What’s the same? What’s different? These are not Pro’s or Con’s by the way. Just things I noticed from using both programs at the elementary level. Like others with math backgrounds (both on this forum and other forums and my dh too) have noticed, at jr high and high school levels, MUS is not going to be the right program for those needing strong math sequence for college. But let me stick with elementary because that's what I know.
MUS – mastery approach with some review worksheets in each lesson so that you practice older skills and not just and only the new current skill. However, there is the user failure danger that can easily happen that you will miss something thinking your student has mastered it and doesn’t need to review. That’s not the program fault.
SING: not really mastery, not really spiral. It’s a blend. Singapore is hard to define in American math terms as it is not American program.
Both programs in my experience, like to introduce concepts and then applications of those concepts. Some reviewers say that means it skips around. I disagree and see it differently. I see both programs do a new computation or concept and then try to pause for a while, let it settle, and during that time, do some applications of the topic. I like that about both of them. For those of us using MUS, what I mean is stuff like skip counts by 2's and then you learn about how to use it with cups to pints to quarts and all of that. We don't jump topic to measurements really. right? well, singapore is the same way on that.
MUS is very strong in computation skills to use manipulatives, drills, etc.
MUS: good for building confidence in teachers for a few teaching techniques. There is something nice about having a teacher show you really quickly how to do something so you can teach it.
Singapore: if you need confidence builders, get the Home Instructor Guide. and yes, you can use your MUS blocks, or Cuisenaire Rods, or any objects. That is strongly encouraged in Singapore. (in fact, that's encouraged in most elementary)
Singapore: the program assumes the teacher is doing drill work with number bonds. You will need to drill facts. MFW recommends flash cards. Check archives for math drill ideas.
You can even use the online MUS drill page if you want. But get to know your number bonds. number bonds means they are taught in families: 4+3=7, 3+4=7, 7-4=3, 7-3=4
Singapore, like MUS, starts with very concrete teaching before the abstract. A common mistake made is that people rush to the abstract in Singapore.
Both programs encourage use of hands on tools for learning.
In the early years MUS in alpha and beta teaches addition and subtraction kinds close together so students see how those are related. Singapore does this too. Then, in gamma, MUS and Singapore really begin their separate journeys. But, some people even try to use MUS and Singapore together and sometimes it works.
Singapore continues to teach related operations together so that multiplication and division are taught as partners. In MUS, gamma is only multiplication. Then, delta is division. In Singapore 2A and on, the operations are taught together in ways that complement each other. So in Singapore while you learn your skip counts by 2’s 3’s 5’ 10’, and then later in 4 6, 7 8, 9,
You are teaching it as number bonds still. so you learn them as 2*3=6, 3*2=6, 6/2=3, 6/3=2 and so on like that.
Word problem and thinking skills: Singapore is known for its strength of word problems that make you think but can still be solve concretely and pictorially. I personally found that MUS worked too quickly to the abstract with variables and inverse coefficient of something or other…. Huh? So, I found that MUS advanced in the math vocab with those words, but didn’t help my dd or me learn how to think about a problem without setting up an equations with X’s and things.
Singapore teaches how to think through a problem. And draw it and doesn’t deal too much with writing equations. I think MUS worked more on the equations and wording and this kept the level of word problems lower than necessary for the age. just my experiences.
Geometry: Singapore does more with geometry than MUS did.
I found I was adding to MUS to make it a more complete program in math. It was strong in computation.
Again, I didn’t ruin my child who used it from Kindy thru Zeta. But I am really thankful to use Singapore for both my smart math kid and my middle daughter. I’ve watched as my middle daughter works through Singapore and am just amazed that she is doing it and thinking about it.
minor things of note:
MUS has no color on teacher book or student book (this is not a good or bad thing by the way)
Singapore - teacher manual has some color and is used as a pre made chalk board. Student pages black and white (like MUS), but few problems per page to cover a lesson.
Review work: mus has 6 worksheets per lesson plus test (if I recall, maybe Wendy will verify or correct that?). 3 of them are classified as review.
Singapore: has reviews/practices at end of each unit, and tests and reviews. It assumes, but doesn't directly say on teacher book that on reviews, we are to encourage reviewing techniques with child. I found it easy to re do review pages from teacher/text book.
May God guide your decision as He knows your children. There are definitely some children who need MUS. And then, there's my child who benefited from switching and using different things at different stages of learning.