I work in a school where most lessons are planned with sensory motor function in mind, where art, language, math, etc are shown to be intertwined, and where students often preform higher on standardized tests, despite me never giving them a single, formally graded test the rest of the year.
For more than half of the children that transfer into my school after spending 3 or 4 years in a public school (factory structured, lecture based model), I have to spend the initial months detoxifying the child, showing them that it's okay to be creative, unsuppressed, and use their interests to learn.
The developing brains of young children are extremely sensitive to visual, tactile experiences that the various arts provide. Their psychology is very different from an adult's, yet many adults often project their own learning styles onto them. This leads to continuously keeping subjects separate (such as art & math). While key concepts should initially be presented in isolation to avoid confusion, the follow up activities should combine multiple areas. In other words, expose the children to everything possible, show them how it all interconnects, and use what the child's mind is sensitive to, practicing multiple areas in conjunction and forming deep understanding.
I find it highly likely that the statistically significant increase in critical thinking, social tolerance, and historical empathy that this study found not only comes from the initial exposure, but also from teachers integrating the experience into follow-up lessons / activities.