Adaptation of a questionnaire to assess the epistemological beliefs of mathematics in secondary school teachers

The objective of the study is to determine the psychometric properties of the Epistemological Beliefs Questionnaire on Mathematics. 171 Secondary School Mathematics Teachers of the Central Region of Cuba participated. The results show acceptable internal consistency. The factorial structure of the scale revealed three major factors, consistent with the Model of the Three Constructs: beliefs about knowledge, about learning and teaching. Irregular levels in the development of the epistemological belief system about mathematics of these teachers were shown, with a tendency among naivety and sophistication poles. In conclusion, the questionnaire is useful for evaluating teacher’s beliefs about mathematics.

Variation in offspring size towards the high elevational range edge of a montane annual

Understanding the ecological determinants of species’ distribution is a fundamental goal of ecology, and is increasingly important with changing limits to species’ range. Species often reach distributional limits on gradients of resource availability, but the extent to which offspring provisioning varies towards range limits is poorly understood. Selection is generally expected to favour higher provisioning of individual offspring in environments with short growing seasons and limited moisture, nutrients, or hosts for parasitism. However, individual provisioning may decline if parent size is limited by resources. This thesis focuses on three major questions: 1) does seed size vary over an elevational gradient? 2) does this variation respond adaptively towards the range limit? and 3) is potential elevational variation environmentally or genetically controlled? I tested variation in seed investment towards the upper elevational limit of the hemiparasitic annual herb Rhinanthus minor, sampled across an elevational range of 1,000m in the Rocky Mountains of Alberta, Canada. I also used a reciprocal transplant experiment to address the heritability of seed mass. Seed mass increased marginally towards higher elevations, while seed number and plant size declined. There was a strong elevational increase in seed mass scaled by overall plant size. Therefore, investment in individual seeds was higher towards the upper range edge, indicating potential adaptation of the reproductive strategy to allow for establishment in marginal environments. Genetic, environmental, and genotype-by-environment interactions were observed in transplanted populations, but the relative proportions of these effects on seed size were unclear.

The efficacy of colour cues in facilitating adaptation to opposing visuomotor rotations

We investigated visuomotor adaptation using an isometric, target-acquisition task. Following trials with no rotation, two participant groups were exposed to a random sequence of 30 degrees clockwise (CW) and 60 degrees counter-clockwise (CCW) rotations, with (DUAL-CUE), or without (DUAL-NO CUE), colour cues that enabled each environment (non-rotated, 30 degrees CW and 60 degrees CCW) to be identified. A further three groups experienced only 30 degrees CW trials or only 60 degrees CCW trials (SINGLE rotation groups) in which each visuomotor mapping was again associated with a colour cue. During training, all SINGLE groups reduced angular deviations of the cursor path during the initial portion of the movements, indicating feedforward adaptation. Consistent with the view that the adaptation occurred automatically via recalibration of the visuomotor mapping (Krakauer et al. 1999), post-training aftereffects were observed, despite colour cues that indicated that no rotation was present. For the DUAL-CUE group, angular deviations decreased with training in the 60 degrees trials, but were unchanged in the 30 degrees trials, while for the DUAL-NO CUE group angular deviations decreased for the 60 degrees CW trials but increased for the 30 degrees CW trials. These results suggest that in a dual adaptation paradigm a colour cue can permit delineation of the two environments, with a subsequent change in behaviour resulting in improved performance in at least one of these environments. Increased reaction times within the training block, together with the absence of aftereffects in the post-training period for the DUAL-CUE group suggest an explicit cue-dependent strategy was used in an attempt to compensate for the rotations.

The contribution of visual feedback to visuomotor adaptation: How much and when?

We investigated the role of visual feedback in adapting to novel visuomotor environments. Participants produced isometric elbow torques to move a cursor towards visual targets. Following trials with no rotation, participants adapted to a 60 degrees rotation of the visual feedback before returning to the non-rotated condition. Participants received continuous visual feedback (CF) of cursor position during task execution or post-trial visual feedback (PF). With training, reductions of the angular deviations of the cursor path occurred to a similar extent and at a similar rate for CF and PF groups. However, upon re-exposure to the non-rotated environment only CF participants exhibited post-training aftereffects, manifested as increased angular deviation of the cursor path, with respect to the pre-rotation trials. These aftereffects occurred despite colour cues permitting identification of the change in environment. The results show that concurrent feedback permits automatic recalibration of the visuomotor mapping while post-trial feedback permits performance improvement via a cognitive strategy. (C) 2008 Elsevier B.V. All rights reserved.

The interference effects of non-rotated versus counter-rotated trials in visuomotor adaptation

An isometric torque-production task was used to investigate interference and retention in adaptation to multiple visuomotor environments. Subjects produced isometric flexion-extension and pronation-supination elbow torques to move a cursor to acquire targets as quickly as possible. Adaptation to a 30 degrees counter-clockwise (CCW) rotation (task A), was followed by a period of rest (control), trials with no rotation (task B0), or trials with a 60 degrees clockwise (CW) rotation (task B60). For all groups, retention of task A was assessed 5 h later. With initial training, all groups reduced the angular deviation of cursor paths early in the movements, indicating feedforward adaptation. For the control group, performance at commencement of the retest was significantly better than that at the beginning of the initial learning. For the B0 group, performance in the retest of task A was not dissimilar to that at the start of the initial learning, while for the B60 group retest performance in task A was markedly worse than initially observed. Our results indicate that close juxtaposition of two visuomotor environments precludes improved retest performance in the initial environment. Data for the B60 group, specifically larger angular errors upon retest compared with initial exposures, are consistent with the presence of anterograde interference. Furthermore, full interference occurred even when the visuomotor environment encountered in the second task was not rotated (B0). This latter novel result differs from those obtained for force field learning, where interference does not occur when task B does not impose perturbing forces, i.e., when B consists of a null field (Brashers-Krug et al., Nature 382:252-255, 1996). The results are consistent with recent proposals suggesting different interference mechanisms for visuomotor (kinematic) compared to force field (dynamic) adaptations, and have implications for the use of washout trials when studying interference between multiple visuomotor environments.

Dual adaptation to two opposing visuomotor rotations when each is associated with different regions of workspace

Studies examining dual adaptation to opposing novel environments have yielded contradictory results, with previous evidence supporting both successful dual adaptation and interference leading to poorer adaptive performance. Whether or not interference is observed during dual adaptation appears to be dependent on the method used to allow the performer of the task to distinguish between two novel environments. This experiment tested if colour cues, a separation in workspace, and presentation schedule, could be used to distinguish between two opposing visuomotor rotations and enable dual adaptation. Through the use of a purpose designed manipulandum, each visuomotor rotation was either presented in the same region of workspace and associated with colour cues (Group 1), different regions of workspace in addition to colour cues (Groups 2 and 3) or different regions of workspace only (Groups 4 and 5). We also assessed the effectiveness of the workspace separation with both randomised and alternating presentation schedules (Groups 4 and 5). The results indicated that colour cues were not effective at enabling dual adaptation when each of the visuomotor rotations was associated with the same region of workspace. When associated with different regions of workspace, however, dual adaptation to the opposing rotations was successful regardless of whether colour cues were present or the type of presentation schedule.

Neuromuscular adaptation during skill acquisition on a two degree-of-freedom target-acquisition task: Isometric torque production

In this study we attempted to identify the principles that govern the changes in neural control that occur during repeated performance of a multiarticular coordination task. Eight participants produced isometric flexion/extension and pronation/supination torques at the radiohumeral joint, either in isolation (e.g., flexion) or in combination (e.g., flexion - supination), to acquire targets presented by a visual display. A cursor superimposed on the display provided feedback of the applied torques. During pre- and postpractice tests, the participants acquired targets in eight directions located either 3.6 cm (20% maximal voluntary contraction [MVC]) or 7.2 cm (40% MVC) from a neutral cursor position. On each of five consecutive days of practice the participants acquired targets located 5.4 cm (30% MVC) from the neutral position. EMG was recorded from eight muscles contributing to torque production about the radiohumeral joint during the pre- and posttests. Target-acquisition time decreased significantly with practice in most target directions and at both target torque levels. These performance improvements were primarily associated with increases in the peak rate of torque development after practice. At a muscular level, these changes were brought about by increases in the rates of recruitment of all agonist muscles. The spatiotemporal organization of muscle synergies was not significantly altered after practice. The observed adaptations appear to lead to performances that are generalizable to actions that require both greater and smaller joint torques than that practiced, and may be successfully recalled after a substantial period without practice. These results suggest that tasks in which performance is improved by increasing the rate of muscle activation, and thus the rate of joint torque development, may benefit in terms of the extent to which acquired levels of performance are maintained over time.

Neuromuscular adaptation during skill acquisition on a two degree-of-freedom target-acquisition task: Dynamic movement

In this experiment, we examined the extent to which the spatiotemporal reorganization of muscle synergies mediates skill acquisition on a two degree-of-freedom (df) target-acquisition task. Eight participants completed five practice sessions on consecutive days. During each session they practiced movements to eight target positions presented by a visual display. The movements required combinations of flexion/extension and pronation/supination of the elbow joint complex. During practice sessions, eight targets displaced 5.4 cm from the start position ( representing joint excursions of 54) were presented 16 times. During pre- and posttests, participants acquired the targets at two distances (3.6 cm [36 degrees] and 7.2 cm [72 degrees]). EMG data were recorded from eight muscles contributing to the movements during the pre- and posttests. Most targets were acquired more rapidly after the practice period. Performance improvements were, in most target directions, accompanied by increases in the smoothness of the movement trajectories. When target acquisition required movement in both dfs, there were also practice-related decreases in the extent to which the trajectories deviated from a direct path to the target. The contribution of monofunctional muscles ( those producing torque in a single df) increased with practice during movements in which they acted as agonists. The activity in bifunctional muscles ( those contributing torque in both dfs) remained at pretest levels in most movements. The results suggest that performance gains were mediated primarily by changes in the spatial organization of muscles synergies. These changes were expressed most prominently in terms of the magnitude of activation of the monofunctional muscles.

The sites of neural adaptation induced by resistance training in humans

Although it has long been supposed that resistance training causes adaptive changes in the CNS, the sites and nature of these adaptations have not previously been identified. In order to determine whether the neural adaptations to resistance training occur to a greater extent at cortical or subcortical sites in the CNS, we compared the effects of resistance training on the electromyographic (EMG) responses to transcranial magnetic (TMS) and electrical (TES) stimulation. Motor evoked potentials (MEPs) were recorded from the first dorsal interosseous muscle of 16 individuals before and after 4 weeks of resistance training for the index finger abductors (n=8), or training involving finger abduction-adduction without external resistance (n=8). TMS was delivered at rest at intensities from 5% below the passive threshold to the maximal output of the stimulator. TMS and TES were also delivered at the active threshold intensity while the participants exerted torques ranging from 5 to 60% of their maximum voluntary contraction (MVC) torque. The average latency of MEPs elicited by TES was significantly shorter than that of TMS MEPs (TES latency=21.5+/-1.4 ms; TMS latency=23.4+/-1.4 ms; P

The Synergistic Organization of Muscle Recruitment Constrains Visuomotor Adaptation

Reaching to visual targets engages the nervous system in a series of transformations between sensory information and motor commands. That which remains to be determined is the extent to which the processes that mediate sensorimotor adaptation to novel environments engage neural circuits that represent the required movement in joint-based or muscle-based coordinate systems. We sought to establish the contribution of these alternative representations to the process of visuomotor adaptation. To do so we applied a visuomotor rotation during a center-out isometric torque production task that involved flexion/extension and supination/pronation at the elbow-joint complex. In separate sessions, distinct half-quadrant rotations (i.e., 45°) were applied such that adaptation could be achieved either by only rescaling the individual joint torques (i.e., the visual target and torque target remained in the same quadrant) or by additionally requiring torque reversal at a contributing joint (i.e., the visual target and torque target were in different quadrants). Analysis of the time course of directional errors revealed that the degree of adaptation was lower (by ~20%) when reversals in the direction of joint torques were required. It has been established previously that in this task space, a transition between supination and pronation requires the engagement of a different set of muscle synergists, whereas in a transition between flexion and extension no such change is required. The additional observation that the initial level of adaptation was lower and the subsequent aftereffects were smaller, for trials that involved a pronation–supination transition than for those that involved a flexion–extension transition, supports the conclusion that the process of adaptation engaged, at least in part, neural circuits that represent the required motor output in a muscle-based coordinate system.

Cost function adaptation: a stochastic gradient algorithm for data echo cancellation

A family of stochastic gradient algorithms and their behaviour in the data echo cancellation work platform are presented. The cost function adaptation algorithms use an error exponent update strategy based on an absolute error mapping, which is updated at every iteration. The quadratic and nonquadratic cost functions are special cases of the new family. Several possible realisations are introduced using these approaches. The noisy error problem is discussed and the digital recursive filter estimator is proposed. The simulation outcomes confirm the effectiveness of the proposed family of algorithms.