Mastery vs Spiral Math: How to Choose the Best Curriculum

One of the questions I get asked often is: what is the difference between a mastery approach and a spiral approach in math curriculum? This is an important distinction. Understanding the difference will help you to be able to choose the best math curriculum for your child. If you’re curious about mastery vs spiral math, keep reading!

how to choose the best homeschool math curriculum for any learning style
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This post was sponsored by CTCMath. I received compensation and a 1-year Homeschool Family membership to CTCMath in exchange for my honest review, but all the opinions in this post are my own.

What is Spiral Math?

In a spiral math curriculum, the introduction of new concepts is a little bit like a spiral. Each new topic is introduced and practiced. After some practice, the next concept is introduced. However, the curriculum will continue to return to each topic frequently for review.

In spiral learning, each time a student returns to a topic, they will learn something new about it that will deepen their understanding. Students might learn how the concept fits with the new material they have studied. They will also learn how to take their knowledge to the next level. The spiral math approach continues to build on each topic every time the student returns to it.

Examples of a Spiral Math Curriculum

Here are some examples of common math curricula that use a spiral approach to teaching math.

  • Saxon Math
  • Teaching Textbooks
  • The Good and The Beautiful
  • Horizons Math
  • Bob Jones University (BJU)

Pros of Spiral Math

Provides lots of review

One of the best reasons to choose a spiral curriculum for math is that it allows lots of opportunities for students to review the concepts they are learning. Kids who need lots of review and repetition to remember new concepts will benefit from spiral programs. This will allow them to continually revisit the topics they have studied.

Keeps concepts fresh

Over time, kids often forget about things that they have learned. Scientific research shows that continual review of a subject helps with our long-term retention, and with the spiral method children have the opportunity to spend lots of time reviewing what they already know.

Helps kids who are struggling

If a child is struggling with a concept in math, a spiral math curriculum allows them to take a break from that topic, learn about something else, and return to the topic later. When they return to the subject for spiral review, they may have a new level of understanding or maturity. This will help them understand the topic in a way they could not before.

Boosts self-confidence

In a spiral program, every lesson includes a review of topics that students are already comfortable with. This can help kids feel more confident in their math skills as they see themselves successfully solving review problems in each math lesson.

Introduces new concepts slowly

When kids are learning new math topics, a spiral curriculum helps them build their understanding of a concept slowly over time. Students can move at a slower pace and learn new concepts in smaller chunks.

Helps students make connections between topics

One of the biggest benefits of a spiral program is that it allows students to make connections between different topics in their math curriculum. When students practice different kinds of math problems in the same lesson, they start to build connections between different areas. They might see how long division uses multiplication and subtraction, for example, when they practice those skills together.

Makes math interesting

With a spiral math program, each new lesson includes a variety of different problems. Rather than focusing on one topic for weeks or months in a row, kids can practice different kinds of math problems, which will make their math lessons more interesting and fun.

Gives kids freedom to explore

Within a spiral curriculum, students will have more freedom to explore topics that they are interested in. The curriculum is usually more flexible and might allow kids to focus more deeply on topics they enjoy.

mastery vs spiral math curriculum

What is Mastery Math?

In a mastery math curriculum, specific topics are introduced one at a time. Students learn about the new concept in many different ways. In addition, teachers make sure that kids understand the topic completely at a deeper level before moving on. Students practice the new concept until they have a strong foundation of knowledge and understanding. They don’t move on until they have mastered the topic completely.

The mastery method is also called sequential or skills-based learning.

Mastery Math Curriculum Example: CTCMath

CTCMath‘s Homeschool Family membership is a comprehensive online math program that uses a mastery approach to learning. The program features short video lessons from master teacher Patrick Murray. I love the way Patrick explains each concept in such a simple and age-appropriate way. The videos do a great job of breaking down complicated subjects and making them easy for my son to understand.

Each lesson also includes practice questions that kids can do online to reinforce each topic. The practice questions are a fun way to make sure that your child has truly mastered the topic. My son loves the confetti that appears on the screen when he gets all the questions correct in a section. He usually asks to do the questions again if he doesn’t get 100%- just so he can see the confetti!

Using CTCMath for Independent Learning

I also love that this is a curriculum that my son can use independently. Although we sometimes work on the lessons together, I know that I can get my son started on his lesson and then walk away if I need to. As a busy homeschool mom, this is one of my favorite things about CTCMath because it helps us stay consistent with practicing math every day.

CTCMath offers a fantastic half-price discount for homeschoolers on their single or family memberships. We love the Homeschool Family membership because it allows everyone in the family to use the program at their level.

Check out my full CTCMath review or sign up for a free trial today!

ctcmath mastery vs spiral math curriculum

Additional Examples of a Mastery Math Curriculum

Here are some examples of common math curricula that use a mastery approach to teaching math.

Pros of Mastery Math

Moves at a slower pace

Mastery math programs move at a much slower pace overall. They give kids plenty of time to understand abstract concepts the first time they are taught and lots of practice. With so much review right away, students master each topic completely before moving on to the next one.

A video curriculum like CTCMath is a great way to teach a mastery math curriculum. I love that my son can rewind the videos and watch them again and again until he understands each concept. When he is struggling with a new lesson, we can just go back and re-watch the video!

Makes sure kids understand

In mastery learning, teachers need to make sure that kids have a complete comprehension of a concept before moving on. They may take more time to explain a concept or to practice it using math manipulatives. Kids have a lot more time to ask questions and understand complex concepts because the curriculum is moving more slowly.

Another great way to help kids understand their math lessons better is by using a multi-sensory approach. My son is a visual learner, so I am always looking for a curriculum like CTCMath that has a visual component. But, I love that he can listen to the videos too. As a former teacher, I know that his brain is more engaged and he will remember more when he is using multiple senses at once!

Prevents gaps in learning

One of the most important things about a mastery program for math is making sure that kids don’t have any gaps in their understanding of math concepts. Because they can’t move on until they have mastered a concept, parents can know that no foundational topics have been skipped.

When kids truly understand each math concept with no gaps in learning, they will feel more confident in their math skills, and often, their attitude about math will improve as well. We have noticed a huge improvement in my son’s attitude since we started using CTCMath!

Builds a solid foundation

Kids who are using mastery math curriculums will have a strong foundation of math skills, no matter what their learning styles. Because the curriculum spends so much time on each topic, kids will understand each one.

It is important to make sure that you are checking for understanding of each topic before moving on in a mastery math curriculum. You can give your child tests or use a curriculum like CTCMath that generates detailed progress reports for parents. This will help make sure that your child has mastered each topic.

Deep understanding includes more theory and concepts

When kids spend so much extra time on each concept, they will develop a deeper understanding of how problems work and why they are solved the way they are. Mastery math courses often include more theory and conceptual understanding.

Less review is needed

When students are using a math mastery curriculum, they often need less review overall. Kids can save time because there is less need for math review activities. This is because it is easier for children to remember concepts that they have already mastered.

Backed by research

Scientific research in the 1990s, which studied math programs in the United States and around the world, showed that a mastery program can be a more effective way to teach math. Using scientific best practice can help make math easier for kids.

Aligns better with public schools

Now, many public schools are using a mastery teaching method in their math classes. That means that choosing a mastery curriculum for homeschooling can help your child stay at grade level in math if you plan to enroll in a public school in the future.

mastery vs spiral math curriculum

Key Differences Between Mastery and Spiral Math Curricula

Understanding these key differences between the different approaches will help you choose the best homeschool math curriculum for your family.


With a mastery math curriculum, students don’t move on to the next topic until they understand what they are studying completely. A spiral math curriculum moves at a quick pace and will focus on new concept building instead of mastery.

Connection vs focus

With a spiral program, students build on their prior knowledge to understand how different topics are interconnected until they have a general mastery of all covered math concepts. In a mastery program, students will focus on each specific topic in great depth. This means they will often have a deeper understanding of the concepts overall.


When using a mastery approach, teachers wait until students have reached the appropriate level in their development and knowledge to introduce a new concept and study it completely. In a spiral approach, teachers believe that kids can learn any concept at any age, as long as it is taught simply and a little bit at a time.

Learning Styles

A spiral curriculum might be best for kids who like to understand how each concept that they are learning is related and connected to the whole. Students who are more methodical and need to understand why things work the way they do might prefer a mastery curriculum.

History of Mastery vs Spiral Math Curriculum

Until the 1960s, most schools in the United States used a spiral math curriculum. Teachers believed that the frequent review that a spiral math curriculum provides would help their students learn better and remember more.

In the 1990s, the United States began conducting the Trends in International Mathematics and Science Study which compared worldwide student performance in math by analyzing test scores in 4th grade and 8th grade. Scientists found that American students struggled on these tests compared to students from other countries. After studying the math programs in these other countries, the United States began to shift towards a mastery model.

Today, many traditional schools continue to use a mastery approach to teaching math.

mastery vs spiral math curriculum

Choosing the Best Homeschool Math Curriculum for Your Family

How can you choose the best math curriculum for your child? Is a spiral curriculum or a mastery curriculum best?

As your child’s parent and their teacher, you know your child better than anyone. Take some time to think about how your child learns and which kind of curriculum would be the best fit for your child.

I would definitely recommend signing up for a free trial of CTCMath or taking advantage of their half price subscriptions for homeschoolers. This is a fantastic mastery curriculum!

Once you make the decision of mastery vs spiral math curriculum, choosing a math curriculum for your family will be much easier.

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