Metacognitive Strategies Related with Logical–Mathematical Thinking for Adolescents with ADHD

This article focuses on the contributions of the still-scarce corroborations available on the social nature of the metacognitive regulation of joint attempts in order to offer systematic means to operationalize and analyze shared regulation. The mathematical knowledge aims to achieve the metacognitive needs of students and, in particular, those with learning difficulties. The present research process aims to explain the relationship between the logical and mathematical thinking of students with ADHD in secondary education schools in Heraklion (Crete) and metacognitive awareness and academic motivation, including questions about pupils’ logical–mathematical skills and logical decisions of life and problem solving. Appropriate psychometric tools are used to evaluate their performance as well as their short and medium-term and consequently their long-term goals. The results of the current study imply that, when students realize that teachers and their parents emphasize the essential process of learning, appropriate strategies can be shown to them to allow them to learn how to solve problems on their own. As a result, it is of great significance to point out the relationship between students’ academic achievement and academic motivation.


Introduction
A chronic neurodevelopmental disorder that affects approximately 5% of schoolaged children is attention-deficit/hyperactivity disorder (ADHD) [1], which is associated with clinically significant impairments in the family, peer and academic domains [2]. Academic difficulties associated with ADHD start early and often remain through middle and high school [3]. The extent of the subject above makes it necessary to study indepth the perception that students have of the subject of mathematics in junior high schools in institutions of Greece on some psychological aspects, such as motivation towards homework, self-concept, self-esteem and peer relationships.
More specifically, the present study determines the connection between the academic performance of students of mathematics, especially the solving of mathematical problems, in the secondary stage (12-15 years old) in institutions in Greece and some aspects such as motivation, self-concept, self-esteem, relationships with peers, students' daily lives and all that the teaching society has.

Cognitive Process Factors of Incentives: Individual Goals to Be Achieved
One of the most common communications between teachers and students is undertaking the invitation of an attentive attitude [4], mainly in which performance is deficient, such as the issue of children with attention-deficit hyperactivity disorder (ADHD). Metacognition and performance create a relationship that can be ascribed to the fact that metacognition relates to students' ability to adjust knowledge and strategies and to regulate their own learning as a result [5]. Furthermore, an individual's ability to use appropriate strategies and procedures also plays an important role in order to quickly and securely drive the organization and execution of the resolution plan. In recent years, studies of a child's ability to choose the right problem-solving strategy have essentially led to an indicator of whether the individual "knows how to learn", i.e., his metacognitive ability [6].
It is important to mention that the current relevance of investigating high-level strategies is related to performance goals which are positively associated with functional behaviors, such as high school performance. In other words, it seems that both learning objectives and performance goals are seen as incentives for approaching, as they are achieved by engaging students in academic activities. In general, the definition of metacognition is one's reflection on his/her way of thinking. Metacognition can be distinguished as thinking about the knowledge and skills that exist in the minds of individuals, who, in our study, are adolescents with ADHD [7].
Some instruments to measure metacognition in youth and adults are the Motivation and Learning Strategies Questionnaire and the Metacognitive Skills Inventory, known respectively as MSLQ and MAI. The MAI, which was used for this research, is an instrument that allows us to examine the metacognitive awareness of children, adolescents and adults, and it was created and validated by Schraw and Denninson (1994) [8]. Since then, this instrument has been widely used in different investigations, especially to demonstrate the relationship between metacognition and learning achievement [9,10].

Mathematics in Cognitive Processes in Students with ADHD
Mathematical competence, in line with recommendations of the European Parliament and the Council of the European Union, is defined as "the ability to develop and apply mathematical thinking in order to solve a range of problems in situations of everyday life" (2018, p. 9) [11]. The differences in the way children acquire mathematical abilities seem significant [12]. The cognitive explanations for these differences, as research has investigated, are both domain-general cognitive factors (i.e., factors related to learning various academic abilities) and domain-specific cognitive factors (i.e., factors specifically related to mathematics learning) as well [13,14]. The relationship between metacognition and general academic performance has been largely considered. Vo et al. (2014) [15] noticed that children's metacognitive skills in the numerical domain predict their general school-based mathematics awareness and suggested that children's metacognition is a domain-dependent cognitive skill in adolescents.
Cooperation in metacognitive learning seems meaningful for students when considering new concepts and developing mathematical causality [16]. On the other hand, academic underachievement is apparent in those with ADHD, with approximately 33-63% of children with ADHD displaying difficulties in many school subjects, such as math [17]. ADHD academic difficulties usually appear early and are often persevered through middle and high school [3]. Furthermore, ADHD-related academic difficulties are correlated with countless negative results, including increased repercussions of failing grades, lower grade point averages and standardized test scores, higher rates of high school dropout and lower college presence, especially when they are compared to typically developing children of the same age [18].
Summarizing the above, the cognitive process factors of incentives are achieved by engaging students in academic activities. Particularly referring to mathematical competence, differences in the ways that children acquire mathematical abilities appear significant, especially when taking into consideration adolescents with ADHD, whose academic underachievement is apparent.
The general objective pursued in this research was to know the perception, namely the way of thinking, that students have of the subject of mathematics in junior high schools in Greece on specific psychological aspects, such as motivation towards homework, selfconcept, self-esteem and peer relationships. The novelty of the present study lies in the fact that metacognitive factors in relation to mathematical competence were studied exclusively in students with ADHD.
Therefore, numerous questions can be brought up, which simultaneously have teaching, academic, psychometrical and daily value. Therefore, a research question that arose was related with the significant difference between the learning design of children with ADHD and their metacognitive skills, which are indirectly related with their life decision plans. In addition, another question was whether there is a significant difference between the learning management of children between the age of 12 to 15 years old with ADHD and their socio-demographic characteristics or their last-year performances in mathematics.
The following research questions were created to attain the aim comprehensively: 1.
Is there any significant difference between students' academic achievement, metacognitive awareness and academic motivation, and their socio-demographic characteristics or their last-year performances in mathematics? 2.
Are there significant differences between the performances of students (girls and boys) from 12 to 15 years old and task motivation? 3.
Are there significant differences between student performances in mathematics and their school area? 4.
Are there significant differences between student performances in mathematics and their last-year performances in mathematics?

Research Setting and Participants
The research sample consists of 12-15 year old students with ADHD (attention-deficit hyperactivity disorder) attending secondary school units (17 schools in total in both urban and non-urban area) in Heraklion, Crete, both in integration and in the general classroom. The sample selection criterion was carried out in an appropriate manner, as indicted by the knowledge of the Educational and Counseling Support Centers, which, in conjunction with the Public Pediatric Medical Centers, are ultimately responsible for the diagnosis, differentiation and development of appropriate interventions and support programs in accordance with legislation [19,20].
In a non-probability sample, such as in the present study, there is no way to calculate the probability that each individual has to be included in the sample. Thus, the selection of the sample was made randomly through the common characteristic of students with ADHD. After dividing the sample into groups, between the schools in urban and nonurban areas, the selection of members was made only on the basis of convenience (simple random sampling), in which the research was held for the most easily accessible people to participate in the research.
The sampling method used is feasibility sampling [21], as it refers to the selection of certain population groups that satisfy specific assumptions, which, for the needs of our research, include students with ADHD.
Below, descriptions of each variable, used separately, are presented. In Table 1, it can be seen that the sample of 110 students participating in this study shows that almost 30% of them are female, and more than 70% are male. In this sample, 36.4% studied in the 1st class of junior high school, and 31.8% were in the 2nd and 3rd class. About 60% of the children participating in this investigation were living in an urban area (city of Heraklion), and the rest of them were living in a non-urban area (40.9%). The table below illustrates the percentages of the last-year performances in mathematics as well. Most of the children (30%) had a performance of 13-14, whereas close to 20% were children with a last-year performance of 11-12 and 15-16. A few low percentages show performances that are lower than 10 (9.1%) and more than 17 (7.3-8.2%).  Table 2 shows that almost half of those who were surveyed have attention-deficit (43.6%), and only 11.8% were diagnosed with attention-deficit, hyperactivity and impulsivity. Moreover, 29.1% of the students showed attention deficit and impulsivity, and 15.5% showed attention deficit and hyperactivity.

Implementation of the Instrument
Concerning the data availability statement, the researchers ensured the consent of the parents and guardians of the pupils; the anonymity of the research participants and their protection, in accordance with the existing legislation of their sensitive personal data [22]; the provision of the possibility for research participants to terminate their participation; as well as the process of collecting research data being compatible with international treaties and conventions related to human rights in education [23]. Thus, all participants were fully informed that their anonymity was assured, why the research was being conducted, how their data were to be used and if there were any risks associated. As with all research involving humans, ethical approval from the Institute of Educational Policy from the ethics committee of the Ministry of Education of Greece was obtained prior to conducting the study, with assignment decision number 73541/D2/13-05-2019.
The scale measuring cognitive process questions, such as depth strategies, metacognitive strategies, surface strategies and self-regulation strategies, consists of 18 questions and is separated into 5 sub-categories.
This scale is part of the MAI validated instrument [24], which makes it possible to identify the metacognitive abilities of subjects through specific specialized questions divided into two categories: knowledge of cognition and regulation of cognition, which, in turn, are divided into other more specific categories: This questionnaire guarantees its validity and reliability, since the reliability value for academic achievement tests should be 0.65 and higher [25]. With respect to the research's internal consistency and reliability, the Cronbach's alpha is 0.87 for the cognitive process questions strategies.

Analysis Strategies
The data obtained are of a quantitive nature and were analyzed with a statistical program, specifically, the SPSS v18, performing descriptive and inferential tests. In this research, a descriptive analysis and an inferential analysis of mean differences, Student's t-tests and ANOVAs were carried out with variables of gender, school area and each student's last-year performance in Math.

Results
This section can be divided by subheadings. It provides a compendious and accurate description of the experimental results, their interpretation and the experimental inferences.
Below, in Table 3, the descriptive results of central tendency (mean and standard deviation) of the items that comprise the Cognitive Process questionnaire are illustrated. The sample of 110 students participating in this study shows a higher mean in Item 11. Therefore, most of them try to ask for help when they do not understand something, and the same sample of students shows the lowest mean in Item 1, which depicts the situation in which students ask themselves questions about the lesson before they start studying.

Results According to Gender
Through the procedure to compare Cognitive Process Questions according to gender by analyzing Student's t-tests (n.s = 0.05), the results shown in Table 4 were yielded.  Another statistically significant Item is the 18th, in which children were asked that, when they finish a job, if they wonder if they have learned as much as possible. This question seems to have a more significant impact for the girls (M = 3.73) than the boys (M = 3.15), [t (108) = −2.184, p = 0.031].

Results According to School Area
In addition, by proceeding to compare the Depth Strategy and Self-Regulation Questions according to school area (Appendix A), Student's t-tests were analyzed (n.s = 0.05). In Item 9, children were asked if they periodically re-examine something they study, in order to help them understand important relationships. Children who lived in the city of Heraklion (M = 2.66) seemed to have the habit of periodically re-examining what they study, more than those who live out of the city (M = 2.07), [t (108) = 2.317, p = 0.022].
A statistically significant result is from Item 13, in which children were asked if they stop and reconsider when new information is confusing. Children who lived in the city of Heraklion (M = 3.57) seemed to react in the above way more than children who lived out of the city (M = 2.87), [t (108) = 3.042, p = 0.003]. There is significance between students with last-year degrees in Mathematics of 15-16 and 19-20 who ask for help when they do not understand something (Item 12). In addition, the difference of the answers given from the students between their last-year grades in mathematics (p-value) was calculated for both groups (15-16 and 19-20), and in this case, the value was 0.044, since students with last-year grades in mathematics of 15-16 changed their strategies when they could not figure out a math problem more than those with grades of 19-20 [F (5, 104) = 2.451, p = 0.038]. It is essential to mention that the Greek grading scale system for the whole secondary education is between 1 and 20 (1 is the lowest grade, 10 is pass and 20 is perfect). In addition, students with attention-deficit stop and re-read when they are confused more than those with attention-deficit, hyperactivity and impulsivity (t = 2.751, p = 0.042).

Discussion
The use and absence of cognitive and metacognitive strategies has been linked in the past to various learning patterns, such as achievement goals, school performance and the degree of persistence in achieving a given goal [26,27]. However, both cognitive and metacognitive strategies are key self-regulated learning strategies associated with positive learning outcomes [26,28] used by students who use strategies to avoid engaging in dysfunctional behaviors [29,30]. Self-regulatory skills require awareness of how they think in a condition of achievement to control their learning behavior and to maintain a high motivation to achieve. Consequently, help-seeking behaviors as well as academic self-undermining are not expected of students using cognitive and metacognitive strategies. Seeking help itself is a self-regulatory strategy and an adaptive behavior in response to a subject's own recognition that he or she needs help to achieve a goal [28,30].
A similar study to the one presented in this investigation was carried out by Alci and Karatas (2011) [31], who used the MAI to determine the metacognitive awareness of teacher candidates according to area and sex. They found that, although numerical mastery students had higher results, the differences were not significant. In the same way, men had a higher average, but the difference was not significant either.
In our study, more girls than boys continued to ask if they could reach their goals (self-questioning and self-control) and stopped and re-read when they were confused (selfcontrol and self-regulation). As a result, in this specific area of motivation (self-questioning, self-control and self-regulation) there exists an indifference between girls and boys.
Young and Fry (2008) [10], in their research, applied the MAI to 45 graduate students and 133 undergraduate students and studied the correlation of this instrument with partial and accumulated grades of one of the courses they were taking. They determined that there is a high correlation between the MAI and the cumulative grade point average, as well as with the final grade, and that there are significant differences in the regulation of cognition between undergraduate and graduate students. They state that the MAI is a powerful tool for teachers to know which students need direct instruction on metacognition, especially in large courses or in virtual modes.
In our study, the routine of children of giving answers about changing their strategies when they cannot figure out a math problem (self-regulation) represents better individuals with last-year performances in mathematics, with scores that were mediocre or good. Children in this category ask themselves questions about the lesson before they start studying (voluntary participation in learning with active involvement and utilization of acquired knowledge) and choose the best way of solving a problem, among many different ways (use of adaptive strategies and cultivation of personal identity in learning). Thus, significant indifference exists between students with mediocre or good last-year performances in mathematics and those with different performances in the above. The innovation of Cruz Pichardo and Puentes Puente (2012) [32], on the use of ICT and the teaching of mathematics, indicates that the use of these technological resources in this subject can help the progress of mathematical competence and reorganize their way of thinking, therefore allowing them to develop metacognition strategies.
The results of the current study indicate that most of the children, when they must solve an exercise, firstly try to figure out what this exercise requires, as well as try to ask for help when they do not understand something. In addition, they try to remember some older information when they solve an exercise or understand a text. Moreover, when it seems more important for them to answer a question in a test, they finally read it again to make sure they gave the answer that the question asked.
Children who live in an urban area seem to have the habit of periodically re-examining something they study in order to help them understand important relationships (selfquestioning, self-control and self-regulation). Children who live in urban areas seem to stop and reconsider when new information is confusing (self-control and self-regulation) more than children who live out of the city. As a result, there exist significant differences between students depending on their performances in mathematics and their school area. Similarly, the results of the research of Taghieh, Tadayon and Taghieh (2019) [33] indicate significant differences between adolescents from urban and rural areas of Eghlid with respect to cognitive and metacognitive strategies used as learning strategies.
The study of Sibley et al. (2019) [34] indicates that the motivational and the goaldirected features of self-regulated learning are affected in children with ADHD. During this developmental period, group differences are less stable. School-based interventions that emerge for high school students with ADHD may integrate reparative metacognitive strategies, such as goal setting and implementation motives [35].

Conclusions
The present research has led to a number of findings concerning the reasons why high school students resort to the use of avoidance behaviors in school, which degrade the learning process and undermine learning outcomes. The findings above lead to the conclusion that self-questioning, self-control as well as self-regulation have a connection with the gender of adolescents. In addition, self-regulation, voluntary participation in learning with the active involvement and utilization of acquired knowledge, the use of adaptive strategies and the cultivation of personal identities in learning represent better individuals with last-year performances in mathematics, with scores that are mediocre or good. Children who live in an urban area have more self-questioning, self-control and self-regulation than those who live out of an urban area. The novelty of the present study lies in the fact that metacognitive factors in relation to mathematical competence were studied exclusively in students with ADHD.
Generalizing the findings of this study is limited, as a convenience sampling procedure was used. It is clear that future research in the field of avoidance behaviors in the school context has much more to contribute, mainly through more holistic and, consequently, more realistic approaches. A more generalized sample can account for both the school context and the family context, which also change in the dynamics of time.
Hence, interventions to improve self-regulated learning among high school students with ADHD may be advanced by targeting metacognition and cognitive flexibility. Despite having several limitations mentioned above, a mathematics curriculum that aims to teach mathematics could use metacognition questioning, self-monitoring and self-evaluating as effective methods. Informed Consent Statement: Informed consent was obtained from all subjects involved in the study. Written informed consent has been obtained from the patient(s) to publish this paper.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.
Acknowledgments: It would be an omission not to thank the Ministry of Education of Greece for authorizing this research, the schools' governing body and the principal and staff who granted us permission to work with the children. The children are also especially thanked for their willingness to participate in this study.

Conflicts of Interest:
The authors declare no potential conflict of interest with respect to the research, authorship and/or publication of the article. Table A2. Results of the ANOVA according to students' last-year performances in math.