A case study exploration of primary teachers' conceptions of whole class interactive mathematics teaching

Research has shown, with respect to the learning of mathematics, that whole class interactive teaching, its form and function, is a complex phenomenon. Teachers develop and exploit pedagogical strategies, which they believe are effective either in engaging their children in mathematical learning or in presenting mathematics to learners. Such strategies, whether later shown to be effective or not, are typically assumed to develop during periods of teacher education or through practice after qualification. Alongside these assumptions is the belief that teachers who are enthusiastic about and have a secure subject knowledge with respect to mathematics will evoke similar enthusiasm, confidence and competence in their learners. However, observations during my years as a teacher educator have led me to conclude that trainee teachers, even those with similar qualifications, frequently behave very differently when put in front of children. Such differences confound the naïve assumption, for example, that similar enthusiasm and confidence will yield similar patterns of teaching practice. Thus, what primary teachers do and why they do it has vexed me for a number of years. I have wanted to know, in particular, what makes teachers teach differently during whole class episodes, not least because my experiences as both teacher and teacher trainer have led me to believe that it is during these periods that teachers induct their children into those mathematics-related beliefs and behaviours that will determine the extent to which they enjoy and engage meaningfully with the subject. Addressing such questions demands an appropriate methodological stance. Consequently an exploratory case study of six teachers, two during a first, essentially pilot phase, and four during a second, was undertaken. All teachers, to facilitate understanding of how exemplary practice differs from one person to another, were considered, against various criteria, as effective. The pilot enabled me to evaluate not only the effectiveness of extant frameworks for analysing classroom behaviour but also my skills as an interviewer and observer of classrooms. The second phase, drawing on what had been learnt during the first, was more open in that existing frameworks were abandoned in favour of allowing the data to speak for themselves rather than being constrained by others’ conceptualisations of effective teaching. Both phases, to examine teachers’ underlying beliefs about mathematics and its teaching, their classroom practice, particularly during whole class episodes, and their rationales for their actions, were addressed by means of a battery of data collection tools. Teachers’ backgrounds and underlying beliefs about mathematics and its teaching were examined through preliminary, life history, interviews framed by a loose set of questions derived from the literature. Interviews were video-recorded. Teachers’ classroom actions were captured by means of a tripod-mounted video camera placed discretely in their classrooms, augmented by a wireless microphone worn by the teacher and a separate, static microphone to capture as much of the children’s talk as possible. Finally, teachers’ rationales and explanations for their actions were examined through the use of video-recorded video stimulated recall interviews. All recordings, whether of classrooms or interviews, were transcribed for later analysis. Analysis during the first phase drew extensively on pre-existing frameworks. While they were helpful in identifying both similarities and differences in teachers’ beliefs, actions and rationales, it became clear that they failed to capture the subtleties and nuances of meaning embedded in the high quality data yielded by the approaches adopted. In so doing it became clear that while data collection approaches were appropriate, analyses needed to be more open in order to allow the data to give up the depth and complexity of their stories. During the second phase, while it was acknowledged that this was not a grounded theory study, analysis drew extensively on the coding strategies of the constant comparison procedures of grounded theory. This approach to analysis yielded results previously unknown in the literature. Quite unexpectedly two groups emerged from the data. Significantly, each was underpinned by teachers’ experiences as learners of mathematics and whether the enjoyment they had gleaned from those experiences was instrumentally located or relationally located. The first group, identified as the mediators, having been engaged, in various ways, with mathematics and derived pleasure from relational experiences expected their children to experience mathematics similarly. Their teaching was based on a desire to develop, in collaborative ways, a deep conceptual knowledge that would form the basis for later procedural skills and, significantly, problem solving. Teachers in the second group, identified as the mediated group, having derived pleasure from their procedural successes as children, saw mathematics and its teaching as skills-based. Their classroom actions and commensurate rationales were focused on surface learning and the replication of the pleasure they had experienced when young. Interestingly, the beliefs of both groups and, to an extent, their classroom actions were independent of any training they had received. The Mediators showed different signs of professional independence and autonomy. They had a clear articulation of their warranted principles and were able to exploit these in the ways that mediated the constraints within which they worked. Moreover, and this presents substantial implications for teacher education, teachers in the Mediated group, exhibited few signs of professional independence; their actions being constantly mediated by the constraints, whether institutional or governmental, within which they worked. They had few articulated principles around which they based their teaching. These differences permeated all aspects of their work

Estimation in the primary mathematics curricula of the United Kingdom: Ambivalent expectations of an essential competence

In this paper, we examine the national curricula for primary mathematics for each of the four constituent nations of the United Kingdom (England, Northern Ireland, Scotland and Wales) for the estimation-related opportunities they offer children. Framed against four conceptually and procedurally different forms of estimation (computational, measurement, quantity and number line), the analyses indicate that computational estimation and measurement estimation were addressed in all four curricula, albeit from a skills-acquisition perspective, with only the Scottish offering any meaningful justification for their inclusion. The process of rounding, absent in the Northern Ireland curriculum, was presented as an explicit learning objective in the English, Scottish and Welsh curricula, although it was only the Scottish that made explicit the connections between rounding and computational estimation. In all curricula, both quantity estimation and number line estimation were effectively absent, as was any explicit acknowledgement that learning to estimate, irrespective of its form, has a developmental role in the learning of other mathematical topics.Output Status: Forthcoming/Available Onlin

The Atacama Cosmology Telescope: A Measurement of the Cosmic Microwave Background Power Spectrum at 148 and 218 GHz from the 2008 Southern Survey

We present measurements of the cosmic microwave background (CMB) power spectrum made by the Atacama Cosmology Telescope at 148 GHz and 218 GHz, as well as the cross-frequency spectrum between the two channels. Our results clearly show the second through the seventh acoustic peaks in the CMB power spectrum. The measurements of these higher-order peaks provide an additional test of the {\Lambda}CDM cosmological model. At l > 3000, we detect power in excess of the primary anisotropy spectrum of the CMB. At lower multipoles 500 < l < 3000, we find evidence for gravitational lensing of the CMB in the power spectrum at the 2.8{\sigma} level. We also detect a low level of Galactic dust in our maps, which demonstrates that we can recover known faint, diffuse signals.Comment: 19 pages, 13 figures. Submitted to ApJ. This paper is a companion to Hajian et al. (2010) and Dunkley et al. (2010

31st Annual Meeting and Associated Programs of the Society for Immunotherapy of Cancer (SITC 2016) : part two

Background The immunological escape of tumors represents one of the main ob- stacles to the treatment of malignancies. The blockade of PD-1 or CTLA-4 receptors represented a milestone in the history of immunotherapy. However, immune checkpoint inhibitors seem to be effective in specific cohorts of patients. It has been proposed that their efficacy relies on the presence of an immunological response. Thus, we hypothesized that disruption of the PD-L1/PD-1 axis would synergize with our oncolytic vaccine platform PeptiCRAd. Methods We used murine B16OVA in vivo tumor models and flow cytometry analysis to investigate the immunological background. Results First, we found that high-burden B16OVA tumors were refractory to combination immunotherapy. However, with a more aggressive schedule, tumors with a lower burden were more susceptible to the combination of PeptiCRAd and PD-L1 blockade. The therapy signifi- cantly increased the median survival of mice (Fig. 7). Interestingly, the reduced growth of contralaterally injected B16F10 cells sug- gested the presence of a long lasting immunological memory also against non-targeted antigens. Concerning the functional state of tumor infiltrating lymphocytes (TILs), we found that all the immune therapies would enhance the percentage of activated (PD-1pos TIM- 3neg) T lymphocytes and reduce the amount of exhausted (PD-1pos TIM-3pos) cells compared to placebo. As expected, we found that PeptiCRAd monotherapy could increase the number of antigen spe- cific CD8+ T cells compared to other treatments. However, only the combination with PD-L1 blockade could significantly increase the ra- tio between activated and exhausted pentamer positive cells (p= 0.0058), suggesting that by disrupting the PD-1/PD-L1 axis we could decrease the amount of dysfunctional antigen specific T cells. We ob- served that the anatomical location deeply influenced the state of CD4+ and CD8+ T lymphocytes. In fact, TIM-3 expression was in- creased by 2 fold on TILs compared to splenic and lymphoid T cells. In the CD8+ compartment, the expression of PD-1 on the surface seemed to be restricted to the tumor micro-environment, while CD4 + T cells had a high expression of PD-1 also in lymphoid organs. Interestingly, we found that the levels of PD-1 were significantly higher on CD8+ T cells than on CD4+ T cells into the tumor micro- environment (p < 0.0001). Conclusions In conclusion, we demonstrated that the efficacy of immune check- point inhibitors might be strongly enhanced by their combination with cancer vaccines. PeptiCRAd was able to increase the number of antigen-specific T cells and PD-L1 blockade prevented their exhaus- tion, resulting in long-lasting immunological memory and increased median survival

The influence of early childhood mathematical experiences on teachers' beliefs and practice

This paper shows how particular forms of formative familial experiences provide prospective teachers with the intellectual tools necessary for undertaking critical analyses of both the received and intended curriculum. Data from a multiple case study shows that beliefs formed through early mathematical experiences stay with individuals to reveal themselves in subsequent beliefs and practice

When the Mathematics gets lost on the Didactics

This study shows how six elementary teachers, construed locally as effective, interpreted and were observed to enact the same curricular and didactical language very differently. One group of three provided high-level cognitively challenging tasks to engage children in mathematics. A second group of three, ensuring their children enjoy mathematics, subordinated mathematical learning to an emphasis on the teaching activity. The actions of this second group made mathematics invisible

Regeneration of the cardiac conduction system

Arrhythmias are a hallmark of myocardial infarction (MI) and increase mortality risk for patients. The cardiac conduction system is increasingly implicated in arrhythmias but how it is altered following MI is not well understood. I hypothesised that there is an impairment of the conduction system in adult infarcted hearts whereas it is rapidly restored in regenerative neonatal hearts to maintain normal rhythm. In this thesis, I demonstrate complete conduction system restoration during neonatal mouse heart regeneration, versus pathological remodelling at non-regenerative stages that map onto the adult heart wound-healing response. By developing tissue-cleared whole- organ imaging and analysis approaches, I initially performed the first description and quantitative characterisation of the intact 3D architecture of the post-natal murine ventricular conduction system. Next, following MI injury, I identified global disruption to the His/Purkinje network, disorganised bundling of conduction fibres and regional loss of connexin-40 one week after birth which contrasted with regeneration of the network and restoration of fibres at immediate post-natal stages. Enriched single-cell RNA-sequencing revealed distinct transcriptional signatures of infarcted regenerating versus non-regenerating conduction cells. I identified that conduction cells undergo transition at a transcriptional and protein level to regenerate the network, as compared to sustained electrical alterations during fibrotic repair. I found that this manifests functionally via transition from normal rhythm to pathological conduction delay beyond the regenerative window. Finally, modelling the non- regenerative phenotype in the infarcted human heart implicated these changes as causative for bundle branch block and increased dyssynchrony of ventricular contraction, as is observed in MI patients. Collectively, the findings of this thesis characterise conduction system growth and maturation following birth, identify pathophysiological electrical remodelling in the His/Purkinje network after MI, elucidate the cellular and molecular profiles of the regenerating conduction system, and demonstrate the consequence of MI-induced conduction system damage for clinical arrhythmogenesis