There are a multitude of math curriculums available for homeschoolers; however, students need to research spiral and mastery methods. Understanding each method makes it easier to select curriculums that will benefit each child.

The spiral approach introduces a new concept, and teachers move on to a new topic even if students did not master the concept; although the concept is revisited as new topics are introduced.   It also interleaves various subjects or topics at the same time. Lessons are intermixed with previously learned concepts, so students have a smaller percentage of problems to solve for a specific idea.

The mastery approach involves a thorough understanding of a topic before moving on to a new concept.  

Advocates for the spiral approach criticize the mastery method, claiming that concepts are not revisited enough and problems are combined with concepts already learned. Just because a curriculum uses the mastery approach, does not mean there is no repetition. When a topic is first introduced, it concentrates on that topic. However, problems are drawn from earlier lessons and intermixed at the end of each lesson. Not mixing the problems from the beginning, allows students to solve a much larger sample of problems for each concept. Both methods, eventually, allow problems to be juxtaposed.

The spiral approach, used in brick-and-mortar schools, covers the same concept every year with increased complexity each time. Some students require repetition to better assimilate math concepts; however, my sons felt too much repetition was unnecessary.