There are two different approaches to math instruction; spiral and mastery. Some children learn math better with one approach instead of the other, but there is no one “best” approach.



The spiral approach refers to a built-in review of previous concepts throughout the curriculum as new topics are introduced.  The student practices new concepts incrementally and reviews previously introduced topics so they build on each other systematically.


  • The child can practice with incremental steps towards understanding new concepts.
  • If the student needs more practice or time to understand a concept, there are many opportunities to review and practice that are built into the materials.
  • Understanding and skill develop over time.
  • The child’s math skills and knowledge does not go stale and he/she is less likely to forget concepts.
  • The child is able to make connections between the different concepts as they are revisited throughout the materials over time.
  • Some children find it more interesting because they are learning something new and different instead of focusing on the same concept for an extended period.


  • Some children find this approach too slow or repetitive.
  • Children may be overwhelmed learning a new concept before completely understanding the previous topic. It may feel like the material is too hard to keep up with and remember.


  • Teaching Textbooks
  • Saxon Math
  • Abeka Math
  • Go Math
  • The Good and the Beautiful Math
  • Horizons Math
  • RightStart Math
  • BJU Math


Mastery requires the student to completely comprehend a topic, forwards and backwards, before moving on to the next topic.


  • Focus on one topic at a time, in a sequential way.
  • The child may work at his/her own pace.
  • This approach builds a strong foundation before adding on new information.
  • Often prevents learning gaps.
  • Commonly used approach by public schools, so may be helpful if the child is enrolled in a traditional school later.


  • Some curricula have minimal review and mastery may be diminished without the review.
  • If the child needs additional resources to gain mastery, he/she could exhaust the materials in the curriculum.
  • Children may become bored or frustrated working on the same concept every day for an extended time.
  • The idea of “mastery” can be challenging or stressful for students as it could be interpreted as requiring perfection.


  • Math U See
  • CTC Math
  • Khan Academy
  • Math Mammoth
  • Beast Academy
  • Singapore Math
  • Art of Problem Solving (AOPS)



There are other curricula that take unique approaches that do not fall under spiral or mastery.

  • Life of Fred
  • Miquon


Smarter Learning Guide – All About Mastery vs Spiral Math

Orison Orchards – Homeschool Math Curriculum

The Simple Homeschooler

Nicole the Math Lady

Homeschool Here