Difference between MUS/Crewton Ramone/Mortensen and Gattegno/Miquon?

[hi.im.em]

Hi all,

I’ve been giving myself a maths re-education while trying to work out how I want to teach it. I want to teach conceptually, playfully and early (start at 4).

 I started with Montessori (too ££) and from there found Mortensen blocks, which I found out have been approved by montessorians of a cheap alternative which are in some ways better and more adaptable than the montessori materials. See paper by montessori teacher Judith Townsend: 

https://www.crewtonramoneshouseofmath.com/support-files/townsend-mortensen.pdf

 

I have enjoyed watching the Crewton Ramone House of Math videos and I think thats the way I want to go. In an ideal world I would buy all the Mortensen Math books to make his videos work as an actual program and give us some structure - but their prices and shipping costs are extortionate. CR says not to bother with the books and just ‘play math’ but that freaks me out. I don’t have his passwords though and he claims his program is more structured inside the paywall, but some of the reviews suggest otherwise. 
 

Gattegno and the C-rods are super accessible in the UK but i’m struggling to nail down the differences. I will refer to the different approaches as Mortensen v Gattegno as they were the originals. CR and MathUSee are spin offs from Mortensen and Miquon is from Gattegno.
 

 So far I have:

-Gattegno and Moretenson both introduce algebra right off the bat. Gattegno doesn’t have any actual numbers until book 3 (just says one green is three whites etc). Mortensen encourages associating the rods with a number and has lines on them so kids can count them. In Mortensen, one of the first games is to build pictures and count them.

Mortensen does algebra traditionally with x and Gattegno uses letters to signify the colour of rods eg 3r = g (three whites is one green). This is to encourage a relational understanding of math. 

MathUSee doesn’t do early algebra and Miquon does some, but uses shapes.

-Mortensen/MathUSee blocks are bigger and easier for little kids to handle. They also have an ‘empty’ underneath that can be used to signify a negative number. Some people on this board say the C-rods are better for being smooth as it discourages counting.

- Mortensen uses a montessori three part lesson, and also moves from the concrete blocks, to pictorial representations of the blocks on paper (square for 100, line for 10 and dot for 1) to finally just working with numbers. I believe singapore does this too. MUS misses the pictorial step. No idea about Gattegno. 

- Mortensen goes right up to 12th grade, not sure about gattegno. I know miquon only goes to third. 

I don’t know Gattegno that well but have I missed things?

If Gattegno is basically the same as Moretenson it makes no sense to shell out for the text books. I could just buy the Gattegno text books and adapt them to MUS blocks? (I think I want to use MUS blocks to make it easy to follow CRs videos, or to switch to MUS for a bit if i’m struggling because ill or have a newborn or something)
 

Another idea I had is to use a vintage text book like Rays or Grubes (it seems like they were more conceptual back then) and use blocks to lay out the word problems and work through the questions (i don't like having to think of my own questions like CR does). That way I would at least know I was covering a certain amount of material. I could print off MUS worksheets for extra practice. 

If anyone has any experience then please, tell me more! It seems like Mortensen is out of fashion (and I can see why with the price!), but it looks like it would fit my teaching style well - I prefer like a bit of structure but not scripted lessons. This is why I ruled out right start but will be getting their games book for drill. 

[HomeAgain]

You would appreciate Anna's Math Page on Facebook.  She works with Mortensen and will have video lessons up.  There are also two ebooks by Crewton on Amazon - kindergarten and Dandy Division, I think, to get to know the system.

Gattegno has two book series that I have found.  The current ones, by Educational Insights (?) have fraction multiplication in book one and numbers up to 20.  The older ones, printed by Lampart Gilbert & Co., are more spread out, with book 9 being equivalent to part of book 2 or 4, I forget which..

Miquon and Gattegno go hand in hand for the first book and then work similar but different toward  book 2.  Math For Love offers additional free exercises for book 1. There is a company on TPT that offers worksheets to go with Gattegno and there are workbooks available in the UK in print by their current Cuisenaire company.  I did just fine making my own materials (like the product chart).

I find the biggest difference in the blocks.  The wooden centimeter blocks offer a few features that the MUS/Mortensen ones do not:

-easily convertible volume quantities.  MUS/Mortensen are 1/2in, so are either counted as "units" or the math must be done in inches first.

-fact families.  2, 4, 8, 10 are part of the warm red family.  3, 6, 9 are the cool blue family.  Red x Yellow = Orange (2x5=10).  That leaves the black sheep: 7, and the white (no family/all families) 1 unit block. 

-Wooden c-rods are meant to be stacked quite high in factors, MUS/Mortensen doesn't use this visual multiplication trick that starts with an imagined rectangle.

-more availability of supplemental materials.  More programs use c-rods than Mortensen blocks and Base-10 fits right in to add another dimension.

 

I had one student go through MUS, one through Gattegno, and 3 through Miquon w/Gattegno.  I prefer the fraction pieces of MUS and the way it teaches, but Gattegno's repeating fractions idea is quite nice, too.

Now, my students are all very clear in math concepts.  Everything was taught visually in different ways to different kids.  They all gravitated to things that sparked their interest.  I think that mattered more than anything.

[lulalu]

We have used Miquon and Gattegno. As far as investment in your shoes I would get a small set of c-rods and go through chapter 1 of book 1 in Gattegno. It is a chapter of play and gives a great foundation. Then you will also be able to see if you can teach from the book. Not everyone is able to as it isn't set up in a manner that says say this and it doesn't give the answers. We love Gattegno! And it works very well for acceleration and slowing down where needed. Being that the books are free online too makes it an easy trial before too much commitment. 

We loved the way Miquon works well alongside Gattegno. I wish Miquon went through all of elementary school. I however, have just been able to create worksheets when we have needed after we finished Miquon. 

I have no experience with MUS or Mortessen. 

 

[8filltheheart]

I would also follow the advice of going low investment first. My kids have hated all manipulatives. They would never engage with them other than as construction toys. Most of them have been mathematically inclined, have grasped concepts easily, and have viewed manipulatives as babyish. My granddaughter, otoh, really does better with manipulatives and they really help her understand mathematical concepts.

Knowing your child and how they learn does make a difference in how to approach teaching. 

[hi.im.em]

Interesting that you think there are more resources for C-rods than MUS blocks @HomeAgain, I had always thought it was the other way around.

The ones you listed look really good.
 

What grade does gattegno go up to? I really like that Mortensen/MUS can go all the way to 12th. 

[HomeAgain]

9 minutes ago, hi.im.em said:

What grade does gattegno go up to? I really like that Mortensen/MUS can go all the way to 12th. 

The last book I have, book 7, is algebra/geometry.  It doesn't go quite as high as MUS, and more topics are woven in at lower levels.  DS did MUS algebra 1 after finishing Gattegno 5.  Several topics had been covered as in depth or more than MUS algebra's version.  We spent a lot of time on different base systems and exponential base 10 values, which I think Mortensen also covers more in depth than MUS.  Last year was a very easy year for ds with MUS. 

Now you have questions. 😄I had MUS on my shelf.  It was less parent-intensive than Gattegno, which requires a firm presence for every lesson.  DS didn't use the blocks.  He didn't need them much at that point and when he did, he used c-rods, base 10, or colored squares.  We did a big chart that showed exponential value in negatives and positives as part of learning last year.  It was pretty cool, but not in any curriculum. Just something to refresh his memory.  BUT, it wasn't a big deal switching from Gattegno to MUS at the high school level.  The lessons were a little slower and more bite-sized, but that was about it.

[*****]

1 hour ago, HomeAgain said:

You would appreciate Anna's Math Page on Facebook.  She works with Mortensen and will have video lessons up.  There are also two ebooks by Crewton on Amazon - kindergarten and Dandy Division, I think, to get to know the system.

Definitely look at Anna's Math Page, I like her approach and if you have questions,  you can easily contact her.  I have also taken a live webinar from CR. I  like the way students learn conceptually through play.  If you have the time, he has great teaching videos, but not always in  sequential order. I dove into Mortensen a few years ago and used very beginning concepts with students for a short time (Sadly, their teacher preferred a textbook approach, so did not use either Mortensen or Math-U-See materials the class already had).   CR doesn't care which blocks you use, either the Mortensen or MUS.  (I never learned with Cuisenaire rods myself, so I preferred the others.) I feel the kids learned which blocks were which much faster than I did and didn't resort to counting each time for very long. 

I feel the algebra concept can be taught when YOU are ready to teach it.  If you are busy helping the kids  to subitize and learning facts, that doesn't necessarily mean you have to teach algebra at that point.

I have not used Miquan or Gattegno, so I can't comment on that. I used MUS with my kids (but adapted what they didn't need. For instance, they did fine naming their teen numbers, so I did not teach them the way MUS suggested, we just continued on...).  I only found out about Mortensen many years later after my kids were in college. I liked how it actually was a concept that started with Montessori. 

You sound excited about teaching conceptually, so this is an exciting time for you! Because you will be a better teacher when you learn alongside of your children! Check out Anna's Math Page and you can find many of CR's videos on Youtube as well as his site.  You will then get a better feel about which approach you want to use as well as from whom, or maybe you will use a combination...don't think too far into the future, high school is a long way away. Just have fun right now and you will know which direction to use as you go along. 

 

[MScott]

If you are looking at Gattegno you must go to Sonya's FB group and websites at ArithmophobiaNoMore, Learning Well Academy and FB group-Homeschool Math with Base Ten Blocks.  She has used Mortensen and Gattegno for years. She has read all of his books and has personally taken training at one of the only schools in the country to still be using Gattegno.  She is a wealth of knowledge and understands Gattengo and the use of the rods like no one else.  She is also friends with Ana. 

I originally started with Mortensen/Crewton and then learned about Gattegno from her and made the switch years ago.  She convinced me the C-rods were better than Mortensen because they didn't have the unit marks on them and having used them for several years with Gattegno's books I have to agree. There is much more you can do with the C-Rods, even though you can still use the Mortensen blocks if you turn them on their side. ou can buy the entire set with c-rods from an online shop in the UK. That is what I did and the rods are amazing quality.  Gattengo does require parental involvement to implement, but the way he teaches math is brilliant! Sonya has done a lot of the leg work and offers several courses for kids using Gattegno material to make it easier for parents, but you absolutely don't have to take them. You can still go through the books on your own and still get so much out of them. 

One other thing, Mortsensen/MathUSee and Miquon basically took Gattegno and made it a curriculum that is more open and go, but unfortunately some things were lost. Having the unit marks on the rods was a big one and another is the notice and wonder aspect. Have you ever watched any of the old Gattegno videos on youtube? Watch those and you'll see what I mean.  Sonya does a wonderful job of explaining all of this on her websites and her FB group, which is very active. She has modules and training that make it easy to see how Gattegno works. I highly recommend joining the FB group and looking and going through the guides. Ask away, she loves helping parents!  I'll drop links below.   

~Melissa

https://www.facebook.com/groups/arithmophobianomore/learning_content

https://www.learningwellathome.com/academy/

https://www.arithmophobianomore.com/

Edited September 12, 2022 by MScott

[MScott]

2 hours ago, HomeAgain said:

The last book I have, book 7, is algebra/geometry.  It doesn't go quite as high as MUS, and more topics are woven in at lower levels.  DS did MUS algebra 1 after finishing Gattegno 5.  Several topics had been covered as in depth or more than MUS algebra's version.  We spent a lot of time on different base systems and exponential base 10 values, which I think Mortensen also covers more in depth than MUS.  Last year was a very easy year for ds with MUS. 

Now you have questions. 😄I had MUS on my shelf.  It was less parent-intensive than Gattegno, which requires a firm presence for every lesson.  DS didn't use the blocks.  He didn't need them much at that point and when he did, he used c-rods, base 10, or colored squares.  We did a big chart that showed exponential value in negatives and positives as part of learning last year.  It was pretty cool, but not in any curriculum. Just something to refresh his memory.  BUT, it wasn't a big deal switching from Gattegno to MUS at the high school level.  The lessons were a little slower and more bite-sized, but that was about it.

I think the Gattegno books get kids through at least the 8th grade, but really since it is algebra first so much is covered already. Most kids can eas into any upper math courses without a problem.  Have you looked through his books? Lots of higher level math. They are free online here https://issuu.com/eswi. Scroll down about half way to see them.  I've circled the textbooks in the photo to show which ones are the textbooks.  I mentioned Sonya's website in my other post, but here on her site she has a page on where to start. https://www.learningwellathome.com/biggest-list-of-cuisenaire-rod-and-gattegno-resources/

 

 

Edited September 12, 2022 by MScott

[8filltheheart]

3 hours ago, hi.im.em said:

What grade does gattegno go up to? I really like that Mortensen/MUS can go all the way to 12th. 

One thing you definitely do not need to do is make a decision based on the option of going all the way through 12th grade.  I have no knowledge of Mortensen, but MUS is one of the absolute weakest high school math programs available.  I have used MUS's alg and geo with all 8 of my kids.  I use it as pre-alg and pre-geo and follow with more comprehensive alg and geo courses.

Make your decision based on what will work best for your child and for you as a teacher for now.  Anything beyond elementary math is a long way away.

[EKS]

16 hours ago, hi.im.em said:

MathUSee doesn’t do early algebra...

If you mean simple "solve for x" type problems, MUS does do them.  We used Beta-Zeta.  

I would not use the MUS high school math products except in special circumstances for the reasons that 8 states above.

[hi.im.em]

2 hours ago, EKS said:

If you mean simple "solve for x" type problems, MUS does do them.  We used Beta-Zeta.  

I would not use the MUS high school math products except in special circumstances for the reasons that 8 states above.

CR, i know, does things like factoring with young kids and collecting like terms. The idea is that they learn the four operations by solving quite complex problems with the blocks. They are pretty heavily guided but it means that these things aren’t foreign to them when they encounter them later. Not sure about how Gattegno does it, but i know he likes to name the blocks by their colours before using numbers, so maybe its implicit algebra/factoring etc but its not spelled out. 

 

[EKS]

32 minutes ago, hi.im.em said:

CR, i know, does things like factoring with young kids and collecting like terms. The idea is that they learn the four operations by solving quite complex problems with the blocks. They are pretty heavily guided but it means that these things aren’t foreign to them when they encounter them later. Not sure about how Gattegno does it, but i know he likes to name the blocks by their colours before using numbers, so maybe its implicit algebra/factoring etc but its not spelled out. 

I don't know anything about the other resources you mentioned, but reading this, two things come to mind. 

First, the teacher is more important than the resource.  If you have a way you want things presented, you can just do that, regardless of what the resource says. 

Second, in my experience with kids who have some natural math ability, concrete representations may be good for a minute or two (sometimes quite literally!), but after that, they seem to actually get in the way of their thinking about the concepts.  I think this is because their natural inclination is to think abstractly, which is probably why they have natural ability.

[hi.im.em]

Oh yea. It’s actually more for my own education at this point. I need the manipulatives, lol.

So the reason i’m looking for a full curriculum is that I want to see where it ends up - what it’s working towards. And also because I want to relearn the stuff I just learned the algorithms for in school with the manipulatives to give myself a conceptual maths education. I feel like I can only teach it well if i know where I’m hoping to end up, ykwm? 
 

Thanks for the tips re Math U See higher grades. 
 

The Gattegno books do freak me out a bit. I’m very visual with maths, i really need to watch a video of it being done. There does look to be lots of CR-style video lessons using the C-rods on youtube though, but am I right in thinking that they are mostly geared towards lower grades? 
 

Interesting re the different types of rods. You almost have me convinced to go c-rods @HomeAgain 😉 

On the other hand I really like the idea of going through all of the CR stuff myself so that i know the method well, and then watching the video lessons together with my daughter (after the initial play stage), pausing to work through his problems. I like his energy. 
 

I already have a small set of C-rods so will do some more messing about with Gattegno text books, but so far he had lost me at fractions 😳. I stopped studying maths at 16, which is allowed in the uk.  

[HomeAgain]

25 minutes ago, hi.im.em said:

 

The Gattegno books do freak me out a bit. I’m very visual with maths, i really need to watch a video of it being done. There does look to be lots of CR-style video lessons using the C-rods on youtube though, but am I right in thinking that they are mostly geared towards lower grades? 
 

 

Watch Gattegno's 3 part videos on youtube.  While the children are younger, 5th grade-ish in the last one, you can see the way he teaches.

The books are almost conversational when compared to his actual teaching.  There are some things that were a bit tougher to work out (we never did quite manage to find the "ease" in his multiplication of large numbers), but I put together pictures of my own for local families using the books.  Things like this, the difference of squares.  It's simple when you see it worked, less simple when trying to work it out from text.

[Clarita]

32 minutes ago, hi.im.em said:

Oh yea. It’s actually more for my own education at this point. I need the manipulatives, lol.

So the reason i’m looking for a full curriculum is that I want to see where it ends up - what it’s working towards. And also because I want to relearn the stuff I just learned the algorithms for in school with the manipulatives to give myself a conceptual maths education. I feel like I can only teach it well if i know where I’m hoping to end up, ykwm? 

In this case I would look for a curriculum that works for you. Don't give too much thought as to how your child will do with it or where they will be in 12 years with it. When my son was 4 I had math curriculum thoughts for him and before he turned 5 he already ruined them. He groans when I bring out the manipulatives for the math lesson. The set of golden beads are used at my house as obstacles for cars and for making "sandwiches". 

[8filltheheart]

Based on your description of yourself, it might be worth noting that some kids experience the same confusion with manipulatives.  Some kids need to learn algorithm before conceptual explanations make sense, knowing the algorithm then turned into a visual makes things click vs. starting with the visual and turning it into problem solving. No single math approach will necessarily be the best for a given child. 

And how you can teach will make a bigger impact than curriculum.   For example, I hate bar diagrams.  Bc I hate them, I am not a good teacher for SM.  I like to present things algebraically. I like Hands On Equations Verbal Problems bc that is how I enjoy teaching.

But, I think Clarita's pt is the most important one.  Kids don't conform to long-term plans.   You'll be much better off thinking about the short-term for your child and step by step for yourself.  

[hi.im.em]

Hmm interesting. The literature i’ve seen suggest that little kids really need manipulatives (montessori et al.) but I can see that once some kids get older they would get annoyed with all the guided discovery and just want to be shown the algorithm. I think that misses a lot of the ‘fun stuff’ of maths though. 

Saying that. I told my husband about the CR trick of ‘all the numbers want to be a ten’ thing that he uses to make mental maths easier, and he was like ‘umm yea everyone does that’. It was news to me. If I have to minus 37 i would minus 30 and 7 not 40 and add 3. But he’s mathy and i’m not. So maybe the stuff that I need to be shown with manipulatives is just obvious to some people.

Maybe I would be best to work through an incremental old school program like rays, looking for videos to illustrate how to do stuff with blocks as needed? I don’t really comfortable teaching material that i don’t have a full handle on myself - and taking myself through some sort of program seems to be the best way of getting from a to b. Then if my daughter can be taught the same way I guess its a bonus.. but fully open to picking a curriculum to suit her learning style nearer the time 

Edited September 12, 2022 by hi.im.em

[8filltheheart]

14 minutes ago, hi.im.em said:

Hmm interesting. The all the literature i’ve seen suggest that little kids really need manipulatives (montessori et al.) but I can see that once some kids get older they would get annoyed with all the guided discovery and just want to be shown the algorithm. I think that misses a lot of the ‘fun stuff’ of maths though. 

I don't think any of us are saying that they should only be shown the algorithm.  Some kids can grasp conceptual concepts quite easily and don't need manipulatives.  For example, simply discussing working from 10s is easier, they can automatically grasp what your husband is saying without having to go through the process of making it 40 and moving the 3.  The latter is what my kids would absolutely hate doing.  They didn't need that step bc they already figured it out mentally.  

My youngest ds (who is now an adult) taught himself multiplication.  I never had to have a single conversation with him about it (other than to chuckle to myself bc he thought he had discovered something else that no one else knew.)  He had figured out that multiplication from playing with Legos.  He informed me that 4 rows of 5 cookies meant 20 cookies or 6 rows of 3 window panes meant 18 window panes.)  He was extremely dyslexic and couldn't read on grade level until 5th grade but completed his first alg course at age 10.  I'd never have guessed how he would learn.   He was a math sponge who simply saw math everywhere.

[hi.im.em]

So what do you think? Persevere with Gattegno since I already have the c-rods and access to the text books? Or get myself some MUS blocks and a password for the Crewton Ramone videos? I have a feeling I will get further with Crewton, so perhaps i should look at it as an investment in my own professional development as a homeschooler. I really want to *teach* my little ones to do maths, but for that I need to put in the time/effort. Also i have no students to practice on so watching a teacher teach is probably the next best thing.

Crewton Ramone/Mortensen probably makes more sense to me just because I have the background knowledge of the Montessori math, I I kind of know the drill (with the three part lesson etc). I will watch the videos of him teaching though, like you say it seems more discovery/socratic based than Mortensen. 

Edited September 12, 2022 by hi.im.em

[hi.im.em]

I would be so out of my depth if I had to teach your mathy son @8filltheheart! Although i suppose once they outstrip you they could just teach you to cement what they learn from their curriculum?

[Clarita]

48 minutes ago, hi.im.em said:

Maybe I would be best to work through an incremental old school program like rays, looking for videos to illustrate how to do stuff with blocks as needed? I don’t really comfortable teaching material that i don’t have a full handle on myself - and taking myself through some sort of program seems to be the best way of getting from a to b. Then if my daughter can be taught the same way I guess its a bonus.. but fully open to picking a curriculum to suit her learning style nearer the time 

If Gattenego works to teach you then that's great continue on because it looks like it could be free and you already have the rods. Since your husband is mathy maybe he could explain the fraction part to you. I guess what I'm trying to say is don't spend too much time/effort/money on a particular method. 

I'm learning phonics alongside my son. What that looks like is I have some reference books/websites (made for adults) on the subject where I can look up information. Then I just use a phonics curriculum that works for my son. I read the teacher's guide before hand, if I get confused I go to the references I have see if I have more of a clue. Hopefully you'll have some friends who would be willing to help you with the math when you struggle. I've given math lessons to my homeschool friends. (My kids are young so I was teaching the friend place value, but my MIL has taught her friends algebra.) 

[EKS]

@hi.im.em, you may want to check out the book Elementary Mathematics for Teachers as well as the corresponding exercises.  

[8filltheheart]

2 hours ago, hi.im.em said:

I would be so out of my depth if I had to teach your mathy son @8filltheheart! Although i suppose once they outstrip you they could just teach you to cement what they learn from their curriculum?

I learned how to teach math with my oldest ds. (Other ds mentioned above is #4 of 8.) I took math through cal 2, but I had forgotten most of it. Alg and geo I relearned fairly easily, but about half way through alg 2, I gave up. I was completely outnumbered with kids and limited time. At that pt,  finding other than me being teacher became easier. 

The main pt is that just bc you are homeschooling, you dont have to overwhelm yourself. You can do things one step at a time. You dont needt to think alg now. Pace yourself and chug along bit by bit.

To encourage you, I am definitely no math genius. My kids excel far beyond me in just about everything, but we homeschool almost all subjects at home and my kids have gone on to be highly successful adults who graduated from college with very high GPAs.  I definitely did not have all the answers when I started. I had never even heard of homeschooling until the day we started!

Edited September 12, 2022 by 8filltheheart

[Malam]

On 9/11/2022 at 11:01 PM, 8filltheheart said:

One thing you definitely do not need to do is make a decision based on the option of going all the way through 12th grade.  I have no knowledge of Mortensen, but MUS is one of the absolute weakest high school math programs available.  I have used MUS's alg and geo with all 8 of my kids.  I use it as pre-alg and pre-geo and follow with more comprehensive alg and geo courses.

Make your decision based on what will work best for your child and for you as a teacher for now.  Anything beyond elementary math is a long way away.

Agreed! There's nothing special about k-12 math, especially starting with prealgebra when syllabi are more standardized across curricula

On 9/12/2022 at 3:32 PM, EKS said:

@hi.im.em, you may want to check out the book Elementary Mathematics for Teachers as well as the corresponding exercises.  

Or Arithmetic for Parents by Aharoni

https://kateshomeschoolmath.com/videos-and-books-learn-to-teach-homeschool-math/

 

See here for more cuisenaire resources:

https://www.learningwellathome.com/biggest-list-of-cuisenaire-rod-and-gattegno-resources/

Edited September 14, 2022 by Malam