The authors suggest that individuals have a "single limited pool of mental resources that support working memory" and "that working memory activities that include difficult processing leave fewer resources to support memory storage". This is truly evident in math word problems. My child reads each word but cannot ferret out the important details so it seems that after about the first 5 or 6 words he is only speaking the words out loud and not comprehending what he is reading. By the time he gets to the actual question sentence he has forgotten what he just read in the sentences before. As a help, I have him try to look these problems not as math but as a mystery where he can look for clues. Now when he reads aloud a problem, any number he sees he says it louder than the other words, which I imagine would be a form of rehersal. After reading through the problem he then goes back and writes down the numbers (what we call facts) and trys to write out the problem. Hopefully by writing down the information it may free up his "limited working memory storage". Unfortunately this process still requires a few prompts to make it happen and this is only in preparation to do the actual problem. It seems that even a simple math word problem is really quite complicated when you break down into individual processes and can see how it can overload a child's working memory just in the details and how information gets pushed out when they search out what steps to take next.
Back in the 60's we learned the multiplication tables in 4th grade. I vividly remember the flash cards and to this day see the image of the cards in my head. I believe the book calls this semantic or stored memory. I don't remember ever learning why 8X8=64, it just was. What was also good was by having the total image of the each multiplication fact memorized it help in remembering the relationship of the numbers which meant that that learning division wasn't really a learning new process, it was just recalling abd re-using longterm memory.
To the question, would memorizing the multiplication tables inside and out, backwards and forwards, so the information becomes longterm memory in a visuo-spatial way, thereby freeing up the child's working memory for the "deciphering the question" be too much for a third grader who struggles in math? We have worked with the cards but have never pushed too hard.