Spiral vs Mastery

[Nm.]

Is there any solid research about one or the other?  I can only find a little bit of research on spiral- but then it seems like its by a spiral company?  Just curious. 

Edited June 15, 2023 by Nm.

[LostintheCosmos]

I'm not sure where the terms "spiral" and "mastery" originated - I've only ever really seen them used by homeschoolers. If you want research on the underlying pedagogical questions, though, you might look for stuff on "spaced repetition" and the "forgetting curve," "interleaved practice," and "overlearning."

[Clemsondana]

I once heard an elementary school teacher say something along the lines of 'If a kid doesn't understand something, that's Ok - just trust the spiral and they'll get it eventually'.  That meaning of spiral seemed nuts to me.  We teach to mastery.  But, there have been times when we take a break from something and come back.  There isn't any 'hoping that they get it next time' - it's a decision to stop going down an nonproductive path, and we then intentionally come back to the material and do it to mastery.  But, with that, we do review.  Most kids can't be adept at something that they don't do for months at a time.  This meant that when my older did geometry, we did some algebra review because I didn't trust that kid would remember it all.  

For us, Singapore Math was a good combo -- we worked to mastery, but there was end-of-unit review and we could revisit anything that was forgotten.  Other programs likely have a different balance, so you'll have to find what works for your family.  

[Nm.]

That’s really helpful.  Perhaps just using those techniques with the programs I use would work.  I think spacing out hard lessons in math mammoth will help a lot.  Work on multiple chapters.  I do really like how much they like tgtb math and how it doesn’t overwhelm them- but my oldest would need level 7.  It is on the easier side.  He does forget a lot- so just being more mindful of review should help when we start math mammoth back up.  I also like how prealgebra is covered in math mammoth 7.  My DH has said that the topics he struggles with is a hard thing for all kids to get.  Multiplying/dividing decimals has been the latest sticking point.  He finally understood after I just spaced out the lessons (not purposefully doing so).

I can also use these techniques with AAR 4 for my son with dyslexia.  I really don’t like switching curriculum.

Edited June 14, 2023 by Nm.

[8filltheheart]

The terms do make sense in terms of how different textbooks are arranged and present material.  There are definite mastery textbooks and there are definite spiral textbooks.  When you have taught both, you can see the distinctions.   SM, MM, MiF....they are all mastery textbooks.  Concepts are arranged in units with a particular focus.  Horizons is spiral.  New concepts are not the focus of a unit.  They are introduced and practiced but that is only a portion of a lesson.  The rest of the lesson includes previously taught concepts.  As the book progresses, the introduced concepts build upon each other, but they are always intertwined with other problems.  It is why flipping through a textbook like Horizons makes it difficult to do a simple assessment bc you can't see the entire progression of teaching in any specific place.

I have only ever seen Saxon teach spirally  at the non-elementary level (but its spiral is more than simple spiral, it is also incremental bc the concepts are broken down into so many small progressions).  The high school level textbooks we have used have all been mastery focused.  

My kids have done well with both approaches, spiral for elementary and mastery for high school.  I'm not sure one is necessarily better than the other.  They are simply different.  But, I have also never really researched any info on the 2.  Just my experience with my kids that it doesn't have seemed to matter much.  (Though, with my granddaughter it might.  She needs a lot of review to maintain or things tend to be completely forgotten.)

[EKS]

Note that there is also a third option (at least when we talk about this on here) which is incremental development.  That's what Saxon does.  It's kind of a spiral superimposed on a larger spiral.  Singapore is an example of a classic spiral, where they generally circle back to concepts every year, expand on them, and add some new ones as well.  Math U See is the most mastery oriented program I'm aware of, where it's all addition/subtraction for two whole years!  Then multiplication for a year, then division, then fractions, then decimals/percents.  Saxon circles back to things every year, but they also split up the learning of a particular concept into a bunch of little pieces and then distribute those pieces with practice in between.  

Edited June 14, 2023 by EKS

[Nm.]

I definitely agree with you@8filltheheart.   I think I want to try intentionally using some of the spiral techniques that seem to help them with math mammoth vs switching curriculum.  I am interested in whether there’s evidence based research in these techniques/styles incase I’m being too stubborn on my mastery stuff 😂 .

I’ve never looked into Saxon.  Is it still incremental in highschool?

Edited June 15, 2023 by Nm.

[EKS]

9 minutes ago, Nm. said:

Is it still incremental in highschool?

I assume so.  I have not used anything above 8/7.  I'm sure someone will chime in here and let us know for sure.

[HomeAgain]

A good program straddles both.

When a student is working to mastery with a technique or concept, it means they have the ability to use that same concept in other ways.  It's saying, great, you have the basics, let's continue to use this idea in a new way.

There is always review because it's a feature of development.  It's like learning to skate.  The child first learns to fall.  That's the absolute first lesson in a good program.  Learn to fall down.  Then take steps forward.  The steps become glides, and as they step, they fall.  The gliding begins to include moving backward.  Same motion, different direction.  Then crossovers forward - the kid is still falling, still gliding, still moving forward and backward as they're incorporating something new.  Nothing is isolated, but every new skill to that point has met a definition of mastery for the development.  There's no "ah, we'll put off any falling this week and incorporate it next week again."  No, everything is used every lesson as the new skill is worked on.

I think one of the things we get hung up on in math is that a program must be one or the other.  It must run through concepts in turn or spend too long on one concept to the detriment of the others. We forget to include the invisible thread that stringing them together and making it cohesive and understandable to the student.  A good course will absolutely bring in the previous work and make it all mastery and continue to include new elements one at a time.

 

[8filltheheart]

16 minutes ago, Nm. said:

Is it still incremental in highschool?

Yes, from what I remember.  My oldest used part of the alg 2 textbook and it was an absolutely horrible fit for him.  I learned quickly that Saxon was not a good match for my kids.

[Nm.]

  DS9 with dyslexia / learning delays seems to do better with mastery + review. 

Edited June 15, 2023 by Nm.

[Ellie]

1 hour ago, Nm. said:

I’ve never looked into Saxon.  Is it still incremental in high school?

Yes.

Also, I think presentation is important, moreso t6han whether it's "spiral" or "mastery." And children who need manipulatives need those manipulatives whether the instruction is spiral or mastery. So that's my first inspection of something: is it heavily based on manipulatives, or is it more traditional. My children would die if they had to manipulate everything.

[Nm.]

https://www.itac.edu.au/blog/teaching-strategies/overlearning#:~:text=Overlearning can be thought of,the origins of each word.

https://granite.pressbooks.pub/teachingdiverselearners/chapter/surface-and-deep-learning-2/

Interesting.. surface learning/ deep learning, over learning.

@EKSI also realize math mammoth and most other programs are technically a  spiral program when looking at the “research”.  They just don’t spiral each day.  Topics are introduced and revisited with increasing difficulty each year.  They certainly don’t teach all of fractions (or any other topic) in one unit.

I think this is an advertising ploy for many companies:

https://www.goodandbeautiful.com/blog/spiral-math/

https://www.abeka.com/blog/spiral-learning/#gref

 

Edited June 18, 2023 by Nm.

[Tanager]

What gets me the most in the elementary years is how each grade breaks up the basic 4 (+,-,*,/). Once my kids understand how to carry numbers I just teach them straight on through from two digit addition to bigger numbers. Same with subtraction, I understand the public schools divide it out so that they catch kids who didn’t get it the year before, but with homeschooling, I know if my kids didn’t get it and we can address it. It drives me crazy that each grade adds another step. Same with multiplication and division once they master the times table I just teach them the steps all the way through to multiple digits. I also find myself combining percents, fractions and decimals when we hit those topics in a book to give them a complete overview. I have yet to find my favorite math curriculum (besides the early years which is Montessori followed by miquon.) 1 kid does Saxon and the other uses Singapore. Both have different math brains.
I wish overlearning had a better name, it sounds so negative, but makes so much sense.

Edited June 14, 2023 by Tanager

[FreyaO]

3 hours ago, Clemsondana said:

I once heard an elementary school teacher say something along the lines of 'If a kid doesn't understand something, that's Ok - just trust the spiral and they'll get it eventually'.  That meaning of spiral seemed nuts to me.  We teach to mastery.  But, there have been times when we take a break from something and come back.  There isn't any 'hoping that they get it next time' - it's a decision to stop going down an nonproductive path, and we then intentionally come back to the material and do it to mastery.  But, with that, we do review.  Most kids can't be adept at something that they don't do for months at a time.  This meant that when my older did geometry, we did some algebra review because I didn't trust that kid would remember it all.  

For us, Singapore Math was a good combo -- we worked to mastery, but there was end-of-unit review and we could revisit anything that was forgotten.  Other programs likely have a different balance, so you'll have to find what works for your family.  

Side note - I went to school in another country and we did Algebra 3x and Geometry 2x per week in parallel. 

[Nm.]

11 minutes ago, FreyaO said:

Side note - I went to school in another country and we did Algebra 3x and Geometry 2x per week in parallel. 

I just read somewhere that learning more than one topic can boost learning.  
https://www.edweek.org/teaching-learning/opinion-the-what-why-how-of-interleaving/2021/05

this would be incredibly easy for me to do with math mammoth.  

Edited June 14, 2023 by Nm.

[EKS]

1 hour ago, Nm. said:

They just don’t spiral each day.

You're talking about continual review.  That's not the same as a spiral.

[Nm.]

1 hour ago, EKS said:

You're talking about continual review.  That's not the same as a spiral.

So abeka, cle, tgtb have continual review?  Makes sense.

[8filltheheart]

I don't know about the other 2, but Abeka is similar to Horizons and is spiral.  Spiral is different than continual review bc there are not mastery units.  No single concept is the main focus for a chpt.  All new concepts are introduced within a lesson full of review concepts.  I don't know how to explain it other than that.  They are distinctly different.

[Nm.]

@8filltheheartthats what homeschoolers define that as.  I think what I’m trying to say is that the interval is just longer for Singapore, math mammoth etc.  It still spirals each year building upon prior knowledge- adding to the depth vs spiraling every day/ few days.  When looking into the research that is touted for spiral- it is kind of weak and doesn’t necessarily vouch for tight spiral curriculum like horizons or CLE.

https://en.m.wikipedia.org/wiki/Spiral_approach  This is what I am talking about (forgive me for using Wikipedia 😂)

[8filltheheart]

Horizons and others also spiral back through old concepts every yr.  I have no idea about research.  I would say that by 6th grade they all end in the same place regardless of spiral vs mastery.

[Tanager]

3 hours ago, FreyaO said:

Algebra 3x and Geometry 2x per week in parallel. 

Taking Geometry with algebra 2 (1 credit each) was common in my high school so that there wouldn’t be an algebra gap. Saxon also combines them.
 

I think it’s really all about an individual. Research on my daughter would look completely different than research on my son. Some kids do much better with a spiral, for my daughter ( possible ADD) saxons spiral got it in her long term memory. Some don’t need a spiral. And some would find it incredibly redundant.

[Clarita]

1 hour ago, Tanager said:

I think it’s really all about an individual. Research on my daughter would look completely different than research on my son. Some kids do much better with a spiral, for my daughter ( possible ADD) saxons spiral got it in her long term memory. Some don’t need a spiral. And some would find it incredibly redundant.

I think it also would depend on the educator. 

In our family, the parents are so mathematically inclined review gets built-in because our normal everyday conversation includes topics in arithmetic through algebra. Between the adults there are often conversations including topics in calculus, statistics, number/set theory, etc. I can see another family and their kids needing more explicit review (introduction to other topics) built into their math curriculum. This is something that I need from our language arts curriculum because it doesn't come naturally to me to discuss it with my kids as we see it in real life. Definitely nowhere near how much I incorporate the math and science review and discussion.  

[Nm.]

I agree with all of you!  Just trying to get to the bottom of some companies’ claims that spiral curriculum is proven to be more effective than what we call “mastery”.. but technically very few curriculums are pure mastery without any review.  Excited to have some new ideas to incorporate into our math -like working out of a couple chapters (interleaving), Spaced repetition, overlearning, etc.  Curriculum is just a tool, it’s nice to have other tools instead of relying on a publisher to come up with something perfect. 

https://www.abeka.com/Homeschool/SpiralLearning/#

*The studies they cited do not really point to “spiral curriculum”, at least to me.

Edited June 15, 2023 by Nm.

[Farrar]

When my kids were younger, I didn't really appreciate how much they would need some spiraling in math. I had the idea that they'd master a thing and that would be that. But the truth was that even in the elementary years when we were schooling yearround (so no "learning loss" over the summer), they still would forget things and need to review and re-up their skills. 

I think the best texts are structured to review some, to get kids to practice old skills in the context of new ones, and to challenge them to deepen their knowledge on something that they've mostly mastered.

But mostly, I think trust a good program and modify the pace and review as needed for your individual kids. 

[LostintheCosmos]

4 hours ago, Nm. said:

https://en.m.wikipedia.org/wiki/Spiral_approach  This is what I am talking about (forgive me for using Wikipedia 😂)

Oh, yeah, Jerome Bruner was really into spiraling the curriculum, I forgot about him. And poking around some more I did find a the use of "spiral" as a descriptor in a few non-homeschool math contexts, including UChicago's infamous Everyday Mathematics. My sense is that Bruner is fairly out of fashion these days - I wonder why the spiral language seems to have stuck around in math more than other subject areas. You do see the concept elsewhere, like in history rotations (not spirals).

I suspect most programs, spiral or mastery, do not provide enough practice for many if not most students and that real overlearning requires way more reps than we generally realize (and that's why we might want to be attentive to tools for making our practice as efficient as possible). Zig Engelmann, the original Direct Instruction guy, estimated that most students actually need about 5x the amount of practice contained in most programs used in schools. My hunch is that (some) homeschool math programs do better than this, but still don't generally provide enough practice, at least if we go by how many of us find ourselves needing to review previously studied topics or have to supplement with extra drill for things like multiplication tables.

[Ellie]

1 hour ago, LostintheCosmos said:

 My hunch is that (some) homeschool math programs do better than this, but still don't generally provide enough practice, at least if we go by how many of us find ourselves needing to review previously studied topics or have to supplement with extra drill for things like multiplication tables.

And don't forget the homeschool mom who picks and chooses which problems her dc do, and have them move on to the next thing once she thinks her dc "understand the concept."

[Clarita]

29 minutes ago, Ellie said:

And don't forget the homeschool mom who picks and chooses which problems her dc do, and have them move on to the next thing once she thinks her dc "understand the concept."

Not every math curriculum thinks overly hard about the practice problems they put in. Some of them do say you can skip problems and provide extra ways for you to incorporate the necessary practice that is not just book work. 

[Nm.]

6 hours ago, Ellie said:

And don't forget the homeschool mom who picks and chooses which problems her dc do, and have them move on to the next thing once she thinks her dc "understand the concept."

Yes!  I started doing that recently and I think I’ll stop.  Just having them rotate topics in math mammoth should ease the frustration/monotony enough.

[Nm.]

8 hours ago, LostintheCosmos said:

Oh, yeah, Jerome Bruner was really into spiraling the curriculum, I forgot about him. And poking around some more I did find a the use of "spiral" as a descriptor in a few non-homeschool math contexts, including UChicago's infamous Everyday Mathematics. My sense is that Bruner is fairly out of fashion these days - I wonder why the spiral language seems to have stuck around in math more than other subject areas. You do see the concept elsewhere, like in history rotations (not spirals).

 

What’s interesting is that his spiral approach resembles Singapore and other programs like it.  Children in the first year or 2 are being introduced to fractions, addition, subtraction, multiplication, division, algebra, etc. it’s revisited each year. It doesn’t seem to advocate for topics to be dispersed throughout the year like “spiral curriculum”. 

Abeka cites two studies for their spiral curriculum and they seem to be more about the need to review and use what you learn (forgetting curve).

Also not saying it doesn’t work to disperse the topics, but there really isn’t any evidence I can find to say it works better.  It seems a disaster for at least my DS9 and DD6.  Can you imagine dispersing phonics like that?  It might work for a few who are naturally inclined..

Why is this important?  It’s not 😂 just helpful for me not to worry I’m missing out on some approach that has been “proven to work.”  Especially when I hear from others it’s evidence based.

To alleviate the forgetting curve- review helps- which I wasn’t doing regularly.

[LostintheCosmos]

2 hours ago, Nm. said:

Why is this important?  It’s not 😂 just helpful for me not to worry I’m missing out on some approach that has been “proven to work.”  Especially when I hear from others it’s evidence based.

Increasing homeschool mom self-confidence in the face of bogus marketing claims is actually VERY important! 🙂

[8filltheheart]

7 hours ago, Nm. said:

It doesn’t seem to advocate for topics to be dispersed throughout the year like “spiral curriculum”. 

.  Can you imagine dispersing phonics like that?  

I'm not sure I follow your post. This is exactly how most phonics programs are set up. Content isnt randomly dispersed. Content is introduced and built upon while reviewing previous skills.

[Clemsondana]

8 hours ago, Nm. said:

What’s interesting is that his spiral approach resembles Singapore and other programs like it.  Children in the first year or 2 are being introduced to fractions, addition, subtraction, multiplication, division, algebra, etc. it’s revisited each year. It doesn’t seem to advocate for topics to be dispersed throughout the year like “spiral curriculum”. 

Abeka cites two studies for their spiral curriculum and they seem to be more about the need to review and use what you learn (forgetting curve).

Also not saying it doesn’t work to disperse the topics, but there really isn’t any evidence I can find to say it works better.  It seems a disaster for at least my DS9 and DD6.  Can you imagine dispersing phonics like that?  It might work for a few who are naturally inclined..

Why is this important?  It’s not 😂 just helpful for me not to worry I’m missing out on some approach that has been “proven to work.”  Especially when I hear from others it’s evidence based.

To alleviate the forgetting curve- review helps- which I wasn’t doing regularly.

What I found interesting about Singapore is that it came back to topics while teaching new information.  It did multiplication every year, for instance, but the first year was just 2s, 3s, and 5s (I think, it's been a while).  The next year added 4s and 6s, etc.  So, it avoided having kids memorize everything from the zeros to the 12s at once, keeping the memorization small.  And it was consistent - you learn to multiply by 2, 3, and 5, then divide by 2, 3, and 5, then tell time (needing to count by 5s to do the minute hand), convert yards to feet, and maybe fractions of halves and thirds, too,   When students do multiplying by 10s and 100s, they then learn metric conversions.  This seems far better than what I see with the kids that I volunteer with, where they just do some multiplication that they never learn every year.  With this, done well, kids master a small set of facts and a few concepts and then use them.   The next year they revisit the concepts and learn new facts.  I hadn't realized how systematic it was at first.  

[Nm.]

54 minutes ago, 8filltheheart said:

I'm not sure I follow your post. This is exactly how most phonics programs are set up. Content isnt randomly dispersed. Content is introduced and built upon while reviewing previous skills.

I’m picturing a lesson on vowel team ea one day +(reviewing a bunch of other stuff), the next day ou, the next day suffix est, etc.  The ones I use spend time on each thing before moving on.  

[8filltheheart]

11 minutes ago, Nm. said:

I’m picturing a lesson on vowel team ea one day +(reviewing a bunch of other stuff), the next day ou, the next day suffix est, etc.  The ones I use spend time on each thing before moving on.  

That is not the way spiral programs work.  

[Nm.]

6 minutes ago, 8filltheheart said:

That is not the way spiral programs work.  

Is this what horizons looks like?

[8filltheheart]

I can't say I ever looked at the TOC to see how things are labeled, but everything is very logical in sequence and presentation.  So, they may work on taking 67 as 6 10s and 7 1s and transforming it into 5 10s and 17 1s in the same lesson as reviewing perimeter.  They would continue the 10s/1s process for multiple lessons (I'm guessing maybe 7-10 lessons) and then subtraction with borrowing is then introduced continuing to use the same process.  In between they might have had review of addition, clocks, etc.  When you work through the books, the building of concepts is progressively moving along. 

It goes back to my pt that when looking through spiral programs you can't just flip through the book in a few minutes to see how the concepts are presented.  You actually have to spend time looking at every lesson to see the building of skills.

I'm not arguing with you at all.  I can see where some kids definitely need mastery presentation to master content.  But, it is definitely not appropriate to label spiral programs as having content randomly dispersed bc it is far from random and is very deliberately designed.  (Well, at least Horizons is.)

Edited June 15, 2023 by 8filltheheart

[Nm.]

Well it could be tgtb is in a class of its own.  It feels very random.. each day has a video with new content, and no more than 2-3 lessons on a given topic (except in review).  I think DD9 could possibly do ok with it but she doesn’t struggle with anything except attitude.

Edited June 15, 2023 by Nm.

[8filltheheart]

Just now, Nm. said:

Well it could be tgtb is in a class of its own.  It is very random.. each day has a video with new content, and no more than 2-3 lessons on a given topic (except in review).  I think DD9 could possibly do ok with it but she doesn’t struggle with anything except attitude.

Keep in mind that TGTB is self-published homeschooling material.  It is not a professionally designed math curriculum.  

[Nm.]

Could be I didn’t give it enough time.  It was created by a math team (not Jenny Phillips) and reviewed by a team of “experts”- one with a PhD in mathematics, MA in math, and some others.  Not that that means anything but they did put a lot of thought and money into the program.  

Edited June 15, 2023 by Nm.

[8filltheheart]

3 minutes ago, Nm. said:

Could be I didn’t give it enough time.  It was created by a math team (not Jenny Phillips) and reviewed by a team of “experts”- one with a PhD in mathematics, MA in math, and some others.  Not that that means anything but they did put a lot of thought and money into the program.  

LOL......Ok.  So a lot of thought went into the program that 

1 hour ago, Nm. said:

 is very random.. each day has a video with new content, and no more than 2-3 lessons on a given topic (except in review)

Sorry.  That is just too funny to not comment on.  I would never use those words to describe any math curriculum that I have ever used.  I have used or spent significant time with math programs that I haven't liked or that I thought were too weak.  But "very random" are not words that I would use for describing my evaluation of them.

[Nm.]

I am just agreeing with you in the sense that there may be a method that’s organized like you find in horizons and I’m not seeing it yet.  

[BusyMom5]

I find that Math really varies by kid and instructor ;)  I have used lots of different programs over the years, both spiral and mastery.  Marketing strategies are designed to sell, so don't listen to anyone's hype about the new latest and greatest curriculum. 

In my own sample of kids, in elementary my favorite combo is Saxon and Math in Focus (previous edition- I'd probably get Primary Mathematics now).  Saxon is very incremental and it has lots of different types of problems each day, which my kids prefer!  Then I like to follow up with a more mastery-based program like MM, MiF, PM that focuses more on one topic at a time.  My kids are good with doing 2 programs a year at the younger ages. 

This past year my youngest started doing math.  I have PM (new 2023 edition), MwC, and Saxon 1.  Her favorite- Saxon.  I asked her why one day- it's the only one that's black and white, it looks more boring. Her reply, she likes doing all kinds of math on the same page, not just all the same kind.  I think this sums up my kids preferences!  Too much of the same thing is boring, they prefer a variety every day.   

The mastery-based programs that we use- I try to just pick certain chapters I think they need to focus on a bit more.  Usually its review, so they speed through it, but they are looking at the entire years Worth of the subject, so it might sink in a little more.  

I tried sooo hard to use MM, but my kids hated it.  I even printed out 2-3 chapters at a time, and would do a few from each chapter each day- making my own spiral.  It just wasn't what my kids wanted.

Teaching math depends on what the teacher needs in order to feel confident,  and what the student needs.  Some of mine love manipulatives and learn better with them.  One HAD to have visuals and lots of repetition.   One still just plays with them and learns much better by drawing pictures.  The whole mastery vs spiral is overblown.  All kids need material to be reviewed frequently.  

[8filltheheart]

@BusyMom5's description of her kids' preferences sums up mine.  They definitely preferred a wide variety of topics every day.  I have used 2 programs simultaneously before (Horizons and MiF) with one of my very stubborn complaining kids.  Long story short, I warned if she didn't stop complaining that I was doubling her load so that if I had to listen to complaining at least it would be valid.  She didn't stop.  I kept my word.  She did 2 math programs 4,5, and 6 grades.)  She stopped complaining 1/2 way through 4th, but then she started saying she liked doing both (get an idea of her personality??  LOL.  No way was she going to think I had won!)  Since she said she liked doing both so much, I just kept on having her.  LOL.  Ah!  The joys of parenting and homeschooling!!  

@Nm. It could very well be you haven't given it enough time.  When I read about people's complaints with Horizons, the complaints usually reflect a mastery presentation expectation which is just not going to be found in the spiral approach.  It really does take working through the books to develop an understanding of how the program is structured.  You could spend some time yourself looking through every lesson to see if the progression starts to make sense to you.  If it doesn't, I'd switch bc you as teacher need to be able to teach it and that requires being able to follow the logic.

[Nm.]

36 minutes ago, BusyMom5 said:

 

The whole mastery vs spiral is overblown.  All kids need material to be reviewed frequently.  

That was the original purpose of my post was to understand if there’s really any evidence either way.  But I’m glad for the other topics because I’m learning a lot I didn’t intend to learn 😉

I think DD9 would prefer lots of different problems each day.  Following up with some chapters of math mammoth makes sense.  Thank you so much ☺️ 

[Nm.]

1 hour ago, 8filltheheart said:

Long story short, I warned if she didn't stop complaining that I was doubling her load so that if I had to listen to complaining at least it would be valid.  

This sounds like a good idea for DD9.  I’m really over the math attitude!!

[Ellie]

22 hours ago, Clarita said:

Not every math curriculum thinks overly hard about the practice problems they put in. Some of them do say you can skip problems and provide extra ways for you to incorporate the necessary practice that is not just book work. 

It's why you (the teacher) need to read the TM to see if there are any instructions for that. In particular, Saxon math, from 54 on up, requires all problems to be done in all problem sets, but most people don't read the intro in the student text to see what it says about that.