Compacting is one differentiation strategy. Before you teach a unit, you give a pre-assessment and find out a handful of your students already know most of what you're going to teach them, several of them know some of it, and some are going to need a bunch of help. You tailor your small group instruction and the work you give students based on assessment results.
In the original Compacting Curriculum Study, Renzulli et al. found that you could eliminate half the curriculum for certain students without impacting their achievement on achievement tests aimed at students a year older, in each case, from the test subjects.
In other words, a fifth grader was identified by their teacher (whether or not formally identified as gifted) as someone who might benefit from compacting. That student was given a 6th grade achievement test. Half the curriculum was eliminated through pre-assessment for that student, and then they took the 6th grade test again. Their achievement did not suffer, and the teacher sometimes ended up compacting for about nine of their classmates.
To compare and contrast this with ability grouping or tracking, your ability groups--if you use them in compacting--are determined by your pre-assessment for each unit. Theoretically, someone who is in the low group for fractions might be in the high group next week with different material.
