دانشگاه علامه طباطبائی روانشناسی افراد استثنایی 2252-0031 15 59 2025 12 22 The Impact of a ThinkMath Intervention Programme on the Early Numerical Skills and Mathematical Performance of First-Grade Iranian Children at Risk for Mathematical Learning Difficulties: A Timely Intervention تأثیر برنامه مداخله به ریاضی فکر کن بر مهارت‌های عددی اولیه و عملکرد ریاضی کودکان ایرانی پایه اول دبستان در معرض خطر مشکلات یادگیری ریاضی: یک مداخله به‌هنگام 237 274 20616 10.22054/jpe.2026.86778.2834 FA کامیار عظیمی دکتری روان‌شناسی تربیتی، دانشگاه شهید چمران اهواز، اهواز، ایران. منیجه شهنی ییلاق استاد گروه روان‌شناسی، دانشگاه شهید چمران اهواز، اهواز، ایران. علیرضا حاجی یخچالی دانشیار گروه روان‌شناسی، دانشگاه شهید چمران اهواز، اهواز، ایران. Journal Article 2025 07 08 Abstract Challenges with basic numerical skills at an early age can lead to substantial gaps in mathematical learning and performance, with detrimental long-term consequences. This study aimed to investigate the impact of a ThinkMath intervention program on the early numerical skills and mathematical performance of first-grade children at risk for mathematical learning difficulties. The current research is a field experiment. In total, 30 first-grade children at risk of mathematical learning difficulties who were studying in the 2022–2023 academic year were randomly assigned to experimental and control groups. The intervention program for children in the experimental group was delivered over 15 sessions of 30 to 45 minutes, while the control group received conventional classroom instruction. Compared to the control group, the experimental group showed significant improvements in early numerical skills (d = 0.73) and mathematical performance (d = 0.66), with medium effect sizes. These effects were also observable six weeks after the intervention (follow-up). Overall, the findings suggest that early numerical skills and mathematical performance in children at risk for mathematical learning difficulties are malleable and can be improved with appropriate mathematics intervention. <strong>Keywords: </strong>Early Numerical Skills; Mathematical Performance; Interventions; at Risk; Mathematical Learning Difficulties.   <strong> </strong> <strong> </strong> <strong>Extended Abstract</strong> Introduction The cognitive epidemiology literature indicates that 5% to 14% of children in the early years of education (Grades 1 to 3) do not demonstrate age-appropriate mathematical performance (Outhwaite et al., 2024) and are identified as children at risk for mathematical learning difficulties (Hellstrand, 2021). The results of the Trends in International Mathematics and Science Study in 2019 show a significant decline in the performance of Iranian students in mathematics (Yaftiyan & Abbasi, 2024). Based on this evidence, addressing children at risk for mathematical learning difficulties in the Iranian education system has come under closer scrutiny (Ghafouri et al., 2024). In this regard, a growing body of research suggests that the mathematical performance of children at risk for mathematical learning difficulties is predicted by early numerical skills (Doabler et al., 2019). Early numerical skills refer to a set of basic abilities, such as verbal counting, number relationships, and comparing numerical quantities (de Chambrier et al., 2021). Meta-analyses suggest that early numerical skills build on one another, such that children who start with the lowest levels of early numerical skills show the least growth in later mathematical performance in the absence of effective intervention (Outhwaite et al., 2024). Currently, one of the timely math interventions is the ThinkMath intervention program, which was developed based on the theoretical model of Aunio and Räsänen (2016) to reduce the achievement gap and prepare children at risk for mathematical learning difficulties for success in math (Mononen & Aunio, 2014, 2016). Despite the aforementioned considerations, the effectiveness of the ThinkMath intervention program as a supplementary curriculum has been tested in a few studies (Aunio et al., 2021; Lopez-Pedersen et al., 2023). However, the effectiveness of the ThinkMath intervention program in less developed countries, such as Iran, remains an unanswered question. Therefore, the present study aimed to investigate the effect of the ThinkMath intervention program on the early numerical skills and mathematical performance of Iranian first-grade children at risk for mathematical learning difficulties. <strong>Research Questions</strong> The research questions of this study included the following: Does the ThinkMath intervention program lead to pre-test/post-test differences between the experimental and control groups in improving basic numerical skills and mathematical performance (immediate effect)? Does the ThinkMath intervention program lead to pre-test/follow-up (6 weeks after training) differences in outcomes between the experimental and control groups (long-term effect)? Methodology The present study is a field experiment with a pretest, posttest, and follow-up design with a control group. The statistical population included first-grade children at risk for mathematical learning difficulties in Kuhdasht city during the 2022–2023 academic year. Thirty children were selected after preliminary screening using a multistage cluster sampling method. The screening process included two standard instruments: the Number Sense Brief Screener (Jordan et al., 2010) and the Number Knowledge Test (Griffin, 2009). Other data collection tools included Raven's Colored Progressive Matrices Test for Children (Raven et al., 1998), the Child Symptom Inventory, Fourth Edition (Gadow & Sprafkin, 1994), the Tests of Early Numeracy (Clarke & Shinn, 2004), and the Number Sets Test (Geary et al., 2009). ThinkMath Intervention Program: The ThinkMath intervention program consists of 15 training sessions, each 30–45 minutes long, held three times a week over 5 weeks in small groups of 4 to 8 children, aiming to prevent mathematical learning difficulties in children aged 5 to 8. Procedure: Ethical approval and research permission from the Ethics Committee of Ahvaz Shahed University (approval number: EE/1400.2.24.37358/Scu.ac.ir) were obtained. In November, the selected children were randomly divided into experimental and control groups. The pretest was conducted in December. The intervention was implemented in January and February, while the control group received conventional classroom instruction. Posttest assessments were conducted after the sessions in February, followed by a 6-week follow-up. Results Before performing the inductive data analysis, statistical assumptions for multivariate analysis of covariance were examined to ensure the validity of the results (Tabachnick & Fidell, 2019). A multivariate analysis of covariance was performed on the data, considering the basic statistical assumptions. The results from the MANCOVA analysis between the experimental and control groups, with pretest scores controlled, showed that these groups differed significantly from each other in at least one of the dependent variables, based on the Wilks's lambda statistic in the posttest. To determine this difference, a univariate analysis of covariance (ANCOVA) was conducted within the multivariate analysis of covariance (MANCOVA) on posttest scores and follow-up dependent variables, with the results presented in Table 4.   <strong>Table 1. ANCOVA results in the context of the MANCOVA on post-test and follow-up early numerical skills and mathematical performance</strong> <strong>step</strong> <strong>variable</strong> <strong>Source</strong> <strong>Sum of Squares</strong> <strong>df</strong> <strong>Mean Square</strong> <strong>F</strong> <strong>p</strong> <strong>Effect size</strong> Post-test Early numerical skills Group 2272.82 1 2272.82 71.098 0.0001 0.732 Mathematical Performance Group 30.79 1 30.79 51.074 0.0001 0.663 Follow-up Early numerical skills Group 1118.710 1 1118.710 70.467 0.0001 0.730 Mathematical performance Group 27.426 1 27.426 42.091 0.0001 0.618 Table 1 shows that the F-values of the univariate analysis of covariance (ANCOVA) for the posttest are statistically significant for both basic numerical skills and mathematical performance. In addition, Table 1 shows that the F-values of the univariate analysis of covariance (ANCOVA) for the follow-up stage are statistically significant for basic numerical skills and mathematical performance. The results indicate a significant difference in the dependent variable scores between the experimental group and the control group. Discussion This study aimed to examine the immediate and long-term effects of a ThinkMath intervention program on basic numerical skills and mathematical performance of first-grade children at risk for mathematical learning difficulties. A potential explanation for the effectiveness of the ThinkMath intervention program in improving children's basic numerical skills is explicit and regular instruction (Mononen et al., 2021). More specifically, explicit and regular instruction has the potential to deeply engage children in important mathematical knowledge content, such as understanding mathematical relationships and counting skills, and to tailor the intensity of the intervention through differentiated instruction matched to the child's needs (Aunio et al., 2021). Another promising finding of this study was that the mathematical performance of the children in the experimental group improved significantly during the intervention compared to the control group. A possible explanation is that improving children's basic numerical skills may have helped enhance their mathematical performance (De Leon et al., 2021). It has been identified that these features are useful educational elements for improving the mathematical performance of first-grade children at risk for mathematical learning difficulties (Nelson & McMaster, 2019; Clarke et al., 2023). Conclusion In summary, the research findings showed that a ThinkMath intervention program, by enhancing children's basic numerical skills at the beginning of the school year (first grade), can lead to improved mathematical performance. In other words, improved numerical skills can serve as a foundation for learning mathematics and enhancing mathematical performance in school. Acknowledgments This article is extracted from the first author's doctoral dissertation in the Psychology Department of Ahvaz Shahed Chamran University, with ethical code EE/1400.2.24.37358/Scu.ac.ir and support from the Institute for Cognitive Science Studies (ICSS). چالش‍های مربوط به مهارت‍های عددی اولیه در سنین پایین می‍تواند منجر به شکاف‍های اساسی در یادگیری و عملکرد ریاضی شود و با پیامدهای بلندمدت زیان‍باری همراه باشد. این مطالعه باهدف بررسی تأثیر برنامه مداخله به ریاضی فکر کن بر مهارت‌های عددی اولیه و عملکرد ریاضی کودکان پایه اول دبستان در معرض خطر مشکلات یادگیری ریاضی انجام شد. پژوهش حاضر از نوع آزمایشی میدانی است. درمجموع، 30 کودک پایه اول در معرض خطر مشکلات یادگیری ریاضی که در سال تحصیلی 1402-1401 مشغول به تحصیل بودند با گمارش تصادفی به گروه‍های آزمایشی و گواه اختصاص داده شدند. برنامه مداخله برای کودکان گروه آزمایشی، طی 15 جلسه 30 تا 45 دقیقه اجرا شد، درحالی‌که گروه گواه آموزش رایج کلاسی را دریافت کردند. گروه آزمایشی در مقایسه با گروه گواه، بهبود‍ معنی‍داری را در مهارت‍های عددی اولیه (73/0 = d) و مهارت‍های ریاضی (66/0 = d) با اندازه اثر متوسط نشان دادند. این تأثیرات شش هفته پس از مداخله (پیگیری) نیز قابل‌مشاهده بود. روی‍هم‍رفته،<strong> </strong>یافته‍ها نشان می‍دهد مهارت‍های عددی اولیه و عملکرد ریاضی در کودکان در معرض خطر مشکلات یادگیری ریاضی، انعطاف‍پذیر هستند و می‌توانند با مداخلات ریاضی مناسب بهبود یابند. https://jpe.atu.ac.ir/article_20616_1ae87ae126bd23a38c54b074620d3f88.pdf