Introduction
Procedural memory is responsible for extracting and learning the rules in sequences constantly presented in the surrounding environment [2]. According to the declarative-procedural (DP) model [2, 4, 5], procedural memory plays a role in learning aspects based on language rules such as grammar [5, 6]. Based on the procedural deficit hypothesis (PDH) the cause of linguistic and non-linguistic deficits observed in developmental language disorder is associated with the damaged procedural memory system in these people [2, 7].
Considering the role of procedural memory in the acquisition of grammar, its damage has been suggested as the main cause of some speech and language disorders, including developmental language disorders. Thus, evaluating and determining children’s performance in this memory is particularly important. Still, this issue has not received the proper attention from speech and language pathologists.
Various tasks have been designed to assess procedural memory that differs based on the modality that the sequence presents (including verbal and gestural) [9-11]. Some researchers have used separate tasks to investigate and compare the procedural memory status of participants in different modalities [14, 15]. Desmottes et al. designed a serial search task and examined procedural memory in both motor and verbal modalities [9]. The advantage of this task is to compare the performance status of the participants in two areas by using one task and similar stimuli.
Learning in procedure memory occurs during the stages initial of learning, consolidation, and retention. The first stage is characterized by a rapid improvement in the person’s performance while learning the pattern in the sequence, which can be seen during the initial attempts in the procedural memory task. The second stage, consolidation, stabilizes the memory path after initial learning [16]. In the third stage, which is called retention, the skill becomes more accurate and automatic through repeated practice. The person can later identify and present the pattern in the sequence without cognitive effort [17].
Among the studies conducted, some researchers investigated procedural learning in addition to the initial learning stage in the consolidation and retention stages [10, 18, 19]. The aim of examining the stages of consolidation and retention is to determine whether procedural memory improves over time and whether there is an increase in the speed of the participant’s performance in the later stages of learning compared to the early stages [10].
Another issue that makes the evaluation of procedural memory important is the direct relationship between procedural memory and grammar in the DP model. Some evidence in support of this model shows this relationship in the initial learning stage in children with normal development [9, 24-28]. On the other hand, some studies did not report this relationship in the initial learning stage [29, 30]. Some studies have examined the relationship between the stages of consolidation and retention, and the results of these studies are also inconclusive [10, 19, 31, 32]. Recent studies suggest that one of the main causes of these different results is the lack of checking the reliability of the tasks used to evaluate procedural memory [33].
So far, no task has investigated procedural memory simultaneously in both verbal and motor modalities and different stages of learning. The advantage of such a task is to increase the validity of the results and the possibility of comparing the performance among other modalities and stages of learning. Also, considering that the results of the studies conducted in the field of the DP model did not show consistent and homogeneous results [24, 25, 30], this task can accurately evaluate procedural memory and provide more knowledge about the relationship between procedural memory and grammar.
This study aims to design a valid and reliable task for evaluating procedural memory. Then, we examine the children’s procedural memory in different modalities and stages of learning and explore the relationship between procedural memory and grammatical skills in Persian-speaking children.

Materials and Methods
Study participants
This research was conducted in the first stage as a methodology study and in the second stage as a descriptive-analytical one. In the first stage, the serial search task was designed and validated to evaluate procedural memory, and in the second stage, the relationship between procedural memory and grammar was investigated. In the first step, after designing the task, its face validity was assessed on 10 children (5 girls and 5 boys) with a Mean±SD age of 96.02±10.87 months (7 to 9 years old). Test-re-test reliability was conducted on 15 children (8 girls and 7 boys) with a Mean±SD age of 98.06±8.72 months (7 to 9 years old), who were selected from Isfahan City schools, Iran using the convenience sampling method.
In the second stage, to investigate the relationship between the performance in the task of procedural memory and grammatical skills, 27 children aged 7-9 years participated. They were selected by a multi-stage mixed sampling method from Isfahan City. 
The inclusion criteria in the two stages included being monolingual and Persian-speaking, 7-9 years old, and with normal vision and hearing. The exclusion criteria included a history of neurological injuries, developmental-neural disorders, delayed psychomotor development, emotional-psychological problems, attention deficit hyperactivity disorder, and delayed speech and language development. After visiting the schools, the inclusion and exclusion criteria were provided to the administrators, and the children were selected based on the administrators’ opinions and the children’s health files.
All children met the inclusion and exclusion criteria based on the demographic information questionnaire, the auditory screening questionnaire, and the speech therapist’s informal assessment [35, 36]. Because of the spread of the coronavirus in March 2020, 7 samples stopped participating in the research. Finally, 20 children (13 girls and 7 boys) participated in the second stage of the study (Mean±SD 95.22±8.04 months).
Study procedure
Phase1: Designing serial searchtask
In the first step, a serial search task was designed, and its validity and reliability were examined.
Selection of stimuli 
First, 14 words with the lowest average age of acquisition, with different initial syllables and from various semantic categories [9] were selected from the Persian picture naming set, and the corresponding color pictures were determined. Then, 20 five-year-old children were asked about their familiarity and agreement with the names of the pictures. Finally, the names of four photos (cat, grapes, sock, house) with the highest name agreement and familiarity were used as auditory stimuli, and their corresponding pictures as visual stimuli in the task design.
The initial design of the task
 The task was designed using the Java programming language suitable for the Android operating system. This task includes six blocks in both modalities. Blocks 1 to 4 are pattern blocks, block 5 is a random block, and block 6 is the final pattern block. Each learning block contains 60 trials presented as a sequence of 6 and repeated 10 times. In the random block, both the sequence of answers and the sequence of the names of the pictures are different from the pattern block [9].
Each trial in this task begins with the visual stimulus’s presentation, consisting of four images in a two-by-two design. Pictures are presented on a Samsung Galaxy Tab A 10 tablet. The program records the reaction time and type of response to each trial. The reaction time is considered from the beginning of saying the word to the time of touching the corresponding picture. From each attempt to another, the location of the 4 pictures on the screen changes, and as a result, the task examines procedural memory in two modalities. In the motor modality, the movement responses performed by touching the hand follow a repetitive sequence, but the sequence of the names of the pictures is semi-random.
In the verbal modality, the names of the pictures follow a repetitive pattern, while the sequence of movement responses made by touching the hand is semi-random. So, in the motor modality the motor sequence is repetitive (2-4-3-1-4-2) and in the verbal modality the verbal sequence is repetitive (cat, grapes, house, sock, house, grapes) (Figure 1).



Two pattern blocks were considered to evaluate procedural learning in consolidation and retention. They are similar to the third and fourth blocks of the learning stage [43]. It is expected that reaction time in the consolidation stage is less than the similar blocks in the learning stage. In the retention phase, it is also less than the reaction time in the consolidation stage [43]. The consolidation stage is evaluated 24 hours after the initial learning stage, and the retention stage is considered one week after the initial learning stage.
Face validity
To determine face validity and solve possible problems, the task was performed in two stages, each on 5 children aged 7-9 years. According to the performance and feedback of the participants, the existing problems were solved.
Reliability
 The reliability of the task was checked using the test-re-test method on 15 participants. Considering that the two pattern blocks in the consolidation and retention stage, were the two pattern blocks 3 and 4 in the initial learning stage, the reliability of the consolidation and retention stage was also calculated using the test-re-test reliability coefficient for these two blocks in the same group of participants. The test-re-test reliability coefficient was calculated using the statistical method of the Pearson correlation coefficient between the scores performed twice in both modalities.
Phase 2: Relationship between procedural memory and grammar
In the second stage of the study, to investigate the relationship between the performance status in procedural memory and grammatical skills, the test of language development-primary (TOLD-P:3) was conducted on each participant. Then, all participants completed the task in three stages of initial learning, consolidation (24 hours after initial learning), and retention (one week after initial learning), first in the verbal modality and then with a 6-week interval in the motor modality [9]. Therefore, each child was exposed to the task 6 times.

Results
Reliability results of the task
The test-re-test reliability results showed that the correlation coefficient for the reaction time variable was 0.84 (P˂0.001) in the verbal modality and 0.8 (P˂0.001) in the motor modality. Also, the correlation coefficient of the response accuracy variable in the verbal modality was 0.81 (P=0.11), and in the motor modality was 0.77 (P=0.026). In the consolidation and retention stage, the correlation coefficient for the reaction time variable was 0.737 (P=0.002) in the verbal domain and 0.743 (P=0.001) in the motor domain. Also, the correlation coefficient of the Responce accuracy variable in the verbal modality was 0.624 (P=0.013), and in the motor modality was 0.916 (P˂0.001).
Results of the stage of the relationship between procedural memory and grammar
Participants’ performance in the serial search task
Before the reaction time analysis, trials with wrong answers were removed, and only the trials with correct answers were included in the reaction time analysis. Figure 2 shows the average reaction time of the participants in both verbal and motor modalities and different stages of learning.



Reaction time analysis in procedural learning
To check the significance of the changes that occurred in the reaction time of blocks 1 to 4 of learning, the results of repeated measures analysis of variance (ANOVA) showed that the main effect of the block was significant (partial η2=0.740; P<0.001; F (3.14)=13.301. But the main effect of the modality was not significant (partial η2=0.185; P=0.075; F(1,16)=3.628). The results of repeated measures ANOVA in checking whether the participants showed significant changes in reaction time by changing the pattern block to random showed that the main effect of the block was significant (partial η2=0.84; P<0.001; F2.15=41.034). The results of the paired t-test showed a significant increase in the average reaction time of block 5 compared to block 4 in the verbal domain (145.47±86.06) and motor modality (191.17±120.49), but the main effect of the modality was not significant (partial η2=0.091; P=0.224; F(1,16)=1.603).
Analysis of reaction time in different stages of learning and the effects of consolidation and retention
The results of 2×3 repeated measures ANOVA to examine the changes in the mean reaction time of participants in different stages of learning showed that the main effect of learning stages (partial η2=0.102; P=0.448; F(2,15)=0.848) and the main effect of the modality (partial η2=0.111; P=0.177; F(1,16)=1.993) were not significant. This result shows that although the participants showed a decrease in the reaction time in the later stages of learning compared to the initial stage, and the children showed signs of consolidation and retention, this reduction was not statistically significant in two modalities (Figure 3).



Relationship between procedural learning and grammatical skills
First, the sequence learning index was calculated for different stages to investigate the relationship between procedural memory and grammatical skills. The sequence learning index in the learning stage for each participant and each modality was calculated using the Equation 1: 
1. Average reaction time of block 5-(average reaction time of block 4+average reaction time of block 6)/2. 
The learning index in the consolidation stage was calculated using the following formula: average reaction time in blocks 3 and 4 of the learning stage-average reaction time in the consolidation stage. Finally, the learning index in the retention stage using the formula of average reaction time in the consolidation phase-average reaction time in the retention phase. The grammar dimension score was calculated by combining the standard scores of the three subtests of grammar comprehension, sentence imitation, and grammatical completion of the TOLD-P: 3 test.
The correlation between the learning index in different stages with the standard scores of grammar comprehension, sentence imitation, grammar completion subtests and overall grammar score were calculated. The results showed that in the motor modality, there was no significant relationship between the grammar subtests and the overall grammar score with the learning index in different stages of learning. In the verbal modality, there was no significant relationship between the learning index in the initial learning stage and retention with grammar, but between the learning index in the consolidation stage of the verbal modality and the grammar comprehension scores (P<0.05, CI=0.069-0.772, r=0.479) and grammar in general (P<0.05, CI=0.016-0.797, r=0.491) there was a significant relationship.

Discussion
The main goal of this study was to design a valid and reliable task to evaluate procedural memory. Also, the status of children’s performance in different modalities and stages of procedural memory learning and the relationship between these children’s performance in the procedural memory task and their grammar skills were investigated.
First, like in the study of Desmottes [9], pictures were selected by considering a set of psycholinguistic features. Using pictures with the highest name agreement and familiarity, a serial search task was designed, face validity was checked and after solving the problems, test-re-test reliability of the task was examined.
The reliability results showed that, like Salehi et al.’s study, the task of this study has good reliability in the variables of reaction time and response accuracy in both verbal and motor modalities and in different stages of learning [18]. Therefore, the serial search task can be used as a valid and reliable task to evaluate different stages of procedural learning in verbal and motor modalities in 7- to 9-year-old Persian-speaking children with the normally developing.
The results of the implementation of the serial search task on the participants in the second stage of the study showed that Persian-speaking children showed procedural learning in both modalities, which was like the results of previous studies [9].
Procedural learning occurred in the form of a significant decrease in the reaction time in the pattern blocks (1 to 4) and a significant increase in the reaction time in the random block [7] compared to the adjacent blocks (4 and 6). This result shows that the designed task correctly examines children’s procedural learning. Also, the modalities main effect was not significant because, like Desmottes’s study [9], these changes occurred in two modalities at a similar rate.
In this study, children showed signs of consolidation and retention, but these effects were not significant. These results are consistent with Hedenius’s study, which said children showed signs of consolidation. Still, these effects were not significant [19]. Adi-Japha’s study noted that children with normally developing did not show a significant decrease in the retention stage compared to the consolidation stage [32]. However, significant effects of consolidation and retention have also been reported [9].
One of the possible reasons for the non-significance of consolidation and retention effects in this study is the diference in the age range of the participants. The age range of the participants of this study was 7 to 9 years, while the participants of Desmottes’s study were in the age range of 7 to 12 years. Considering that the volume of the gray matter of the brain increases from the age of 6 to 10 years and then decreases, this decrease is partly the result of the overall increase of the white matter of the brain tissue.
Garvey et al. hypothesized that an increase in the white matter of the brain tissue leads to a decrease in the conduction time of the nerve message, which can manifest itself as a decrease in reaction time and an increase in motor control [47, 48]. Probably because the participants of this study were in the age range of 7-9 years (average age: 8 years), they had not yet reached maturity in motor timing. Therefore, in the stages of consolidation and retention, they cannot perform significantly better than in the stage of learning.
There was no correlation between performance in procedural memory and grammar in all stages of learning in the motor modality. It seems that the type of input provided is effective in the absence of a significant relationship. Based on the results of some behavioral studies [23, 50], a significant relationship between procedural learning performance and language processing is seen when the presented sequence is verbal. In this study, the relationship between grammar and trend memory in verbal modality was observed..
According to the results of this study, there was no relationship between procedural memory and grammatical skills in the verbal modality in the initial learning and retention stage. This result is in line with previous studies [10, 19, 25, 32]. However, some studies reported contradictory results [9, 26, 25, 51]. One of the possible reasons that can be presented for the existing contradiction is the type of grammar task used in this study.
In some studies that showed the relationship between grammar and procedural memory performance, specific grammatical structures that are more complex and less likely to be fully mastered by the participants were used. For example, Kidd’s study, which reported the relationship between procedural memory and grammatical skills, used the passive structure [25]. The authors of this study concluded that procedural memory is related to the understanding of passive and object relative clauses, but it is not related to the understanding of active and subject relative clauses [24].
The grammar test used in this study examines the comprehension and expression of sentences with common syntactic structures and the use of common morphological forms. It does not specifically examine a specific syntactic structure. Different results may be obtained in the correlation analysis if detailed, and more complex syntactic structures are used to evaluate the grammar. On the other hand, it should be noted that the sample size of the study participants can also be effective on the recent results.
Another result of this study was that in the consolidation stage in the verbal modality, the performance in understanding grammar and grammar, in total, was related to the increase in performance in procedural memory. This result is in line with the results of Hedenius’ study, which showed the relationship between grammar and sequence learning in the consolidation stage using the alternating serial reaction time task [19]. This result confirms the trend procedural part of the DP model in the consolidation stage and only in the verbal modality.
The DP model provides a theoretical framework. Based on this framework, if there is a relationship between procedural memory and grammatical skills, techniques to improve procedural memory can be used to learn grammar. This perspective provides speech and language pathologists with a new view on treating children with grammatical disorders [45]. Therapists can use techniques that promote learning in procedural memory, such as spaced repetition (having a time interval between the repeated presentation of an item) [52] to improve the learning of grammatical structures and especially to retain those structures in memory [53, 54].

Conclusion
The serial search task is a valid and reliable task for evaluating procedural memory in Persian-speaking children. This task could show the procedural learning of children in two modalities. It also showed a decrease in the consolidation and retention stages compared to the initial learning stage, although this decrease was not significant. Also, the results of this study showed the relationship between grammar and procedural learning in the verbal modality and the consolidation stage.

Ethical Considerations

Compliance with ethical guidelines
This research has been approved by the Ethics Committee of the University of Social Welfare and Rehabilitation Sciences and received an ethical code (IR.USWR.REC.164.1397. Before conducting the study, the parents of all participants completed and signed the informed consent form.

Funding
This article is taken from the first author’s PhD thesis in the University of Social Welfare and Rehabilitation Sciences, Speech Therapy Department.

Authors' contributions
Conceptualization and methodology: Maryam Malekian, Talieh Zarifian, and Yalda Kazemi; Validation and data analysis: Maryam Malekian; Research and review: Maryam Malekian and Akram Ahmadi; Writing the draft, editing, and finalization: All authors.

Conflict of interest
The authors declared no conflict of interest.

Acknowledgments
The authors are grateful for the efforts of Karim Rahimian, who designed the software, Mohammad Gholami, who performed the statistical analysis and interpreted the data, and Tabassom azimi, who helped in analyzing the data and writing the article. 
 

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