Performativity and affectivity: Lesson observations in England's Further Education colleges

Teaching and learning observations (TLOs) are used in educational environments worldwide to measure and improve quality and support professional development. TLOs can be positive, for teachers who enjoy opportunities to ‘perform’ their craft and/or engage in professional dialogue. However, if this crucial, collaborative developmental element is missing, a TLO becomes intrinsically evaluative in nature and creates complex emotions – within and beyond the classroom. For some teachers, affective reactions to perceived managerial intrusion into their professional space has a negative impact on them, and in turn, their students’ learning. International research on TLOs has focused on schools or universities. My research centres specifically on England’s Further Education colleges (FE). Through Interpretive Interactionism, I investigate the different expectations, relationships and identities of teachers and (mis)conceptions of ‘authenticity’ in TLOs. Teaching involves our unique (dis)embodied ‘performativity’ (Butler, 2004) or ‘emotional practice’ which is interpreted and judged by others (Denzin, 1989). Using the concept of ‘aesthetic labour’ (Witz, et al., 2003), I argue that rather than promoting positive transformation through reflection, TLOs promote a rejection of emotional ‘genuineness’ that causes anxiety through a fracturing of personal and professional identities. Improving the effectiveness of TLOs should perhaps encompass explicit dialogue about the affectivity involved in the process

The autoconjugacy of a generalized Collatz map

Many of the 2-adic properties of the 3x+1 map generalize to the analogous mx+r map, where m and r are odd integers. We introduce the corresponding autoconjugacy map, prove some simple properties of it and make some further conjectures in the general setting, including weak versions of the periodicity and divergent trajectories conjectures

Dynamic Motion Modelling for Legged Robots

An accurate motion model is an important component in modern-day robotic systems, but building such a model for a complex system often requires an appreciable amount of manual effort. In this paper we present a motion model representation, the Dynamic Gaussian Mixture Model (DGMM), that alleviates the need to manually design the form of a motion model, and provides a direct means of incorporating auxiliary sensory data into the model. This representation and its accompanying algorithms are validated experimentally using an 8-legged kinematically complex robot, as well as a standard benchmark dataset. The presented method not only learns the robot's motion model, but also improves the model's accuracy by incorporating information about the terrain surrounding the robot

Performativity & affectivity: lesson observations in England’s further education colleges

Teaching and learning observations (henceforth ‘observations’) are commonly used in a broad range of educational environments to assess teaching quality and support professional development. Research centred on observations in England’s Further Education colleges (FE), suggests these strategies are often ineffective because of tensions between ‘authentic’ teaching and the inherent performativity required by some managerialist policies (Ball 2003). This psychosocial study draws on interpretive interactionism (Denzin 1989) to explore lived emotional experiences of FE staff involved in observations and perceptions of embodied ‘performativity’. My research involved in-depth semi-biographical interviews with FE staff (n=14) which explored emotional experiences of teaching and learning within the context of their roles as observer and/or observee. Using my personal reflections as an FE teacher, together with my creative writing skills, fictionalised accounts are presented to demonstrate anonymised consolidations of the participants’ narratives (Sparkes 2002). Using conceptual tools from Bourdieu (1991) and the lens of psychoanalysis (Mollon 2002) I draw on Richardson’s (1997) ‘writing as a method of inquiry’ and Ochberg’s (2002) non-linear approach to data analysis to explore shared and disparate themes within the accounts, reflections and fictionalised texts. Vocational and personal learning experiences are argued to form a fundamental aspect of the professional habitus of FE staff (James, Biesta 2007). Outcomes from my innovative approach, illuminates this interplay of factors, specifically within the affectivity in the performativity of observations. Hence these findings provide an original contribution to knowledge in this area, by demonstrating how the potential tension in observations is situated in the personal significance of perceptions of an ‘in/authentic self’, rather than the performativity per se. Fictionalisation could be a useful tool to further explore lived emotional experiences of teaching and learning. Indeed, raising awareness of the perceived performativity intrinsic within the affectivity of observations could hold benefits for teaching practice more widely

Designing Professional Learning Tasks for Mathematics Learning Trajectories

In this paper, we present an emerging set of learning conjectures and design principles to be used in the development of professional learning tasks that support elementary teachers’ learning of mathematics learning trajectories. We outline our theoretical perspective on teacher knowledge of learning trajectories, review the literature concerning mathematics professional learning tasks, offer a set of initial conjectures about teacher learning of learning trajectories, and articulate a set of principles to guide the design of tasks. We conclude with an example of one learning trajectory professional learning task taken from our current research project

Learning and Using Multimodal Stochastic Models : A Unified Approach

This dissertation presents a principled approach to representing and using instance-based knowledge. Perceptions and actions are probabilistically modelled in a unified structure which allows for simultaneous perception modelling and reasoning about desired actions. In particular, a new method for online instance-based learning of such models is presented and analyzed. This method, called Dynamic Gaussian Mixture Estimation (DGME), adapts a model's complexity to the process being modelled. The models produced by DGME are evaluated on several classification, prediction, and control applications, and its characteristics are compared with other state-of-the-art methods. In the context of control applications, an additional novel method, Gaussian Mixture Control (GMC), is introduced for precisely controlling systems that exhibit multimodality

The Unevolved Main Sequence of Nearby Field Stars and the Open Cluster Distance Scale

The slope and zero-point of the unevolved main sequence as a function of metallicity are investigated using a homogeneous catalog of nearby field stars with absolute magnitudes defined with revised Hipparcos parallaxes, Tycho-2 photometry, and precise metallicities from high-dispersion spectroscopy. (B-V)-temperature relations are derived from 1746 stars between [Fe/H] = -0.5 and +0.6 and 372 stars within 0.05 dex of solar abundance; for T_e = 5770 K, the solar color is B-V= 0.652 +/- 0.002 (s.e.m.). From over 500 cool dwarfs between [Fe/H] = -0.5 and +0.5, Delta(B-V)/Delta[Fe/H] at fixed M_V = 0.213 +/- 0.005, with a very weak dependence upon the adopted main sequence slope with B-V at a given [Fe/H]. At Hyades metallicity this translates into Delta M_V/Delta[Fe/H] at fixed B-V = 0.98 +/- 0.02, midway between the range of values empirically derived from smaller and/or less homogeneous samples and model isochrones. From field stars of similar metallicity, the Hyades ([Fe/H] = +0.13) with no reddening has (m-M)_0 = 3.33 +/- 0.02 and M67, with E(B-V) = 0.041, A_V = 3.1E(B-V), and [Fe/H] = 0.00, has (m-M)_0 = 9.71 +/- 0.02 (s.e.m), where the errors quoted refer to internal errors alone. At the extreme end of the age and metallicity scale, with E(B-V) = 0.125 +/- 0.025 and [Fe/H] = +0.39 +/- 0.06, comparison of the fiducial relation for NGC 6791 to 19 field stars with (B-V) above 0.90 and [Fe/H] = +0.25 or higher, adjusted to the metallicity of NGC 6791, leads to (m-M)_0 = 13.07 +/- 0.09, internal and systematic errors included.Comment: 32 pages, 8 eps figures, latex; accepted for PAS