تأثیر راهبردهای آموزشی خطی و غیرخطی بر تغییرپذیری هماهنگی پرتاب آزاد بسکتبال در کودکان

Extended Abstract
Background and Purpose
Training motor skills presents notable challenges due to the complexity of exercises and individual differences among learners. Traditional linear methods often focus on replicating movement patterns and execution processes, assuming that imitating expert models leads to optimal outcomes. However, this assumption frequently fails, especially in diverse populations. Excessive repetition and isolated muscle activation—particularly in children—may result in maladaptive motor behaviors and overuse injuries. In contrast, contemporary approaches such as Nonlinear Pedagogy, including the Constraints-Led Approach (CLA) and Differential Learning (DL), emphasize variability and adaptability. These methods better equip athletes for dynamic, unpredictable environments typical of field sports. Research indicates that coordination development through differential learning occurs more efficiently and rapidly than with linear techniques. Accordingly, modern pedagogical strategies offer a more holistic and individualized framework for motor skill acquisition. This study investigates the comparative effects of linear and nonlinear instructional methods on learning basketball free throw performance, aiming to identify which approach yields superior skill development.
 
Methods
This study involved 45 healthy male students aged 9–10 years from elementary schools in Kerman, selected through a combination of random and convenience sampling. Inclusion criteria required participants to be in good health with no visual or motor impairments, ensuring a uniform baseline for motor performance assessment. Participants were randomly assigned to three instructional conditions representing distinct coaching approaches. Over four weeks, each group participated in weekly 40-minute training sessions, organized as a 10-minute warm-up, 30 minutes of targeted practice, and a brief cool-down. Of the initial cohort, 28 students who completed all sessions were retained for post-intervention analysis, providing a complete data set for evaluating learning and coordination outcomes.
 
The linear training group received instruction through holistic demonstrations of whole-pattern movements coupled with command-style feedback. Corrections were provided only when attempts fell outside predefined performance boundaries, reinforcing a tolerance for minor errors while emphasizing overall movement efficiency. Demonstrations began with an overarching view of the complete movement and progressively broke down into constituent segments across four sessions to facilitate cognitive and motor chunking. By contrast, the CLA (constraint-led approach) and DL (dynamic limbs) groups were exposed to systematically varied task constraints designed to foster motor variability and adaptability. These constraints included alterations in ball size and material, hoop height, shooting distance, and target type, as well as alternating dominant and non-dominant hands, varying foot positioning, changing visual conditions (eyes open vs. eyes closed), adjusting support levels, and modifying body orientation during shooting. The aim was to explore how varied perceptual-motor contexts influence skill acquisition and transfer.
Baseline assessments captured each participant’s height, and nine inertial measurement unit (IMU) sensors were affixed to anatomical landmarks on the upper limbs and trunk to enable comprehensive kinematic analysis. After calibration, participants completed ten practice trials prior to the pre-test, which consisted of ten basketball free-throw attempts scored under a modified Ifred accuracy protocol (Ifred, 1976). The intervention consisted of eight 45-minute sessions spread over four weeks, followed by a post-test mirroring the pre-test to assess changes in shooting accuracy and coordination. Data were analyzed using repeated-measures ANOVA and dependent t-tests, focusing on the RMSe (root mean squared error) values of the coordination index. Statistical processing employed MATLAB and SPSS to ensure robust cross-method validation. The results indicate that the CLA and DL groups yielded greater improvements in coordination variability and transfer to novel task contexts compared with the linear training group, suggesting that structured variability and constraint manipulation can enhance motor learning in pediatric populations. Implications for school-based physical education and the design of age-appropriate, adaptable coaching curricula are discussed, along with limitations and directions for future research.
 
Results
The present analysis indicates that both the Constraints-Led Approach (CLA) and Differential Learning (DL) methods produced substantial improvements in coordination variability across the elbow, wrist, and shoulder joints during basketball free-throw performance in boys aged 9–11 years. Across the three instructional conditions, the CLA group exhibited the most pronounced enhancement in joint coordination variability, surpassing both the DL and linear training groups. Statistical comparisons demonstrated that the CLA group achieved significantly higher gains in variability than the DL group, whereas no significant difference emerged between the DL and linear training conditions in this metric. These findings suggest that the structured perturbation of practice conditions inherent to CLA can more effectively diversify motor strategies and promote exploration of viable coordination patterns.
Regarding performance outcomes, both CLA and DL groups showed notable improvements in free-throw accuracy after the intervention period. Yet, there was no statistically significant difference in accuracy scores between the CLA and DL modalities, indicating comparable efficacy for accuracy gains within nonlinear instructional frameworks. In contrast, the linear training group failed to exhibit meaningful progress in free-throw accuracy, highlighting the limited effectiveness of conventional repetitive instruction for skill acquisition in this younger cohort. The lack of improvement in the linear condition underscores the potential inadequacy of rote practice for fostering transferable motor skills amid developing youths.
A key finding is the association between enhanced coordination variability and improved motor performance within nonlinear training contexts. The CLA-driven enhancement in coordination variability correlated with better execution under dynamic and unpredictable task demands, aligning with the hypothesis that increased movement variability can facilitate adaptive responses. The deliberate manipulation of task constraints — including variations in ball size and material, hoop height, shooting distance, and body orientation — appears to be central to promoting exploratory movement strategies and the emergence of individualized, efficient motor solutions. These results reinforce the value of nonlinear pedagogical frameworks in youth sport settings, where fostering variability and adaptability may yield more robust motor learning than linear approaches that emphasize repetition and imitation.
Together, the evidence supports incorporating task variability and personalized challenges into practice designs to accelerate coordination development and improve performance in complex motor tasks such as basketball free throws. Implications for coaching, curriculum design, and future research directions are discussed, with attention to dose–response relationships, developmental considerations, and long-term transfer to game contexts.
 
Conclusion
This study highlights the superiority of nonlinear training methods—particularly the Constraints-Led Approach—in enhancing motor coordination and performance in young basketball players. CLA-based instruction led to the most significant improvements in joint coordination variability and free throw accuracy, outperforming both DL and linear methods. The findings support the theoretical premise that movement variability fosters adaptive motor learning, especially in dynamic sports environments. While DL also showed positive effects, its impact on coordination variability was not significantly different from linear training. These results suggest that manipulating task constraints is a powerful strategy for promoting individualized learning and skill acquisition in children. Coaches and educators are encouraged to adopt nonlinear pedagogical approaches in youth sports programs to optimize motor development and performance. Future research should explore long-term effects and applicability across different age groups and sports disciplines to further validate the efficacy of these methods.
Article Message
This study highlights the effectiveness of modern motor learning approaches in youth sports coaching. The findings support the integration of nonlinear pedagogy into coaching practices, emphasizing the value of task variability and constraint manipulation for developing motor skills in young athletes.
Ethical Considerations
This study was approved by Research Ethics Committee of Sport Sciences Research Institute
 (code: IR.SSRI.REC.1401.1515).
Authors’ Contributions
All authors contributed equally across all stages of the research.
Conflict of Interest
The authors declare no conflicts of interest.
Acknowledgments
The authors gratefully acknowledge all individuals who supported this research.