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Research Report
Brain activity and learning of mathematical rules—Effects on the frequencies of EEG Wolfgang Skrandiesn, Alexander Klein Institute of Physiology, Justus-Liebig University, Aulweg 129, 35392 Giessen, Germany
art i cle i nfo
ab st rac t
Article history:
We investigated the change of evoked EEG frequencies induced by learning to solve
Accepted 5 November 2014
mathematical tasks by applying divisibility rules. The performance on easy (divisibility by 2, 3, or 5) and hard tasks (divisibility by 9 or by 11) was compared. In a behavioral
Keywords:
experiment on 52 adults we found a significant increase in performance from 67% to 90%
Learning
correct responses induced by rule learning. Subsequently, the EEG data recorded from 30
Mathematics
additional volunteers were analyzed. EEG recordings were performed in two parts: First,
EEG
subjects had to solve 200 tasks without knowing the divisibility rules. Then the rules were
Wavelet analysis
explained, followed by another set of 200 tasks. EEG was measured simultaneously in 30
Alpha/theta
channels, artifacts were removed offline, and the data before and after rule learning were compared. A wavelet transformation with the Morlet-5 wavelet was computed, and the scalp topography of the maximal frequency and its occurrence time was compared. Largest effects were observed with frequencies between about 6 and 18 Hz. In the frequency band between 12 and 30 Hz maximal frequencies were significantly different after successful learning over frontal and centro-parietal scalp areas of the right hemisphere. These changes were paralleled by decreased response times. In summary, our data illustrate a significant relation between successful learning divisibility rules and changes in the frequency content of the task-related EEG. Significant effects were observed after a very short training period of less than 10 min. This article is part of a Special Issue entitled SI: Brain and Memory. & 2014 Published by Elsevier B.V.
1.
Introduction
Human cognition depends to a large extent on the ability to learn new facts or rules. Such learning is based on cortical plasticity that plays an important role for the adaptation to the physical environment and for changes in performance of cognitive abilities. Psychophysical and electrophysiological
studies on human visual perception have demonstrated that sensory discrimination ability improves by training in adult subjects. Perceptual learning is accompanied by changes of event-related brain activity (cf. Skrandies and Jedynak, 1999; Skrandies et al., 2001; Ludwig and Skrandies, 2002; Shoji and Skrandies, 2006). In different experiments we could show that learning of meaningful material results in significant alterations
n
Corresponding author. E-mail address: [email protected] (W. Skrandies).
http://dx.doi.org/10.1016/j.brainres.2014.11.015 0006-8993/& 2014 Published by Elsevier B.V.
Please cite this article as: Skrandies, W., Klein, A., Brain activity and learning of mathematical rules—Effects on the frequencies of EEG. Brain Research (2014), http://dx.doi.org/10.1016/j.brainres.2014.11.015
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of electrophysiological brain responses (Shinoda and Skrandies, 2013). In general, learning is defined as “changes in behavior resulting from prior experience” (Thompson and Donegan, 1987) that in the present experiments are measured as performance on mathematical problems. Specifically, we examined the effects of learning of mathematical rules on multichannel EEG signals that were obtained before and after learning. The neurophysiological correlates of processing mathematical tasks have been studied previously by recording EEG and event-related potentials from healthy subjects. With task-related ERP recordings the occurrence of early components and of late slow wave activity has been repeatedly described (see for example, Skrandies et al., 1999; Galfano et al., 2009; Luo et al., 2009; Nunez-Pena et al., 2011). With recordings of the spontaneous EEG, brain activity in the theta and alpha frequency range has been reported to be related to mental arithmetic-induced workload (Sammer et al., 2007; De Smedt et al., 2009). Until now, only very little is known about the effects of learning mathematical rules on the frequencies of performance-related EEG signals while there are reports on the effects of cognitive processing on brain activity. In a study on eight participants Murata (2005) evaluated the influence of mental workload on EEG in continuous matching tasks. Data from only three recording sites were reported. In a wavelet analysis of the data the author found that increasing mental workload mainly affects the time at which strongest responses were seen while total power of alpha and beta activity increased with task difficulty. Mathematical reasoning was also analyzed by wavelet transforms of EEG where cortical activity was compared between a rest and a task condition (Sakkalis et al., 2006). In this study, brain activity was increased during the task. Such effects were observed mainly over frontal and central scalp regions. Results on brain potentials and the effects of extensive practice of mental arithmetic tasks were reported by Pauli et al. (1994). The authors illustrate how practice affected the amplitude and offset latency of the event-related slow wave component. Since this constituted an ERP experiment, the frequencies of the task-related EEG were not analyzed. In order to study the effects of learning we chose a task in which subjects could rapidly improve in performance. There are mathematical rules that are commonly in full detail unknown to most students but the rules can be learned easily. Divisibility rules are an example for this (Miller and Takloo-Bighash, 2006). In order to determine whether a given number can be divided by 2, 3, or 5, no explicit rules need to be applied since the answer is obvious to most adult persons. Divisibility by 9 or by 11 appears to be more complex and cannot be solved quickly. A number is divisible by 9 if and only if the sum of the digits is divisible by 9, and in order to determine the divisibility by 11 one needs to compute the sign-alternating sum of its digits. When these rules are known to a subject, such tasks become easy. In addition, time restriction allows to easily modulate task difficulty and performance. Thus, task difficulty has some gradual variation. We note that the teaching of divisibility rules is part of the curriculum of German high schools, however, the explicit knowledge of such rules is very poor (see Methods). In a behavioral experiment on 52 adults we first confirmed that learning to apply divisibility rules occurs rapidly and
yields a high rate of learning success. For practical reasons, such an experimental paradigm that allows for rapid learning was the prerequisite for the subsequent electrophysiological experiments. In the present EEG study we investigated, how improvement in performance on a mathematical task is accompanied by changes in EEG frequencies which were elicited during mental performance. We will show that mental arithmetic elicits both, high and low frequencies in the human EEG. However, the main learning effects appear in the low beta range over frontal scalp areas of the right hemisphere.
2.
Results
2.1.
Behavioral data
The subjects were allowed to work on the tasks for 8 min before and 8 min after learning the rules. Before, a mean number of 56.3 tasks were solved, while after rule learning the mean number of finished problems increased to 79.1 tasks. With hard tasks the subjects improved in performance by a factor of 2 after they had learned the rules (from a mean of 19.4 to 40.03 correctly solved tasks within 8 min). As expected, for the easy tasks improvement was not significant (93.10% correct responses before, 97.95% after learning) while for hard tasks performance significantly increased (from 66.63% to 90.17% correct responses). Thus, there was a significant interaction between “time” and “task” (F(1,51)¼ 37.99; po10 5 ) which is illustrated in Fig. 1A. Very similar results were observed for the 30 subjects who participated in the EEG study. There was an overall increase in performance after learning. Again, this increase was smaller for easy (82.20% correct before, 88.56% after learning, t¼6.07, po10 6 ) than for hard tasks (57.09% correct before, 66.67% after learning, t¼6.17, po10 6 ). We note that both changes were significant, however, for easy tasks the change was only about 6.36% while with hard tasks subjects improved by 9.58%. A trend for learning was confirmed by an interaction between “time” and “task” in a repeated measures ANOVA (F(1,29)¼ 3.12; po0:08). The response times for correct answers were also significantly affected as is shown in Fig. 1B. There was a significant interaction between “time” and “task” (F(1,29)¼ 27.06; po10 5 ). Hard tasks yielded significantly higher response times than easy tasks, and response times decreased significantly after rule learning. This effect was significantly different for hard and easy tasks. For hard tasks the improvement was about 400 ms while with the easy controls the response times were reduced by only about 100 ms. We note that the behavioral results were not expected to be identical in both studies, since there were slight differences in the experimental design (time restriction for a response in the EEG study, no time restriction in the questionnaire study). Still all behavioral data demonstrate that the subjects' performance increased significantly over time.
2.2.
Electrophysiological data
First, we illustrate the time and frequency resolution of our wavelet computation. Fig. 2A shows the scalogram resulting
Please cite this article as: Skrandies, W., Klein, A., Brain activity and learning of mathematical rules—Effects on the frequencies of EEG. Brain Research (2014), http://dx.doi.org/10.1016/j.brainres.2014.11.015
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Fig. 1 – (A) Mean of correct responses in the behavioral study. Before and after rule learning there is a significant increase in performance which is more pronounced for hard (learning) tasks (see text for details). Means and SEM of 52 subjects. (B) Mean response times of the subjects in the EEG study. There are significant effects on response times which are similar to the results in A. Means and SEM of 30 individuals.
from one full sine wave of 2, 4, 8, and 16 Hz, respectively. The color codes indicate signal strength normalized to the maximal amplitude. Wavelet transforms were computed for the EEG data of each subject and experimental condition for each electrode. The wavelet analysis showed that in most recording channels strong responses were elicited in both low and high frequency bands between about 8 and 30 Hz. At higher frequencies no consistent activation could be measured. Fig. 2 illustrates the grand mean over all subjects of the wavelet scalograms at the 30 electrode sites. The data illustrated were recorded with hard (learning) tasks after rule learning. Strong activation can be seen starting as early as 50 ms after the beginning of the presentation
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of the task. The raw data obtained in the other experimental conditions had a similar but not identical appearance. From Fig. 2 it is obvious that there are low frequencies up to about 10 Hz as well as high frequencies which occur between about 12 and 30 Hz. The wavelet data of all subjects were inspected in order to define frequencies of interest. It turned out that there was no consistent brain activity present at frequencies higher than 30 Hz. For further quantitative analysis we defined two frequency bands where all subjects displayed strong activity. We determined, for each subject and experimental condition, the frequency values with maximal amplitude. At each channel, we selected the occurrence time of maximal amplitude between 0 and 500 ms for low (between 1 and 12 Hz) and high frequencies (between 12 and 30 Hz). In this way we obtained information about the strongest response in terms of EEG frequency. In addition, this procedure yielded information on the occurrence time of strongest electrophysiological responses. These data were then directly compared between experimental conditions. The aim of the analysis was to determine whether frequencies changes as a consequence of experimental manipulation. Of course, this is different at different electrode sites. Thus, maximal frequencies were plotted topographically. Fig. 3A and B illustrates the distribution of frequencies for the lower band while Fig. 3C and D shows the results obtained with the higher frequencies. These are mean data computed for all subjects separately for the experimental conditions (“before/after learning”; “hard/easy tasks”). Most of the activity in the lower frequency band occurred between 5 and 9 Hz (absolute minimum: 5.14 Hz; absolute maximum: 8.65 Hz; mean over all subjects and experimental conditions: 7.05 Hz). Over frontal midline and left scalp areas there was a distribution of low frequencies (between 5 and 7 Hz) while parietal and central scalp areas were dominated by frequencies between 8 and 9 Hz (see Fig. 3A and B). As is evident, this global pattern was similar for all experimental conditions. For easy tasks we see a small change over frontal areas of the right hemisphere with a frequency increase from about 7–8 Hz. A stronger change is induced by hard tasks where over right frontal areas frequencies increase significantly from 6.7 to 8.5 Hz. With the higher frequencies major activation was observed between 12 and 18 Hz (absolute minimum: 12.61 Hz; absolute maximum: 18.19 Hz; mean over all subjects and experimental conditions: 14.78 Hz). Independent of experimental condition, frontal and precentral areas over the left and right hemisphere showed the strongest responses that occurred between 17 and 18 Hz. The occipital, parietal and central scalp areas displayed a broad symmetrical distribution with a frequency of about 13.5 Hz (see Fig. 3C and D). The general pattern of the distribution of maximal frequencies is similar for hard and easy tasks. However, the changes induced by learning were different. With easy tasks there is a significant increase of the strongest frequency over right frontal and right centro-parietal scalp areas (from about 12 to 15 Hz). The learning effects seen with hard tasks were different where mean frequencies decreased from about 18.2 Hz to 15.5 Hz. The latencies (i.e., occurrence times of strongest responses in the frequency domain) were only very subtly affected for control stimuli. With hard (learning) tasks, there was a tendency for
Please cite this article as: Skrandies, W., Klein, A., Brain activity and learning of mathematical rules—Effects on the frequencies of EEG. Brain Research (2014), http://dx.doi.org/10.1016/j.brainres.2014.11.015
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Fig. 2 – (A) Wavelet scalogram illustrating the time and frequency resolution for a full sine wave of 2, 4, 8, and 16 Hz. (B) Example of wavelet scalograms recorded at 30 electrode sites (see head scheme on top). The inset on the lower right illustrates the time (0–500 ms) and frequency axes (1–30 Hz, logarithmically scaled) with the wavelet data obtained at channel 30. The recordings were obtained after learning to solve hard tasks. Mean data of 30 subjects.
smaller latencies after rule learning over occipital areas. This was similar for both frequency bands that were analyzed. The changes induced by rule learning appear to be different for hard and easy tasks. This is evident from Fig. 3 where learning has a different influence on the EEG frequencies. In order to determine whether there were systematic effects on the frequencies elicited during task processing we computed a 30 2 2 analysis of variance (ANOVA) with repeated measurements with the factors “electrode” (30), “task” (hard/easy tasks), and “time” (before/after rule learning). The data obtained between 1 and 12 Hz and between 12 and 30 Hz were analyzed separately. As expected, the influence of electrode position was highly significant (with F(29, 841)¼5.95; po10 4 ) for low frequencies
and F(29, 841)¼ 10.29; po10 6 ) for high frequencies. For frequencies between 1 and 12 Hz there were no other effects. However, for the higher frequencies there was a significant interaction between “task” (hard/easy tasks), and “time” (before/after rule learning) (F(1,29)¼ 10.82; po0:0026). This is shown in Fig. 4A. With the easy tasks there is a frequency increase with time while with the hard tasks the maximal EEG frequencies become smaller after learning. We are aware of the fact that due to the small number of subjects the statistical power of the ANOVA results might be limited. Still we see statistically significant results that appear to be consistent with the experimental questions. The significant result in Fig. 4A indicates a global effect since the data of all electrodes were considered. In an exploratory data
Please cite this article as: Skrandies, W., Klein, A., Brain activity and learning of mathematical rules—Effects on the frequencies of EEG. Brain Research (2014), http://dx.doi.org/10.1016/j.brainres.2014.11.015
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Fig. 4 – (A) Mean frequencies of maximal amplitude between 12 and 30 Hz recorded before and after rule learning with hard and easy tasks. (Means and SEM of 30 subjects). There is a significant global interaction for the data of all electrodes. The effects of time (before vs. after rule learning) are different for hard and easy tasks. (B) Significant interactions between “task and “time” that occur at specific electrode sites. The numbers give the resulting F- and p-values. Note that the significant interactions illustrated pattern as illustrated in Fig. 4A. Results of the data of 30 subjects.
Fig. 3 – Scalp distribution of mean frequencies of maximal amplitude recorded before (left) and after rule learning (right). (A) Easy; 1–12 Hz; (B) hard; 1–12 Hz; (C) easy; 12–30 Hz; (D) hard; 12–30 Hz. Mean data of 30 subjects. Color bars indicate a frequency range from 5 to 9 Hz in A and B, and a frequency range from 12 to 18 Hz in C and D. Mean data of 30 subjects.
analysis we computed ANOVAs for each electrode separately. Significant interactions between “time” (before/after) and “task” (hard/easy) are interpreted as an indication that rule learning affected hard (learning) and easy (control) tasks in different ways. Such interactions occurred only over the right hemisphere at frontal and central electrode sites. The significant F- and pvalues obtained for frequencies between 12 and 30 Hz are summarized in Fig. 4B. Note that F(1,29)¼4.185 is associated with po0:05, and F(1,29)¼7.68 corresponds to po0:005. All significant interactions illustrated in Fig. 4B showed the same direction of the effects as those presented in Fig. 4A. In addition, it is obvious that the distribution of significant effects is not
random but follows a systematical topographical pattern, similar to the data illustrated in Fig. 3.
3.
Discussion
In both the behavioral and in the electrophysiological data we found a significant interaction between “time” and “task”. This indicates that there are differences between the easy control and hard learning stimuli that occur before and after learning to successfully apply the divisibility rules. We interpret such an interaction as evidence for applying the learned rules. The behavioral data of all 82 participants show that there is a significant increase in performance immediately after learning a mathematical rule. In addition to changes in task performance, the response times were affected for the learning stimuli. Although we did not retest all subjects after longer intervals, cursory reports suggest that the learned strategy remains in long-term memory of the subjects. The rapid improvement in test performance is similar to our earlier observations on
Please cite this article as: Skrandies, W., Klein, A., Brain activity and learning of mathematical rules—Effects on the frequencies of EEG. Brain Research (2014), http://dx.doi.org/10.1016/j.brainres.2014.11.015
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perceptual learning (see for example, Skrandies and Jedynak, 1999; Shoji and Skrandies, 2006; Skrandies, 2006) and on the learning of semantic meaning of previously unknown Japanese Kanji characters (Shinoda and Skrandies, 2013). Also with perceptual learning or the learning of semantic meaning a training period of less than 30 min yields a significant improvement in behavioral performance. In our data we observed frontal theta activity (around 5 or 6 Hz) in the EEG during the solving of mathematical tasks. Such activity has been described to be related to workload induced by mental arithmetic (Sammer et al., 2007; De Smedt et al., 2009). As the wavelet scalograms illustrate, such electrical brain activity can be seen very early after the presentation of the task. Strongest activity occurs well below 100 ms after the onset of the visual presentation of the task. This is in line with earlier reports on ERP components of small latency which are affected by perceptual learning. Similar to the learning effects in the behavioral experiments we also found an interaction between “time” and “task”. This, however, was restricted mainly to higher frequencies: In our data significant effects that reflected successful learning of the mathematical rules were seen mainly in the beta band (see Figs. 3 and 4). In a review paper, Klimesch et al. (2005) had reported that not only theta activity but also so-called high alpha oscillations occur during working memory tasks. This alpha activity has been suggested to be important for the reactivation of long-term memory codes. However, in our experiments we are not concerned with taskrelated brain activation but with the differences induced by successful learning. Thus, the results do not contradict the previous notion of the importance of lower EEG frequencies for task performance. Readers should note in particular that different frequency bands (like theta or beta) probably reflect different brain processes. The changes of maximal frequency induced by rule learning at different recording sites indicate a functional interaction of various complex, not necessarily synchronous, underlying processes. The significance levels reached illustrate, however, that the respective changes are consistent over different subjects. As the behavioral data illustrate, subjects showed improved performance mainly for rule learning of the hard tasks. This was accompanied by a slight but significant decrease in frequencies which was restricted to right frontal and centroparietal areas (see Fig. 4). This topographical distribution suggests that mainly frontal and centro-parietal scalp areas of the right hemisphere are related to learning. A similar tendency of some ERP components elicited by simple mental arithmetic, to be located over the right hemisphere has been reported earlier (Skrandies et al., 1999). Maruyama et al. (2012) studied the cortical representation of activity measured with MEG and fMRI during processing of simple algebraic expressions. In this study also right parietal and precentral cortical areas showed task-related activation. In a similar line, Sakkalis et al. (2006) reported that differences between rest and a mathematical reasoning task were observed mainly over frontal and central scalp regions. In summary, the present electrophysiological data illustrate how learning processes are related to changes in electrical brain activity during task performance. The
behavioral improvement in task performance occurs shortly after the subjects have learned the divisibility rules, and it appears most interesting that such an improvement is paralleled by changes of the EEG. In this way our results confirm and extend earlier reports on electrophysiological correlates of human learning.
4.
Experimental procedure
4.1.
Subjects and tasks
A total of 82 healthy adults with normal vision and intellectual ability (German university students) were studied: 52 persons (31 males, 21 females; mean age: 21.9 years; SD: 1.88) years) participated in a behavioral study, from 30 additional subjects (13 males, 17 females; mean age: 25.0 years; SD: 4.49 years) we obtained EEG data while they solved mathematical problems. Informed consent for participation was obtained at the beginning of the measurements. According to a German version of the Oldfield Handedness Inventory (Oldfield, 1971), there were 28 right-handed subjects; one was left-handed and one was ambidextrous. As non-structured interviews revealed, all participants were naive with respect to the mathematical rules used for the hard tasks while they claimed to know about the divisibility by 2, 3, and 5. Thus, at the beginning of the experiments subjects had no explicit knowledge of the rules involved. There were “easy” and “hard” tasks: Easy tasks comprised the decision about the divisibility of a number with 4 digits at most by 2, 3 or 5. For these tasks we did not expect any systematic change over time, thus, these can be considered as control condition for rule learning. For the hard tasks a decision about the divisibility of a number by 9 or 11 was requested. In the behavioral experiment, the subjects received a printed list of tasks and were allowed to work on this for 8 min. Then we explained the rules of how to determine divisibility, and some practical examples were given. Afterwards, the subjects were allowed to answer a new set of problems for another 8 min. The number of completed tasks within 8 min and the number of correct answers was noted and compared statistically. The design of the EEG experiments was similar; here the tasks were presented on a computer monitor (e.g. 11j3425), and the subjects pressed a button with their right hand on a USB keyboard located on the right side on a table in front of them indicating “yes” or “no” (i.e., the first number divides the second without remainder or not). A response was required within 3 s after presentation. This time restriction allowed to modulate task difficulty. The presentation of the tasks was in blocks of 20 tasks (lasting 1 min), each followed by a break of about 1 min. The subjects had to solve a total of 200 tasks, then the rules were explained, and another 200 tasks were presented. Hard and easy tasks occurred in a random sequence with an equal probability of 50%.
4.2.
EEG recording
The electrophysiological experiment was performed in a dark and silent recording room. The subjects put their head into a
Please cite this article as: Skrandies, W., Klein, A., Brain activity and learning of mathematical rules—Effects on the frequencies of EEG. Brain Research (2014), http://dx.doi.org/10.1016/j.brainres.2014.11.015
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chin-forehead rest and fixated a spot in the center of the screen binocularly at a viewing distance of 1.1 m. Task stimuli with high contrast were presented in the center of a computer monitor. The EEG was recorded from 30 electrodes in an electrode cap (Easycap, Germany) with an electrode array of a 7 6 matrix with the corners omitted (see head scheme in Fig. 2). The most anterior row of electrodes was at 5% anterior to Fz, and the most posterior row of electrodes was at the inion. The interelectrode-distance was 15% of the nasion–inion distance. The electrode located 5% posterior to Cz served as recording reference, for analysis all data were referred to the average reference. Impedance was kept below 10 kΩ. EEG was amplified (Braintronics ISO-1032 amplifier), band-passed between 0.5 and 70 Hz, and digitized at a rate of 500 Hz. In addition to the EEG information about the tasks, timing, correctness of the response, and response times were recorded simultaneously by digital I/O. This allowed for an analysis of response times and of the subjects' performance during the recordings.
4.3.
Analysis
After the experiment, EEG segments which included artifacts were rejected from analysis. Eye blinks were identified by extreme value statistics (Klein and Skrandies, 2013). Artifacts other than blinks were detected by transforming the distribution of the whole data back to a standard normal distribution (van Albada and Robinson, 2007), and then eliminating epochs in which the mean amplitude exceeded the twosided (or the variance exceeded the one-sided) p ¼0.01 thresholds. EEG data obtained with responses longer than 3 s were discarded. In this way we obtained four data sets for each subject: “task” (hard/easy) “time” (before/after rule learning). EEG was recomputed to the average reference for topographical analysis. Time-frequency analysis employing a Morlet-5 wavelet, defined in the frequency domain as
ψ^ ω0 ðωÞ≔e ðω ω0 Þ
2
=2
2 2 e ðω0 þω Þ=2 ;
ω0 ≔5
was used in order to determine the frequency content following stimulus presentation over an epoch of 500 ms (Goupillaud et al., 1984). See Fig. 2A for an illustration detailing the time and frequency resolution. The computations for wavelet analysis were performed with the open source software package GNU-Octave (Eaton et al., 2011). Based on our previous results on ERP correlates of learning, we expected rapid stimulus processing, so we concentrated on low latencies. Since wavelet analysis results in a large expansion of the data values (frequencies time points electrodes), reasonable data analysis is possible only after some data reduction. To this end we determined for each electrode the frequency in the scalogram where the largest amplitude occurred between 0 and 500 ms after stimulus presentation. After visual inspection of all wavelet results (see Fig. 2), we selected two broad frequency bands for analysis: from 1 to 12 Hz (sub-beta), and from 12 to 30 Hz (beta). The determined frequencies at each of the 30 electrodes were then compared between experimental conditions.
7
Since the occurrence times of the maximal frequencies showed large variation, we only statistically analyzed changes of frequency. For statistical analysis the program package Statistica was employed.
Acknowledgments We wish to thank Ms. S. Flöggen and Mr. M. Sivanathan for assistance with data collection.
r e f e r e nc e s
De Smedt, B., Grabner, R.H., Studer, B., 2009. Oscillatory EEG correlates of arithmetic strategy use in addition and subtraction. Exp. Brain Res. 195, 635–642. Eaton, J., Bateman, D., Hauberg, S., 2011. GNU Octave Free Software Foundation. Galfano, G., Penolazzi, B., Vervaeck, I., Angrilli, A., Umilta`, C., 2009. Event-related brain potentials uncover activation dynamics in the lexicon of multiplication facts. Cortex 45, 1167–1177. Goupillaud, P., Grossmann, A., Morlet, J., 1984. Cycle-octave and related transforms in seismic signal analysis. Geoexploration 23, 85–102. Klein, A., Skrandies, W., 2013. A reliable statistical method to detect eyeblink-artefacts from electroencephalogram data only. Brain Topogr. 26, 558–568. Klimesch, W., Schack, B., Sauseng, P., 2005. The functional significance of theta and upper alpha oscillations. Exp. Psychol. 52, 99–108. Ludwig, I., Skrandies, W., 2002. Human perceptual learning in the peripheral visual field: sensory thresholds and neurophysiological correlates. Biol. Psychol. 59, 187–206. Luo, W., Liu, D., He, W., Tao, W., Luo, Y., 2009. Dissociated brain potentials for two calculation strategies. Neuroreport 20, 360–364. Maruyama, M., Pallier, C., Jobert, A., Sigman, M., Dehaene, S., 2012. The cortical representation of simple mathematical expressions. Neuroimage 61, 1444–1460. Miller, S., Takloo-Bighash, R., 2006. An Invitation to Modern Number Theory. Princeton University Press. Murata, A., 2005. An attempt to evaluate mental workload using wavelet transform of EEG. Hum. Fact. 47, 498–508. Nun˜ez-Pen˜a, M.I., Gracia-Bafalluy, M., Tubau, E., 2011. Individual differences in arithmetic skill reflected in event-related brain potentials. Int. J. Psychophysiol. 80, 143–149. Oldfield, R.C., 1971. The assessment and analysis of handedness: the Edinburgh inventory. Neuropsychologia 9, 97–113. Pauli, P., Lutzenberger, W., Rau, H., Birbaumer, N., Rickard, T.C., Yaroush, R.A., Bourne, J.L., 1994. Brain potentials during mental arithmetic: effects of extensive practice and problem difficulty. Brain Res. Cogn. Brain Res. 2, 21–29. Sakkalis, V., Zervakis, M., Micheloyannis, S., 2006. Significant eeg features involved in mathematical reasoning: evidence from wavelet analysis. Brain Topogr. 19, 53–60. Sammer, G., Blecker, C., Gebhardt, H., Bischoff, M., Stark, R., Morgen, K., Vaitl, D., 2007. Relationship between regional hemodynamic activity and simultaneously recorded EEGtheta associated with mental arithmetic-induced workload. Hum. Brain Mapp. 28, 793–803. Shinoda, H., Skrandies, W., 2013. Topographic changes in eventrelated potentials because of learning of meaningful kanji characters. Neuroreport 24, 555–559.
Please cite this article as: Skrandies, W., Klein, A., Brain activity and learning of mathematical rules—Effects on the frequencies of EEG. Brain Research (2014), http://dx.doi.org/10.1016/j.brainres.2014.11.015
8
brain research ] (]]]]) ]]]–]]]
Shoji, H., Skrandies, W., 2006. ERP topography and human perceptual learning in the peripheral visual field. Int. J. Psychophysiol. 61, 179–187. Skrandies, W., Jedynak, A., 1999. Learning to see 3-D: psychophysics and brain electrical activity. Neuroreport 10, 249–253. Skrandies, W., Jedynak, A., Fahle, M., 2001. Perceptual learning: psychophysical thresholds and electrical brain topography. Int. J. Psychophysiol. 41, 119–129. Skrandies, W., Reik, P., Kunze, C., 1999. Topography of evoked brain activity during mental arithmetic and language tasks: sex differences. Neuropsychologia 37, 421–430.
Skrandies, W., 2006. Psychophysics and electrophysiology of human perceptual learning: a summary. Suppl. Clin. Neurophysiol. 59, 81–87. Thompson, R.F., Donegan, N.H., 1987. Encyclopedia of Neuroscience, chapter Learning and memory. Birkha¨user, Boston, pp. 571–574. van Albada, S.J., Robinson, P.A., 2007. Transformation of arbitrary distributions to the normal distribution with application to EEG test–retest reliability. J. Neurosci. Methods 161, 205–211.
Please cite this article as: Skrandies, W., Klein, A., Brain activity and learning of mathematical rules—Effects on the frequencies of EEG. Brain Research (2014), http://dx.doi.org/10.1016/j.brainres.2014.11.015
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www.elsevier.com/locate/brainres
Research Report
Brain activity and learning of mathematical rules—Effects on the frequencies of EEG Wolfgang Skrandiesn, Alexander Klein Institute of Physiology, Justus-Liebig University, Aulweg 129, 35392 Giessen, Germany
art i cle i nfo
ab st rac t
Article history:
We investigated the change of evoked EEG frequencies induced by learning to solve
Accepted 5 November 2014
mathematical tasks by applying divisibility rules. The performance on easy (divisibility by 2, 3, or 5) and hard tasks (divisibility by 9 or by 11) was compared. In a behavioral
Keywords:
experiment on 52 adults we found a significant increase in performance from 67% to 90%
Learning
correct responses induced by rule learning. Subsequently, the EEG data recorded from 30
Mathematics
additional volunteers were analyzed. EEG recordings were performed in two parts: First,
EEG
subjects had to solve 200 tasks without knowing the divisibility rules. Then the rules were
Wavelet analysis
explained, followed by another set of 200 tasks. EEG was measured simultaneously in 30
Alpha/theta
channels, artifacts were removed offline, and the data before and after rule learning were compared. A wavelet transformation with the Morlet-5 wavelet was computed, and the scalp topography of the maximal frequency and its occurrence time was compared. Largest effects were observed with frequencies between about 6 and 18 Hz. In the frequency band between 12 and 30 Hz maximal frequencies were significantly different after successful learning over frontal and centro-parietal scalp areas of the right hemisphere. These changes were paralleled by decreased response times. In summary, our data illustrate a significant relation between successful learning divisibility rules and changes in the frequency content of the task-related EEG. Significant effects were observed after a very short training period of less than 10 min. This article is part of a Special Issue entitled SI: Brain and Memory. & 2014 Published by Elsevier B.V.
1.
Introduction
Human cognition depends to a large extent on the ability to learn new facts or rules. Such learning is based on cortical plasticity that plays an important role for the adaptation to the physical environment and for changes in performance of cognitive abilities. Psychophysical and electrophysiological
studies on human visual perception have demonstrated that sensory discrimination ability improves by training in adult subjects. Perceptual learning is accompanied by changes of event-related brain activity (cf. Skrandies and Jedynak, 1999; Skrandies et al., 2001; Ludwig and Skrandies, 2002; Shoji and Skrandies, 2006). In different experiments we could show that learning of meaningful material results in significant alterations
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Corresponding author. E-mail address: [email protected] (W. Skrandies).
http://dx.doi.org/10.1016/j.brainres.2014.11.015 0006-8993/& 2014 Published by Elsevier B.V.
Please cite this article as: Skrandies, W., Klein, A., Brain activity and learning of mathematical rules—Effects on the frequencies of EEG. Brain Research (2014), http://dx.doi.org/10.1016/j.brainres.2014.11.015
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of electrophysiological brain responses (Shinoda and Skrandies, 2013). In general, learning is defined as “changes in behavior resulting from prior experience” (Thompson and Donegan, 1987) that in the present experiments are measured as performance on mathematical problems. Specifically, we examined the effects of learning of mathematical rules on multichannel EEG signals that were obtained before and after learning. The neurophysiological correlates of processing mathematical tasks have been studied previously by recording EEG and event-related potentials from healthy subjects. With task-related ERP recordings the occurrence of early components and of late slow wave activity has been repeatedly described (see for example, Skrandies et al., 1999; Galfano et al., 2009; Luo et al., 2009; Nunez-Pena et al., 2011). With recordings of the spontaneous EEG, brain activity in the theta and alpha frequency range has been reported to be related to mental arithmetic-induced workload (Sammer et al., 2007; De Smedt et al., 2009). Until now, only very little is known about the effects of learning mathematical rules on the frequencies of performance-related EEG signals while there are reports on the effects of cognitive processing on brain activity. In a study on eight participants Murata (2005) evaluated the influence of mental workload on EEG in continuous matching tasks. Data from only three recording sites were reported. In a wavelet analysis of the data the author found that increasing mental workload mainly affects the time at which strongest responses were seen while total power of alpha and beta activity increased with task difficulty. Mathematical reasoning was also analyzed by wavelet transforms of EEG where cortical activity was compared between a rest and a task condition (Sakkalis et al., 2006). In this study, brain activity was increased during the task. Such effects were observed mainly over frontal and central scalp regions. Results on brain potentials and the effects of extensive practice of mental arithmetic tasks were reported by Pauli et al. (1994). The authors illustrate how practice affected the amplitude and offset latency of the event-related slow wave component. Since this constituted an ERP experiment, the frequencies of the task-related EEG were not analyzed. In order to study the effects of learning we chose a task in which subjects could rapidly improve in performance. There are mathematical rules that are commonly in full detail unknown to most students but the rules can be learned easily. Divisibility rules are an example for this (Miller and Takloo-Bighash, 2006). In order to determine whether a given number can be divided by 2, 3, or 5, no explicit rules need to be applied since the answer is obvious to most adult persons. Divisibility by 9 or by 11 appears to be more complex and cannot be solved quickly. A number is divisible by 9 if and only if the sum of the digits is divisible by 9, and in order to determine the divisibility by 11 one needs to compute the sign-alternating sum of its digits. When these rules are known to a subject, such tasks become easy. In addition, time restriction allows to easily modulate task difficulty and performance. Thus, task difficulty has some gradual variation. We note that the teaching of divisibility rules is part of the curriculum of German high schools, however, the explicit knowledge of such rules is very poor (see Methods). In a behavioral experiment on 52 adults we first confirmed that learning to apply divisibility rules occurs rapidly and
yields a high rate of learning success. For practical reasons, such an experimental paradigm that allows for rapid learning was the prerequisite for the subsequent electrophysiological experiments. In the present EEG study we investigated, how improvement in performance on a mathematical task is accompanied by changes in EEG frequencies which were elicited during mental performance. We will show that mental arithmetic elicits both, high and low frequencies in the human EEG. However, the main learning effects appear in the low beta range over frontal scalp areas of the right hemisphere.
2.
Results
2.1.
Behavioral data
The subjects were allowed to work on the tasks for 8 min before and 8 min after learning the rules. Before, a mean number of 56.3 tasks were solved, while after rule learning the mean number of finished problems increased to 79.1 tasks. With hard tasks the subjects improved in performance by a factor of 2 after they had learned the rules (from a mean of 19.4 to 40.03 correctly solved tasks within 8 min). As expected, for the easy tasks improvement was not significant (93.10% correct responses before, 97.95% after learning) while for hard tasks performance significantly increased (from 66.63% to 90.17% correct responses). Thus, there was a significant interaction between “time” and “task” (F(1,51)¼ 37.99; po10 5 ) which is illustrated in Fig. 1A. Very similar results were observed for the 30 subjects who participated in the EEG study. There was an overall increase in performance after learning. Again, this increase was smaller for easy (82.20% correct before, 88.56% after learning, t¼6.07, po10 6 ) than for hard tasks (57.09% correct before, 66.67% after learning, t¼6.17, po10 6 ). We note that both changes were significant, however, for easy tasks the change was only about 6.36% while with hard tasks subjects improved by 9.58%. A trend for learning was confirmed by an interaction between “time” and “task” in a repeated measures ANOVA (F(1,29)¼ 3.12; po0:08). The response times for correct answers were also significantly affected as is shown in Fig. 1B. There was a significant interaction between “time” and “task” (F(1,29)¼ 27.06; po10 5 ). Hard tasks yielded significantly higher response times than easy tasks, and response times decreased significantly after rule learning. This effect was significantly different for hard and easy tasks. For hard tasks the improvement was about 400 ms while with the easy controls the response times were reduced by only about 100 ms. We note that the behavioral results were not expected to be identical in both studies, since there were slight differences in the experimental design (time restriction for a response in the EEG study, no time restriction in the questionnaire study). Still all behavioral data demonstrate that the subjects' performance increased significantly over time.
2.2.
Electrophysiological data
First, we illustrate the time and frequency resolution of our wavelet computation. Fig. 2A shows the scalogram resulting
Please cite this article as: Skrandies, W., Klein, A., Brain activity and learning of mathematical rules—Effects on the frequencies of EEG. Brain Research (2014), http://dx.doi.org/10.1016/j.brainres.2014.11.015
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Fig. 1 – (A) Mean of correct responses in the behavioral study. Before and after rule learning there is a significant increase in performance which is more pronounced for hard (learning) tasks (see text for details). Means and SEM of 52 subjects. (B) Mean response times of the subjects in the EEG study. There are significant effects on response times which are similar to the results in A. Means and SEM of 30 individuals.
from one full sine wave of 2, 4, 8, and 16 Hz, respectively. The color codes indicate signal strength normalized to the maximal amplitude. Wavelet transforms were computed for the EEG data of each subject and experimental condition for each electrode. The wavelet analysis showed that in most recording channels strong responses were elicited in both low and high frequency bands between about 8 and 30 Hz. At higher frequencies no consistent activation could be measured. Fig. 2 illustrates the grand mean over all subjects of the wavelet scalograms at the 30 electrode sites. The data illustrated were recorded with hard (learning) tasks after rule learning. Strong activation can be seen starting as early as 50 ms after the beginning of the presentation
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of the task. The raw data obtained in the other experimental conditions had a similar but not identical appearance. From Fig. 2 it is obvious that there are low frequencies up to about 10 Hz as well as high frequencies which occur between about 12 and 30 Hz. The wavelet data of all subjects were inspected in order to define frequencies of interest. It turned out that there was no consistent brain activity present at frequencies higher than 30 Hz. For further quantitative analysis we defined two frequency bands where all subjects displayed strong activity. We determined, for each subject and experimental condition, the frequency values with maximal amplitude. At each channel, we selected the occurrence time of maximal amplitude between 0 and 500 ms for low (between 1 and 12 Hz) and high frequencies (between 12 and 30 Hz). In this way we obtained information about the strongest response in terms of EEG frequency. In addition, this procedure yielded information on the occurrence time of strongest electrophysiological responses. These data were then directly compared between experimental conditions. The aim of the analysis was to determine whether frequencies changes as a consequence of experimental manipulation. Of course, this is different at different electrode sites. Thus, maximal frequencies were plotted topographically. Fig. 3A and B illustrates the distribution of frequencies for the lower band while Fig. 3C and D shows the results obtained with the higher frequencies. These are mean data computed for all subjects separately for the experimental conditions (“before/after learning”; “hard/easy tasks”). Most of the activity in the lower frequency band occurred between 5 and 9 Hz (absolute minimum: 5.14 Hz; absolute maximum: 8.65 Hz; mean over all subjects and experimental conditions: 7.05 Hz). Over frontal midline and left scalp areas there was a distribution of low frequencies (between 5 and 7 Hz) while parietal and central scalp areas were dominated by frequencies between 8 and 9 Hz (see Fig. 3A and B). As is evident, this global pattern was similar for all experimental conditions. For easy tasks we see a small change over frontal areas of the right hemisphere with a frequency increase from about 7–8 Hz. A stronger change is induced by hard tasks where over right frontal areas frequencies increase significantly from 6.7 to 8.5 Hz. With the higher frequencies major activation was observed between 12 and 18 Hz (absolute minimum: 12.61 Hz; absolute maximum: 18.19 Hz; mean over all subjects and experimental conditions: 14.78 Hz). Independent of experimental condition, frontal and precentral areas over the left and right hemisphere showed the strongest responses that occurred between 17 and 18 Hz. The occipital, parietal and central scalp areas displayed a broad symmetrical distribution with a frequency of about 13.5 Hz (see Fig. 3C and D). The general pattern of the distribution of maximal frequencies is similar for hard and easy tasks. However, the changes induced by learning were different. With easy tasks there is a significant increase of the strongest frequency over right frontal and right centro-parietal scalp areas (from about 12 to 15 Hz). The learning effects seen with hard tasks were different where mean frequencies decreased from about 18.2 Hz to 15.5 Hz. The latencies (i.e., occurrence times of strongest responses in the frequency domain) were only very subtly affected for control stimuli. With hard (learning) tasks, there was a tendency for
Please cite this article as: Skrandies, W., Klein, A., Brain activity and learning of mathematical rules—Effects on the frequencies of EEG. Brain Research (2014), http://dx.doi.org/10.1016/j.brainres.2014.11.015
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Fig. 2 – (A) Wavelet scalogram illustrating the time and frequency resolution for a full sine wave of 2, 4, 8, and 16 Hz. (B) Example of wavelet scalograms recorded at 30 electrode sites (see head scheme on top). The inset on the lower right illustrates the time (0–500 ms) and frequency axes (1–30 Hz, logarithmically scaled) with the wavelet data obtained at channel 30. The recordings were obtained after learning to solve hard tasks. Mean data of 30 subjects.
smaller latencies after rule learning over occipital areas. This was similar for both frequency bands that were analyzed. The changes induced by rule learning appear to be different for hard and easy tasks. This is evident from Fig. 3 where learning has a different influence on the EEG frequencies. In order to determine whether there were systematic effects on the frequencies elicited during task processing we computed a 30 2 2 analysis of variance (ANOVA) with repeated measurements with the factors “electrode” (30), “task” (hard/easy tasks), and “time” (before/after rule learning). The data obtained between 1 and 12 Hz and between 12 and 30 Hz were analyzed separately. As expected, the influence of electrode position was highly significant (with F(29, 841)¼5.95; po10 4 ) for low frequencies
and F(29, 841)¼ 10.29; po10 6 ) for high frequencies. For frequencies between 1 and 12 Hz there were no other effects. However, for the higher frequencies there was a significant interaction between “task” (hard/easy tasks), and “time” (before/after rule learning) (F(1,29)¼ 10.82; po0:0026). This is shown in Fig. 4A. With the easy tasks there is a frequency increase with time while with the hard tasks the maximal EEG frequencies become smaller after learning. We are aware of the fact that due to the small number of subjects the statistical power of the ANOVA results might be limited. Still we see statistically significant results that appear to be consistent with the experimental questions. The significant result in Fig. 4A indicates a global effect since the data of all electrodes were considered. In an exploratory data
Please cite this article as: Skrandies, W., Klein, A., Brain activity and learning of mathematical rules—Effects on the frequencies of EEG. Brain Research (2014), http://dx.doi.org/10.1016/j.brainres.2014.11.015
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Fig. 4 – (A) Mean frequencies of maximal amplitude between 12 and 30 Hz recorded before and after rule learning with hard and easy tasks. (Means and SEM of 30 subjects). There is a significant global interaction for the data of all electrodes. The effects of time (before vs. after rule learning) are different for hard and easy tasks. (B) Significant interactions between “task and “time” that occur at specific electrode sites. The numbers give the resulting F- and p-values. Note that the significant interactions illustrated pattern as illustrated in Fig. 4A. Results of the data of 30 subjects.
Fig. 3 – Scalp distribution of mean frequencies of maximal amplitude recorded before (left) and after rule learning (right). (A) Easy; 1–12 Hz; (B) hard; 1–12 Hz; (C) easy; 12–30 Hz; (D) hard; 12–30 Hz. Mean data of 30 subjects. Color bars indicate a frequency range from 5 to 9 Hz in A and B, and a frequency range from 12 to 18 Hz in C and D. Mean data of 30 subjects.
analysis we computed ANOVAs for each electrode separately. Significant interactions between “time” (before/after) and “task” (hard/easy) are interpreted as an indication that rule learning affected hard (learning) and easy (control) tasks in different ways. Such interactions occurred only over the right hemisphere at frontal and central electrode sites. The significant F- and pvalues obtained for frequencies between 12 and 30 Hz are summarized in Fig. 4B. Note that F(1,29)¼4.185 is associated with po0:05, and F(1,29)¼7.68 corresponds to po0:005. All significant interactions illustrated in Fig. 4B showed the same direction of the effects as those presented in Fig. 4A. In addition, it is obvious that the distribution of significant effects is not
random but follows a systematical topographical pattern, similar to the data illustrated in Fig. 3.
3.
Discussion
In both the behavioral and in the electrophysiological data we found a significant interaction between “time” and “task”. This indicates that there are differences between the easy control and hard learning stimuli that occur before and after learning to successfully apply the divisibility rules. We interpret such an interaction as evidence for applying the learned rules. The behavioral data of all 82 participants show that there is a significant increase in performance immediately after learning a mathematical rule. In addition to changes in task performance, the response times were affected for the learning stimuli. Although we did not retest all subjects after longer intervals, cursory reports suggest that the learned strategy remains in long-term memory of the subjects. The rapid improvement in test performance is similar to our earlier observations on
Please cite this article as: Skrandies, W., Klein, A., Brain activity and learning of mathematical rules—Effects on the frequencies of EEG. Brain Research (2014), http://dx.doi.org/10.1016/j.brainres.2014.11.015
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perceptual learning (see for example, Skrandies and Jedynak, 1999; Shoji and Skrandies, 2006; Skrandies, 2006) and on the learning of semantic meaning of previously unknown Japanese Kanji characters (Shinoda and Skrandies, 2013). Also with perceptual learning or the learning of semantic meaning a training period of less than 30 min yields a significant improvement in behavioral performance. In our data we observed frontal theta activity (around 5 or 6 Hz) in the EEG during the solving of mathematical tasks. Such activity has been described to be related to workload induced by mental arithmetic (Sammer et al., 2007; De Smedt et al., 2009). As the wavelet scalograms illustrate, such electrical brain activity can be seen very early after the presentation of the task. Strongest activity occurs well below 100 ms after the onset of the visual presentation of the task. This is in line with earlier reports on ERP components of small latency which are affected by perceptual learning. Similar to the learning effects in the behavioral experiments we also found an interaction between “time” and “task”. This, however, was restricted mainly to higher frequencies: In our data significant effects that reflected successful learning of the mathematical rules were seen mainly in the beta band (see Figs. 3 and 4). In a review paper, Klimesch et al. (2005) had reported that not only theta activity but also so-called high alpha oscillations occur during working memory tasks. This alpha activity has been suggested to be important for the reactivation of long-term memory codes. However, in our experiments we are not concerned with taskrelated brain activation but with the differences induced by successful learning. Thus, the results do not contradict the previous notion of the importance of lower EEG frequencies for task performance. Readers should note in particular that different frequency bands (like theta or beta) probably reflect different brain processes. The changes of maximal frequency induced by rule learning at different recording sites indicate a functional interaction of various complex, not necessarily synchronous, underlying processes. The significance levels reached illustrate, however, that the respective changes are consistent over different subjects. As the behavioral data illustrate, subjects showed improved performance mainly for rule learning of the hard tasks. This was accompanied by a slight but significant decrease in frequencies which was restricted to right frontal and centroparietal areas (see Fig. 4). This topographical distribution suggests that mainly frontal and centro-parietal scalp areas of the right hemisphere are related to learning. A similar tendency of some ERP components elicited by simple mental arithmetic, to be located over the right hemisphere has been reported earlier (Skrandies et al., 1999). Maruyama et al. (2012) studied the cortical representation of activity measured with MEG and fMRI during processing of simple algebraic expressions. In this study also right parietal and precentral cortical areas showed task-related activation. In a similar line, Sakkalis et al. (2006) reported that differences between rest and a mathematical reasoning task were observed mainly over frontal and central scalp regions. In summary, the present electrophysiological data illustrate how learning processes are related to changes in electrical brain activity during task performance. The
behavioral improvement in task performance occurs shortly after the subjects have learned the divisibility rules, and it appears most interesting that such an improvement is paralleled by changes of the EEG. In this way our results confirm and extend earlier reports on electrophysiological correlates of human learning.
4.
Experimental procedure
4.1.
Subjects and tasks
A total of 82 healthy adults with normal vision and intellectual ability (German university students) were studied: 52 persons (31 males, 21 females; mean age: 21.9 years; SD: 1.88) years) participated in a behavioral study, from 30 additional subjects (13 males, 17 females; mean age: 25.0 years; SD: 4.49 years) we obtained EEG data while they solved mathematical problems. Informed consent for participation was obtained at the beginning of the measurements. According to a German version of the Oldfield Handedness Inventory (Oldfield, 1971), there were 28 right-handed subjects; one was left-handed and one was ambidextrous. As non-structured interviews revealed, all participants were naive with respect to the mathematical rules used for the hard tasks while they claimed to know about the divisibility by 2, 3, and 5. Thus, at the beginning of the experiments subjects had no explicit knowledge of the rules involved. There were “easy” and “hard” tasks: Easy tasks comprised the decision about the divisibility of a number with 4 digits at most by 2, 3 or 5. For these tasks we did not expect any systematic change over time, thus, these can be considered as control condition for rule learning. For the hard tasks a decision about the divisibility of a number by 9 or 11 was requested. In the behavioral experiment, the subjects received a printed list of tasks and were allowed to work on this for 8 min. Then we explained the rules of how to determine divisibility, and some practical examples were given. Afterwards, the subjects were allowed to answer a new set of problems for another 8 min. The number of completed tasks within 8 min and the number of correct answers was noted and compared statistically. The design of the EEG experiments was similar; here the tasks were presented on a computer monitor (e.g. 11j3425), and the subjects pressed a button with their right hand on a USB keyboard located on the right side on a table in front of them indicating “yes” or “no” (i.e., the first number divides the second without remainder or not). A response was required within 3 s after presentation. This time restriction allowed to modulate task difficulty. The presentation of the tasks was in blocks of 20 tasks (lasting 1 min), each followed by a break of about 1 min. The subjects had to solve a total of 200 tasks, then the rules were explained, and another 200 tasks were presented. Hard and easy tasks occurred in a random sequence with an equal probability of 50%.
4.2.
EEG recording
The electrophysiological experiment was performed in a dark and silent recording room. The subjects put their head into a
Please cite this article as: Skrandies, W., Klein, A., Brain activity and learning of mathematical rules—Effects on the frequencies of EEG. Brain Research (2014), http://dx.doi.org/10.1016/j.brainres.2014.11.015
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chin-forehead rest and fixated a spot in the center of the screen binocularly at a viewing distance of 1.1 m. Task stimuli with high contrast were presented in the center of a computer monitor. The EEG was recorded from 30 electrodes in an electrode cap (Easycap, Germany) with an electrode array of a 7 6 matrix with the corners omitted (see head scheme in Fig. 2). The most anterior row of electrodes was at 5% anterior to Fz, and the most posterior row of electrodes was at the inion. The interelectrode-distance was 15% of the nasion–inion distance. The electrode located 5% posterior to Cz served as recording reference, for analysis all data were referred to the average reference. Impedance was kept below 10 kΩ. EEG was amplified (Braintronics ISO-1032 amplifier), band-passed between 0.5 and 70 Hz, and digitized at a rate of 500 Hz. In addition to the EEG information about the tasks, timing, correctness of the response, and response times were recorded simultaneously by digital I/O. This allowed for an analysis of response times and of the subjects' performance during the recordings.
4.3.
Analysis
After the experiment, EEG segments which included artifacts were rejected from analysis. Eye blinks were identified by extreme value statistics (Klein and Skrandies, 2013). Artifacts other than blinks were detected by transforming the distribution of the whole data back to a standard normal distribution (van Albada and Robinson, 2007), and then eliminating epochs in which the mean amplitude exceeded the twosided (or the variance exceeded the one-sided) p ¼0.01 thresholds. EEG data obtained with responses longer than 3 s were discarded. In this way we obtained four data sets for each subject: “task” (hard/easy) “time” (before/after rule learning). EEG was recomputed to the average reference for topographical analysis. Time-frequency analysis employing a Morlet-5 wavelet, defined in the frequency domain as
ψ^ ω0 ðωÞ≔e ðω ω0 Þ
2
=2
2 2 e ðω0 þω Þ=2 ;
ω0 ≔5
was used in order to determine the frequency content following stimulus presentation over an epoch of 500 ms (Goupillaud et al., 1984). See Fig. 2A for an illustration detailing the time and frequency resolution. The computations for wavelet analysis were performed with the open source software package GNU-Octave (Eaton et al., 2011). Based on our previous results on ERP correlates of learning, we expected rapid stimulus processing, so we concentrated on low latencies. Since wavelet analysis results in a large expansion of the data values (frequencies time points electrodes), reasonable data analysis is possible only after some data reduction. To this end we determined for each electrode the frequency in the scalogram where the largest amplitude occurred between 0 and 500 ms after stimulus presentation. After visual inspection of all wavelet results (see Fig. 2), we selected two broad frequency bands for analysis: from 1 to 12 Hz (sub-beta), and from 12 to 30 Hz (beta). The determined frequencies at each of the 30 electrodes were then compared between experimental conditions.
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Since the occurrence times of the maximal frequencies showed large variation, we only statistically analyzed changes of frequency. For statistical analysis the program package Statistica was employed.
Acknowledgments We wish to thank Ms. S. Flöggen and Mr. M. Sivanathan for assistance with data collection.
r e f e r e nc e s
De Smedt, B., Grabner, R.H., Studer, B., 2009. Oscillatory EEG correlates of arithmetic strategy use in addition and subtraction. Exp. Brain Res. 195, 635–642. Eaton, J., Bateman, D., Hauberg, S., 2011. GNU Octave Free Software Foundation. Galfano, G., Penolazzi, B., Vervaeck, I., Angrilli, A., Umilta`, C., 2009. Event-related brain potentials uncover activation dynamics in the lexicon of multiplication facts. Cortex 45, 1167–1177. Goupillaud, P., Grossmann, A., Morlet, J., 1984. Cycle-octave and related transforms in seismic signal analysis. Geoexploration 23, 85–102. Klein, A., Skrandies, W., 2013. A reliable statistical method to detect eyeblink-artefacts from electroencephalogram data only. Brain Topogr. 26, 558–568. Klimesch, W., Schack, B., Sauseng, P., 2005. The functional significance of theta and upper alpha oscillations. Exp. Psychol. 52, 99–108. Ludwig, I., Skrandies, W., 2002. Human perceptual learning in the peripheral visual field: sensory thresholds and neurophysiological correlates. Biol. Psychol. 59, 187–206. Luo, W., Liu, D., He, W., Tao, W., Luo, Y., 2009. Dissociated brain potentials for two calculation strategies. Neuroreport 20, 360–364. Maruyama, M., Pallier, C., Jobert, A., Sigman, M., Dehaene, S., 2012. The cortical representation of simple mathematical expressions. Neuroimage 61, 1444–1460. Miller, S., Takloo-Bighash, R., 2006. An Invitation to Modern Number Theory. Princeton University Press. Murata, A., 2005. An attempt to evaluate mental workload using wavelet transform of EEG. Hum. Fact. 47, 498–508. Nun˜ez-Pen˜a, M.I., Gracia-Bafalluy, M., Tubau, E., 2011. Individual differences in arithmetic skill reflected in event-related brain potentials. Int. J. Psychophysiol. 80, 143–149. Oldfield, R.C., 1971. The assessment and analysis of handedness: the Edinburgh inventory. Neuropsychologia 9, 97–113. Pauli, P., Lutzenberger, W., Rau, H., Birbaumer, N., Rickard, T.C., Yaroush, R.A., Bourne, J.L., 1994. Brain potentials during mental arithmetic: effects of extensive practice and problem difficulty. Brain Res. Cogn. Brain Res. 2, 21–29. Sakkalis, V., Zervakis, M., Micheloyannis, S., 2006. Significant eeg features involved in mathematical reasoning: evidence from wavelet analysis. Brain Topogr. 19, 53–60. Sammer, G., Blecker, C., Gebhardt, H., Bischoff, M., Stark, R., Morgen, K., Vaitl, D., 2007. Relationship between regional hemodynamic activity and simultaneously recorded EEGtheta associated with mental arithmetic-induced workload. Hum. Brain Mapp. 28, 793–803. Shinoda, H., Skrandies, W., 2013. Topographic changes in eventrelated potentials because of learning of meaningful kanji characters. Neuroreport 24, 555–559.
Please cite this article as: Skrandies, W., Klein, A., Brain activity and learning of mathematical rules—Effects on the frequencies of EEG. Brain Research (2014), http://dx.doi.org/10.1016/j.brainres.2014.11.015
8
brain research ] (]]]]) ]]]–]]]
Shoji, H., Skrandies, W., 2006. ERP topography and human perceptual learning in the peripheral visual field. Int. J. Psychophysiol. 61, 179–187. Skrandies, W., Jedynak, A., 1999. Learning to see 3-D: psychophysics and brain electrical activity. Neuroreport 10, 249–253. Skrandies, W., Jedynak, A., Fahle, M., 2001. Perceptual learning: psychophysical thresholds and electrical brain topography. Int. J. Psychophysiol. 41, 119–129. Skrandies, W., Reik, P., Kunze, C., 1999. Topography of evoked brain activity during mental arithmetic and language tasks: sex differences. Neuropsychologia 37, 421–430.
Skrandies, W., 2006. Psychophysics and electrophysiology of human perceptual learning: a summary. Suppl. Clin. Neurophysiol. 59, 81–87. Thompson, R.F., Donegan, N.H., 1987. Encyclopedia of Neuroscience, chapter Learning and memory. Birkha¨user, Boston, pp. 571–574. van Albada, S.J., Robinson, P.A., 2007. Transformation of arbitrary distributions to the normal distribution with application to EEG test–retest reliability. J. Neurosci. Methods 161, 205–211.
Please cite this article as: Skrandies, W., Klein, A., Brain activity and learning of mathematical rules—Effects on the frequencies of EEG. Brain Research (2014), http://dx.doi.org/10.1016/j.brainres.2014.11.015
