This is a remarkable article, a method I certainly would use.
After brushing this way I would use the tooth-drops we advise since years instead of –potentially toxic tooth-paste, always swallowed to some extent by children.

Dry Brushing Beats Dental Plaque
‘Dry brushing’ — brushing teeth without toothpaste — may be a more effective plaque remover than brushing with paste, one expert says. This study found that 128 individuals who dry-brushed over a six-month period saw plaque deposits on their back teeth drop by 67%, compared with plaque build up found on their teeth before the dry-brushing regimen began. Gum bleeding due to gingivitis (gum disease) also fell by 50%.
One should use a soft, dry brush which seems to scour away built-up bacterial plaque better than a moistened one. If bristles feel stiff, ‘relax’ them by running your thumb through them before brushing. Begin inside, finish out. The inner surfaces of the bottom row of teeth should be brushed first, before saliva buildup develops. Proceed to the inner top level of teeth next, then move to the outer surfaces. The dry-brushing process should take about a minute and a half.