As a neuropsychologist, I specialize in the science of brain-behavior relationships. It's my mission to make these things relevant for you in real life. The following are some of my  thoughts on the connection between neuroscience and dyslexia tutoring:

Dyslexia tutoring approaches that are based in the science of reading, such as Orton-Gillingham-based methods, capitalize on this principle in the following ways: 

Success => Dopamine => I want to try that again.

1. Systematic approach meets the student at their current point of mastery, makes no assumptions, and slowly builds on mastery but only at the pace that is determined by the student.
2. This creates a pattern of success.
3. We know that successful task completion (no matter how small) creates a little burst of dopamine in the brain. Dopamine is one of the key neurotransmitters involved in reward and motivation.
4. Repeated connection between a task, successful completion, and the associated dopamine reaction: make the behavior more likely to occur in the future. 

Repeated sound-symbol practice => stronger white matter pathway => more efficient reading

1. Multisensory approaches, with frequent error-free/guess-free repetitions, bolster pathways in the brain.
2. We see this in neuroimaging studies, which document growth in the white matter tracts of the reading network pre- and post-Orton-Gillingham tutoring.
3. The pathway of fibers that connects the symbol/letter recognition part of the brain with the sound/word part of the brain becomes stronger with time.
4. This is what leads to increased efficiency in reading.

Our brains are learning superheroes. For individuals with dyslexia, it's just a matter of learning how that brain learns and then teaching in that way.