The research method was semi-experimental, employing a pre-test-post-test design with a control group. The target statistical population included all children aged 5 to 7 years in Shahrood City. The sample size consisted of 30 children aged 5 to 7 years, selected using a random cluster sampling method and randomly divided into two groups of 15: experimental and control. The researcher's learning test, which contained 30 questions, was the tool used for data collection. The validity of this test was confirmed through content validity by two experts in the field of education and two experienced preschool teachers. Additionally, the reliability of the test was assessed using Cronbach's alpha, with a value estimated at 0.80. To analyze the research hypotheses, the analysis of covariance statistical test was conducted using SPSS version 20 software. Prior to the intervention, consent was obtained from the teachers, and the program was implemented over 16 sessions. The findings indicated that gamified deliberate practice positively affects the learning of mathematical concepts among preschool children aged 5 to 7 years in Shahrood City (p < 0.05). Based on the results of this research, it is recommended to use a deliberate practice strategy to enhance the learning of mathematical concepts in preschool centers for children aged 5 to 7 years. Furthermore, preschool teachers should receive the necessary training to effectively implement deliberate practice.
Keywords: Child, Deliberate practice, Math, Preschoolers, practice
Introduction
Preschool is a crucial developmental stage for children, significantly impacting their future growth and education (Evtimov & Petrović, 2021). Mathematics, in particular, is one of the foundational skills that preschoolers begin to develop and that continue to influence their educational journeys. Mastery of mathematical concepts at this early age is vital, as it enhances children's cognitive abilities and equips them to think logically, strategically, creatively, and critically (Stozharova, 2024). Many math skills are developed in the preschool years, and children's early experiences with math form the foundation for math learning. However, many preschoolers often face challenges, particularly in distinguishing between addition and subtraction.
 This confusion is serious—it can lead to difficulties in daily life (Peng et al., 2020) and markedly affect academic performance in elementary school. A widely accepted belief in educational circles is that learning mathematics necessitates practice, which allows students to engage in problem-solving and manage cognitive demands when faced with more complex tasks. One intervention method proposed for enhancing learning in this area is "deliberate practice" which consists of targeted, goal-oriented activities aimed at improving specific skills.
This structured form of practice is meticulously planned, enabling learners to assimilate information effectively and practice frequently (Williams & Hodges, 2019). Overall and based on what has been stated, it can be said that research on the role and impact of deliberate practice is not extensive, and most studies have focused on procedural skills, with fewer examinations of conceptual skills. Given the limited research regarding the efficacy of deliberate practice, especially for children under 7 years old, this study aimed to explore its impact on preschool children's mathematical understanding, specifically among those aged 5 to 7 years.
Materials & Methods
This study used a semi-experimental method with a control group. The population consisted of all 5-7-year-old male and female preschool students in Shahrood city. The sample included 30 students (15 boys and 15 girls), with an average age of 5-7 years, selected through random cluster sampling and randomly assigned to control and experimental groups. Inclusion criteria were being aged 5-7 and not having a math or other disorders. The exclusion criterion was missing more than one session during the study. The data collection tool was a researcher-made test designed to measure understanding of single-digit number concepts (6 questions), number reduction (6 questions), number increase (6 questions), categorization (6 questions), and pattern recognition (6 questions). The test's validity was confirmed through content validity, and its reliability was verified using Cronbach's alpha, which was 0.80.
 The experimental group participated in eight weeks of training, with two 45-minute sessions each week using the deliberate practice, while the control group engaged in regular exercises. Data were analyzed using descriptive statistics (frequency, mean, percentage) and inferential statistics, specifically covariance analysis, using SPSS version 20.
Discussion & result
The findings showed that the mean scores of the experimental group in the post-test and follow-up were higher than those of the control group. The results from covariance analysis indicated that deliberate practice had a significant and positive effect on preschool children's understanding of single-digit numbers (F=75.12, df=1/27, p<0.05), number reduction (F=70.08, df=1/27, p<0.05), number increase (F=71.44, df=1/27, p<0.05), categorization based on multiple features (F=84.18, df=1/27, p<0.05), and pattern recognition (F=76.21, df=1/27, p<0.05). These findings align with the research of McMullen et al. (2023), Balan & Sjöwall (2023), Cameron et al. (2019), Simanowski & Krajewski (2019), Brinums et al. (2017), Lehtinen et al. (2017), Clarke et al. (2016), and Mononen et al. (2014).
 The results suggest that children's capacity to focus on mathematical concepts through tasks that regulate procedural skills and working memory development plays a crucial role. Such deliberate practice, characterized by features like continuity and meaningful feedback, helps children develop problem-solving skills and handle more complex mathematical ideas. As the difficulty in practice gradually increases, children gain confidence and perseverance, facilitating learning. Moreover, the structure of deliberate practice helps orient learners’ minds toward the subject and enhances working memory capacity (MeinZ & Hambrick, 2010). Studies also indicate that structured exercises positively impact mathematical performance when consistently applied (SpitzeR, 2021). Through deliberate practice, children's cognitive development, including mathematical ability, improves. Unlike mechanical or repetitive drill, deliberate practice involves significant thinking, problem-solving, and reflection to analyze and conceptualize skills (Lehtinen et al., 2017). This type of practice fosters a deep understanding of the subject and shares many traits with self-directed learning. Additionally, because deliberate practice is teacher-led (Ericsson, 2020), this aspect further contributes to its effectiveness in enhancing children's performance in learning mathematical concepts.
Conclusion
It was found that deliberate practice positively influences children's ability to learn mathematical concepts among 5- to 7-year-olds. Based on the results of this study, teachers and educators are recommended to incorporate deliberate practice into preschool programs to ensure the development of essential basic mathematics skills. Integrating this approach into math assignments can help facilitate children's understanding and comprehension of mathematical concepts. By enabling children to succeed in learning fundamental math skills, this method also lays the foundation for fostering a positive mindset towards mathematics.