Elementary math programs written by mathematicians

[lulalu]

Ok we have only half of the last Miquon book left 😢 we have loved it! I really wish it went through all of elementary. So anyways ds will be in 3rd next year, and I am looking at programs. We have used Gattegno books too and will continue with that. But I  wondering if we can make a list of programs written by mathematicians. Or at least written by those whose focus is math. 

I can think of:

Beast Academy

Math Mammoth

Saxon

RightStart

Singapore

 

Are there some that are still solid math instruction written by a broad curriculum provider? I hear CLE is a good math program right? 

[maize]

Jo Boaler's Mindset Mathematics series; she's a Stanford professor whose research focuses on effective mathematics instruction, especially developing a problem-solving mindset.

[Homeschoolmom3]

Also check out Marilyn Burns books I have used a lot of hers and I like Hands on Equations and he also offers Fraction sense which I have looked at that looks promising I plan on using if for my. Fourth grader next year https://www.borenson.com

 

[lulalu]

Any thoughts on CLE math? Does it make you think? I can't tell from the samples how much thinking there is. I don't mind some circling, matching and so forth, but I don't want all problems like that. Some I want to involve the student doing all the work and thinking. I hope that makes sense. But the appeal of open and go is nice. So far I have used Miquon which we will finish very soon, making my own sheets, RightStart games, and Gattegno. But I have a hard time just following curriculum. I like flexibility. And I know I will tweak stuff. 

[lulalu]

34 minutes ago, mms said:

 

You might look into MEP, which is available free. After Miquon it is probably my all time favorite published math curriculum.

I have tried MEP several times. I loved the Reception. But I tried 1 and just couldn't get into a routine with it. Then this year printed year 2 out and got about a month in and quit. I can't put my finger on what it is that doesn't work, but it just doesn't work for me. 

[lulalu]

2 hours ago, mms said:

 

Also, at a certain point progressing at a steady, consistent pace is far more important than any particular program. I jumped around way too much with my oldest looking for a curriculum unicorn. In retrospect, I should have picked something and stuck with it, adjusting for the weaknesses as we went along.

This is what I was wanting to avoid- switching up programs. I so wish Miquon kept going. My big hang up is I know what works for me- non scripted, open ended, discovery based. But finding stuff that is done well is hard. 

I may just need to get something to stick with and add in or take out as we go along. Games have been a great learning tool here. I know I would add in a game day no matter what we use. 

[lulalu]

40 minutes ago, square_25 said:

 

Very much this. At some point, math is math. You want to make sure your child is understanding the concepts and progressing, but there's always more than one way to get there, and often the "magic tool" that promotes understanding is simply time and experience using the ideas in a way that make sense to the kid. 

DD7 is gifted in math, and that was still true for her. There were concepts that she just needed time to chew over. And chew over and over, until she got it. My explanations were not a key part of her understanding, whatever direction I came from. 

Yes, but some programs really are not well done. I have looked at a lot (I taught before becoming a mother). Some homeschool ones on the market really don't present concepts well. 

With CLE I keep looking at the samples, and I like how it is all in one workbook and directions are clearly written. But I can't tell if the student has to think or just do a lot of matching and circle the right answer type problems. Also, it seems to just do a lot of procedure work

[lulalu]

1 minute ago, square_25 said:

I don't think Beast Academy is nearly as well done as Miquon, from what I've seen from Miquon, but have you looked at it much? 

I have looked at the samples, and did the free month online. I do think ds would love it. We got through the first chapter in 2A easily, which I know it will get more challenging. We would use the books though, I have a dislike for online learning. My worry is that it is made for gifted mathy kids. DS loves math, and I really do think he has a great sense of numbers, relationships, and procedures. But it isn't like he is doing 4th grade level now (finishing 2nd grade) or anything highly advanced. What he knows, he knows deeply, and he can use what he knows to figure stuff out. Gattegno does start off in a very different order too so he has had a lot of algebra already. He kind of is all over the place. 

Right now my thoughts for going forward are between Beast or MM or CLE with me adding in the things we already have that are working. I am leaning towards Beast because I do think it would look much closer to what we have been doing. And he needs some things to stretch him with his willingness to try hard things. 

But I also then go back to the idea of me mostly making my own stuff and using Gattegno, and games. It is a lot of work, but then I am able to just make it exactly what ds needs to work on. But really I think I need a break from doing that as the bulk of our work, and just make stuff when needed. 

 

[8filltheheart]

29 minutes ago, lulalu said:

I have looked at the samples, and did the free month online. I do think ds would love it. We got through the first chapter in 2A easily, which I know it will get more challenging. We would use the books though, I have a dislike for online learning. My worry is that it is made for gifted mathy kids. DS loves math, and I really do think he has a great sense of numbers, relationships, and procedures. But it isn't like he is doing 4th grade level now (finishing 2nd grade) or anything highly advanced. What he knows, he knows deeply, and he can use what he knows to figure stuff out. Gattegno does start off in a very different order too so he has had a lot of algebra already. He kind of is all over the place. 

Right now my thoughts for going forward are between Beast or MM or CLE with me adding in the things we already have that are working. I am leaning towards Beast because I do think it would look much closer to what we have been doing. And he needs some things to stretch him with his willingness to try hard things. 

But I also then go back to the idea of me mostly making my own stuff and using Gattegno, and games. It is a lot of work, but then I am able to just make it exactly what ds needs to work on. But really I think I need a break from doing that as the bulk of our work, and just make stuff when needed. 

 

I can't remember where my dd was in math when I bought BA2. She was that age, but I can't remember now what math she was doing  But, I know neither one of us liked it at all.  It actually made me decide to not look at any of the upper level BA books (and dd is gifted in math).  I'm on the fence about AoPS for her for alg (she will doing pre-alg next yr as a 5th grader).  I talked to her older brother who loved AoPS about it and expected him to be all over her taking AoPS, but he wasn't.  He said that he believes that his math skills are what they are bc he used a combo of materials for high school level math.  He had already completed Foerster's alg 1 and 2 before I learned about AoPS. He started with AoPS in 8th grade with their alg 3 course.  He said that Foerster's word problems were just as much an integral part of his being successful in physics and math as AoPS proofs.  

Anyway, that is a long way of saying that just bc people post that BA and AoPS are the best out there does not mean that they are the best for your particular situation, your student, or even for covering all aspects of math.  My perspective is similar to @mms's and that it is really more about me being there as teacher than what we use.  I can teach math concepts without a textbook, but I never would.  Scope and sequence are things I do not want to have to think about.  I teach the concepts and make sure they understand the whys that they are doing, but then I let the textbook do its work.  I use things like Hands On Equations to supplement to challenge their understanding.

Elementary math is not some mythological apparition that requires someone to have special powers to conquer.  It isn't as if there is only 1 right way to lead to solid understanding.  It is just elementary math.  Make sure they develop number sense and understand what they are doing, and it will be fine.  If a math program is difficult for you to teach or takes too much time for you to teach effectively, it is probably the wrong choice.  I hate SM, for example.  I don't like bar diagrams.  Since I hate teaching it, it is not the right program for me to teach!  I think algebraically, so programs like HOE which teach them to set up algebraically are a much better fit. Guess what, it hasn't mattered.  Just bc my kids have learned to set up problems without using bar diagrams hasn't made a bit of difference in their mathematical understanding and I saved myself 26+ yrs of frustration of having to teach elementary math via a method I dislike!  🙂  Find what works for you, and really, none of the rest matters as long as your kids can think through problems to solve.

 

Edited May 30, 2020 by 8FillTheHeart

[Roadrunner]

Ha. I have always felt that Beast was a great supplement but not a great primary program. Never could explain why I felt that though, but it just felt shaky for this not mathematician mom. We loved Singapore here (even the bar diagrams 🤭). We mostly only worked Intensive Practice books and my DS transitioned to AoPS prealgebra without a hiccup. He said bar diagrams made him see all the equations in his head, although I suspect he would have done just fine without them. 
And to echo @8FillTheHeart DS, mine feels somewhat shaky on word problems (or as he says, I don’t like word problems, would rather work on a proof) having done only AoPS starting in 4th grade. 

I’m I see people recommend Beast exclusively now on Facebook for everybody (struggling kid, gifted kid, bored kid... just name it). I shake my head, but I don’t have anything articulate to offer. 

[lulalu]

1 hour ago, Roadrunner said:

Ha. I have always felt that Beast was a great supplement but not a great primary program. Never could explain why I felt that though, but it just felt shaky for this not mathematician mom. 

I have heard this a lot. The other hang up I have is the price. If it won't feel full enough it is a lot of money. 

 

Then I have heard often to use it a year behind. After doing a free month online we didn't hit anything ds needed work on or that was too difficult in the 2nd grade level. So, I wouldn't know if getting level 2 or 3 would be best for next year when he is in 3rd. 

[lulalu]

Ok- I read through the linked post above about CLE. Looks like it may not be clearly written in explaining concepts. For those that have used it, did you see mistakes in how concepts are taught often? The link above talks about how it incorrectly explains multiplying fractions. 

[purpleowl]

I do find BA conceptually sound and have loved levels 3-5 for my girls, as a primary/only program. My perception is that while the comics are intended to be fun, the problems are intended to be *engaging*, and that's what DD#1 and DD#2 need/ed.

I don't think it's ideal for every kid. I don't think ANY program is ideal for every kid. You teach the kid you have, as the parent/teacher you are. It's one of the great things about homeschooling. 

Based on what you've described, @lulalu, it sounds like BA is worth trying. I'd suggest getting just 3A to try it out, and if that goes well, get additional books to continue. 

[lulalu]

2 hours ago, 8FillTheHeart said:

I can't remember where my dd was in math when I bought BA2. She was that age, but I can't remember now what math she was doing  But, I know neither one of us liked it at all.  It actually made me decide to not look at any of the upper level BA books (and dd is gifted in math).  I'm on the fence about AoPS for her for alg (she will doing pre-alg next yr as a 5th grader).  I talked to her older brother who loved AoPS about it and expected him to be all over her taking AoPS, but he wasn't.  He said that he believes that his math skills are what they are bc he used a combo of materials for high school level math.  He had already completed Foerster's alg 1 and 2 before I learned about AoPS. He started with AoPS in 8th grade with their alg 3 course.  He said that Foerster's word problems were just as much an integral part of his being successful in physics and math as AoPS proofs.  

Anyway, that is a long way of saying that just bc people post that BA and AoPS are the best out there does not mean that they are the best for your particular situation, your student, or even for covering all aspects of math.  My perspective is similar to @mms's and that it is really more about me being there as teacher than what we use.  I can teach math concepts without a textbook, but I never would.  Scope and sequence are things I do not want to have to think about.  I teach the concepts and make sure they understand the whys that they are doing, but then I let the textbook do its work.  I use things like Hands On Equations to supplement to challenge their understanding.

Elementary math is not some mythological apparition that requires someone to have special powers to conquer.  It isn't as if there is only 1 right way to lead to solid understanding.  It is just elementary math.  Make sure they develop number sense and understand what they are doing, and it will be fine.  If a math program is difficult for you to teach or takes too much time for you to teach effectively, it is probably the wrong choice.  I hate SM, for example.  I don't like bar diagrams.  Since I hate teaching it, it is not the right program for me to teach!  I think algebraically, so programs like HOE which teach them to set up algebraically are a much better fit. Guess what, it hasn't mattered.  Just bc my kids have learned to set up problems without using bar diagrams hasn't made a bit of difference in their mathematical understanding and I saved myself 26+ yrs of frustration of having to teach elementary math via a method I dislike!  🙂  Find what works for you, and really, none of the rest matters as long as your kids can think through problems to solve.

 

Yes, I don't think Beast is the end all be all of programs. I haven't really felt pulled to it because it gets talked about so often as THE best. But they had a free month and I looked at samples. DS liked the month online (although I would get the books, I just like to have books over internet). And I do think he would like it all from what I saw.

He doesn't need much work to get a concept. But he does need review every month or so. Right now that is basically what I am doing myself and making sheets for. He needs review and then there are a few things I find important that I don't see often in programs- Roman Numerals, Word roots used (tri, bi, quad, etc) and a few other things. 

[Roadrunner]

5 minutes ago, lulalu said:

I have heard this a lot. The other hang up I have is the price. If it won't feel full enough it is a lot of money. 

 

Then I have heard often to use it a year behind. After doing a free month online we didn't hit anything ds needed work on or that was too difficult in the 2nd grade level. So, I wouldn't know if getting level 2 or 3 would be best for next year when he is in 3rd. 

Beast includes things that are just not found anywhere and those parts are super fun! We haven’t used grade 2 or grade 5 (they weren’t published on time for us), but I would say grade 3 had things in it that really made my DS exited. I vaguely remember skip counting and thinking how silly it was going to be and then being floored about how cool it ended up being. I don’t know what to say, but we felt SM gave us a foundation and Beast gave us love. Also for my youngest kid, SM’s long division was very confusing. Then he took one look at Beast’s long division and said, oh, this is what I do in my head! So I am glad we shelled out $$$ but I am also glad we didn’t ditch SM for it.

[8filltheheart]

I guess I don't see it as all that unique???  My kids have magic squares, cross words, solving for riddles, etc in their math books even though their math books are very much just traditional math books. Dd had already mastered Roman numerals through 1000 when I bought BA.  It all seemed just....meh....not fun and inspiring.  I think using it behind probably actually makes the program lose its appeal.  (I think that is what happened with one of my dd's. She took AoPS alg after already having completed Foersters and she just didn't think there was anything great about it. She liked Foerster's teaching approach more.  She didn't encounter anything "unique" or "compelling" in it.  It was just more algebra.  😉 )  

[daijobu]

3 hours ago, square_25 said:

 

My biggest issue with BA is my usual issue with AoPS: they are extremely enthusiastic about math and spend a lot of time making it fun, but they spend a lot less time thinking about which concepts are actually hard and take time, so they rush through those. 

 

 

Thanks for writing this.  Can you provide some examples in the AoPS textbooks (not the BA level) where they do an inadequate job of explaining difficult concepts?  

[ByGrace3]

We only used CLE for one year. It was straightforward, spiral, and traditional. It was not conceptual. For a math intuitive person -- they can learn using most things and it wouldn't matter. However, it would not have worked for my non mathy kids-- they needed the conceptual hand holding of Math Mammoth (as did I as I myself am not math intuitive). I learned so much from MM! 

We have experience with both Right Start and Math Mammoth and they both have a great focus on making sure the concept is presented well and understood. You cannot pattern memorize in MM. It is significantly made up of multi level/multi step problems. 

[Xahm]

We use Beast Academy as our primary math for my almost 8 year old and the 6 year old will be starting soon. We've stopped for a time and filled in with Math Mammoth, partly to get more practice and partly because level 2 ramped up so quickly my daughter needed to grow into it. She handled 2a easily as a young 5 year old, but by 2c it wasn't a fun challenge, it was miserable. I think one reason it's being recommended to everyone and his brother right now is that there is a high demand for online math programs amongst new homeschoolers especially, and most such programs are really weak and/or really dull.

[mellifera33]

5 hours ago, lulalu said:

 

Then I have heard often to use it a year behind. After doing a free month online we didn't hit anything ds needed work on or that was too difficult in the 2nd grade level. So, I wouldn't know if getting level 2 or 3 would be best for next year when he is in 3rd. 

 

It seems to almost be homeschool lore that any hs math program is so advanced that it should be used a year behind. I just don't see it most of the time. BA covers the topics usually covered in third grade, but breezes past some and goes deep in others. We love BA here, but I see levels 2 and 3, at least, as being firmly on grade level. When we need extra practice or review with a particular topic, I usually pull a few pages from MEP to fill in. 

[8filltheheart]

22 minutes ago, square_25 said:

 

It's not that the topics aren't on grade level. It's just that some of the harder puzzles can be better to grapple with if you're, say, already very fluent in adding two digit numbers, as opposed to still struggling to do so.

Sometimes, having to put together new conceptual ideas and ALSO having to struggle and use deeper thinking skills can be overwhelming. I always run things that require "backwards" thinking a bit behind things that require forwards thinking. Like, I think calculating 13 + 18 is considerably easier than solving 

13 + __ = 31, 

even though in some sense they are the same thing. That's because by the time you've added lots of numbers, you have much better sense of how that works. But if you're still pretty shaky on place value, that equation might be quite tricky and you may not know how to start. 

Are there truly standard elementary math programs that don't teach problems like that?  My kids started solving for N vs ____ in 2nd grade.  

I'm with @mellifera33 that the "so advanced use a yr behind" is an overblown statement in homeschooling circles.

[wendyroo]

42 minutes ago, square_25 said:

 

It's not that the topics aren't on grade level. It's just that some of the harder puzzles can be better to grapple with if you're, say, already very fluent in adding two digit numbers, as opposed to still struggling to do so.

Sometimes, having to put together new conceptual ideas and ALSO having to struggle and use deeper thinking skills can be overwhelming. I always run things that require "backwards" thinking a bit behind things that require forwards thinking. Like, I think calculating 13 + 18 is considerably easier than solving 

13 + __ = 31, 

even though in some sense they are the same thing. That's because by the time you've added lots of numbers, you have much better sense of how that works. But if you're still pretty shaky on place value, that equation might be quite tricky and you may not know how to start. 

I agree.

I have always used Beast Academy a year "behind" Math Mammoth.  Then again, in our case, we are using both of them way "ahead" as well.

For example, each of my boys finished Math Mammoth 1 and most of 2 during kindergarten.  Then they finished the rest of 2 and 3 during first grade.  My current first grader has started Math Mammoth 4, but only recently has he had the executive function and flexible thinking to tackle Beast Academy 2 (independently, I'm sure with sufficient support he could have done it last year, but it still would have been very frustrating).

For example, today he was working in Beast Academy 2b.  The problem was:

Lizzie is practicing addition with a game.  She starts by writing three numbers on a piece of paper.  Each turn, she crossed out one number and adds the other two, writing the sum somewhere on her paper.  After four turns, Lizzie's paper looks like this: 6, 33, 60, 21, 15, 26, 27 (the illustrated numbers are not in any sort of order or line).  What three numbers did Lizzie start with?

The actual math involved in that is trivial addition, but it takes a lot of logic, problem solving, and organized thinking to figure out where to even start.  That is the only problem that DS got done today, and even that required a lot of scaffolding from afar.  It took a long time and some tears.  I do think that level of challenge is good for him (mathematically and emotionally), but it would have been far too much a year ago when he was easily cruising through Math Mammoth 2.

 

[Roadrunner]

4 hours ago, square_25 said:

 

I'm less experienced with the textbooks than the online classes, since the classes are only loosely based on the books. I know that with the online classes, I see it all the time. For instance, I've been teaching Intro C&P, and I'm absolutely sure we didn't spend enough time on the multiplication principle. (The idea that if you have a choices for one thing, and be choices for another, then we have ab choices for the pairs.) And I can see this in later classes, where kids frantically try to remember whether to add or multiply, because they didn't have the chance to develop their intuition. 

This isn't everyone, of course, and I'm sure it depends on how much time a kid is spending outside of class on the work and how quick they pick up concepts. 

With the textbooks, I imagine one could make up for it by going slower or going back to a concept. That's harder with the online classes. 

this is the reason my kid has taken almost all AoPS courses either after completing the textbook or when he is near completion.

[Spy Car]

Reading this thread makes me nostalgic.

Bill

 

[Roadrunner]

1 hour ago, Spy Car said:

Reading this thread makes me nostalgic.

Bill

 

Great Saxon Singapore wars of the past! 😂

 

[lulalu]

11 hours ago, xahm said:

 I think one reason it's being recommended to everyone and his brother right now is that there is a high demand for online math programs amongst new homeschoolers especially, and most such programs are really weak and/or really dull.

I think it was recommended a lot before they had the online format. I have heard for years on this board and fb how it is great for gifted kids. 

[lulalu]

On 5/5/2020 at 10:02 PM, maize said:

Jo Boaler's Mindset Mathematics series; she's a Stanford professor whose research focuses on effective mathematics instruction, especially developing a problem-solving mindset.

Have you used this? I looked at the sample on kindle. It looks interesting. 

Would this make a full year? Or would I need to add a lot? Or maybe this is better as an extra and add some variety. Can it be done with just one child or is a group needed? 

[Spy Car]

1 hour ago, Roadrunner said:

Great Saxon Singapore wars of the past! 😂

 

Good times 

Bill

[8filltheheart]

5 hours ago, Roadrunner said:

Great Saxon Singapore wars of the past! 😂

 

LOL!!!! And reading before K/not reading before K (and these poor slouches never catching up.) 😉  (Unfortunate outcomes of Berkeley physics for one and recipient of a top competitive scholarship for another of my math and reading deprived students from back in those days. 😎)

Edited May 31, 2020 by 8FillTheHeart

[Roadrunner]

2 hours ago, square_25 said:

Yeah, that makes sense to me. 

Mind you, I am not convinced the textbooks guide you over the hard stuff perfectly, either, and I have lots of kids who find class clearer than the text. But at least you can take your time over the book.

Yes, classes most definitely add value for us. First, I am never sure my kid self studied well what he said he did, and since there is nobody in the house capable of checking, I need outside sanity check. Also DS always finds class makes material clear, and going over it the second time, and getting feedback on proofs, is valuable to him. 
I don’t think my kid could even succeed in a class without the textbook, but the pace of the classes doesn’t give us time to do both book and course problem sets simultaneously, hence delay. 

[wendyroo]

On 5/30/2020 at 9:58 AM, square_25 said:

 

I haven't used CLE, so in some sense, I'm not informed. But having looked at the samples... I would assume that if a kid didn't feel like understanding the concepts, they could get by with pattern matching. A lot of the program seems like that. 

Let me find you @wendyroo's post about this, one sec. 

Ah-ha, here it is: 

 

For what it's worth, that DS does still have CLE as one of his math options each day (along with a number of other choices), but he hasn't chosen it since before Christmas.  He has a contentious, love-hate relationship with Math Mammoth, but by and large that is what he chooses almost every day.  He is also working though Hands on Equations Verbal Problems and Hands on Geometry.

He just started Math Mammoth 6, and I am already dreading the end of the era when he finishes it...it has certainly not been a peaceful journey, but it has gotten the job done, and transitioning him to something new will not be pleasant.

[Roadrunner]

Has anybody seen/worked with U of Chicago translations of Russian and Japanese math?

https://ucsmp.uchicago.edu/resources/translations/

[Spy Car]

35 minutes ago, mms said:

I think @Spy Car used some of those (Do I remember that correctly Bill?).

Hey @square_25, isn’t the Russian book the one by M Moro that we would have used in third grade?

 

We used the First Grade materials of a Japanese math program that was not published by UofC. It was something like Tokyo Sesi-seiko, but I think I'm slightly off. A major Japanese textbook, IMS.

I never used the UofC texts, Russian or Japanese.

Bill

 

[Roadrunner]

1 hour ago, mms said:

I think @Spy Car used some of those (Do I remember that correctly Bill?).

Hey @square_25, isn’t the Russian book the one by M Moro that we would have used in third grade?

They had grades 1 and 2 as well of the Russian math, but they no longer list them. 
 

And there is an amazing Russian math 6! 
http://www.perpendicularpress.com/math6.htmlI am pretty sure this is the one we used in school. 

 

[Roadrunner]

I remember (still have notebooks saved)having to copy the problem and write out step by step solution (regrouping addition and subtraction for example). I am convinced not having workbooks that you just fill in with a number and having to show the process was key in early grades. 

Edited June 1, 2020 by Roadrunner

[Roadrunner]

@mms @square_25 the very popular Russian Math schools that are popping up everywhere, do you know if those are based on old Soviet textbooks? Because I also hear new ones are garbage. It’s the textbooks by Kolmogorov, Nurk... that were excellent. I thought maybe they would also be selling the translations,  it I don’t see them anywhere.

[lulalu]

So, what is different about Russian math? 

And the scope and sequence? 

Curious minds want to know 😁

[Roadrunner]

17 minutes ago, square_25 said:

I think you can also do that with manipulatives or visuals, though :-). I didn't make DD7 write things out, but I did make her explain the steps to me, so she couldn't simply pattern match. 

mine just rolled their eyes on manipulatives. They considered it “beneath” them. And of course they refused to write anything out, because their workbook didn’t tell them they needed to do it. You know, looking back, I don’t know how I have survived my kids, or how I am still surviving them. 🙄

[Roadrunner]

@mms you had blanks in the book? Hmmm. I have my 1st grade notebook where I have handwritten 

x + 3 = 5

x = 5-3

x = 2

 

[lulalu]

On 6/1/2020 at 7:14 PM, mms said:

Aren’t you in Central Asia? Anywhere near one of the old republics?

So, when I went through school there was no kindergarten and school started in 1st grade (7 years old). 1st grade math starts off with MEP reception type activities and was very gentle, gradually working up to addition and subtraction to 100.  But, students are solving puzzles from the beginning; parentheses and inequalities are introduced early on; missing addends and subtrahends, and multi-step word problems are common throughout.  There is almost no instruction in the book because the teacher was expected to teach. Basically, the arithmetic concepts are limited but what is expected is pretty sophisticated.

Second grade added in multiplication, division and fractions to 100 and then the four operations to 1000. Again, limited arithmetic but deep thinking.

Third Grade delved deeper into the four operations and introduced area and perimeter as well as time and speed/distance problems. Also, variables replaced blank boxes for the missing number. 
 

Skipped fourth grade, not sure why.

Fifth and Sixth were prealgebra, though it wasn’t called that: just fifth and sixth grade math 😉 The sixth grade book is available in English at the link provided by Roadrunner.

 

 

 

This sounds kind of like what I have intuitively done with DS. It is kind of what Gattegno does too. Although Gattegno Book 1 has fractions and all operations. Book 1 only works with numbers to 20. I feel this was a natural way to go deep and really know what the operations do. 

Edited June 29, 2020 by lulalu

[lulalu]

5 minutes ago, mms said:

I just wish Gattengo wasn’t scripted!

I can't do scripted programs. But I have found Gattegno to be not too scripted, and easy to put in my own words. It is the only scripted program I can use.