They care very much. Most other countries follow the US pretty closely.
I have a weird thing going on in my personal life where every so often a Chinese friend will suddenly ask me about something in American domestic politics that I've never heard of. And every so often I'll ask about something in Chinese domestic politics that they've never heard of.
People in other places do not care that much (setting aside the worrying possibility that this kind of thinking may be later imported to their own countries), but given the prominence of English in worldwide communication and the massive role of American media, they will read the news and either laugh or frown.
American internal problems are much more visible to the outside world than, say, Italian ones.
>They don't have to care to laugh at us for dumbing down our kids.
Why laugh? I guess they will be glad they will winning the competition. If anything, they will encourage the US to continue on the same path, they'll might even praise it.
I have a weird thing going on in my personal life where every so often a Chinese friend will suddenly ask me about something in American domestic politics that I've never heard of. And every so often I'll ask about something in Chinese domestic politics that they've never heard of.