What does 'expand on' mean in the context?

Question

The Merrima Webster defines expand on as to speak or write about (something) in a more complete or detailed way : elaborate on, but the meaning in the context appears to me quite different. I think it just means to increase in extent, number, volume, or scope (a definition of expand by the same dictionary). Which fits the context better?

Though we are marching toward a more global society, various ethnic groups traditionally do things quite differently, and a fresh perspective is valuable in creating an open child. Extensive multicultural experience makes kids more creative (measured by how many ideas they can come up with and by association skills) and allows them to capture unconventional ideas from other cultures to expand on their own ideas. As a parent, you should expose your children to other cultures as often as possible. If you can, travel with your child to other countries; live there if possible. If neither is feasible, there are tons of things you can do at home, such as exploring local festivals, borrowing library books about other cultures, and cooking foods from different cultures at your house once a month, interviewing someone you know who is from a different country, watching a TV show online from a different country, and practicing words in a different language.

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Answer 1

I have always understood "Expand on" to mean the same as the given definition. For instance:

• Standard newspaper style begins each item with a headline and a nutgraph (nutshell paragraph) that provide all the essential information. Following paragraphs then expand on that by providing more and more specific details. (The idea is that the item could be literally cut off with scissors at any point and still be suitable for publication.)
• Some editions of the Encyclopedia Britannica began articles that could be understood by almost anyone (e.g. suitable for a grade 9 "research" essay), and then followed them with a much more detailed or technical article (suitable for college level readers).
• Today, people do the same thing when they provide a "TL;DR:", followed by the long version.

Just because someone has published a book doesn't mean that their spelling, grammar, idiomatic word usage, etc. is 100% perfect.

I suspect that by "to expand on their own ideas" would have been better written as "to expand their own ideas", or "to add to their own ideas", or even "to complement their own ideas".