Well, towards American values, of course....
You see, the notion of progress or improvement is meaningless without some standard toward which said progress or improvement is made. And in the case we're discussing, the standard is always us. To put it bluntly, to whatever degree some African nation begins to resemble a western one after embracing Christianity, it can therefore be said that the nation in question has improved or made progress.
(And coupled with such cheers over improvement, of course, are jeers over the hopelessly backward and primitive ways the newly-Christianized culture has thankfully left behind.)
For my own part, this all seems quite ethnocentric and racist, not to mention extremely selective when it comes to evaluating Christianity's influence. For example, to gush over the fact that even black people can be trained to listen to Bach instead of savagely killing one another is to assume that Bach's music (along with that of other white European composers) is objectively good. And moreover, such criteria also forgets that Christians themselves are often rather bloodthirsty and prone to beat the drums for war.
Come to think of it, wasn't our religion used as justification for killing and enslaving the very people whom we claim our religion is supposed to civilize? "Isn't it ironic, don'tcha think?"
On that note, how are we to deal with the fact that America, upon which Christianity has enjoyed near-exclusive rights of influence for 400 years, is still in the business of exploiting Asia's and Africa's poor? Now I suspect the retort will be something along the lines of "Well, that's not Christianity's fault, it's the fault of other political and economic factors." OK, so let me get this straight: If there's something good about America then Christianity gets the credit, but if there's something bad, Christianity avoids the blame? Sounds like the game has been rigged from the get-go.
I think it would be prudent at this point to remind us all of what Christianity actually is. Christianity is a religion (not a world-and-life view) whose central tenet is that God assumed a human nature in order to live, die, and rise again to save sinners. If that's a fair summary, then I must admit that it completely escapes me how such a faith can be expected to instill in its adherents an appreciation for fine cuisine or, for that matter, an appreciation for silverware with which to eat it.
If we're being honest in our transformationism, we should lay at the foot of the church both the credit for our society's virtues as well as the blame for its vices. But even better, in my opinion, would be to let the earthly kingdom worry about earth, and let the church provide water, word, and wine to those whose thirst can be quenched by nothing else.