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These Year 3 doubling challenge worksheets encourage pupils to complete empty boxes by doubling given numbers twice from the two times table. They are reminded to consider how the numbers double each time, following the pattern in the 2, 4 and 8 times tables.

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Free Year 3 Add and Subtract 1s Reasoning and Problem Solving

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Add and subtract numbers mentally, including: three-digit number and ones; three-digit number and tens; three-digit number and hundreds

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Enhancing cognitive dimensions in gifted students through future problem-solving enrichment programs

• Open access
• Published: 09 September 2024
• Volume 5 , article number  248 , ( 2024 )

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• Khaled Elballah 1 ,
• Norah Alkhalifah 2 ,
• Asma Alomari 2 &
• Amal Alghamdi 2  

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This study has undertaken a scrutiny of research pertaining to enrichment programs based on future problem-solving skills, aimed at enhancing the cognitive dimensions of gifted students between the years 2010 and 2023. The study used a sample of 10 studies; 3 correlational studies and 7 quasi-experimental studies. The study employed the descriptive-analytical approach by following a meta-analysis method. The study aimed to discern the effectiveness of enrichment programs based on future problem-solving skills in developing the cognitive dimensions of the gifted. The study's findings have indicated a significant impact of enrichment programs based on future problem-solving skills in the development of the cognitive dimensions of the gifted, as per both correlational and quasi-experimental designs. Moreover, statistically significant differences were found related to the variables of educational level and gender in accordance with both correlational and quasi-experimental designs. The study also advocates the need for further research in this domain to facilitate the generalization of the novel findings of this study within the gifted field.

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1 Introduction

The special needs of gifted students and the challenges they encounter compel us to offer them tailored education that aligns with their potential. According to relevant literature, numerous programs and practices are employed in educating gifted students. In recent years, gifted education has witnessed substantial growth in programs, providing students with various enrichment opportunities. Among these opportunities are enrichment programs that come in various forms, often interactive and centered around higher-order thinking skills. This allows students requiring additional intellectual stimulation to remain engaged and interested in their classrooms [ 3 ]. Enrichment programs focusing on future problem-solving skills are a significant component of gifted education. Many studies have called attention to such problem-based programs. Given the challenges faced by modern societies due to rapid and continuous changes, gifted individuals in the twenty-first century find it imperative to possess future problem-solving skills. These skills involve individuals actively exploring the future by connecting the past with the present, attempting to anticipate the future based on current information and data, and creating current and future solutions to these issues. Future thinking is an active process encompassing all situations, involving planning toward future objectives, passing through stages of imagination, prediction, visualization, planning, and decision-making [ 2 ].

Enrichment programs centered on future problem-solving skills focus on enhancing cognitive processes, such as creative thinking, critical thinking, future-oriented thinking, imaginative thinking, and motivation for achievement. These programs are suitable for experienced students and support the educational process interactively. Their curriculum encompasses essential steps that students should follow when solving future problems. These steps start with identifying future challenges, selecting the most prominent challenges, generating solutions and ideas, setting criteria and applying them, and conclude with developing an action plan, equipping students with the tools and strategies to address these problems [ 48 ]. In this regard, [ 20 , 33 ] underline the significance of future problem-solving enrichment programs in gifted education, emphasizing that it represents a novel and captivating approach for gifted students to enhance their self-efficacy, acclimate to higher-order thinking skills, and cultivate their creative self. This, in turn, improves their creative thinking, mitigates the potential for boredom and monotony, and broadens their knowledge while introducing them to new areas of interest. Johnsen [ 28 ] posits that gifted education programs must prioritize offering rich experiences characterized by depth, challenge, and flexibility. They should challenge the capabilities of gifted students and develop their higher-order thinking skills, focusing on holistic development of their mental, skill-based, emotional, and independent thinking capacities in problem-solving situations. Such characteristics can be found in enrichment programs that revolve around genuine future problems to nurture these skills.

Regarding research, several studies have directed their attention to exploring future problem-solving competencies. For instance, [ 20 ] assert the effectiveness of enrichment programs centered on future problem-solving in enhancing students' creative self-efficacy. Additionally [ 7 ], affirms the effectiveness of an enrichment program based on the Kolb model in developing problem-solving skills among gifted students in the cognitive dimensions.

On another side, studies have examined the characteristics of gifted students participating in future-thinking problem-based programs [ 55 ]. Conducted a study that revealed that children participating in a program based on diverse future-thinking skills acquired the ability for profound observation, extensive general knowledge, exceptional verbal, logical, detailed, and creative thinking, and a flexible approach to problem-solving. Despite the positive impact identified by numerous previous studies in the context of future problem-solving programs, there have been variations, particularly concerning gender, educational level, and other skills, as evidenced by the findings of certain studies [ 11 ]. Furthermore, this methodological approach has not garnered significant attention from researchers in Arab countries, despite the researchers' affirmation of the importance of sequential analyses [ 47 ]. Emphasize that Meta analyses can provide unique contributions to the field of gifted education. Firstly, the results are reliable, stemming from replicable methodological steps [ 25 ]. Secondly, by summarizing the current state of evidence, Meta analyses offer researchers the opportunity to place their insights within the larger context. Thirdly, Meta analyses allow researchers to examine the effects of a large number of independent variables and potential influences simultaneously [ 45 ]. Asserts that Meta analyses are a more comprehensive method for conducting program evaluations in gifted education, as it enables the study of a wide array of independent and moderating variables simultaneously, facilitating a better understanding of the results of various studies.

1.1 Research questions

This study employed a meta-analytic approach to synthesize findings concerning problem-solving skills in the domain of gifted education. The purpose was to address the following inquiries:

What is the effect size average of the impact of enrichment program interventions based on future problem-solving skills for gifted students in fostering their cognitive dimensions, according to correlational designs?

To what extent does the effect size average of the impact of enrichment program interventions targeting future problem-solving skills for gifted students vary in terms of their cognitive dimension development according to correlational designs, as a result of participant type (males, females, both) and educational level (elementary, middle, high school)?

What is the effect size average of the impact of enrichment program interventions based on future problem-solving skills for gifted students in fostering their cognitive dimensions, according to quasi-experimental designs?

To what extent does the average magnitude of the impact of enrichment program interventions targeting future problem-solving skills for gifted students vary in terms of their cognitive dimension development according to quasi-experimental designs, as a result of participant type (males, females, both) and educational stage (elementary, middle, high school)?

1.2 Significance of the study

The significance of this study resides in its substantive contribution to the field of gifted education research, mitigating the rare of studies employing such analytical methodologies. Furthermore, it answers the clarion call voiced by numerous scholars in the Arab world regarding the importance of conducting meta-analytical studies within the educational field [ 1 ]. This study will play a pivotal role in the realization of the directives set forth by the American Psychological Research Guide, which underscores the criticality of employing meta-analysis as an adjunctive statistical method for scrutinizing statistical significance. Through this meta-analysis, we shall elucidate the effective factors upon the education of gifted students. Consequently, it will bestow unparalleled contributions to the field of gifted education by means of descriptive multivariate analyses, which proffer a more comprehensive evaluation of gifted education programs. They empower researchers to scrutinize a wide spectrum of independent variables and moderating variables concurrently [ 50 ].This study will serve as the cornerstone upon which plans for the development and activation of the roles of gifted care programs in fostering cognitive dimensions are constructed. This is because any developmental blueprints hinge upon a comprehensive portrayal of the existing reality from all its facets. Moreover, this study will offer guidance for future research endeavors and inquiries into enrichment program typologies.

1.3 Research terminologies

1.3.1 meta-analysis.

This study uses the meta-analysis methodology, defined as statistical analysis for a comprehensive spectrum of research findings. Its principal objective resides in the synthesis of abstracts or information extracted from an expansive body of research, with the overarching intention of fostering cohesion among studies that share a common thematic concern. This methodological approach serves to facilitate a more profound understanding of the rapid proliferation of antecedent research endeavors. The nomenclature employed to signify meta-analysis has demonstrated a degree of lexical diversity, encompassing designations such as transcendental analysis and meta-analysis [ 15 ].

1.3.2 Enrichment programs

Enrichment programs, as defined by [ 6 ], refer to an assemblage of educational programs used by educators to nurture the development of students' competencies. These proficiencies encompass a varied spectrum, including cognitive aptitudes, social skills, and other skills that enhance the educational experiences of students.

1.3.3 Future problem-solving skills

Future problem-solving, as elucidated by [ 4 ], draws upon Torrance's (2003) definition of this term, characterizing it as the acumen employed for the analysis and formulation of strategies directed at the resolution of problems, challenges, or difficulties, and undefined obstacles projected to manifest in the future, extending over a temporal future of no less than twenty-five years.

1.3.4 Gifted students

The National Association for Gifted Children (NAGC) has defined gifted and talented students as those who perform—or can perform—at higher levels than others of the same age, experience, and environment in one or more areas. These talented people must modify their educational experience to learn and achieve their potential. Furthermore, gifted and talented students can have the following features:

They come from all ethnic and cultural groups and from all economic classes.

It requires obtaining adequate educational opportunities to achieve their potential.

May have learning and processing disorders that require specialized intervention and adaptation.

Need support and guidance to develop socially, emotionally and in different areas [ 35 ].

1.3.5 Cognitive dimensions

Cognitive dimensions, as expounded by [ 9 ], encompass an array of concepts, ideas, and systematically organized mental operations resident within a child's cognitive consciousness. These operations discriminate the cognitive realm and are predicated upon skills such as recall, categorization, and decision-making. These skills, in turn, are rooted in the skills of thinking, conceptualization, and organizational aptitude.

1.4 Study procedures

1.4.1 study design.

The study used the descriptive-analytical approach applying the meta-analysis method, as it was suitable for the nature of this study. Meta-analysis is considered an advanced approach for comprehensive summarization of previous studies and research. It significantly contributes to the interpretation of the huge literature that extends beyond the confines of academia. It is a descriptive-analytical methodology aimed at extracting underlying findings from multiple outcomes derived from individual studies with specific attributes. This involves conducting a survey of studies related to the subject matter of the study, examining their theoretical framework, as well as the research problem, hypotheses, procedures, and results. Subsequently, criteria were established for selecting studies that warrant reanalysis and the appropriate decisions [ 19 ].

1.4.2 Study sample

The sample comprised ten research articles published between 2010 and 2023 in diverse international journals.

Shokraneh [ 45 ] recommended documenting the strategies and steps employed in meta-analysis to facilitate repetition or new updates for meta-analysis. In this study, the analytical strategies and steps adopted were as follows:

2.1 Firstly, data collection

Studies published between 2010 and 2023 were included, using a two-stage process. The first stage involved conducting computer-based research using the following keywords: "gifted," "gifted education programs," "gifted education," "gifted student," "thinking skills," "future problem-solving skills," "gifted programs," "cognitive dimensions," "cognitive resilience," "decision-making," "achievement," and "metacognition." Studies that included these keywords in their titles or abstracts were initially selected and individually reviewed to identify additional references.

Manual searches were conducted across several journals, with articles related to gifted students, including but not limited to the Journal of Secondary, Journal for the Education of the Gifted, Roeper Review, Gifted Child Quarterly, Gifted Education, Journal of Advanced Academics, Journal of King Saud University, Journal of Umm Al-Qura University, International Journal of Educational Research at the United Arab Emirates University, Educational Journal at Taif University, and Dar Al-Mandhuma Database. Additionally, searches were conducted on the Google Scholar scientific researcher database, ERIC database, and the Google search engine. The previous search results yielded a total of 288 research articles. In the second stage, criteria for including studies in the current research were applied, resulting in a reduction to ten research articles.

2.2 Secondly, inclusion and exclusion criteria

The study applied inclusion criteria based on the following guidelines:

Selection of studies published between 2010 and 2023 in Arabic and foreign journals.

Selection of complete studies (open-access journals).

Selection of studies with clearly defined correlational or quasi-experimental methodologies.

Selection of studies that explicitly stated the sample size.

Selection of studies that employed educational tests as Pearson correlation coefficients, "t-tests," and "F-tests."

Selection of studies with available statistical data indicating the relationship between the interventions of enrichment programs based on future problem-solving skills for gifted students and the development of their cognitive dimensions or their impact (correlation coefficients, sample size, mean, standard deviation). The previous studies were examined, resulting in the inclusion of ten studies investigating the impact of enrichment program interventions based on future problem-solving skills for gifted students and the development of their cognitive dimensions, according to the criteria specified above. It is to be noted that articles removed during the systemic process included the duplicated articles, articles identified as ineligible for the research by the automation tools and other articles that were removed for some other reasons such as missing information or bad quality of the articles or irrelevant to the study topic. It is also important to note that 41 articles were excluded from the analysis because of the missing information or bad quality of the articles or irrelevant to the study topic.

3 PRISMA flow diagram of the systematic search

Figure 1 describes the process stages used to select the articles used in this research. It is to be noted that two sources have been used in the process of selecting of data namely articles from databases and registrars. Furthermore, it is to be noted that articles removed during the systemic process included the duplicated articles, articles identified as ineligible for the research by the automation tools and other articles that were removed for some other reasons such as missing information or bad quality of the articles or irrelevant to the study topic.

PRISMA flow diagram of the systematic search

Table 1 describes the studies in the research sample included in the meta-analysis.

3.1 Thirdly, the encoding of study characteristics

A coding protocol was established to reflect information regarding the principal attributes of the study, experimental conditions if applicable, and the participants and samples. The features of the outcomes [ 21 ]. Consequently, the encoding of the modified variables in the present study stands as follows:

3.1.1 A—Study design

The encoding of the study design was categorized into:

Correlational research: If these studies investigate the correlational relationship between interventions of enrichment programs for gifted students and the development of their cognitive dimensions.

Quasi-experimental research: If these studies explore the impact of enrichment programs based on future problem-solving skills for gifted students in developing their cognitive dimensions.

3.1.2 B—Participant type

The encoding of participant type was categorized as (males, females, males and females together).

3.1.3 C—Educational level

The encoding of educational stage was categorized as (elementary, middle, secondary).

3.2 Fourthly, data analysis strategy

The study used effect size criteria provided by [ 17 ], and in accordance with that, the effect size is categorized as follows: from 0 to 0.10 weak, from 0.11 to 0.30 modest, from 0.31–0.50 moderate, from 0.51to 0.80 large, and represents greater than 0.81 as very large.

Furthermore, the common effect size of previous studies was calculated by determining the model used and represented by the random or fixed-effects model, which is determined by the test of heterogeneity that detects whether the observed variance in effect sizes (Q) significantly differs from the variance due to sampling error [ 21 ]. Accordingly, it is necessary to find the value of Q and compare it to the degree of freedom value (df = n-1) in the Chi-square value tables as follows: If the value of Q is less than the Chi-square value, it is interpreted that the effect sizes of the studies are homogeneous, and the common effect size is calculated according to the fixed-effects model. However, if the value of Q is greater than the Chi-square value, it is interpreted that the effect sizes of the studies are not homogeneous, and the common effect size is calculated according to the random-effects model.

In the current study, the random-effects model was used to align with the study's objectives, and the test of heterogeneity was conducted, as well as the application of categorical moderator analysis to examine whether the common effect size of enrichment programs based on future problem-solving skills for gifted students in the development of their cognitive dimensions showed significant differences based on study type, participant type, and educational stage. Moreover, it was determined whether the moderator was significant based on the level of significance value (Q) in the light of the random-effects model.

3.3 Fifthly, effect size calculation

The effect size in quasi-experimental studies was calculated as the difference between the means of the experimental and control groups divided by the common standard deviation. Additionally, Pearson's correlation coefficient was used as a measure of effect size for correlational studies.

3.4 Sixthly, publication bias assessment

Publication bias refers to the irregular representation of studies published in the literature, resulting from a higher probability of publishing studies with significant effects. This bias can influence the results of meta-analysis [ 42 ]. Researchers in meta-analysis studies have examined a set of peer-reviewed scientific studies published in journals, although there are similar studies that have not had the opportunity to be published in those journals for one reason or another, raising doubts about the possibility of bias in the results they reach. Hence, the importance of assessing publication bias becomes evident. For this purpose, Egger's regression test was used, which is a test of regression analysis for non-symmetrical funnel plot. It relies on the value "t" and its significance, so if the "t" value is not significant, it indicates no bias.

3.5 Seventhly, heterogeneity assessment

Heterogeneity analysis is a common approach in meta-analysis. It examines the likelihood of observing the variation displayed by effect sizes if sampling error is what makes them different [ 21 ]. In the current research, heterogeneity was evaluated using the Cochran's Q test, and the I 2 statistic [ 27 ]. The Q statistic follows a Chi-square distribution with degrees of freedom (n-1), while the I 2 statistic represents a percentage of the total variation across studies attributed to heterogeneity rather than chance. The test also examines the null hypothesis of homogeneity, stating that all studies evaluate the same effect [ 27 ].

3.6 Data analysis

The researchers of the current study used the Comprehensive Meta-Analysis (CMA) V.3.3.07 software to analyze the data extracted from previous studies (n = 10).

4.1 First question results

“What is the effect size average of the impact of enrichment program interventions based on future problem-solving skills for gifted students in fostering their cognitive dimensions, according to correlational designs?"

To answer this question, the researchers used the following:

The heteroscedasticity test was employed to ascertain whether the observed variability in effect sizes within the research and study sample significantly deviated from the expected variability attributable to sampling error. This determination was crucial in identifying the appropriate model for aggregating effect sizes, as illustrated in Table  2 .

Table 2 clearly demonstrates the outcome of the heterogeneity test, which attests to its statistical significance (P = 0.037). The observed value stands at Q = 10.39 with degrees of freedom df = 2, markedly exceeding the critical Chi-squared (X 2 ) table value at a 95% confidence level. Furthermore, the heterogeneity ratio index (I 2  = 80.14%) underscores a substantial degree of heterogeneity among the various studies, indicating a dearth of common effect size. This, in turn, suggests a marked incongruity among the studies. Given the considerable variation in effect sizes across different studies, it is imperative to subject them to analysis in accordance with the random effects model. In this model, the common effect is construed as the mean value of these respective effects [ 16 ].

Moreover, the tabulated data in Table  2 unveil that the common effect size, as posited by the random effects model, is estimated at 0.531 with a standard error of 0.004 and a 95% confidence interval spanning from 0.317 to 0.694. This estimate is consistent with the characterization of a substantial effect size, as delineated by [ 17 ]. Consequently, the influence of enrichment programs tailored for intellectually gifted students, particularly concerning the development of their cognitive dimensions through the utilization of a correlational design, is indeed of considerable large.

In the assessment of publication bias, researchers employed the regression analysis test by Egger, yielding a coefficient "t" (1.15), with one degree of freedom, with P value of 0.455. This value bears no statistical significance, signifying the absence of publication bias.

4.2 Second question results

“To what extent does the effect size average of the impact of enrichment program interventions targeting future problem-solving skills for gifted students vary in terms of their cognitive dimension development according to correlational designs, as a result of participant type (males, females, both) and educational level (elementary, middle, high school)”

To answer this question the researchers used Analysis of Modified Variables, as follows:

The researchers employed a modified analysis to discern whether the impact of enrichment program interventions on the cognitive dimensions of gifted students varies depending on the type of participants (males, females, both), and the educational level (primary, middle, secondary). This revelation is elucidated through Table  3 .

It is evident from Table  3 that statistically significant disparities in the effect size of enrichment program interventions on the cognitive dimensions of gifted students are attributed to the gender of the participants (males, females, both), in favor of females (P = 0.004), and the educational stage (primary, middle, secondary), in favor of the secondary level (P < 0.001).

4.3 Third question results

“What is the effect size average of the impact of enrichment program interventions based on future problem-solving skills for gifted students in fostering their cognitive dimensions, according to quasi-experimental designs?”

An assessment of heterogeneity test was employed to ascertain whether the observed variability in effect sizes within the research and study sample significantly deviated from the expected variability attributable to sampling error. This determination was crucial in identifying the appropriate model for aggregating effect sizes, as illustrated in Table  4 .

Table 4 reveals that the heterogeneity test results signify significance (< 0.001 = p). The value (Q = 139.1) is accompanied by degrees of freedom (6), surpassing the critical Chi-squared value (X 2 ) and indicating a 95% confidence interval. Moreover, the heterogeneity ratio (I 2  = 96%) indicates a substantial degree of heterogeneity among studies. This suggests that the research and study samples do not share a common effect size, highlighting their inherent heterogeneity. Given the variation in effect sizes across studies, it is imperative to analyze them according to the random-effects model, where the common effect is the average of these effects [ 16 ]. Furthermore, Table  4 demonstrates that the common effect size, according to the random-effects model, is 0.745 with a standard error of 0.003 and a 95% confidence interval ranging from 0.436 to 0.789. This places the common effect size within the realm of substantial effect sizes, as indicated by [ 17 ]. Consequently, the impact of enrichment programs for gifted students on cognitive dimensions development, employing a quasi-experimental design, is large.

Publication Bias Assessment: The researchers employed Egger's regression analysis test, yielding a "t" value of 0.3211 with degrees of freedom (5) at a p- value 0.7623. This statistically non-significant value suggests an absence of publication bias.

4.4 Fourth question results

“To what extent does the average magnitude of the impact of enrichment program interventions targeting future problem-solving skills for gifted students vary in terms of their cognitive dimension development according to quasi-experimental designs, as a result of participant type (males, females, both) and educational stage (elementary, middle, high school)?”

To answer this question, the researchers used the Analysis of the modified variables: Researchers employed modified analysis to discern whether the effect of enrichment program interventions for gifted students on the development of their cognitive dimensions differs depending on the type of participants (males, females, males and females together), and the academic stage (primary, intermediate, secondary). This is evident from Table  5 ,

It is apparent from Table  5 that there are statistically significant differences in the average effect size according to the type of participants (males, females, males and females together), in favor of both males and females together (P < 0.001). Additionally, statistically significant differences were found according to the academic level (primary, intermediate, secondary) in favor of the secondary level (P = 0.001).

5 Discussion

The primary aim of the present study was to conduct a rigorous analysis with the intent of elucidating the impacts of enrichment program interventions on the development of prospective problem-solving skills and the cognitive dimensions within a cohort of gifted students. This was achieved through the employment of both correlational and quasi-experimental research designs, with the purpose of unveiling the moderating factors intrinsic to these effects. For this purpose, a total of ten research inquiries were subjected to scrutiny, encompassing three correlational studies and seven quasi-experimental investigations conducted from 2010 to 2023. The ensuing discourse will center upon the findings pertaining to each of the study's research questions, which are as follows:

This section starts with the first question enquiring about the effect size average of the impact of enrichment program interventions based on future problem-solving skills for gifted students in fostering their cognitive dimensions, according to correlational designs. The results, in response to this question, have determined that the common effect size, as per the random-effects model, attains a value of 0.531 with a standard error of 0.004 and 95% confidence intervals (0.317, 0.694). This effect size, for future problem-solving program interventions, resides within the realm of substantial effects, in accordance with what [ 17 ] has elucidated. Consequently, the influence of future problem-solving program interventions on the development of cognitive dimensions in gifted students, utilizing the correlational design, is indeed large. Researchers expound that future problem-solving programs are efficacious in the cultivation of cognitive dimensions among gifted students, guiding them towards success in both their personal and professional lives. It is noteworthy that education specialists must direct enrichment programs to meet the needs of gifted students in this field and design programs commensurate with the knowledge and skills of gifted students at various educational stages. Moreover, these programs must be oriented toward enhancing critical and creative thinking skills among gifted students in both academic and non-academic domains, while providing the requisite resources to accomplish these objectives. Interest in the development of future problem-solving programs for gifted students is steadily increasing, as problem-solving is deemed an exceedingly crucial skill in the modern age. Cognitive dimensions for problem-solving skills encompass critical and creative thinking, idea and problem analysis, theoretical and practical thinking, and the ability to make appropriate decisions [ 24 , 46 ]. Research suggests that future problem-solving programs contribute to the development of critical and creative thinking capabilities among gifted students. Indeed, [ 8 ] study demonstrated that enrichment programs for future problem-solving assist gifted students in developing their analytical and critical thinking skills, thereby enhancing their academic performance. Future problem-solving programs also aid in the development of theoretical and practical thinking. A study conducted in 2021 revealed that enrichment programs for future problem-solving help gifted students enhance their ability to analyze problems theoretically and practically, thereby enabling them to make sound decisions in diverse situations [ 54 ]

Furthermore, the current study's findings align with those conducted by [ 43 ], which showed that enrichment programs for future problem-solving facilitate gifted students in developing their ability to make appropriate decisions, thereby assisting them in achieving success in their personal and professional lives.

Then, we discuss the second question enquiring about the extent to the effect size average of the impact of enrichment program interventions targeting future problem-solving skills for gifted students vary in terms of their cognitive dimension development according to correlational designs, as a result of participant type (males, females, both) and educational level (elementary, middle, high school. To respond to this question, researchers used a modified analysis to discern whether the impact of future problem-solving intervention programs for gifted students on the cultivation of their cognitive dimension skills, as per correlational designs, indicated statistically significant differences in effect size attributed to the participant variables (males, females, males and females together), favoring the female participants, and the educational stage (elementary, middle, secondary), favoring the secondary stage. Researchers expound upon these findings by acknowledging the divergent aptitudes and requirements of gifted students across various educational stages. Indeed, students in the lower echelons may necessitate a greater emphasis on fundamental skills, while those in the higher echelons yearn for more substantial challenges. The nature of talent also varies among students participating in enrichment programs, with some demonstrating academic inclinations and others displaying artistic or socio-emotional proclivities. These differences significantly influence their responses to program interventions. The enrichment programs exhibit variances in terms of content, session duration, resource availability, and the expertise of supervisors, all of which contribute to disparities in the magnitude of the effect. Thus, disparities in the effect size of enrichment programs can be attributed to multiple variables related to the nature of the students, program content, and methodologies, as elucidated by experimental designs in this domain. Studies conducted in this domain [ 5 , 56 ] have demonstrated the pivotal role played by participant characteristics in determining the effect size of enrichment programs on the cognitive dimensions of gifted students. Results have shown statistically significant differences in the effect size of enrichment programs in favor of females. This might be attributed to gender disparities in educational interests, proclivities, and career aspirations, all of which influence the responses of gifted students to enrichment program interventions. Regarding the educational stage, studies [ 32 , 38 ] have indicated substantial variations in the effect size of enrichment programs across different educational stages. It has been revealed that the secondary stage yields superior results in the development of cognitive dimensions in gifted students compared to other stages. This can be attributed to variations in academic achievement levels and cognitive maturity among different educational stages, which impact the responses of gifted students to enrichment program interventions.

Enrichment programs for gifted students aim to provide educational opportunities that transcend standard curricula and intellectually challenge advanced learners. The effectiveness of such programs has been the subject of diverse research studies. Many studies have shown that participation in enrichment programs positively impacts the academic performance of gifted students. Research conducted by [ 29 ] found that students who participated in enrichment programs exhibited higher academic achievements, increased motivation, and enhanced critical thinking skills compared to their non-participating peers. Enrichment programs often offer opportunities for gifted students to explore their talents and develop advanced skills in specific fields. Research conducted by [ 39 ] elucidated that specialized enrichment programs focusing on specific areas such as mathematics, science, or the arts can accelerate learning and develop expertise.

The third question enquiring about the effect size average of the impact of enrichment program interventions based on future problem-solving skills for gifted students in fostering their cognitive dimensions, according to quasi-experimental designs, is then discussed. Hence, to address this question, an analysis of heterogeneity was employed to discern whether the observed variability in the research sample exhibited significant disparities beyond the anticipated variance due to observational error. The findings unequivocally elucidate the significant influence of enrichment programs for gifted students on the cultivation of their cognitive dimensions. These programs center their focus on stimulating critical and imaginative thinking in gifted students, who are the quintessence of cognitive evolution. They proffer challenges that nurture their loftier intellectual capacities and kindle unconventional problem-solving approaches and innovative ideation, thereby augmenting their cognitive capital [ 26 , 44 ]. Furthermore, these educational initiatives encompass projects and experiential learning activities, affording students the opportunity to construct knowledge through practical application. The enrichment programs hone gifted students' acquisition of advanced cognitive skills, encompassing critical thinking, problem resolution, and decision-making, thereby impacting the evolution of their cognitive dimensions [ 40 , 41 ]. Researchers elucidate that enrichment programs for gifted students wield a formidable influence on the augmentation of their cognitive dimensions. These programs are geared toward nurturing critical and creative thinking, which constitute the bedrock of cognitive development. They instill challenges designed to foster higher mental faculties, stimulating students to employ alternative methods in problem-solving and conceiving fresh ideas, thereby amplifying their cognitive endowment.

These programs hinge upon skills-based learning, affording gifted students opportunities to construct knowledge through experiential acquisition. They train students in the acquisition of elevated cognitive skills such as critical thinking and problem resolution, which significantly contribute to the enhancement of their cognitive dimensions. For these reasons, a multitude of studies have demonstrated the efficacy of enrichment programs in advancing the cognitive dimensions of gifted students.

The study's results concur with several extant research endeavors, much like the study conducted by [ 30 , 34 ], which evinced that the enrichment training program substantially facilitated the acquisition of critical thinking and problem-solving skills among gifted students. A study by [ 34 ] revealed a marked increase in the levels of critical and creative thinking among gifted students. The findings of a study by [ 31 ] demonstrated that enrichment programs significantly contributed to the enhancement of cognitive thinking skills, such as critical thinking and problem-solving, among gifted students.

Finally, this result related to question four, enquiring of to what extent the average magnitude of the impact of enrichment program interventions targeting future problem-solving skills for gifted students vary in terms of their cognitive dimension development according to quasi-experimental designs, as a result of participant type (males, females, both) and educational stage (elementary, middle, high school is discussed. To respond to this question, researchers undertook an elucidation of results, which unveiled statistically significant discrepancies in the mean effect size upon participant type (males, females, males and females together), favoring both males and females jointly. Furthermore, statistically meaningful distinctions about the educational level (elementary, middle, secondary) were unearthed, favoring the secondary level.

The findings in these studies revealed statistically significant disparities in the mean magnitude of the impact based on participant type and educational level. Concerning participant type, studies discovered disparities in the impact size of enrichment programs in favor of both males and females jointly, indicating that enrichment programs can be beneficial to both genders alike. Researchers expound this by suggesting that gifted individuals in the realm of sciences, such as critical and creative thinking, foster within themselves the zeal and enthusiasm to further their learning in this domain. The enrichment program proffers a diverse array of educational enriching activities, thus aiding in honing the students' skills in various scientific fields. The selection of students partaking in the enrichment program is contingent upon their distinguished prowess in the sciences, signifying their aptitude to assimilate and apply advanced scientific concepts more effectively. Regarding educational level, studies [ 14 , 22 ] found disparities in the impact size of enrichment programs in favor of the secondary level, implying that enrichment programs may be more efficacious in nurturing the cognitive abilities of gifted students in subsequent educational stages. This may be attributable to variations in mental and educational maturity levels and interests across educational stages.

This can be expounded upon by positing that gifted students possess greater experience in various academic subjects and exhibit higher levels of mental and intellectual maturity, rendering them more adept at comprehending and applying complex concepts and skills offered in enrichment programs.

Additionally, the educational interests of gifted students evolve across educational stages, as they become more specialized in specific fields and develop particular skills. Hence, enrichment programs that concentrate on these fields and skills may be more effective in enhancing their intellectual capacities [ 36 ]. These findings align with the study conducted by [ 23 ] to evaluate the effectiveness of the enrichment program employed by high school students in advancing their athletic intelligence and sports thinking. The results demonstrated significant enhancements in the levels of athletic intelligence and sports thinking among students who participated in the enrichment program. They also concur with a study by [ 8 ] assessing the efficacy of the enrichment program utilized by elementary and middle school students in improving their scientific skills. The study aimed to evaluate the effectiveness of the scientific enrichment program in enhancing the levels of scientific, intellectual, and creative thinking among gifted students in elementary and middle schools. The results of the enrichment program were assessed using scientific intelligence and scientific and creative thinking assessments, and the results of students who participated in the enrichment program were compared with those of a group of students who did not participate. The results indicated that the enrichment program achieved positive results in improving the levels of scientific intelligence and scientific and creative thinking in students.

6 Conclusion

In this study, the researchers analyzed the outcomes of previous research published between the years 2010 and 2023. These works delved into the future problem-solving skills within the domain of nurturing the gifted. This analysis was conducted via the meta-analysis approach, which hinges on the examination of results from prior studies, coupled with quantitative evaluation through various statistical procedures. These include impact assessment, magnitude assessment, and control of potential publication bias. After thorough examination of databases and journals, as many as 288 studies relevant to the study's title and objectives were identified. Studies that did not align with the prescribed study criteria were excluded, resulting in a reduction of the studies to ten. The study primarily focused on ascertaining the effectiveness of interventions pertaining to future problem-solving programs in developing the cognitive dimensions of gifted students. This evaluation was conducted according to correlational and quasi-experimental designs. Furthermore, the investigation sought to determine the average variance in the impact size of these future problem-solving interventions on the development of cognitive dimensions among gifted students, categorized by participant gender (male, female, and mixed) and academic stage (primary, middle, and secondary). The study's findings in this regard indicated that the effectiveness of future problem-solving program interventions, under both correlational and quasi-experimental research designs, demonstrated a high degree of effectiveness. As for the examination of the average variance in the impact size of future problem-solving program interventions on the development of cognitive dimensions, considering the participant type and academic stage, the results displayed disparities based on the research designs. Studies adopting correlational research designs pointed to differences based on academic stage, favoring the secondary stage, and gender-based differences favoring females concerning participant type. On the other hand, studies employing quasi-experimental research designs showed variations based on academic stage consistent with the findings from correlational research, favoring the secondary stage. However, concerning the participant type, there were statistically significant differences favoring both males and females.

7 Recommendations

In light of the findings derived, the researchers proffer the following suggestions:

Studies of this nature, as pursued in the current research, are exceedingly scarce in the realm of gifted education, and their outcomes cannot be universally extrapolated. Hence, an imperative requirement manifests for the execution of further investigations to validate result precision.

Those entrusted with the formulation of enrichment programs for the gifted ought to be rooted in the cultivation of future problem-solving competencies, while taking into account a multitude of factors, notably their alignment with the age bracket, gender, and societal cultural context. It has been observed that differential impact surfaces across the more advanced developmental stages.

8 Future proposed studies

Future studies suggest that meta-analysis studies are needed to reveal the effect of future problem-solving skills on other variables (psychological, social, and emotional) through experimental and correlational designs. It is also recommended that more meta-analysis studies on enrichment programs based on future problem-solving on studies published in peer-reviewed journals to clarify the effect of culture and form a clear picture of the results.

9 Limitations of the study

Like any other study, this research has some limitations. For example, the study targeted only the previous literature available in Arabic and English, ignoring her studies conducted in different languages, which may have some biases. It is to be noted that the studies related to males were very few compared to those about females or both sexes. The study included only those with open sources due to the difficulties in accessing non-open source articles. Furthermore, while searching, about 32 reports were not retrieved, which might have some influence on the study findings.

Data availability

The data used to support the findings of this study are available upon request. However, please note that the data for this article were generated as part of a project funded by King Faisal University. Due to the nature of the funding and to protect intellectual property rights, the data cannot be shared without prior permission from King Faisal University.

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This work was supported by the Deanship of Scientific Research, Vice President for Graduate Studies and Scientific Research, King Faisal University, Saudi Arabia [Grant No. 241554].

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Contribution: The contributions of each author to the research paper are as follows: Khaled Elballah—Formal Analysis—Funding Acquisition Norah Alkhalifah—Investigation.—Research Methodology Asma Alomari—Conceptualization—Data Curation Amal Alghamdi—Project Administration—Resources—Software.

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Elballah, K., Alkhalifah, N., Alomari, A. et al. Enhancing cognitive dimensions in gifted students through future problem-solving enrichment programs. Discov Sustain 5 , 248 (2024). https://doi.org/10.1007/s43621-024-00470-5

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