Source: ENRICHri thanks and credits Granite State Home Educators (NH) for use of this article. We couldn’t have said it better ourselves! *Some of the resources are not secular.

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.

SPIRAL

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.

Pros:

• 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.

Cons:

• 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.

Spiral Math Programs:

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

MASTERY

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

Pros:

• 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.

Cons:

• 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.

Mastery Math Programs:

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

Other Programs

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

• Life of Fred
• Miquon