Transfer of learning between unimanual and bimanual rhythmic movement coordination: transfer is a function of the task dynamic

Abstract

Under certain conditions, learning can transfer from a trained task to an untrained version of that same task. However, it is as yet unclear what those certain conditions are or why learning transfers when it does. Coordinated rhythmic movement is a valuable model system for investigating transfer because we have a model of the underlying task dynamic that includes perceptual coupling between the limbs being coordinated. The model predicts that (1) coordinated rhythmic movements, both bimanual and unimanual, are organised with respect to relative motion information for relative phase in the coupling function, (2) unimanual is less stable than bimanual coordination because the coupling is unidirectional rather than bidirectional, and (3) learning a new coordination is primarily about learning to perceive and use the relevant information which, with equal perceptual improvement due to training, yields equal transfer of learning from bimanual to unimanual coordination and vice versa [but, given prediction (2), the resulting performance is also conditioned by the intrinsic stability of each task]. In the present study, two groups were trained to produce 90° either unimanually or bimanually, respectively, and tested in respect to learning (namely improved performance in the trained 90° coordination task and improved visual discrimination of 90°) and transfer of learning (to the other, untrained 90° coordination task). Both groups improved in the task condition in which they were trained and in their ability to visually discriminate 90°, and this learning transferred to the untrained condition. When scaled by the relative intrinsic stability of each task, transfer levels were found to be equal. The results are discussed in the context of the perception–action approach to learning and performance.

Appendix: Additional measures of coordination performance

Measures of mean error and variability have been used in some studies to evaluate coordination performance and learning. We report these measures and show that they are difficult to interpret in the current context in contrast to the proportion of time-on-task (PTT) measure that we have used. Similar to Maslovat et al. (2010), we computed the relative phase distributions windowed at intervals of 20° ranging from 0° to 180° and produced a histogram showing where participants were spending time when trying to move at 90° both before and after training (see Fig. 4a, b). We used this graph to interpret the mean error and variability.

Fig. 4

Relative phase distributions for baseline and post-training for bimanual 90° separated by group: a) baseline; b) post-training

The problem for the measures is as follows. As participants begin to try to perform 90° coordination, they often fail to remain in the neighbourhood of 90° and transition to spend significant time at either 0° or 180°. As they learn and improve in performance, they succeed better in staying near or at 90° (as shown directly by the PTT measure) although they may still occasionally transition to 0° or 180°. There are individual differences in whether a performer tends to transition either to 0° or to 180° or to both. If it is both rather than just 0° or 180°, for instance, then the resultant overall variability can be increased. However, this is not relevant to the level of success in performing the task, which is to stay at or near 90°. It is all the same if the movement is at 0° or 180° instead of 90°. Also, if the performer spends similar amounts of time at 0° and at 180°, then the mean can be 90°, whereas if the performer transitions more reliably to 0°, then the mean can biased towards 0°. Again, these differences are not of direct relevance to the success in performing the task. For these reasons, measures of mean error and variability are problematic for evaluating performance in this learning task.

First, we describe the relevant measures of mean error and variability.

Data analysis

Relative phase is a circular variable (the distribution of possible values lies on a circle) that creates a problem for computing standard means and standard deviations. Circular statistics provide trigonometric solutions to these problems by treating each data point in a relative phase time series as a vector of unit length and an orientation that matches the relative phase at that time point. Mean direction is effectively the result of concatenating these vectors and computing the orientation of the vector between the origin and the tip of the final data point vector. The mean vector length or uniformity (U) (Fisher 1993) measures the variability as the length of the resultant vector divided by the number of data points (and which therefore ranges from 0 to 1). This latter was transformed into a linear variable (SDψ) that varies between 0 and infinity using the following transformation:

$${\text{SD}}\psi {\, =\, }\left( { - 2\log_{\text{e}} U} \right)^{1/2}$$

Results

First, to examine performance before and after training, we computed relative phase distributions (that is, the proportion of time spent at relative phases between 0° and 180° using 20° bins) by condition (unimanual 90°, bimanual 90°) and separated by group. We illustrate the resulting individual differences in Fig. 4. When performing the bimanual task at baseline, as expected, neither training group consistently produced a relative phase at or near 90°. As shown in Fig. 4a, the group that would subsequently be trained at the bimanual task tended to transition to and spend time at 180°, while the group that would be trained at the unimanual task tended to transition to and spend time at 0°. This was merely an individual difference between the groups that was, however, reflected in the pattern of results for the mean direction at baseline. (Note that individual differences also appeared in results at baseline for the unimanual task.) As shown in Fig. 5a, the training groups exhibited significant differences in mean direction that reflected the individual differences. To analyse the mean direction, we used a two-way mixed-design analysis of variance (ANOVA) with group (unimanual training, bimanual training) as a between-subjects factor and condition (unimanual 90°, bimanual 90°) as a within-subject factor. The result was a significant main effect of group (F _(1,12) = 4.98, p < .05). However, this difference was not relevant to the level of success in performing the task to be learned. Accordingly, we had found no differences when performance was evaluated using the PTT measure of success in performing the 90° task.

Fig. 5

Mean vector direction (in degrees) at baseline and post-training separated by condition and group: a) baseline, bimanual versus unimanual 90°; b) post-training, bimanual versus unimanual 90°

We used the same ANOVA design to analyse SDψ and found no significant main effects or interactions. This indicated that there was no difference in consistency between the groups at baseline as shown Fig. 6a. (Note that there could have been a difference if participants in one of the groups had tended to transition equally often both to 0° and to 180°, but this difference, if significant, also would not have been relevant to the evaluation of success in performing the task to be learned.)

Fig. 6

SDψ at baseline and post-training separated by condition and group: a) baseline, bimanual versus unimanual 90°; b) post-training, bimanual versus unimanual 90°

Next, we analysed mean direction and SDψ at post-test. For mean direction, as shown in Fig. 5b, there were no significant main effects or interactions. However, as shown in Fig. 4b, the unimanually trained group still spent more time at 0° (in the bimanual task), while the bimanually trained group spent more time at 90°. This yielded a result in the analysis of SDψ where there was a significant group by condition interaction (F _{(1, 12)} = 7.82, p < 0.02) as shown in Fig. 6b. A comparison of baseline and post-test yielded a main effect of session for SDψ (F _(1,12) = 13.50, p < 0.05), but not for mean direction. Nevertheless, both measures must be taken into account when evaluating success in learning this task. The reason is that stable but highly inaccurate performance can result from spending time only at 0° or only at 180° and that apparently accurate but highly unstable performance can result from spending equal time at 0° and at 180°.

So finally, using the two measures (mean direction and SDψ), it remained unclear how to evaluate the relative transfer of training, appropriately scaled by intrinsic differences in stability between the tasks. PTT measures the goal of the learning task directly, providing a single measure of success in performing the 90° task. It also yielded good measures of transfer. Thus, this was the preferable measure to use.