I should have clarified . . .
The way I have set up my iPOD is as one large Playlist with a couple hundred songs. However, I have loaded/listed the songs in groups (e.g. 1 - 10 are classical, 11 - 20 are jazz, 21 - 30 are new age, etc.) My idea is to click on where I want to start in the Playlist and then (simply!) have the tunes play one after the other in the listed order. That is, if I start at Song #11, then I would expect #12 to follow, then #13, etc. However, the random shuffling has a mind of its own. For example: It will start at 8, then it jumps to 23, then 4, then 68, then 8 (again), then 9, etc. Most annoying. No rhyme nor reason.
My 4th Generation is not an iPOD SHUFFLE; it is the iPOD TOUCH - which has the shake/shuffle feature. (The "shake" can be turned off in Settings; however, "shuffling" cannot be).
The tips found in the links provided in earlier posts are for different Control/Settings panels. My iPOD does not have iTUNES (pink/blue icon), but an app called MUSIC (orange icon) - which came pre-installed. The iTUNES and MUSIC app layouts are not the same, as far as I can tell.
I found a workaround of sorts: I created a new Playlist containing only a select group of 20 songs. It still randomly goes through the list - shuffles the order of play - but no tunes outside of this list are played.
It just baffles me that the function of shuffling cannot be de-activated for the whole device (and re-activated, when desired). You know, the way one can lock or unlock screen rotation on an iPAD, for example.