boys), aged 5–8 years (mean age = 6.53 years) and the parent who spent more time with them (25 fathers, 33 mothers, mean age 40.67 years) wore Omron HJ-720IT pedometers for seven consecutive days. Two ANOVAs for repeated measures were applied to examine PA differences between genders and week phases (weekdays vs. weekend days) in children and parents. Moreover, one sample t-tests were used to compare participants’ PA to the recommended PA, while linear regression analyses were utilized to examine whether parental PA in each week phase was associated with children’s PA. Results: Children accumulated more steps on weekdays than at the weekend (F1,56 = 18.58, p < 0.001, η2 = 0.27), while boys presented higher PA than girls (F1,56 = 12.42, p = 0.001, η2 = 0.20), and accomplished the recommended daily PA, in contrast to girls. Mothers and fathers presented similar PA (p = 0.67, η2 = 0.004), with more steps on weekdays than at the weekend (F1,56 = 9.22, p = 0.004, η2 = 0.16). However, their PA was significantly lower than the recommended. Finally, there were no statistically significant associations between parents’ and boys’ ambulatory activity either on weekdays (p = 0.938) or at the weekend (p = 0.095). On the contrary, parents’ PA explained 47% of girls’ PA on weekdays (R = 0.68, F1,28 = 22.81, p < 0.001) and 23% at the weekend (R = 0.48, F1,28 = 6.40, p = 0.02) Conclusions: Boys appear to be more physically active than girls in Greece, whereas mothers and fathers present similar ambulatory activity. Moreover, parents’ PA is related to that of their daughters and not to that of their sons. Taking into account that both girls and parents did not meet PA recommendations, family-based interventions are needed for both children and parents benefit. © 2018, Czech National Institute of Public Health. All rights reserved

Preservice teachers’ expressed awarenesses: emerging threads of retro-spection of learning and pro-spection of teaching

AbstractIn this paper, we report an enquiry into elementary preservice teachers’ learning, as they engage in doing mathematics for themselves. As a group of researchers working in elementary Initial Teacher Education in English universities, we co-planned and taught sessions on growing pattern generalisation. Following the sessions, interviews of fifteen preservice teachers at two universities focused on their expressed awareness of their approach to the mathematical activity. Preservice teachers’ prospective planning and post-teaching evaluations of similar activities in their classrooms were also examined. We draw on aspects of enactivism and the notion of reflective “spection” in the context of teacher learning, tracing threads between preservice teachers’ retro-spection of learning and pro-spection of teaching. Our analysis indicates that increasing sensitivity to their own embodied processes of generalisation offers opportunities for novice teachers to respond deliberately, rather than to react impulsively, to different pedagogical possibilities. The paper contributes a new dimension to the discussion about the focus of novice elementary school teachers’ retrospective reflection by examining how deliberate retrospective analysis of doing mathematics, and not only of teaching actions, can develop awarenesses that underlie the growth of expertise in mathematics teaching. We argue that engaging preservice teachers in mathematics to support deliberate retrospective analysis of their mathematics learning and prospective consideration of the implications for teaching can enable more critical pedagogical choices. </jats:p

Tracing threads of awareness in initial teacher education: Peer-collaboration.

This paper reports on a UK project exploring the learning of preservice primary teachers whilst they engaged in doing mathematics and how this experience shaped their subsequent teaching. During university-based sessions, we presented a number of visual growing patterns for preservice teachers to investigate collaboratively and to consider possible approaches to use in their teaching. We draw on aspects of enactivism and the notion of reflective spection in the context of teacher learning, tracing threads between preservice teachers’ retro-spection of their own learning and pro-spection of their approach to teaching. Our findings suggest that preservice teachers emphasize the importance of collaboration in ‘seeing’ what others ‘see’ and that this influences their teaching