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Merton Bland regularly posts to the TESL-L list. Unfortunately, little of what he has to say is helpful. One of his favorite arguments goes something like this: "If our job is to bifurcate the native and target languages, any instrument (such as a bilingual dictionary) which forges chains to tie the two together is counterproductive." He backs this up with arguments like this: "A true bilingual does his processing of each language in a different hemisphere of the brain." Sometimes he changes hemispheres to lobes.
If there's a need for "bifurcation", it is in separating evidence from ideology.
The claim that a second language is processed in the other hemisphere of the brain is completely absurd as the studies cited below will show. The idea that it is processed in a distinct lobe may or may not be more correct, but it remains misleading.
It is generally agreed that there are five major lobes in the brain. The definition of 'lobe', however, is rather ambiguous and minor lobes are discussed, but not always agreed upon. Furthermore, two areas of the brain that are mainly involved in language are Wernicke's area, which spans the region between temporal and parietal lobes, and Broca's area, which is in the frontal lobe. In other words, language activity usually occurs in different lobes in monolinguals, too, not just in bilinguals.
While late L2 learners do seem to activate different (though typically adjacent) areas of the brain, the research on the overlap or lack thereof of L1 and L2 brain activation is equivocal. A summary by Vivian Cook of some available studies is here.
Bland's point is that teachers should avoid connections between the L1 and L2 (through translation) to dissociate them in the brain. Yet, one idea that seems to come from these brain studies is that the most successful bilinguals are actually those who seem to have the greatest overlap, not the greatest separation. This might mean that connections are good, not bad. Or not. Either way, they are likely inevitable.
Personally, I don't think the brain studies are ready to tell us much about how we should go about teaching language, but they're fun to look at.