It's a good bet that they're aphids.

If so, you can squish them; or wipe them off; or spray insecticidal soap, diluted according to label directions, directly on them.

Whatever your choice, repeat as needed.

If they were aphids I thought they would move. They are completely stationary. Please let me know either way if that information changes (or not) the above answer. Thank you!

They look like scale. Hand wipe each affected leaf c 1:10 alcohol:water solution.They should come easily off the leaves.
Repeat process in 5 days or so.

Do you have a magnifying glass? If so, please look at the spots and tell us if they have legs.

Seriously doubt they're scale -- still betting on aphids which don't necessarily move all that much.

As luck would have it my kids actually have a magnifying glass and near as I can tell they don't have legs, but they do seem to be fuzzy when viewed up close. Also, the underside of the leaves is almost solid white (should be green) and it is only a problem on new growth leaves. The existing foliage appears unaffected. hopefully these clues will help. I would like to treat it asap, but also want to make sure I'm helping and not making things worse... Thank you!

White spots on leaves should be distinguished from the white or light gray powder caused by Powdery Mildew.

You said they could be easily wiped off. Please do so. Or wash them off w/ a harsh water spray.

Repeat as needed.

Another thought -- or take them to your county's Extension Services office.

If you do so, please post the answer to update us all.

You can locate that office w/ this map:
http://www.csrees.usda.gov/Extension/

Here is a link that might be useful: locate your county's Extension Service office