LOG means "level of giftedness" or some variant thereof.
My youngest, like your ds, has wildly swinging achievement scores. In our case, we're really leaning toward divergent thinking processes. She rarely looks at problems the way the test designer did and can therefore come up with some really creative, but sometimes wrong, answers.
Re science being higher than math, they are testing different things, but about 1/2 of the science test is "thinking skills." Did he do poorly on both the math problem solving and math computation parts of the ITBS (that may not be the exact wording)? The problem solving part would fall more into the "thinking skills" area again where I would expect to see more overlap btwn scores.
