In a seminal paper on the subject, Bloom wrote that that 1:1 tutoring is "too costly for most societies to bear on a large scale" and reported on their efforts to find more scalable solutions. This has become known as Bloom's 2 Sigma Problem.
Like many others working on education technology, I believe that Bloom's 2 Sigma results can be achieved and even surpassed by appropriate use of computer technology. From a number of initiatives, we're getting results that confirm this belief. While approaches vary, they have common elements:
Mastery Learning: That's what Bloom called it. Other terms are Competency Based Pathways and Proficiency Based Learning. There are nuanced differences but the basic premise is that students don't advance until they have demonstrated competency in the current topic.
Asynchronous Learning: Students advance from topic to topic independently. To do mastery learning properly, this is a requirement. However, it doesn't mean that there aren't sync points. For example OLI Courses support students spending variable amounts of time (according to their skills and background) learning the basic material. This way they arrive in class equally prepared for the live debates that are so critical to teaching certain subjects. Some classes resync every Friday with those students who are ahead assisting those who are taking more time. Results from the Khan Academy and School of One are showing us that individual students aren't consistently fast or slow. The slow and fast students trade places from day to day or week to week and overall variability tends to balance out.
Emphasis on Principles more than Facts: A student who has command of the underlying principles of a subject can often derive the facts. And in today's world, memorizing facts is of diminishing importance. It's too easy to look them up.
Strategic Intervention: The teacher is more important than ever. After all, learning is fundamentally a human-to-human process. Deploying online curricula in such a way that supports independent work frees teachers to spend more time one-on-one with students. They are enabled to focus on things only teachers can do: diagnosing misunderstanding, demonstrating the value of the subject, motivating and rewarding achievement and developing a personal relationship with each student. Paradoxically, technology has potential humanize the classroom. In a very important TED talk, Salman Khan says that we should move from measuring the student to teacher ratio to measuring the "student to valuable human time with the teacher ratio." (Quote is at 14:30 but watch the whole thing.) Teacher Dashboards are an important mechanism for informing teachers about where they need to apply their skills.