The discussion here refers to the Light Blue series books  the complete curriculum for grades 17. This does NOT apply to Blue or Golden or Green Series books.
Saxon math's "incremental approach" or short spiral means that nearly every lesson introduces a new concept or skill, yet the curriculum only includes a few exercises about the new concept and most of the problems in each lesson are for previously learned concepts.
In contrast, Math Mammoth focuses on a concept or topic for several lessons and provides plenty of exercises for the concept at hand.
I love the way a new concept is introduced and then practiced, practiced, practiced! My kids hated Saxon, because it would introduce a new concept, then only give them 5 problems to do to go with the new concept then the rest of the lesson was a review from previous lessons. By the next day, they forgot the concept that they had learned the day before and were really lost after having to learn a new concept that day. Saxon just goes to fast without giving the students time to master the concept they are introducing. I really love how your books give my children the practice that they need to master the concept BEFORE moving on! My 11 yearold has learned to like math again thanks to you! Thank you!
Stacey Clay
See also My opinion on Saxon math.
Just like Saxon, Abeka is a spiral program with a "short" spiral where there aren't many practice problems for any new concept right after the concept is explained.
Math Mammoth and Singapore Math are similar in the sense that both are masterybased, emphasize conceptual understanding, mental math strategies, and both use the "bar diagram" method for word problems.
The above comparison on scope does not apply to SM Primary Mathematics Standards Edition, which follows the old California standards and is therefore more advanced, nor to the SM Primary Mathematics Common Core Edition, which should have a very similar scope to Math Mammoth.
We have used both Singapore US and Standards Edition. I have to be honest, we love Math Mammoth! You are right, I do think that Singapore Standards does move a bit quicker than Math Mammothwhich doesn't necessarily mean it is a good thing. Unfortunately, I noticed that sometimes Singapore Standards introduces a concept and then wisks you on to the next concept. I didn't think it was a big deal at first, but when it comes to a concept such as vertex, edge and so forth, I think we should have spent a little more time on it (especially when it was introduced to my son for the first time at the end of 2nd grade.)
As mentioned, we also have used the US edition. I think Math Mammoth does as good, if not a even better job, at explaining concepts than the US edition. However, I have bought Singapore Math through 5th grade. But since I couldn't resist your offer on the Homeschoolers buyers coop, I bought the Light Blue Series. Therefore, I am using both programs. As of now, since we finished our school year for Math, I am taking my daughter through Math Mammoth on any areas she needed more indepth practice. She just completed Singapore US edition 3. After going through the concepts learned on Math Mammoth, she seems to have a deeper understanding. We are grateful to you for that!
My son will be finishing the Standards Edition 2nd grade soon. Then, I will take him through any areas that he needs more practice on with Math Mammoth this summer. Eventually, I suspect that we will switch over completely to Math Mammoth. It just seems easier for me to teach and easier for them to digest. And, both my kids are mathy kids. But, we just like Math Mammoth better.
Yours truly,
Loralie
MathUSee uses a complete mastery approach. I will outline their system for lower grades below:
Level  Focus 
Alpha (1st grade)  Singledigit addition and subtraction. 
Beta (2nd grade)  Multidigit addition and subtraction. 
Gamma (3rd grade)  Multiplication 
Delta (4th grade)  Division. 
Epsilon (5th grade)  Fractions. 
Zeta (6th grade)  Decimals and percents. 
Math Mammoth complete curriculum series is not as totally masteryoriented as MathUSee. My approach is a blend of some spiraling with mastery. Math Mammoth includes and develops SOME concepts over several grades (for example, the connection between addition and subtraction or the concept of place value), whereas some topics are taught with mastery approach (for example, addition facts or times tables).
An example: In MathUSee, children learn multidigit addition up to 5 digits in level 2 (Beta). In Math Mammoth, we find some easy twodigit addition problems in 1st grade, then two and threedigit addition in 2nd grade, and lastly addition with bigger numbers in 3rd and 4th.
This comparison is lengthy, please complete reading it here.
Miquon is not a complete math program but supplemental. It consists of workbooks with very interesting problems. I do like their problems and the various approaches. Math Mammoth introduces new concepts at a slower pace than Miquon. Miquon is an excellent supplement to kids who excel in math.
I homeschool my two boys (2nd and 4th grade), and have a three and four year old as well. My oldest son completed all three years of Miquon Math and did quite well. I did find, however, that while it's very creative in presenting math concepts, it's short on drill and explanation. So in picking his next curriculum I wanted something that explained concepts thoroughly and gave enough practice (but not endless pages!) so he feels he has mastered the concepts. We are now almost finished with chapter 3 of Math 4A, and it has gone very well. I've been really pleased how you've explained concepts like the multiplication algorithm, and he is understanding it, too!
My second grader was struggling with addition and subtraction in Miquon, so we jumped out of it for awhile and completed "Add & Subtract 2A". It was a real help (I like those rainbows!), and now we are back in Miquon until (and if) another problem arises. Your curriculum and Miquon seem to complement each other quite well.
We also used the Decimals 1 collection to help prepare for the state standardized test.
Respectfully,
Cara Hogervorst
Life of Fred is a fine supplement but not a full curriculum so it's not exactly comparable to Math Mammoth. It doesn't contain enough practice to be a full curriculum.
Please also see the "word of warning" review written on this page.
I feel LOF is best left as a FUN supplement — even to supplement Math Mammoth. However, for most children, it is not the best choice for an only math curriculum.
CLE employs a "short spiral" where there are only a few problems on any new topic, and most of the student work is review of other topics. They even state on their website: "Each lesson introduces one or more bitesized new number concepts. Most of the student work consists of continuous review to ensure that the concepts stick."
Based on the (quite ample) samples on CLE's website, the curriculum presents math as a set of formulas and facts to memorize, and does not explain why something works or where different concepts come from.
Math Mammoth is "masteryoriented", meaning that the curriculum focuses on one topic or theme (such as place value) for a while, before switching to another topic (such as geometry). So in this sense Math Mammoth and CLE are near opposites.
However, you can use Math Mammoth in somewhat of a spiral manner, and many people indeed do that. Simply choose 23 chapters that your child is working on at any given time, instead of studying only one chapter. The chapters need chosen carefully: for example because some topics require a mastery of another. For example, before studying the concept of division, the child has to understand the concept of multiplication and preferably master most of the multiplication tables. But it usually works just fine to have a child study geometry/measuring/time/money at the same time as addition/subtraction/multiplication/division.
Math Mammoth gives you the freedom and possibility to focus on a topic if necessary  OR use it in a somewhat "spiral" fashion mixing up topics. You cannot do that with a spiral curriculum where the topics are already mixed up for you.
I have not seen RightStart math except the few samples on their website, but I have seen their geometry course, which I thought was really good.
In general I've gotten the impression that RightStart is well thought of and rigorous. The big difference is that it's not workbook or worksheetbased but instead teacherled and scripted. In other words, RS is teacherintensive and teacherled.
I've written Math Mammoth so that the explanations are right in the student text and written TO the student, aiming it to be as selfteaching as possible.
I have been using MMGrade 1 Light Blue series with my preschooler. She is 4.5 but an accelerated learner. We love MM. I use it along with Right Start math and they complement each other so well. I can't thank you enough for making it so affordable.
My biggest challenge with RSM is understanding where we are in our learning process. RSM presents concepts in a spiral format and that coupled with scripted lessons was making it so difficult for me to track the progress. We love RSM but when a single lesson could talk about three different activities, it was difficult to see where we are and where my daughter needs help without losing focus. MM is perfect to bridge the gap.
The mastery approach of MM helps me a ton. I use RS scripted lessons to help me in teaching math. My daughter loves doing MM worktexts. It helps me to look at the skills my daughter need to acquire at each stage and understand where she needs help. I also like the flexibility to work on multiple topics when my daughter needs a change. We do clock and money while we play addition games to gain expertise. She is almost done with place value. I make it spiral according to our needs and still have clarity on the progress we make. I am loving it.
Thank you so much.
Geetha.
We have been using Right Start math and love the good conceptual understanding, leading to easier memorization of the math facts through the mental image the concepts lead to. However, I have not liked that there aren't too many worksheets and that the lessons are totally dependent on me to teach them. My children are woefully behind in math because there have been too many days we haven't had time to do lessons. I put them in Teaching Textbooks when they're old enough for that, but to give a good foundation before that I use Right Start. Your worksheets are exactly what we needed to supplement our Right Start lessons and to give the student something to keep moving forward with even on days I can't sit down with them for a whole lesson. In fact, it looks like you use many of the same “tricks” that Right Start teaches. I am excited to have a good math program to work through with them that doesn't require so much from me. I am so pleased with Math Mammoth that I am planning to start my first grader with that in the fall and use Right Start as a supplement (the opposite of what I intended in the first place). The only thing I can think of that I would like better about Math Mammoth is if the objects pictured were grouped by fivesthat really helps to visualize the number in one's head.
Another thing I really LOVE about Math Mammoth is that there is not a teacher's manual for me to wade through to try to figure out what I'm supposed to teach the child and how to get it across to him or her. All instruction is right there on each page. But you also have a summary at the beginning of each chapter that gives additional info for me, and I only have to read it once! Fabulous!
Thank you for a great program at such a low cost.
Elizabeth Kobelia
Teaching Textbooks excels in one category: it provides full solutions to all problems. In comparison to Math Mammoth:
My son switched to Math Mammoth this year from Teaching Textbooks. He had completed Teaching Textbooks 6, but we had to start back with Math Mammoth 5 when we switched. That tells you how far behind TT is. My son loved TT, but even a nonmath person like me could see that TT was not giving him any practice in mathematical reasoning. He was getting A's on every lesson and test, but if I gave him a problem that was worded differently, or one that required him to do something even slightly complex with the information he had learned  he was stumped. It took him a few weeks to adjust to the much more rigorous work in MM, but after finishing the first half of level 5, he is doing very well  often understanding concepts and figuring out problems way before I do. And I am learning a lot too  grade 5 is just about where I got lost in math and I never got found. I wish I had had Math Mammoth!
Thanks Maria
Connie and Sam Downer
[Besides Math Mammoth,] I also bought Teaching Textbooks for 3rd grade & after looking through it, I think I'm going to stick with your program. I had originally bought it for my son for second grade & then I was going to move on to the Teaching Textbooks since it advertises independent learning. I work at home doing my husband's company's books, so I don't have huge blocks of time to teach. After looking it over though, it isn't as challenging as yours. Thanks again for making the cost of yours so nice. I printed out the chapter they are working on & hole punched it & placed in a folder. I am making each chapter last about 23 weeks of work so kids don't seem too intimidated by a huge book and can just concentrate on doing 34 pages a day. Working great. Thanks.
Channa
I am not very familiar with Developmental Mathematics. I found that www.christianbook.com has samples of each of their books, which is nice. All the samples and the problems in them generally looked fine to me, but that really doesn't give you a full picture of how the concepts are developed over time. It says they use picture problems at first, then written problems, and lastly word problems in each booklet.
There are similarities, such as having one book concentrating on the basic concept of multiplication or division.
One difference is: Developmental Mathematics does not cover clock, measuring, or geometry (!). Statistical concepts such as bar graphs are only in booklet 16  the last one. So you need to find some other resources for those topics.
I would be curious to know how Developmental Mathematics deals with problem solving for problems that require several steps and the usage of several operations. I would guess that Math Mammoth might be better in developing student's overall understanding of tying mathematical concepts together and using them in various kinds of problems (I hope someone having used both could chime in!). I do consider the lack of geometry a significant lack in Developmental Mathematics.
I have only used Developmental Math and since using Mammoth Math I am relearning how to explain math concepts along with my children. It is a great independent math curriculum that requires very little prep work if any. Developmental Math was great until I realized the lack of explaining certain concepts. Mammoth Math shows many different ways to do the same problems and gives the child the choice to use which makes sense to him. The most beneficial part, I feel is Maria's newsletter and blog so that you can ask questions and get help when you need it. The cost can't get better than Mammoth Math either.
Thanks for your committment to us homeschoolers
Raina McGrath
Basically Math Mammoth complete curriculum is masteryoriented but there is also some "spiraling" of similar topics over the grades. You could call it "slow spiraling".
However, I don't want to spiral too slowly either. Some topics are better studied with total mastery approach, with no repetition over the grades, or the books would grow to be 500page monsters. I'm aiming for a balanced approach with mastery vs. spiraling.
Also, the sequence (order of topics) of Math Mammoth is similar to curricula used in schools. It is not going to be exact, of course, since I have some of my own ideas and preferences also, when it comes to the sequence. By following loosely a typical sequence of elementary math curricula, parents find it easy to relate to the topics in the various grade levels, students find it easier to switch to Math Mammoth from other curricula, and school teachers are able to use my materials to supplement or to replace the curriculum at their school.
I am so grateful to have discovered Math Mammoth earlier this school year and for the wonderful job you have done in creating this curriculum, Maria.
We live overseas and so have limited access to the variety of curricula and materials that are available in N. America. That, along with limited internet in the past, made it very difficult for me, a new homeschool mom 3 years ago, to figure out what curriculum we should use.
As a result, we have been through the gamut of math programs. Someone recommended MathUSee, so I bought the primer for my daughter when she began Kindergarten. In lesson 10 it jumped to teach place values, while my daughter was still struggling to recognize the basic numbers. I had to set it aside. I discovered Making Math Meaningful, which was a good handson approach for learning math concepts orally, but I knew we had to move beyond this.
Last year, my daughter and another child were taught together using Saxon Math. I think it was good for her at the time and solidified alot of basic concepts, but when I looked at the Math Mammoth first grade test and such, I realized that Saxon Math did not progress as far as MM.
This year I am back to teaching my kids, and I happened to have some Singapor Math US edition workbooks on hand. I started my daughter on SM 1B to make sure she was where she needed to be after using Saxon Math. I was surprised to find that much of it was new to her. As we worked through the book, I found that topics were covered much too quickly with no explanation, then progressed further to other new topics. I knew my daughter had not grasped them at all, so I went looking online for how I should help her. It was in this search that I discovered Math Mammoth.
In order to make sure our bases were covered, I started my daughter on the grade 1 Math Mammoth, though she has been able to cover many of the sections fairly quickly, then spend more time on concepts new to her. I also started my son on MM grade 1 and even though he is newer to studying math, I have found the workbook moves at a good pace (not too fast or slow) and he enjoys it. I am pleased with the many angles that are used to help the kids to learn each concept. They're getting it! I love the way the workbook includes the instructions in it, too and is so straight forward to use. It's wonderful to have finally found a program that works us and that I know is helping my kids learn what they need to know.
I was especially pleased to find a curriculum that I could download and print at home, since it's difficult for us to get printed resources here from the US.
Thank you, Maria!
Helen
From Horizons to Math Mammoth  a story where Horizons math was not working, and Math Mammoth became the solution.
My younger daughter used Horizons math from grade K through 3rd. She was doing well until 3rd grade when she began to feel like everything was moving too fast without enough time to absorb the lessons. The work was skimming the surface and then continuing on without true understanding. We were getting very frustrated. I switched to Math Mammoth for fourth grade, and it was a tough transition. But now we are over halfway through the year, and my daughter is so much more confident. She really understands what she is working on and has better "number sense". I appreciate the amount of work problems included, and feel like she is benefiting greatly from the more mastery approach. I feel like she is lightyears ahead of where she was just a few months ago.
I am also switching my older daughter to MM. She is in 7th grade and started Teaching Textbooks prealgebra this year. She got halfway through the year when I realized that she was not grasping concepts well. TT seemed to be skimming even more than Horizons with very little depth, and almost no word problems. I am putting her in MM, but having her go back to grade 6 because MM is more advanced. Even though she does not love going back to 6th grade math, I think that she will have so much more indepth knowledge when she is done. I'm looking forward to having her start the new MM 7 prealgebra next year!
Robyn Willard
I just wanted to share what I have been doing for my kindergartner's math. I am using Ray's Arithmetic Year One (all oral) as my main math program. However, I am finding the Math Mammoth Light Blue Grade 1A material to fit very nicely with their scope and sequence and provides a different avenue for the student to practice the material. Ray's Year One is spent building a strong foundation in number recognition, addition, and subtraction from 110, not just from rote memory but from understanding the concepts. Grade 1B should align nicely with Ray's Year Two as well although I have not looked at them side by side only by an overview of the topics. Ray's Year Two emphasizes addition and subtraction to 100, again with understanding not just rote drill.
Cynthia
Addition & subtraction to 100 is covered only partially in Math Mammoth Grade 1B and in more detail in Math Mammoth Grade 2A.
We have used Miquon, Horizons, and Developmental Math. It was not until Math Mammoth that I began to feel confident teaching math and the kids stopped complaining about math time. I have 8 children so it is important to me that I can be a resource for them, but not have to sit holding their hands all during each lesson. I love that I can print the books at home as we need them. I can print extra practice for those kids who need the extra work while letting the kids who get it go on at their own pace. We love Math Mammoth. It has lightened my load considerably while giving me the confidence that my children are getting all the math they need to succeed in their future lives.
Comparisons to what we used before:
Math Mammoth is MUCH less expensive
Math Mammoth is easier for me to use
My children like doing the lessons and get confused less often.
I find printing the books easier than shopping all over for the cheapest place to buy all the books I need. Math Mammoth lets my children master a topic totally before forcing several new things on their minds.
Thank You Maria for sharing your knowledge with other moms.
Natalie Bias
We have been using Math Mammoth 2 for about 2 months now. I just wanted to say that I really like the program. Best of all, my 8yo son is doing well with it. We used Moving with Math for a couple years. I liked it, but felt like it didn't have enough repetition and was pretty slow in the K and 1 levels. I like the Singapore concept, but my son was overwhelmed. We've tried it several times but there is just not enough repetition and it moves quickly. Just when my son would figured out one concept, they switched it around and he was quickly confused.
I think Math Mammoth is designed well. We do 12 pages each day. I like how you give enough problems to get the concept but then slightly add to it to present another concept. My son actually seems to enjoy the slight challenge, but we've rarely had tears like Singapore gave us!
Thanks,
Wendy Howell
I'm eager to hear your "comparison" comments, if you've used several curricula, including Math Mammoth!
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