Yes! Adults tend to devise instructional methods that please other adults -- thus the abhorrence of memorization. But Maria Montessori figured out, over a century ago, that there is a stage in a child's development where the brain is particularly adept at memorizing and, as your author points out, the child actually enjoys it if progress is being made.
You've brought out a very important point.
Children really like poetry that has rhyme and meter. I don’t know if girls still do jump rope, but that was all rhyme and meter years ago. I loved that sort of poetry when I went to and English school for one year, many years ago.