Math: Mastery, Spiral, or Confused?

Math is one of those subjects that tends to cause struggles for homeschool families.

The sheer number of math curriculum companies and titles out there don’t help. It may seem “everyone” is using a particular curriculum and it is producing such gifted, wonderful scholars, and isn’t that just what you want your kids to be? Don’t beat yourself up. Math is the leading cause of insanity in homeschool moms.

You knew that, right?

Math: Mastery, Spiral, or Confused?|HSBAPost

Changing to a certain curriculum almost never is THE answer. It’s just not that easy. So what’s the difference in these math programs, anyway? There are two main sequencing styles among curriculum publishers:  Mastery and Spiral.


Mastery-based programs tend to focus on a topic or a set of topics for a period of time, and then move on to others. Some programs break them into chapters. Others break them into worktexts, where they complete 10 worktexts in a school year and each focuses on a different topic. One in particular takes on a topic for the entire school year.

Throughout these programs there is some review, possibly a “Cumulative Review” toward the end of each unit, but the main focus is on moving forward through the topics. Mastery-based programs include:

  • Alpha Omega Lifepacs
  • Bob Jones Math
  • Keys To…
  • Math Mammoth Blue Series
  • Khan Academy
  • Math-U-See
  • Modern Curriculum Press
  • Developmental Math


Spiral teaching programs have review built into the daily lessons. The lessons will have a focus of one or two new concepts, and there will be problems for students to work out from the current lesson. There will also be other problems pulled from previous lessons so that there is constant review. No topic is left alone for long.

Spiral programs include:

  • Abeka
  • Christian Light
  • Saxon
  • Horizons
  • Teaching Textbooks

Which method is best?

That depends entirely on your students. Some kids need to have time to focus on just one concept at a time, until they fully grasp it. Once they do, they are ready to move on.

The nice thing about math is that it is progressive.  One concept builds upon another, and another, until they have reached higher math and are using all of the previous concepts to work at a higher level.

The struggle comes in when the program moves too fast through the concepts.  This is where you need to know your child’s learning style.

Does she take a long time to understand concepts? She may do better with a program that works through with mastery in mind. Does she require a lot of review? A spiral method may be just the thing.

On the other hand, some kids struggle with “jumping around” from concept to concept so much and some just don’t like so much review.

Sometimes you have a child that needs both.

When working with a child that needs lots of time to master concepts, but tends to forget things if left too long, there are practice books and online programs you can use to keep her skills sharp in between. When used for a short time but consistently each day, there should be no loss of skills between units that use them. Xtra Math is one of our favorite sites for skill practice.

What about gaps?

Honestly, there will always be gaps, no matter which curriculum you use, or what school they go to. Gaps are invitable because there is no way to teach EVERYTHING that is available to be learned. The key is to be consistent.

Here’s the thing. It doesn’t matter what curriculum you use. (Gasp! Blasphemy!) Pick one and stick with it. Eventually they all cover everything your kids will need to learn. It’s the moving from one program to another that leaves the biggest holes.

How many math programs have YOU used?



Check out more homeschool math ideas from the iHomeschool Network:

guide to homeschooling math

Dawn (23 Posts)

Dawn is still happily homeschooling after 16 years. She teaches her two sons, 13 & 11, enjoying every minute of "the second time around". She lives in Eastern Washington with her husband, the youngest 2 of their 6 kids, and an assortment of barking, squeaking, and clucking critters. She writes at her homeschool/parenting blog The Momma Knows and her new chapter, Dawn Marie Perkins. You can also find her on Twitter @DawnMPerkins, , and Pinterest.

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  1. says

    We live in the UK where spiral curricula are the norm. We have found that each topic is revisited once a year and often a topic which caused chaos, a year previously, is grasped easily second time round. If a topic is difficult, we pull out the book from the year before, and use that until it is grasped.

    For us this has worked well and has meant that we haven’t had children stuck on one topic for months.

    • Sharon says

      If a topic is only revisited once a year, you aren’t using a spiral program. Rare review still sounds like the mastery method to me. Mastery doesn’t have to mean that review is never done. It just means that more time is spent learning a new concept well instead of reviewing what you didn’t learn well the first time.

  2. says

    Without knowing, we use both methods. We use different math programs, the one is with text books which works on the mastery method (as I learned today) and doing math on two programs on the computer – of which one is IXL.
    I love the way you started with “math is the leading cause of insanity in homeschool moms”, because when we do text book math on Wednesdays I feel like running away most of the time. As I mentioned on my site with the tips to make the 9 times table easy, my son is great with math, but my daughter just does not get it (but by Grace and going day by day we’ll get there)
    Thanks for sharing this insight.

  3. Jenny says

    We are having math issues. My 9 year old was doing fine with Fred for awhile, but eventually stalled with her learning. She doesn’t want to reread the stories. She hates extra math. However, we did find Reflex Math and she is liking that. We are just doing basic addition and subtraction right now, but as long as she likes it I don’t mind. I need to find something else to use with it, but I have no idea what.

    • says

      Jenny: Just find a review method that works. It really doesn’t matter which one! If he doesn’t like Xtra Math, there is TimezAttack or IXL (and others), there are Calculadders (worksheet skill drills) and most teaching supply stores have a large assortment of practice workbooks inexpensively too. Just pick something she can tolerate and work with it.

  4. Irene says

    I have 9 year old twin girls using different math curriculums. I started them both on Horizons Math in Kindergarten moving to Abeka in first grade due to the cost. My one daughter Jennifer did well with Abeka while my other daughter Teresa needed more solidification of a topic. So this year (2nd grade)I switched her to Math Mammoth and it works great for her. I am looking into Teaching Textbooks for Jennifer because while she likes the style of Abeka I think a computer based program will be better for her. So yeah with 2nd graders we are on our 3rd math curriculum.

      • says

        Have you tried Time4Learning with your twins? What do they think of it? I am curious what made you use it for one child and not the others.

        • Irene says

          My son Brian is a very independent learner and we butt heads a lot. Time4Learning works well for his learning style and takes stress off both of us. Teresa has tried it but declared it boring. Jen has vision issues that make work on electronics very hard so T4L is out for her.

    • says

      And enjoying being 5 is GREAT! :) My very favorite first math curriculum is Math U See. The lessons are short and easy for the young ones. My kids LOVED it. We used it K-3rd for 5 kids.

      • Nicole says

        Hi Dawn,
        Can you tell me what you used and why after the 3rd grade for your children. We currently use MUS for my 3rd and 1st grader but feel like we need more review of past covered concepts that we are not getting with MUS. So I am debating switching to a spiral curriculum or supplementing with worksheets. I don’t have a lot of time to be finding worksheets for the needs that present at the moment, I have 4 children 8 and under and another on the way in a month. Any advice is appreciated! Thanks

        • says

          Nicole: Since your child is in third grade, you could try a review program online, such as XtraMath. XtraMath is set up to take about 10 minutes a day, and it keeps track of the facts your child has mastered and keeps them reviewing while working on mastering new ones. It’s free and most kids really like it. This is what we use for fact review.

  5. Michelle says

    I have a 7th grader and a 2nd grader. In Kindergarten we did living math and simple worksheets. In first grade we started Math Mammoth which goes up until 6th grade. My oldest is now using Thinkwell 7th grade math. My younger daughter is using Math Mammoth.

  6. Mrs.Momof6 says

    We have used four total programs.. wow, I didn’t realize that! My first program was Abeka, which I bought as a set for my highly gifted 4 year old (he did the 1st grade program). Since he devoured that year’s curriculum in about 4 months, I decided that a boxed curriculum was going to be too costly to keep him interested. So we made our own curriculum the next year and I used Modern Curriculum Press, grade 3. Which he hated… it was a lesson in perseverance, because I didn’t know at the time that it was a remedial math, with LOADS of repetitive work, and I didn’t know he was so gifted in math… so then we got Saxon, because it was given to me free. Again, he was bored to tears, and was able to suck through the program in less than a year. Interestingly I now know the MCP was mastery based, and Saxon was spiral, but he had trouble with both of them. He loves mastery, but he hates unnecessary drill n kills… So we used Khan and Saxon… till I finally found Art of Problem Solving, which is a mastery based math program, with a higher level of challenge, and an online program similar to Khan, which allows him to work through faster, with less drill n kill. He is now in Algebra, he’s 10.

    My girls coming up have had Modern Curriculum Press… this year I am switching to Spectrum workbooks, because they are cheaper and I have three girls. I think Spectrum is a spiral, and MCP was a mastery. One of my three girls does great in the mastery program, one not so great. I don’t know why. I think… the girl who does well, likes repetition of things she already knows, because it encourages her that she will get them all right. The girl who doesn’t like it, I think she is bored, but there are some topics I am not sure she is getting. I wanted to go back to Abeka just for the math, but, the COST… so Spectrum it is this coming fall… Then I will have used 5 different math curricula in 6 years, with 4 kids. Wow… and I thought I was consistent.

    • says

      Funny how that happens, right? You just use what works, and if you need to change to reach a child at their level/learning style, so be it!

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