Making mathematics phenomenal : Based on an Inaugural Professorial Lecture delivered at the Institute of Education, University of London, on 14 March 2012

Mathematics is often portrayed as an 'abstract' cerebral subject, beyond the reach of many. In response, research with digital technology has led to innovative design in which mathematics can be experienced to some extent like everyday phenomena. I examine how careful design can 'phenomenalise' mathematics - that is to say create mathematical artefacts that can be directly experienced to support not only engagement but also focus on key ideas. I argue that mathematical knowledge gained through interaction with suitably designed tools can prioritise powerful reasons for doing mathematics, imbuing it with a sort of utility and offering learners hooks on which they can gradually develop fluency and connected understanding. Illustrative examples are taken from conventional topics such as number, algebra, geometry and statistics but also from novel situations where mathematical methods are juxtaposed with social values. The suggestion that prioritising utility supports a more natural way of learning mathematics emerges directly from constructionist pedagogy and inferentialist philosophy

Disturbances in the spontaneous attribution of social meaning in schizophrenia

Background. Schizophrenia patients show disturbances on a range of tasks that assess mentalizing or 'Theory of Mind' (ToM). However, these tasks are often developmentally inappropriate, make large demands on verbal abilities and explicit problem-solving skills, and involve after-the-fact reflection as opposed to spontaneous mentalizing. Method. To address these limitations, 55 clinically stable schizophrenia out-patients and 44 healthy controls completed a validated Animations Task designed to assess spontaneous attributions of social meaning to ambiguous abstract visual stimuli. In this paradigm, 12 animations depict two geometric shapes' interacting' with each other in three conditions: (1) ToM interactions that elicit attributions of mental states to the agents, (2) Goal-Directed (GO) interactions that elicit attributions of simple actions, and (3) Random scenes in which no interaction occurs. Verbal descriptions of each animation are rated for the degree of Intentionality attributed to the agents and for accuracy. Results. Patients had lower Intentionality ratings than controls for ToM and GO scenes but the groups did not significantly differ for Random scenes. The descriptions of the patients less closely matched the situations intended by the developers of the task. Within the schizophrenia group, performance on the Animations Task showed minimal associations with clinical symptoms. Conclusions. Patients demonstrated disturbances in the spontaneous attribution of mental states to abstract visual stimuli that normally evoke such attributions. Hence, in addition to previously established impairment on mentalizing tasks that require logical inferences about others' mental states, individuals with schizophrenia show disturbances in implicit aspects of mentalizing

Brain regions concerned with perceptual skills in tennis: An fMRI study

Sporting performance makes special demands on perceptual skills, but the neural mechanisms underlying such performance are little understood. We address this issue, making use of fMRI to identify the brain areas activated in viewing and responding to video sequences of tennis players, filmed from the opponent’s perspective. In a block-design, fMRI study, 9 novice tennis players watched video clips of tennis play. The main stimulus conditions were (1) serve sequences, (2) non-serve behaviour (ball bouncing) and (3) static control sequences. A button response was required indicating the direction of serve (left or right for serve sequences, middle button for non-serve and static sequences). By comparing responses to the three stimulus conditions, it was possible to identify two groups of brain regions responsive to different components of the task. Areas MT/MST and STS in the posterior part of the temporal lobe responded either to serve and to non-serve stimuli, relative to static controls. Serve sequences produced additional regions of activation in parietal lobe (bilateral IPL, right SPL) and in right frontal cortex (IFGd, IFGv), and these areas were not activated by non-serve sequences. These regions of parietal and frontal cortex have been implicated in a “mirror neuron” network in the human brain. It is concluded that the task of judgement of serve direction produces two different patterns of response: activations in MT/MST and STS concerned with primarily with the analysis of motion and body actions, and activations in parietal and frontal cortex associated specifically with the task of identification of direction of serve

Robot Navigation in Unseen Spaces using an Abstract Map

Human navigation in built environments depends on symbolic spatial information which has unrealised potential to enhance robot navigation capabilities. Information sources such as labels, signs, maps, planners, spoken directions, and navigational gestures communicate a wealth of spatial information to the navigators of built environments; a wealth of information that robots typically ignore. We present a robot navigation system that uses the same symbolic spatial information employed by humans to purposefully navigate in unseen built environments with a level of performance comparable to humans. The navigation system uses a novel data structure called the abstract map to imagine malleable spatial models for unseen spaces from spatial symbols. Sensorimotor perceptions from a robot are then employed to provide purposeful navigation to symbolic goal locations in the unseen environment. We show how a dynamic system can be used to create malleable spatial models for the abstract map, and provide an open source implementation to encourage future work in the area of symbolic navigation. Symbolic navigation performance of humans and a robot is evaluated in a real-world built environment. The paper concludes with a qualitative analysis of human navigation strategies, providing further insights into how the symbolic navigation capabilities of robots in unseen built environments can be improved in the future.Comment: 15 pages, published in IEEE Transactions on Cognitive and Developmental Systems (http://doi.org/10.1109/TCDS.2020.2993855), see https://btalb.github.io/abstract_map/ for access to softwar

Purposeful Explanation and Causal Gaps

In this paper, I argue that a commitment to science and the methodo- logical commitment to causal closure do not require a rejection of the idea that the choices of souls explain the occurrence of certain events in the physical world. Stated slightly differently, I maintain that one can both affirm science and believe that souls causally interfere in the course of events in the physical world. Such an affirmation and belief are compatible. In short, science vis-à-vis the methodological principle of causal closure poses no problem for souls as explanatory agents

The Impact of Power Training on Balance and Visual Feedback Removal

Because power training has been known to augment stability, the purpose of this study was to assess whether the removal of visual input affects lower limb muscle power production in young women who are resistance trained to the same degree it affects the untrained. This provided insight as far as the need for resistance training protocols in a largely untrained visually impaired population. To study this, fourteen college-aged female participants (18-23 years) performed a seated double-leg press on a leg sled machine, isolating power production of the lower limbs. After establishing baselines, which involved finding an average of power produced during five trials, the subjects were asked to close their eyes for the following set of five pushes. The power production was assessed by utilizing a Tendo Unit, with placement on one of the limbs of the machine, to measure power output during leg extension (measured in Watts). Statistics analyzed in SPSS determined the average power deficit of the athletic population to be 11.57 Watts, whereas the general population had an average power deficit of 37.43 Watts. The deficits experienced by each respective group upon visual removal were significantly different from one another, as evidenced by a p-value of .048. This accentuated the power-trained group’s resilience. A suggested training plan regimen including cardiorespiratory, resistance, flexibility, and neuromotor exercises has been appended for persons experiencing visual impairment and seeking to better their balance through power

The role of motion analysis in elite soccer

The optimal physical preparation of elite soccer (association football) players has become an indispensable part of the professional game especially due to the increased physical demands of match-play. The monitoring of players’ work-rate profiles during competition is now feasible through computer-aided motion analysis. Traditional methods of motion analysis were extremely labour intensive and were largely restricted to university- based research projects. Recent technological developments have meant that sophisticated systems, capable of quickly recording and processing the data of all players’ physical contributions throughout an entire match, are now being used in elite club environments. In recognition of the important role motion analysis now plays as a tool for measuring the physical performance of soccer players, this review critically appraises various motion analysis methods currently employed in elite soccer and explores research conducted using these methods. This review therefore aims to increase the awareness of both practitioners and researchers of the various motion analysis systems available, identify practical implications of the established body of knowledge, while highlighting areas that require further exploration