New to home school Math - what is the "spiral approach"?

[Hillcrest Academy]

I have come across the 3 major math curricula - Singapore, Saxon and MUS, and have tried MUS Primer and is doesn't work with my DD6. I'm going to try Singapore Earlybird next.

 

I was wondering, however, how one would describe the different approaches. I have read of a "spiral" approach, and can guess what it means, but would really appreciate if someone could explain it. I think I also recall a "mastery" approach.

 

What are the approaches and which approach would each of these curricula have been?

 

TIA!

~Caryn~

[OnTheBrink]

Spiral approach is when you hit on different topics, reviewing previous topics, as you go along. Saxon is spiral; Singapore is spiral, Rod and Staff is spiral. Visualize is thus: take a paper plate and with a pen, divide it into 4 pie pieces. Label each piece as addition, subtraction, multiplication, division. Then, cut the paper plate into a spiral. Holding the top, let it hang down, like a long spiral snake. Look at it from the top; you'll see that the long spiral is sectioned by the 4 skills. As you go deeper into the spiral, you go deeper into each skill.

 

Mastery is staying on one topic until it's mastered, then moving to the next skill, with a small amount of review as you go along. MUS, Making Math Meaningful, Key To... series, are all mastery-based.

[Hillcrest Academy]

Thank you! That is along the lines of what I was thinking.

 

Hmm. The spiral approach makes sense to me.

[Julie in GA]

Singapore and Rod & Staff, however, are closer to a mastery approach than Saxon. They will repeat the spiral each year, but Saxon spirals around several times each year, making it an "incremental" approach.

[Hillcrest Academy]

Oh boy - just when I thought I had it down!:glare:

 

So how does the incrimental approach differ from the spiral approach? Do I understand it correctly in thinking that with the spiral approach it may do one spiral per year, but with incrimental it does more than one spiral in one year?

 

If so, what would the benefits of an incrimental approach be?

[Kathie in VA]

I tend to think of the difference as how 'review' is used. With a spiral approach, a new topic is taught about every day. Then they work some problems using the new lesson, then there are lots of problems that review past lessons. Basically if they don't fully get the new lesson down cold it's okay because they will get more chances as it comes up again in future reviews. So these 'reviews' are only a review for the kids that have mastered the material, others end up using the review problems as another chance to finally learn the lesson. I think incremental spends a bit more time on the new information but still uses the reviews to really learn the lesson. Mastery programs do not have a new lesson everyday. Instead they teach something new and then work basic problems related to the new lesson till it's about mastered. Then they work on more advanced problems related to the new lesson but also includes skills learned in past lessons (math really does build). If a separate review is included, it is really there just to review and put together all that was learned up to that point. Some mastery based programs use more review then others.

 

BTW: I think Saxon is Incremental, MUS and Singapore are Mastery, Horizons is Spiral.

 

hth

[Suzanne in ABQ]

I agree. I wouldn't ever describe Saxon and Singapore as having the same approach. They're quite different.

 

Saxon introduces topics in tiny little nibbles, does a few problems for practice, then spends the majority of the lesson reviewing the previously introduced tidbits of topics. You don't have "chapters" in which you learn specific concepts. After awhile, you are learning several concepts at the same time, practicing different kinds of problems within the same lesson. This works really well for some kids.

 

Singapore, OTOH, introduces a skill level for each concept (say, addition and subtraction within 10), and teaches you to master it. You then go on to use the skills learned in that skill level of addition/subtraction to learn multiplication and division within an appropriate skill level. (I can't remember how they define the skill levels for mult/div). The next year, the skill level increases (addition and subtraction within 20). You master that, and then use that skill to learn the next level of multiplication and division. The other concepts (measurement, geometry, graphs, etc) are covered the same way. The concepts are revisited each year, but the skill levels are mastered before moving on to different concepts. The chapters are divided by concept, and there is never a doubt as to what you are trying to learn. At the end of each chapter, they have several "Practices" in which you review the skills in that chapter. Periodically, they have comulative "Reviews", which cover material from all previous chapters.

 

I don't know if I'm making sense (I should be in bed), but I hope this is helpful.

 

Is there a convention coming up, or some way you (original poster) can look at the different programs to compare for yourself?

[Suzanne in ABQ]

I'm curious. For years, Singapore has been classified as "mastery", compared to Saxon, which has been described as "spiral". Only recently (the last few weeks) have I seen Singapore and Saxon both classified the same (spiral). This really suprises me because for years, on this very board, there were "passionate" discussions about the differences between the two programs, and how the mastery approach of Singapore is so far superior/inferior than the spiral approach of Saxon.

 

My questions: I'm very aware of the vast differences between Singapore and Saxon. What is it that makes Singapore more like Saxon, and less like MUS or MMM, that you classify it as spiral instead of mastery? Do MUS and MMM really teach addition to absolute mastery before moving on to the next concept? And, if so, how far do they take it? Do they teach addition up to columns of multi-digit numbers before moving on to subtraction, or simple multiplication? I'm asking because I've never seen either MUS or MMM. I don't understand how any arithmetic program can teach little kids to absolute mastery before moving on.

 

Thanks for your insight.

Suzanne

[angela in ohio]

Singapore is a mastery approach. Mastery is the traditional approach we all grew up with - each year you may learn similar topics as the last, but they are dealt with in separate chapters. Saxon (and A Beka & Horizons) have a different format, where topics are reviewed that same year, thourghout the year. Because a program repeats topics from one year to the next does not make it spiral. Saxon could be considered a subset of the spiral approach, as it is also incremental.

[Closeacademy]

Singapore is not spiral. It may cover similiar topics in the same order each year but it is at a higher level.

 

For instance: For levels 2 through 4, the first topic in each level is place value but place value in level 2 is three-digit, and level 4 is 5 digit numbers.

 

Level 1 spends a lot of time in various parts on first numbers within 20 then within 50 then within 100.

 

Each level also has a main focus that you need to master in that level or you will be lost when you get to the next level.

 

Level 1 that would be addition and subtraction

Level 2--addition and subtraction with regrouping and multiplication and division

Level 3--multiplication with regrouping and division with remainders

Level 4--fractions

Level 5--decimals

Level 6--has a bunch of different topics not touched on by the lower levels.

 

Now it does cover measurement and such each year but by level 3 they are doing very difficult problems with it and have to really have their other math skills down to get through it.

 

I would say that Singapore is mastery because if you do not master it in the lesson where it is brought up then you will not be able to do the math that comes after. There is some review in the books but it is not a daily thing. And other than on the review pages in the text or workbook will you see a list of problems that are mixed review like you will see on a review page in Saxon, Rod and Staff or Rightstart math.

 

Singapore is mastery not spiral. If it was spiral like Saxon or Rightstart we would not be using it because like scripts just getting a nugget of math each day and moving on to something else the next day and finally getting back to that first nugget 5-6-10 days down the road is just maddening to us. But it can work very well for others.

 

Just my 2 cents.:001_smile:

[Hillcrest Academy]

OK, now I'm completely confused ;)

 

I do have a convention at the end of the month which I'm very excited to go to. I will definitely have a look there.

 

I'm looking for a program that introduces a concept and works for mastery before moving on. The way I "lost" math as a kid was not understanding some foundational basics before they moved on, and I just never got it after that. I had enough to pass but it was a frustration and has left me "math handicapped" for life.

 

I don't want a program that takes many years before it touches on some concepts. I want them to learn everything at it's basic level, and then move on in difficulty in steps, doing everything (or most things!) before moving on to the next difficulty.

 

What would that be?

[lighthouseacademy]

Here is a wrench to throw in- RightStart. I consider RightStart spiral by the definitions here.

[nmoira]

 

I'm curious. For years, Singapore has been classified as "mastery", compared to Saxon, which has been described as "spiral". Only recently (the last few weeks) have I seen Singapore and Saxon both classified the same (spiral). This really suprises me because for years, on this very board, there were "passionate" discussions about the differences between the two programs, and how the mastery approach of Singapore is so far superior/inferior than the spiral approach of Saxon.

Singapore spirals once per year. You could look at it as spiral with mastery (as opposed to something like Everyday Math which doesn't expect mastery). The important thing about Singapore is that topics don't spiral frequently and that mastery of concepts presented is expected. Saxon, at least in the early years, is incremental. This can greatly frustrate kids that either need to see the whole picture to "get it" or who just "get it."

[nmoira]

 

Here is a wrench to throw in- RightStart. I consider RightStart spiral by the definitions here.

I dunno how to classify it... RightStart is a different animal. If you look at it by level, it's definitely mastery, but if you look at it by lesson, it's spiral.

[Melissa in CA]

...getting a nugget of math each day and moving on to something else the next day and finally getting back to that first nugget 5-6-10 days down the road is just maddening to us.

 

Same here!! My boys absolutely hated Saxon for this very reason. Because no mastery of true understanding is expected when a concept is first taught, it seemed like they were constantly having to revisit/relearn several concepts everyday...including the current days new concept. It was maddening; all the flipping back and relearning. Ack! At least in the newer versions of Saxon they began to list the lesson number next to the problem so you knew which lesson to flip back to to answer said problem. With my older boys they did not have this when we first began Saxon, it was like going on a hunt everyday. I cannot express how much they detested this program...and being the wonderful unobservant not-willing-to-look-elsewhere-because-virtually-EVERYONE-used-Saxon-so-it-must-be-the-very-best kind of mother, I tortured them with it for two looooooong years. ;)

 

Give me concept chapters, thank you very much, which will teach the concept in a deep and meaningful way, then add in review questions in later chapters to keep it all fresh. I don't know if this is called mastery or spiral, but I call it wonderful. :D