I am not a math person. Math has been the subject that daunts me most when I think about the big picture of homeschooling. Or, at least, it did. Now that I’m 9 years into this gig (if you start counting with Kindergarten) and I have an 8th grader who is about to finish Algebra, I’m neither daunted nor worried.
I am so glad that when my oldest was 4 or 5, I had two real-life friends rave about Math-U-See. Not only did they rave, but one of them sat me down and had me watch the “adding 9s” lesson. I was sold then and there.
Perhaps part of the reason I like Math-U-See is that it is pretty much the opposite of Saxon, and I hated Saxon as a homeschooled student. MUS has short lessons; Saxon lessons are exhaustingly tedious. MUS focuses on mastery; Saxon is a spiral approach. MUS uses manipulatives to teach, even in 5th & 6th & 7th grade, making math very concrete; Saxon is abstract, and as a student I was quickly lost in the words and what they meant. MUS has no instruction in the student text, instead parent & student are supposed to view the DVD instruction together and the teacher’s manual gives suggestions for teaching the concept to the student (without a script); Saxon presents each concept (abstractly) in pages of dry text in the student book, which if done as independent work, can quickly leave the student lost (and it might take 10 or more lessons before she realizes she’s lost, and then it might feel hopeless and like something it’s better not to draw attention to – and the “she” is actually “me”).
So, here’s my song of praise to Math-U-See:
I love Math-U-See’s manipulatives.
Math-U-See is based on the foundational principle that math should be concrete before it is abstracted. Abstract comes after understanding, but understanding follows concrete demonstration and concrete work. The name itself refers to the fact that it is all about literally seeing – through manipulatives, even into algebra – how math works. There is no memorizing of formulas or answers before it is demonstrated that the student concretely understands the why and how behind the functions, and can do them (and teach them) with the manipulatives.
The manipulatives themselves are clever. There is a bar-block, almost like a large Lego, for each unit and also for tens and hundreds. Unlike cuisinaire rods, each block has squares equal to its value, aligned in such a way that they can be stacked.
With these blocks, the DVD instructor (and author of the curriculum, a homeschool dad who didn’t like any of the math options available) demonstrates that “equals” means “same as.” He sets up a four-block and above it two two-blocks and shows they are the same length, they are equal, and equal is written as two same-length lines. When we get to subtraction, he puts up an eight block, then turns a four block upside down on top of the eight (the back side has hollow squares, and now the demonstration looks like a subtraction sign). How many squares are left after 4 are gone?
With these blocks, learning x + 3 = 5 is also simple, and taught very early on. Set it up with the blocks, the five on the bottom, the three on the top. What do you need to make them equal, to make it look like an equal sign?
Making shapes with the blocks also makes it clear what “area” and “perimeter” mean and why the math gets you the right answer.
Multiplication is taught with skip counting and pattern recognition as well as with the blocks. Multiplication is finding area. 3 x 3 means “3 by 3” or three up and three across, and when you construct that, you can see it is the same as 3 3s and totals 9.
Even fractions get their own special manipulatives that make it clear why a fraction of a fraction (that is, fractions multiplied) is smaller rather than larger, why you have to have the same denominator to add, and how 1 can be represented by fractions. Fractions were still painful for my students so far, but I felt better equipped as a teacher to go back to the basics, to explain with clear terms, and to stick with it until they mastered it (rather than moving on as soon as they had a “C”).
There are even Algebra manipulatives! However, my first and so-far only Algebra student hasn’t used them. He watches the video teacher’s demonstration and jumps right into abstract – he’s ready for that kind of thinking. He understands the concepts and gets most problems correct, so I don’t force him to use the manipulative himself.
I love Math-U-See’s emphasis on place value.
Math-U-See begins with the concept of place value and returns to place value to teach every new function. Without place value, you can’t understand why numbers do what they do when you start combining them, so it is important.
Math-U-See has some handy sayings for learning place value – like “Every number has a place” and “place means value.” The numeral 9, for example, means 9 units if it’s in the unit place, but it means 9 tens if it’s in the tens place. It has been quite helpful to have this vocabulary to show my beginning-regroupers that 12 + 8 does not equal 2. Without the zero, that means 2 units, not two tens – you need the zero to put the 2 in the ten place.
Place value is also helpful when they want to work equations from left to right, like reading and writing. No, with math you have to start at the unit place and move up the “street” from there.
Place value brings greater clarity to long division, too. And when you hand your student graph paper on which to do his figuring (highly recommended), you can always remind him, “Keep each number in its right place!” and he might sigh and slump, but he knows what you’re talking about.
I love Math-U-See’s mastery approach.
Personally, I was burned as a math student by just cruising along at a lesson-a-day pace, self-correcting and able to call a grade “good enough.” For a time, I was able to just get the right answer, often enough, to keep going until one day I was halfway through the book and totally stuck.
With Math-U-See, there are concrete ways to demonstrate understanding. This curriculum is designed to help students see how numbers work, not just drill in steps to get the right answer. Saxon was written to help kids test well. Math-U-See was written to help kids understand why formulas work.
The mastery approach is epitomized in the fact that MUS books do not have grade levels. You start your child when he’s ready and you move at his pace. There is no such thing as “behind” or “ahead,” only where your student is. Math-U-See wants your kids to have all the facts drilled, understood, and quickly correct before moving into more abstract math. That might take a year, it might take longer, but don’t move on until they have it.
In our home, sometimes it appears there is mastery (evidenced by 100% on math pages on the first attempt), but later it becomes evident they’ve forgotten. So we go back and review until there’s mastery – again. Better to keep those foundations shored up than to build on a shaky foundation. In the end, the building will be higher and stronger.
Math-U-See is set up at approximately a lesson-a-week format, although they never explain it in those terms, because the point is mastery, not a book-a-year pace. This is how it works for us:
- Day 1: Watch the lesson, work the first few problems with mom (for elementary students), complete page xA. If they get it and want to move on, they have to also complete a Systematic Review page and get 100% on it. If they don’t get 100% on the first try, they have to correct the page until it is 100% – leaving errors unsolved is not acceptable.
- Day 2: If it seems like they need more practice with the concept, I give them the B page. If it seems like they understand it, I give them a systematic review page. Either way, if they get 100% on the first attempt, they pass that lesson. If they do not get 100% on the first attempt, they rework their errors until they do have 100%.
- Day 3: Same as Day 2.
- Day 4: Same as Day 2.
And so on…because they’re reworking every error, they’re incentivized to work correctly the first time – sloppy work that leads to errors will always have to be fixed, so it never saves time. Because all errors have to be worked until they are correct, we are always aware and working on the concepts they are having trouble with. I often watch them rework errors, and in that way have seen when more review in multiple-digit multiplication or fractions or some other foundational concept is the tripping point.
When I see a specific skill needs to be reviewed, we take a break from the current lesson and go back to practicing the foundational skill that is causing the errors – yes, sometimes that’s even meant practicing number formation because 4s look like 9s or 6s look like 0s.
This approach does require teacher awareness and involvement. Welcome to homeschooling – we signed up for this gig.
I love Math-U-See’s DVD instruction.
Now, although I have to be aware of what’s going on and how my kids are doing, I don’t have to pull up the inner resources to teach concepts directly to each one of them.
Instead, they learn the concept by watching the author of the program teach it – engagingly, with humor, with multiple concrete examples and explanations. I couldn’t pull that off myself, but watching him do so helps give me a starting point and a vocabulary when I do sit down with a child and his math page.
Plus, I can have them review by rewatching lessons – and unlike myself, recorded Mr. Demme is still just as cheerful and still just as ready to crack a joke the third time as the first.
That’s a plus.
I love using the same math curriculum for all my children.
Currently, I have 1 student in Algebra, 1 in Zeta, 1 who will start Gamma as soon as she passes xtramath addition, 1 who just started Beta, and 1 who is learning to write her numbers and count.
I know some choose different math curriculums for different kids, but unless you have a really compelling reason and pressing situation, I recommend choosing the curriculum that resonates with you as the mother-teacher. Learn one system, know the ropes, be able to adapt and teach math with the curriculum (even if there’s a DVD teacher provided), and you’ll experience better success than if you expect the curriculum to do everything for you and your student. What can you teach? What math curriculum can you be grateful for every time you pull it out? Stick with that one and you’ll have a greater likelihood of consistency and success.
Switching math curriculums comes with a high cost, as different programs teach with different vocabulary, in different orders, and in different ways. For awhile, you’re not necessarily learning math, just learning a new system of learning math. Better to find a program that fits you, then teach it to each of your children.
As for me and my house, we love Math-U-See.