Submovement Analysis in Learning Cursive Handwriting or Block Print[1]
Hans-Leo TEULINGS & Diana ROMERO
NeuroScript, Tempe, Arizona, USA
hlteulings@NeuroScriptSoftware.com
Abstract. Pen movements were recorded in healthy adults during learning of a sequence of vertical down strokes, a zigzag pattern, or a cursive-script pattern. The strokes had to be performed by moving the pen from target to target while visual feedback was offered via a computer monitor. The movement patterns were segmented into up and down strokes and each stroke was segmented into primary and secondary submovements, i.e., a preprogrammed, ballistic part and a feedback controlled part, respectively. Results show that learning takes place during the course of 16 trials as stroke duration decreased. Submovement analysis confirmed the usual increase in the relative duration and size of the primary submovement. However, this increase was only observed in the zigzag and the cursive writing patterns, which are continuous patterns, but not in the vertical down strokes, which is a discontinuous movement. This suggests that submovement analysis may show powerful learning effects in multi-stroke, continuous movement patterns.
1. Introduction
The ability to rapidly produce a specific handwriting pattern can be compared to learning to produce a sequence of goal-directed movements. The production of an accurate goal-directed movement with a pen to a visible target as fast and precise as possible requires that the visuo-motor system preprograms the initial part of the movement, with subsequent fine adjustments of amplitude and direction based on visual feedback. If the movement requires a change in direction or increase in amplitude, a small deceleration and acceleration of the pen movement may be measured. The initial ballistic movement towards the vicinity of the target is called the primary submovement. The feedback-controlled adjustment(s) are called secondary submovements. The ballistic submovement is fast but inaccurate. The feedback-controlled adjustments are accurate, but consume time. The optimized submovement model (OSM, Meyer et al., 1988) proposes that the motor system minimizes total movement duration through planning an optimal combination of primary and secondary submovements. This optimization was verified in pen movements (Teulings, in prep.). During the process of learning a goal-directed movement, the relative duration and size of the primary submovement increase, signifying the motor system's increased ability to preprogram stroke size and direction correctly (Thomas, Yan, and Stelmach, 2000; Seidler-Dobrin and Stelmach, 1998). These studies suggest that while learning of a single-stroke movement, the relative duration and size of the primary submovement increases.
Another measure proposed to be able to quantify learning is normalized jerk, which is a dysfluency measure (Teulings et al., 1997). With practice movement duration reduces and due to the low-pass filtering of the musculo-skeletal system, dysfluency should reduce.
The writing patterns we tested were inspired by the motor tasks that pupils in primary schools perform during handwriting instruction. Commonly, pupils initially learn block print and eventually cursive script. A frequent movement unit in block print is a straight, vertical downward stroke followed by a pen lift. Cursive script consists mostly of loops and movement reversals without pen lifts. To learn a complex task like handwriting, it may be advantageous for the learner to be able to combine strokes into "units". Multi-stroke units, forming known cursive letters, have been observed by Teulings at al (1983). This study shows that when two cursive-script letters were presented in choice-reaction time (RT) conditions (without or with partly precue), only the identical letters showed an RT advantage. In another study (Stelmach & Teulings, 1988), where sequences of zig-zag stroke patterns were used, no evidence for multi-stroke units was observed. These studies suggest that learning of multi-stroke patterns, such as handwriting letters, may be different from multi-stroke zigzag sequences.
In an explorative study we want to investigate whether traditional measures of movement duration, relative duration and size of the primary submovement, and normalized jerk are able to detect progress in motor learning in multi-stroke patterns.
2. Experiment
Participants. Twelve adult university students and teachers (8 women, 4 males, and ages 21 to 44 years, all right–hand dominant) participated after informed consent.
Equipment. Stimuli were presented using a Princeton E0900, 48-cm CRT display (visible 45 cm) set at 1600x1200 dots and 72 Hz vertical refresh rate. The display was vertical in front of the participant at 50 cm distance. Writing movements were recorded using a Wacom Intuos2, XD-0608-U display with an active area of 20.32 cm x 15.24 cm. The sampling rate was 102 Hz. The resolution was 0.001 cm and the RMS error <0.1 cm. Data were collected on a 2.5 GHz Intel4 PC with Windows XP. The recording and analysis of pen movements were done using MovAlyzeR (Teulings, 2003).
Stimuli. The stimulus was presented in real-size on a computer monitor located in front of the participant. It consisted of 14 circles, representing a cursive writing pattern "ehye", with a body height of 0.7 cm, and ascender or descender heights of 1.4 cm from the baseline. The circle diameters were 0.3 cm, which turned green when the pen approached the circle within 0.1 cm if it was in the right sequence and red it was not in the right sequence. The visual feedback had the same size as the required patterns on the digitizer.
Conditions. Three stroke multi-stroke writing patterns were performed that required the participant touching all circles in a sequence from left to right, and from top to bottom. The movement patterns can thus be considered as a to-be-learned sequence of goal-directed movements:
(1) Separate-stroke pattern (See Figure 1, left): Place a dot in Circle 1, then lift the pen and produce vertical lines from top to bottom in consecutive circle pairs, lifting the pen after each line, and then place a dot in Circle 14.
(2) Zigzag pattern (See Figure 1, center): Connect Circles 1, 2, 3, ... with straight strokes.
(3) Cursive-script pattern (See Figure 1, right): Write cursively "ehye". Start at Circle 1, e-loop top at Circle 2, bottom at Circle 3, etc.
Procedure. The participants were sitting at a desk with the digitizer on top and the computer monitor in front of them. Recording started when the pen touched the tablet and ended when the pen was lifted for more than one second. Each condition was repeated 16 times. The sequence of conditions was randomized. The participant initially performed the trials as an exercise, during which the experimenter trained the proper execution of each of the conditions, with the instruction that the writing patterns had to be performed as rapidly and accurately as possible. Data was processed immediately after a trail was recorded, and the experimenter could monitor whether the trials were consistent. When the subject produced a sufficient number of consistent trials, the training series was terminated and the recording of the experimental data commenced. The experiment took 15 minutes.
Analysis. Writing patterns were low-pass filtered at 10 Hz (transition band 5 Hz to 16 Hz), differentiated, and velocity and acceleration curves were estimated. Stroke segmentation was at points where the vertical velocity passed through zero. Submovement analysis appears little sensitive for the choice of the low-pass filter frequency around 10 Hz (Teulings, in prep.). Subsequent zero crossings within 0.04 seconds were discarded. A stroke was further segmented into primary and secondary submovements by the first negative-to-positive zero crossing of the vertical acceleration (in positive or upward strokes) after the absolute peak velocity. Duration and vertical size were estimated for the entire stroke and for each submovement. The relative duration of the primary submovement was defined as T1/T and S1/S, respectively, where T1 and S1 are the duration and size of the primary submovement and S and T the size and duration of the entire stroke, respectively.
Trials were automatically discarded if they were not consistent, e.g., if the number of strokes was less or more than 13 or if the "ehye" pattern did not form the proper sequence of clockwise, counterclockwise looping, acute, or obtuse movement reversals or did not form the proper sequence of short and long strokes. In total 11% of the 576 trials were discarded.
To reduce the effects of discarded trials in the learning curves as a function of trial, discarded trials were replaced by the last, valid trial, or, in case it was the first trial, by the first valid trial. Finally, Trials 1-4, 5-8, 9-12, 13-16 were pooled, yielding a sequence of 4 data points during the course of 16 trials.
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3. Results
An example of a recorded writing pattern and its segmentation are shown in Figure 2. Average stroke duration as a function of trial number shows a gradual reduction in all conditions (regression coefficients are negative, t(11)>2.62, p<0.05), demonstrating evidence of learning (See Figure 3). During the learning process, relative duration and size of the primary submovement are increasing in the zigzags and the cursive script patterns (regression coefficients are positive, t(11)>2.70, p<0.05) but not in the vertical strokes (t(11)=1.24, p>0.2) (See Figure 4, left). Similarly, the relative size of the primary submovement increases with practice (regression coefficients are positive, t(11)>2.53, p<0.05) in the zigzag and cursive patterns, but not in the vertical strokes, t(11)<1). Figure 5 shows the gradual reduction of normalized jerk during practice. Normalized jerk reduced in the separate-stroke and the cursive-script patterns (t(11)<3.23, p<0.01) but non-significantly in the zigzag pattern (t(11)=1.56, p>0.1).
4. Discussion
The participants learned during 16 replications 3 different writing patterns (conditions) connecting the same set of 14 points: (1) Separate, vertical strokes, similar to the typical movements required in printing. (2) Zigzags consisting of straight strokes that do not require pen lifts, and (3) a cursive script pattern ("ehye"). The results indicated that learning takes place over the course of 16 trials as shown by a reduction of the average stroke duration, an increase in the relative duration and size of the primary submovement, and a reduction of normalized jerk. However, not all patterns show these trends to the same extent and it also differs fore the different measures of learning. While stroke duration appeared to reduce in all patterns, submovement analysis did not show a significant learning effect in the sequence of separate, goal-directed strokes. This is remarkable as submovement analysis was developed for goal-directed strokes. Other studies (e.g., Thomas, Yan, and Stelmach, 2000; Seidler-Dobrin and Stelmach, 1998) have shown that in "single-stroke" goal-directed movements, the relative duration of the primary submovement increased during learning. A possible reason that we did not observe this effect in a more complex, multi-stroke pattern is that the vertical stroke sequence is simple compared to the other patterns so that this simple patterns was already learned more than enough while the more complex patterns were just learned well enough to be able to produce them. At odds, however, seems that compared to the zigzag pattern, the separate-stroke pattern had still ample space for improvement in terms of increasing duration and size of the primary submovement. Similarly, normalized jerk showed no learning effect in the zigzag. A possible reason is that the zigzag pattern was already very fluent at the beginning of the experiment so that additional learning would require a lot more trials. In summary, this study shows that submovement analysis is a powerful method to quantify progress in motor learning of fluently connected multi-stroke patterns.
5. References
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Seidler-Dobrin, R.D.,& Stelmach, G.E. (1998). Persistence in visual feedback control by the elderly. Experimental Brain Research, 119, 467‑474
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Teulings, H.L. (in prep.). Optimization of Movement Duration in Handwriting Strokes in Different Directions in Young, Elderly, and Parkinsonian Subjects.
Teulings, H.L. (2003). Movalyzer2.6 [Computer program]. http://www.neuroscriptsoftware.com.
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Thomas, J.R., Yan, JH., and Stelmach, G.E (2000). Movement substructures changes as a function of practice in children and adults. Journal of Experimental Child Psychology, 75(3), 228-244.