# Mastery vs. Spiral Math

### #1

Posted 17 May 2010 - 03:03 PM

Do kids get tired of staying with a single topic until it's mastered? How do you know when it's mastered? What math programs are mastery?

If there is a thread that has already covered all of this, LMK!

TIA!

### #2

Posted 17 May 2010 - 03:14 PM

Anyway, I'm going to try a mastery approach next year when we hs full time and see if that goes better.

### #3

Posted 17 May 2010 - 03:32 PM

I find that for things that a child is not naturally inclined toward, mastery works very well. It gives them enough time to "master" something before moving onto the next higher level.

I think the mastery approach can work for either type of child (just speed up for the natural learner, slow it down for a child who struggles), but in my experience spiral is sometimes a "death sentence" for the child who has not mastered what they need to master before the curriculum moves on.

We use a mastery approach in almost everything we study. I love the flexibility of it... I can speed it up if they are understanding and doing well. I can slow it down when they need more practice or review. I'm guaranteed that whatever we are studying now is built solidly on what we have studied in the past. If I did my job as a teacher and made sure the kids mastered it the first time it is relatively easy to teach new material because it's just the next step.

I also love the connections my kids see (or I can point out to them) between what they have learned in the past and what they are learning now. When my oldest ds got to long division he finally saw what all his work in the 4 basic operations led to. He also sailed through long division because he had all his facts memorized. At that point it's just making sure you pay attention to place value (something he also had an excellent understanding of because we covered it and mastered it.)

We use MUS and MM which are mastery programs. It hasn't bothered my kids to stay on a topic until mastered, but they don't know anything else. I don't really care if they don't like it though... I'm pretty set on them mastering the basics! And, you can tell they've mastered it when they can do it accurately most of the time. Some people use tests and grade them based on percentages. I don't give tests. If they get something wrong on their daily work I go over it with them that day so we can correct the problem right away. That system has worked well for us.

**Edited by robsiew, 17 May 2010 - 04:16 PM.**

### #4

Posted 17 May 2010 - 04:35 PM

### #6

Posted 17 May 2010 - 05:36 PM

It depends how "spiral" is the spiral. If you're talking about the incremental end (e.g. Saxon), I don't think this is the best choice for most math adept children: There's no big picture, and seemingly no point other than endless review problems. Math adept kids tend to flourish in programs like Singapore which present concepts in discrete units, programs in which it's possible to plough through easily understood concepts because they don't have to worry about skipping over other "new" material. Mastery needn't be a death knell, but you must be willing to let the child move ahead at their own speed and according to their ability.In my experience, if a child is naturally wired toward a skill, the spiral approach works well. They can catch on quickly to the concept presented, need little practice and when it comes around again they understood it well enough before to bring that background knowledge into the new higher level skill taught.

### #7

Posted 17 May 2010 - 05:49 PM

### #8 Guest_Cheryl in SoCal_*

Posted 17 May 2010 - 06:12 PM

Does K12 not have review? I don't know about all mastery programs but I know MUS has 3 sheets of systematic review per lesson. While my experience is the opposite as yours (spiral horrible, mastery awesome) I wouldn't use (or recommend) a mastery program that doesn't have review for the very reason you mention. Even though I LOVE mastery I doubt I'd love (or even like) every mastery program because they are just not all the same.We have always done spiral math programs here (either Horizons or Abeka). This year we went to a mastery program through K12 and it has been a disaster. I have to reteach many concepts because we learned addition/subtraction with regrouping earlier this year but by the time we got back to it, dd8 forgot how so I had to reteach. The same with dd6. We did money ad nauseum earlier in the year and now she can no longer count quarters. We are back to Horizons/Abeka and my children do much better here. I won't attempt the mastery thing again, at least not for a very long while.

We like a mastery program that teaches conceptually.

### #9

Posted 17 May 2010 - 06:28 PM

### #10 Guest_Cheryl in SoCal_*

Posted 17 May 2010 - 06:37 PM

I just wanted to reassure you that MUS has review. In the elementary books it's the D, E & F worksheets for each lesson.he did very well. We switched to Teaching Textbooks at some ppint and he sailed because there was so little review. The only other math program I tried with him was Saxon which is spiral as well, but he did not do so well. Many people complain about the amount of drill and review in Abeka, but my ds thrived with it. Every child is different! I currently own Saxon K, Abeka K, Singapore EarlyBird and am in the process of purchasing Math-U-See for my dd. We tried the Saxon and she didn't like it, Abeka she does well with, and Singapore she also enjoys.

I want MUS to try it and see how she does with a hands-on program. I do much prefer something with review, so we will stick with some sort of spiral.

### #11

Posted 17 May 2010 - 06:47 PM

And yet I know many math-adept dc who love Saxon. Go figure.It depends how "spiral" is the spiral. If you're talking about the incremental end (e.g. Saxon), I don't think this is the best choice for most math adept children: There's no big picture, and seemingly no point other than endless review problems. Math adept kids tend to flourish in programs like Singapore which present concepts in discrete units, programs in which it's possible to plough through easily understood concepts because they don't have to worry about skipping over other "new" material. Mastery needn't be a death knell, but you must be willing to let the child move ahead at their own speed and according to their ability.

### #12

Posted 17 May 2010 - 07:21 PM

Does K12 not have review? I don't know about all mastery programs but I know MUS has 3 sheets of systematic review per lesson. While my experience is the opposite as yours (spiral horrible, mastery awesome) I wouldn't use (or recommend) a mastery program that doesn't have review for the very reason you mention. Even though I LOVE mastery I doubt I'd love (or even like) every mastery program because they are just not all the same.

We like a mastery program that teaches conceptually.

The K12 program does have some review but not enough for my children. They really need a little practice every day as opposed to some practice every so often. They really do much better with either Horizons or Abeka.

### #13

Posted 17 May 2010 - 08:02 PM

Math programs like MEP , Singapore, Bob Jones, Math U See, Right Start and Rod and Staff, and Math Mammoth are mastery math programs. These types of programs seem to suit children who need to focus on one concept at a time, and they are usually good with math to begin with. There is some to no review of past concepts. It continues to move forward from the last concept learned.

For some children this may mean they study subtraction in one chapter. Subtraction with a number line, subtraction using unifix cubes, subtraction using strategies such as 'think , if 10-9=1 so 9-9 must be 0.' type strategies. Then the next chapter will be on addition, then the next chaper maybe geometry , then the next chapter will come around to subtraction again and this time they will learn to subtract one digit problems, then two digit problems ,, etc. For some children this is plenty of review , they get the math and life is good.

For other children they sometimes can't focus on one topic for to long, the teaching of to many strategies may make their head feel like its going to explode and they need more review.

My oldest is a mastery math kind of gal. She gets math understands it , it makes sense. My younger two are spiral review kind of gals. Focusing to long on a topic and not having daily review , well just forget it. They lose it , don't understand it. I've tried and tried but this type of math does not work with them. Period.

If you have a child that loves math , is good with math and numbers I would recommend mastery programs( just be sure to remember to do drill with math facts though). This type of math makes sense to them and they will thrive.

If you have a child that has difficulty with math, needs lots of review. Then spiral programs are better. You can always try mastery later on as they get older. When they are more ready.

### #14

Posted 17 May 2010 - 08:20 PM

### #15

Posted 17 May 2010 - 08:20 PM

It depends how "spiral" is the spiral. If you're talking about the incremental end (e.g. Saxon), I don't think this is the best choice for most math adept children: There's no big picture, and seemingly no point other than endless review problems. Math adept kids tend to flourish in programs like Singapore which present concepts in discrete units, programs in which it's possible to plough through easily understood concepts because they don't have to worry about skipping over other "new" material. Mastery needn't be a death knell, but you must be willing to let the child move ahead at their own speed and according to their ability.

That's a good post.

Bill

### #16

Posted 17 May 2010 - 09:16 PM

I guess I don't understand the resistance to doing stuff they already know how to do. We do it all the time in other areas of life, like cooking, crafts, dancing, or playing a musical instrument. Why wouldn't children who enjoy math, enjoy doing a varied selection of math problems?

On a different note, true mastery methods (where you master a concept, then move on and don't go back to it) seem to be pretty rare. Even Singapore describes itself as a "spiral method." It's just that they spiral year-to-year, rather than day-to-day.

**Edited by Eleanor, 17 May 2010 - 10:59 PM.**

### #17

Posted 18 May 2010 - 12:15 AM

[I'm not referring solely to Saxon here.]I guess I don't understand the resistance to doing stuff they already know how to do.

It's not a question of doing stuff they already know how to do, but rather one of learning a bit, then maybe a bit more, then doing something else, then learning a bit more -- learning and relearning it and reinforcing it. The difference is that after finishing a unit in Singapore or another mastery program, the student is expected to know the concept and apply it, period. It's reinforcement through use, if you will, but mastery is still expected.

"Spiral" in US educationese usually means spiralling within a single school year. These classifications have been debatedOn a different note, true mastery methods (where you master a concept, then move on and don't go back to it) seem to be pretty rare. Even Singapore describes itself as a "spiral method." It's just that they spiral year-to-year, rather than day-to-day.

*ad nauseum*in places like the Kitchen Table Math blog. However, I like one compromise I read at KTM: Singapore could be considered spiral with mastery, whereas a program like EM would be spiral without mastery. Incrementalism is a whole other ball game.

### #18

Posted 18 May 2010 - 12:29 AM

### #19

Posted 18 May 2010 - 02:35 PM

I can see this sort of difference in myself and DH, and also in DD and DS. We could all be described as "math adept" based on aptitude tests and levels of achievement, but the males seem to learn math in a different way from the females. (Not saying that this is always the case; just how it seems to have worked out for our family.) For instance, we're currently using Singapore level 1 for both children. DS does great with it -- something just "clicks," and then he zips through all the problems -- but it's sort of hit and miss with DD. I'm finding that I have to spend a lot of time coming up with alternate explanations. This is especially striking given that she already did Earlybird last year, whereas he's completely new to this style of teaching.

We did a bit of Horizons with DD at one point and she really liked it, though I was prejudiced against it because it seemed too slow-moving and spiraly (which, as I kept reading, was supposed to be a no-no for bright DC). It didn't seem to make sense for her to spend so much time filling in pages and pages of review on stuff she'd already learned. But she actually enjoyed doing this, and now I'm thinking she needs that sort of structure, to help her consolidate her learning and strengthen her understanding of the concepts. I'm wondering if this is akin to the "overlearning" that can be helpful for dyslexic DC.

Thinking back, maybe the fact that I was taught math the "wrong way" in public school (mostly verbal/procedural/drill based, pretty slow moving without much chance for acceleration) was what gave me the extra edge to excel at it, despite my less than stellar spatial abilities. If I'd had a "better" math curriculum, maybe I would have been a so-so student, or even struggled with it. Who knows?

Anyway, based on some anecdotes I've read on these boards, I've just ordered CLE for DD, and will just use Singapore as a supplement for her (though it will still be DS's main curriculum). Looking forward to seeing how this works.

### #20

Posted 18 May 2010 - 03:15 PM

Is anyone familiar with Professor B?

### #21

Posted 18 May 2010 - 03:32 PM

In my experience, if a child is naturally wired toward a skill, the spiral approach works well. They can catch on quickly to the concept presented, need little practice and when it comes around again they understood it well enough before to bring that background knowledge into the new higher level skill taught.

I find that for things that a child is not naturally inclined toward, mastery works very well. It gives them enough time to "master" something before moving onto the next higher level.

I think the mastery approach can work for either type of child (just speed up for the natural learner, slow it down for a child who struggles), but in my experience spiral is sometimes a "death sentence" for the child who has not mastered what they need to master before the curriculum moves on.

I totally agree with this. I use a spiral math program for my daughter since she tends to catch on really quickly, but a mastery program for my son because he needs more practice when a new skill is being introduced.

Lisa

### #22

Posted 18 May 2010 - 04:02 PM

CLE is Christian Light; you can see samples at http://www.clp.org/Is CLE the same as Christian Light Publications? Is there anywhere online to see sample pages?

Is anyone familiar with Professor B?

We have the Professor B materials, and I really like what I've seen of his way of teaching, but it turned out that my children wanted to start learning math before they'd developed the motor skills that are necessary for the early lessons. He spends a lot of time on rapid-fire drills where they have to show the numbers from 1 to 10 in different ways with their fingers, which is surprisingly difficult for little ones (but fun for those who can do it). I'm hoping we can go back to it later on.

### #23

Posted 18 May 2010 - 04:07 PM

### #24

Posted 18 May 2010 - 05:13 PM

In a former life, I had a brief fling with Enki education. On the whole it was a ridiculous venture, but the one thing I have brought with me from my Enki indiscretion is that kids can benefit from setting something aside for a bit to let it consolidate in their minds. I have definitely found that to be true with my kids and math, and I intentionally structure our math schedule to allow for that.

Tara

**Edited by TaraTheLiberator, 18 May 2010 - 05:23 PM.**

typo

### #25

Posted 18 May 2010 - 05:16 PM

Math programs like ... Right Start ... are mastery math programs.

(ellipses mine)

We use RS and I definitely don't consider it a mastery program.

Tara

### #26

Posted 18 May 2010 - 05:27 PM

In my experience, if a child is naturally wired toward a skill, the spiral approach works well. They can catch on quickly to the concept presented, need little practice and when it comes around again they understood it well enough before to bring that background knowledge into the new higher level skill taught.

I find that for things that a child is not naturally inclined toward, mastery works very well. It gives them enough time to "master" something before moving onto the next higher level.

I think the mastery approach can work for either type of child (just speed up for the natural learner, slow it down for a child who struggles), but in my experience spiral is sometimes a "death sentence" for the child who has not mastered what they need to master before the curriculum moves on.

I agree. My kids seem to catch on to concepts pretty quickly. I can't imagine them doing all 5 pages of MUS. When we did MUS, I just had them do the final page of the lesson every day. I can't imagine how much they would dread doing 20 problems of something they already mastered 3 days ago.

Laura

### #27

Posted 18 May 2010 - 07:07 PM

Math programs like MEP , Singapore, Bob Jones, Math U See, Right Start and Rod and Staff, and Math Mammoth are mastery math programs. These types of programs seem to suit children who need to focus on one concept at a time, and they are usually good with math to begin with. There is some to no review of past concepts. It continues to move forward from the last concept learned.

For some children this may mean they study subtraction in one chapter. Subtraction with a number line, subtraction using unifix cubes, subtraction using strategies such as 'think , if 10-9=1 so 9-9 must be 0.' type strategies. Then the next chapter will be on addition, then the next chaper maybe geometry , then the next chapter will come around to subtraction again and this time they will learn to subtract one digit problems, then two digit problems ,, etc. For some children this is plenty of review , they get the math and life is good. n always try mastery later on as they get older. When they are more ready.

If this is how mastery is defined, then I really wouldn't put MEP in that category. We're using MEP Year 1 and we do addition and subtraction all in one lesson. The program has added only one new number at a time, so for instance we will only be adding and subtracting up to 4 for a while, then up to 5, then 6, etc. In the same lesson as adding

*and*subtracting numbers up to 6, we'll have a section on identifying different types of polygons or finishing a string of beads in the same pattern in which it was started. We definitely don't cover only one topic at a time for several lessons - or even for one lesson, for that matter.

### #28

Posted 18 May 2010 - 09:18 PM

And therein lies the problem: There are no generally agreed upon definitions, only archetypal programs, but many -- most? -- programs don't fall at these extremes:If this is how mastery is defined

Mastery: MUS

Spiral: Everyday Math, CLE

Incremental: Saxon

**Edited by nmoira, 19 May 2010 - 10:00 AM.**

### #29

Posted 18 May 2010 - 10:10 PM

### #30

Posted 18 May 2010 - 10:32 PM

It really depends on the child and the program. Programs like Saxon , CLE( Christian Light Education) , Abeka are spiral and they teach concepts a little bit at a time, reviewing and spiraling back around and building upon the concept. Usually these programs do well with children who need lots of review.

Math programs like MEP , Singapore, Bob Jones, Math U See, Right Start and Rod and Staff, and Math Mammoth are mastery math programs. These types of programs seem to suit children who need to focus on one concept at a time, and they are usually good with math to begin with. There is some to no review of past concepts. It continues to move forward from the last concept learned.

For some children this may mean they study subtraction in one chapter. Subtraction with a number line, subtraction using unifix cubes, subtraction using strategies such as 'think , if 10-9=1 so 9-9 must be 0.' type strategies. Then the next chapter will be on addition, then the next chaper maybe geometry , then the next chapter will come around to subtraction again and this time they will learn to subtract one digit problems, then two digit problems ,, etc. For some children this is plenty of review , they get the math and life is good.

For other children they sometimes can't focus on one topic for to long, the teaching of to many strategies may make their head feel like its going to explode and they need more review.

My oldest is a mastery math kind of gal. She gets math understands it , it makes sense. My younger two are spiral review kind of gals. Focusing to long on a topic and not having daily review , well just forget it. They lose it , don't understand it. I've tried and tried but this type of math does not work with them. Period.

If you have a child that loves math , is good with math and numbers I would recommend mastery programs( just be sure to remember to do drill with math facts though). This type of math makes sense to them and they will thrive.

If you have a child that has difficulty with math, needs lots of review. Then spiral programs are better. You can always try mastery later on as they get older. When they are more ready.

We use singapore and love it. I do not see how it could be labeled as a mastery program, though. I definitely see MUS as a mastery program. Singapore's approach is incremental but is teaching addition and subtraction at the same time so the child is really getting to see the relationships between numbers. It has review. The amount of review depends on how you implement the program. Overall I see the spiral approach with this program. I cannot speak to spiral vs mastery approaches in general. However, I can tell you the benefit of this program has been that my dd is getting familiar with concepts that she will need in later years while the numbers are still small. There is time for her mind to expand and grow a little in between each "spiral" change. She does not have to master it inside and out at that lesson or even the next. We comeback to it a little later, review it and then add to it. For instance, we did some very basic add., just a few lessons, then some very basic sub, a few lessons, then went back to the addition, reviewed it and upped it a little, then subtraction, reviewed it and upped the concept, repeat. They always relate and reinforce the addition and subtraction relationship with number bonds. But each time we step away and come back, she grasps it a little better.

It just depends on the child. I don't think that one approach is better then another. It doesn't matter how great a philosophical approach to math education is if your child can't learn that way.

I think it is hard to tell with some children what approach will work best. I think it also depends on the parent and how they like to teach or not teach. I can definitely tell you that Singapore will not work the way it is designed to if you don't actually "teach" it. This program does very little good if you just hand the book to your dc and say go do this page without showing them the way this approach comes to its conclusion. Sure, the child could look at the picture of 14 apples, cross out 3 of them, and count the remainder. But it is the methodology that they are really supposed to be learning not just to right down the correct number. This, I think, is the important concept that sets math programs apart. You have to find a program that uses a methodology that you can teach and your children can grasp.

### #31

Posted 18 May 2010 - 10:47 PM

It's probably already been said, but what is MEP?

Mathematics Enhancement Programme. It is a math curriculum from the UK that is based on a hightly esteemed Hungarian math program. MEP is part of an iniatiative intended to raise the standards of maths education in Britain. The Centre for Innovation in Mathematics Teaching, the institute that maintains the program allows home educators to use their full (and very highly interesting) program without cost (aside from ones need to print the files).

The MEP materials are notable for their great Lesson Plans, which are filled with good ideas, and problems for students that really challenging their reasoning skills. It is often described as "puzzle-like" or "makes their brain hurt (in a good way) math."

Bill

**Edited by Spy Car, 18 May 2010 - 10:51 PM.**

### #32

Posted 18 May 2010 - 11:07 PM

I wish I could find a spiral grammar program. Too many of them clump nouns together, then punctuation, then various verbs, etc.. To me that's a disastrous way to learn grammar. Maybe it works when the concepts are first introduced, but in order to master them, constant review is necessary - in my opinion. I feel the same way about math.

But honestly, the best math program is whatever works well for an individual child.

Bill, thank you for the explanation of MEP - it sounds awesome!

**Edited by Teachin'Mine, 18 May 2010 - 11:09 PM.**

### #33

Posted 18 May 2010 - 11:41 PM

I wish I could find a spiral grammar program. Too many of them clump nouns together, then punctuation, then various verbs, etc.. To me that's a disastrous way to learn grammar. Maybe it works when the concepts are first introduced, but in order to master them, constant review is necessary - in my opinion. I feel the same way about math.

Why not use Saxon's grammar program. It's also called Hake Grammar. It's set up the same way as their math.

### #34

Posted 19 May 2010 - 07:16 AM

It depends how "spiral" is the spiral. If you're talking about the incremental end (e.g. Saxon), I don't think this is the best choice for most math adept children: There's no big picture, and seemingly no point other than endless review problems.

I think the mastery approach can work for either type of child (just speed up for the natural learner, slow it down for a child who struggles), but in my experience spiral is sometimes a "death sentence" for the child who has not mastered what they need to master before the curriculum moves on.

This is true... but on the other side of the coin, my gifted "mathy" kid considered the spiral approach a "death sentence" because it would limit how deeply he could delve into the material before moving on to something different. It frustrated him to no end. He wanted to explore every possibility,make connections, and experiment with other ways of working the math... but when we would do this, when the topic came back around, we would find that he already went further in his understanding than the "next step". By the time we were finished one round of the spiral in Saxon, he had mastered most of the book... and we found ourselves flipping through looking for something "new".

Then there is my dd who can handle either spiral or mastery, and really doesn't have issues with either... kids are so different!

**Edited by babysparkler, 19 May 2010 - 07:21 AM.**