## 5 Limitations and Prospects  
This study found that a coordinative exercise training program improved the prefrontal cortex function and the updating ability of the WM in young children. We believe this study has useful information for helping children and their parents choose extramural sports activities, and researchers in the field to design their future work. However, the limitations of the study should be recognized.  
First, the sample size of the present study was limited. We calculated the sample size before intervention, but the uncontrollable factor was that some young children dropped out of the program during the long-term intervention. Although the effect size of most results was acceptable, these results must be interpreted with caution due to the small sample size, and the conclusions should be validated on larger data sets. Second, it is worth noting that only three channels were used herein. The number and positioning of the optodes may have limited the findings. [PERSON] et al. [3] indicated that several cortical regions were activated robustly during the n-back task. This possibility needs to be investigated in the future. Third, a large variance in the hit rates of both groups in the pre-test may prevent group differences from being considered significant. This variance may be caused by the individual difference in young children's self-control ability and attention stability during the task [55]. This possibility could also be reflected in the long reaction times in young children. It should be testified by examining children who were slightly older in order to observe whether there were performance differences between the two groups in the hit rates a few years later when responses were more stable.  
Additionally, this study focused on the visual WM of young children. The materials used in the 1-back task were squares. Future research should attempt to use vocal or auditory materials to explore the relationship between coordinative exercises and auditory WM. Finally, most previous studies were focused on the relationship between different types of exercises and the entirety of the WM in children. Future research is necessary to deliver some empirical evidence for aspects that are actually being affected.  
The following is available online at [[http://www.mdpi.com/2076-3417/10/1/407/s1](http://www.mdpi.com/2076-3417/10/1/407/s1)]([http://www.mdpi.com/2076-3417/10/1/407/s1](http://www.mdpi.com/2076-3417/10/1/407/s1)), Table S1: Post hoc test results of repeated ANOVA of 2 (group: experimental group and control group) \(\times\) 2 (test time: pre-test and post-test) for six indexes of the physical fitness.  
[PERSON] analyzed behavioral experiment results and wrote the paper, and [PERSON] carried out experiments. [PERSON] reviewed and revised the paper, and [PERSON] designed the experiment and analyzed the fNIRs data. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Natural Science Foundationof China (NSFC, grant number 31771244); the National Natural Science Foundationof China (NSFC, grant number 11701029); the Education Work Committee of the Beijing Committee of the Communist Party of China (grant number 2016000020124G094); and the Beijing Education Committee (grant number SM201810029001); research funds of the Beijing Institute of Sports Science (2017); and research funds of the State Key Laboratory of Cognitive Neuroscience and Learning.  
The authors declare no conflict of interest.