Introduction

Humans frequently need to learn what hand movements produce a desired outcome. This is most obviously seen during childhood, but learning takes place throughout the lifespan and can be observed in adults–whether the adult is acquiring a new skill or learning to use their non-preferred hand when recovering from a traumatic event (e.g. a stroke). The principles that underpin such learning have not yet been elucidated. The purpose of the present study was to explore whether learning to produce a novel two-dimensional spatial pattern with the tip of a handheld stylus is easier when tracing or copying the pattern. A real world example of this task would be a European educated adult learning to write Chinese characters.

Two common methods used to teach adults to write Chinese characters are tracing (a process known as ‘mo’) and copying (a process known as ‘lie’). Tracing provides excellent continuous feedback information about the correct path that the hand should follow, and so a trajectory close to optimal will be experienced. This might be highly beneficial for learning (as a veridical sensation of the necessary movement is experienced), but conversely, the lack of a need to remember details of the shape being followed might reduce any learning effects. In contrast, copying a shape might initially result in sub-optimal paths being drawn (because of a lack of direct visual error feedback), but this task may involve a greater degree of memory and recall and so could result in better motor memory for the required movement pattern in the longer term.

There is good evidence that the act of writing facilitates memory of letters when compared to a control condition of typing (Longcamp et al. 2005, 2006, 2008). It remains unclear, however, whether copying or tracing produces better learning outcomes, and current theories of motor learning do not help to identify which method is best. On the one hand, computational models of motor learning emphasise the importance of feedback received from successfully completing a task—with this feedback supporting the optimisation of feedforward internal models (Wolpert and Flanagan 2010). Such theories suggest that since tracing provides better feedback, then improved motor learning will occur. On the other hand, theories of learning transfer by identical elements (Thorndike and Woodworth 1901) might predict that copying would have advantages over tracing. Thorndike and Woodworth’s theory suggests that practising one skill will benefit another skilled behaviour if it has ‘identical elements’ to the practised action. There is good evidence to support Thorndike and Woodworth’s theory with studies showing generalisation of motor learning (e.g. Abeele and Bock 2001) but with ‘transfer’ restricted to similar skills (e.g. Abeele and Bock 2001; Thoroughman and Shadmehr 2000). One issue that appears to be an important determinant of an element being ‘identical’ is the information used to complete the task. Proteau et al. (1987) found that participants became more dependent on visual feedback after learning an aiming task where visual feedback was present and used these results to argue that a major characteristic of motor learning is its relative specificity to the information sources available when the learning occurs. Likewise, Charvin and Proteau (1996) found that there was an advantage to the presence of visual feedback during learning but that this did not transfer to a test of acquisition immediately after training where visual feedback was absent. The specificity of learning appears to predict that copying has an advantage over tracing, as copying pushes the actor to generate the shape based on memory (which is the skill that needs to be learned), whilst tracing makes the actor use the visual feedback (which will not be available when the letter needs to be produced from memory).

There have been previous studies that have raised the question of whether copying or tracing is a superior way of learning a novel shape in children (e.g. Askov 1975; Kirk 1980; Wright and Wright 1980). The general conclusion from these studies (as articulated by Kirk 1980) is that copying is the better method of teaching children to learn novel shapes (e.g. letters). Inspection of published studies, however, shows a set of conflicting results, where some authors claim copying is superior and some claim tracing produces better outcomes. Notably, the supporting evidence is sparse, and claims regarding copying or tracing superiority appear to be mainly based on intuition rather than solid empirical evidence. Most critically, none of the extant studies have employed rigorous kinematic analysis techniques to address this question in an objective empirical fashion. The advantage of kinematic analysis techniques is now well recognised and has been usefully employed in a number of important studies (Morasso 1981; Miall and Haggard 1995; Topka et al. 1998).

We examined whether there is an advantage to tracing or copying in adults when learning a novel set of patterns using sophisticated kinematic techniques. We studied performance immediately after practice, and also in a retention test a week later to see whether any longer-term advantages would be manifest. This issue is of specific empirical and theoretical interest as outlined previously, but this experiment also establishes techniques that allow related issues (learning in children) to be explored in future studies.

Methods

Participants

An opportunity sample of sixteen right-handed participants with normal or corrected-to-normal vision (7 women and 9 men, mean age = 23.7 ± 5.13) from the University of Leeds were recruited to complete a two-session study that included a learning-and-test session and a retention session 1 week later. All participants provided informed consent prior to commencing the study. The study was conducted in accordance with the ethical standards laid out in the 1964 Declaration of Helsinki. Ethical approval was obtained from the Institute of Psychological Sciences, University of Leeds.

Experimental setup

Visual tasks were designed and displayed using specialist software (KiniLab, Culmer et al. 2009). A digitising tablet (Toshiba Portege M700-13P, Screen: 260 × 163 mm, 1,280 × 800 pixels, 32 bit colour and a 60 Hz refresh rate) was used to present the tasks as well as record motor performance through KiniLab. The screen of the tablet was rotated and folded to provide a horizontal writing surface. The writing surface contained integrated sensors that measured the planar position of the pen-shaped input stylus. The position of the stylus was captured and processed using KiniLab at 120 Hz.

Participants were asked to sit comfortably, and the digitising tablet was positioned on a desk, in a landscape orientation, in front of them. The participant had the option of altering the height of the chair to adjust for the height of the tablet on the desk. Prior to experimental trials, participants were allowed to hold the stylus to become familiar with writing with it on the tablet for a few minutes.

Procedures

Participants were randomly assigned to one of two groups: copying (3 men, 5 women) or tracing (6 men, 2 women). They were asked to either copy or trace four patterns as accurately as possible using the stylus. Each pattern was labelled (A, B, C or D), and participants were asked to remember the label for each: a simple line (A), a wave (B) or two different combinations of discrete connected shapes (C and D; see Fig. 1a). The study included a practice-and-test session that lasted approximately 50 min and a 15 min retention test 1 week later. It is difficult a priori to determine the difficulty of the stimuli and a suitable duration of training, but pilot work suggested that performance with these stimuli improved over the time periods used. Participants were aware that there would be a retention test, but one woman in the copy group failed to take part, and her data were excluded from the retention analysis.

Fig. 1
figure 1

Examples of the experimental trials designed in KiniLab. a The four possible patterns; b the Tracing task; c the Copying task, where the pattern to copy was presented above in a box to give participants spatial information about the pattern; d the copy or trace test

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During the practice-and-test session, participants copied or traced a pattern four times and were then tested immediately afterwards by attempting to replicate the pattern they had just practised. Once they had finished this test, the original pattern was presented over the traced or copied path for 5 s as feedback. Participants performed four practice trials followed by a test (practice-test trials) and did this three times for each pattern: this constituted a block. Participants completed a total of three blocks of practice-test trials (Practice block 1–3 and Test block 1–3). The patterns were randomised within the blocks and between participants, except for the straight-line that was presented only at the beginning of the experimental session and at the end of each block as a control. Overall participants practiced copying or tracing all patterns 36 times and performed 12 tests (day 1) with feedback and a further 4 tests on the retention day.

Participants were asked to come back a week later to perform a second session that included retention tests. Participants performed the tests for each pattern twice, and no feedback was provided throughout the session.

Trial methodology

Participants were asked to place the stylus on the start position when ready to start the trial. Once the stylus was placed on the centre of the start button for 500 ms, the pattern (either A, B, C or D) appeared on the screen with the finish button cueing the participant to start copying or tracing the pattern presented (Fig. 1b, c). The next trial commenced once the participants reached the finish button. Trial time out occurred 2 min after the stylus was positioned over the start button.

During the test trials, the cue to start was presented with the word “Test” followed by the label of the pattern to reproduce (A, B, C or D) and the finish button (Fig. 1d). The original pattern was presented, once the participants reached the finish button. The next trial commenced following the feedback period. The retention tests were also cued by the word “Test” and the labels A, B, C or D, but no feedback was provided.

Data processing and analysis

Kinematic data were collected and processed by KiniLab. Data (X and Y coordinates of the stylus) were sampled at 120 Hz and filtered using a second-order low-pass Butterworth filter with a cut-off frequency of 10 Hz. Data collection commenced when participants positioned the stylus on the start button, and the trial ended when participants reached the finish button. We pooled performance across patterns C and D in order to examine the most effective way of learning to recreate difficult patterns (patterns A and B are not considered further).

Indices of performance

It is not trivial to quantify the accuracy of a reproduced pattern: an accurate reproduction requires the correct relationship between the drawn lines, including loops and changes in direction but also drawn at correct scale. We therefore calculated both the dimensional accuracy and shape accuracy by matching the path made by the participant (the input path) with the reference path that they were attempting to reproduce. We used a technique called ‘point-set registration’, whereby point-sets were generated for the input and reference paths by discarding temporal information and resampling the X and Y coordinates at a spatial resolution of 1 mm using linear interpolation. A robust point-registration method (Myronenko and Song 2010) was then used to determine the rigid transformation (consisting of translation, rotation and isotropic scaling components) that best transforms the input path to match the reference path. A compound dimensional accuracy index was determined by removing any identified translation and evaluating the mean distance between corresponding points in the original and transformed input point-sets. Similarly, shape accuracy was calculated by evaluating the mean distance between points in the transformed input path and the reference path. We used the compound dimensional index and the shape accuracy index as our performance measures (the first measuring the ability to reproduce the dimensions, the second measuring the ability to reproduce the shape).

Statistics

A mixed group (2) by block (3) ANOVA was used with an a priori alpha level of 0.05. We compared dimensional and shape accuracies between groups and across trial blocks to determine any learning effects during the practice session. In addition, shape accuracy and deformation comparisons were made between the tests implemented during the practice session and the tests performed 1 week after. Shape accuracies and deformation metrics are expressed as means ± standard deviations.

Results

Practice

First, we considered performance of the copying and tracing groups in the practice trials. Deformation analysis revealed significant differences between groups during practice (Fig. 2c). As anticipated, traced paths required less deformation to fit the reference path than copied paths (group main effect F 1,14 = 43.11, P < 0.001). There were no differences in deformation across block, nor was there an interaction indicating no systematic change to this spatial measure of performance during practice. Tracing also resulted in improved shape accuracy compared to copying (F 1,14 = 79.62, P < 0.001; Fig. 2a), but there were no significant differences between practice blocks nor were there interactions. Performance in these trials provided a useful baseline measures against which to compare performance in the test trials that occurred after each practice block. Shape accuracy when copying was 3 mm, and we might expect good test trial performance to approach this value.

Fig. 2
figure 2

a Shape accuracy during practice trials and b test trials; c Deformation during practice trials and d test trials. In the practice session, the tracing group exhibited superior performance as reflected in lower shape accuracy and deformation scores. The horizontal dashed lines (in panelsb and d) indicate average practice performance copying the pattern. Bars in all cases = standard errors

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The test trials required participants to reproduce the previously copied or traced pattern without a visual display of the pattern (Fig. 1d). Figure 2b shows that whilst shape accuracy measures during test blocks were worse than during practice trials, there was a significant improvement across blocks (F 2,28 = 19.62, P < 0.001). It appears in Fig. 2b that tracing group performance was better than the copying group, though the difference was only marginal (F 1,14 = 4.46, P = 0.053). There were no significant interactions between block and group. The deformation analysis confirmed group differences at test (Fig. 2d; F 1,14 = 4.85, P < 0.05) with the recalled patterns of the tracing group requiring less deformation. There were not, however, any changes across testing sessions (F 2,28 = 0.70, ns) nor interactions (F 2,28 = 0.39, ns) suggesting little influence of repeated practice over this aspect of pattern reproduction. The main effects suggest that there is an initial advantage to remembering previously traced patterns, but the lack of any reliable interactions indicates that both tracing and copying led to improvements in performance at similar rates.

Retention

To determine whether copying or tracing the patterns influenced longer-term retention, we asked participants to return 1 week later to carry out a retention test. The shape accuracy analysis (Fig. 2b) showed that retention performance was not significantly better than Test1 (F 1,13 = 0.972, ns), and both groups were worse compared to Test3 (F 1,13 = 4.78, P = 0.05). The deformation analysis (Fig. 2d) was consistent with this finding with no statistically reliable difference between Test3 and retention (F 1,13 = 0.81, ns; the copying group was quite variable which may have suppressed group differences). There were no differences in accuracy or deformation measures in the retention test between the tracing and copying groups suggesting that both training types led to similar long-term performance.

Discussion

The main aim of our experiment was to investigate whether practicing drawing a pattern by tracing or copying differentially improved learning of a pattern. As expected, the tracing group exhibited superior performance compared to the copying group when actually generating each pattern (as indexed by measures of both shape and dimensional accuracy). The critical question was whether there were differences in the participants’ ability to reproduce the shape when the template disappeared. We found that the higher accuracy obtained when tracing translated to an improved ability to recall the dimensions and shape when the pattern first disappeared and the participant needed to draw from immediate memory. There was, however, no evidence of increased rates of learning in the tracing group (there was no interaction between test block and group), and there was no group difference at the 1-week retention test.

It was not possible a priori to predict whether tracing or copying would produce better learning. Copying appears to have the advantage of forcing individuals to memorise the shape as part of the task–which might be thought to enhance subsequent recall. There are theoretical reasons to suppose that forcing participants to use information (a memory of the shape) might produce better outcomes since this is the information that will ultimately be required (Thorndike and Woodworth 1901; Proteau et al. 1987). On the other hand, tracing provides immediate online feedback, and this is known to be an important part of the learning process (Wolpert and Flanagan 2010). In the current experimental set-up, the short-term advantages of receiving continual online feedback appear to outweigh any advantages of memorising the shape whilst copying. We note that the different theoretical perspectives are complementary, and our results do not conflict with theories of identical element transfer learning—they just suggest that the veridical feedback appears to be more important under these particular task constraints. In our experiment, participants did not experience a large number of practice trials, and this may have influenced information use. Given a longer training period (and more practice trials), it is possible that participants would have become more dependent upon the information available at the time of practice. It could be predicted that such dependence would not only improve the performance of the copying group, but also impair performance of the tracing group when tested without feedback (see the ‘guidance hypothesis’ of Salmoni et al. 1984). In short, it is not certain that tracing would be the most suitable training strategy over longer periods, but this remains an empirical question worthy of further exploration. Future studies could also use these techniques to probe the implications of practice specificity in learning tasks of this type.

The issue of whether tracing is better than copying or vice versa when learning to produce a novel shape is of fundamental importance with regard to teaching handwriting skills. There has been to date a dearth of studies that have documented differences between copying and tracing. This has been in large part because of the lack of suitable technology. The current study shows the power of kinematic analysis techniques made possible through computer tablet technology and the development of software systems such as KiniLab (Culmer et al. 2009). The use of KiniLab has demonstrated a clear superiority for learning through tracing rather than copying in the shorter term. But there are a number of caveats that must be highlighted with respect to this finding. First, the data were collected in neurologically intact adults who had already mastered the control problems involved in generating the appropriate forces through a handheld stylus. It is now important to learn whether the same pattern of results is found in young children who are still learning to write. Second, the better performance for tracing was only present in the immediate recall test. There were no reliable differences found between copying and tracing performance, when retention was tested 1 week later. It remains to be determined whether this reflects a lack of power in the experimental design, whether the task was too hard (so neither group properly learned the shape as suggested by the lack of difference between the first immediate recall and memory 1 week later) or whether the immediate differences simply never translate to longer-term advantages for tracing. Likewise, it is not clear why the immediate advantages of tracing did not produce a steeper learning curve for tracing when compared to copying. This might also be related to the power of the current experimental design.

In a series of elegant experiments, Longcamp and colleagues have shown that the act of writing produces better memory for shapes than typing (Longcamp et al. 2005, 2006, 2008). In a more recent study, Longcamp et al. (2008) used fMRI techniques to investigate brain activation in the handwriting condition. Greater activation was found in those brain regions known “to be involved in the execution, imagery and observation of actions, in particular the left Broca’s area and bilateral inferior parietal lobules”. These findings provide good evidence that the movements involved in writing facilitate the visual memory of graphic shapes and letters. These neural findings highlight the need for us to better understand whether the method used to write (i.e. copying or tracing) influences the neural activation involved in learning novel patterns.

In summary, this study raises many questions regarding differences between copying and tracing. Nevertheless, it shows that there are differences between these tasks in terms of short-term recall even if these differences disappear after 1 week. Importantly, the study demonstrates that it is possible to empirically explore these issues using sensitive kinematic performance measures. These techniques can then be employed to better understand the differences between tracing and copying using a myriad of different shapes over a wide range of time scales (we note that a common saying in Chinese suggests that 100 days of practice is required to learn to write Chinese characters). The approach can also be used to study differences as a function of age. We anticipate that the study of copying and tracing will yield important insights into human motor control that will have important applications within educational settings.