A few short comments: (1) Middle school math is *really* hard. In the following blog post, I list out the standard method for subtracting mixed numbers: seven steps, many of which have sub-steps of their own. Then I show a better way to help your child approach such a problem by using his common sense. Subtracting Mixed Numbers: A Cry for Help In my experience, Saxon teaches the standard method, but it doesn't give much support for a common-sense approach. Your job as a teacher is to provide some balance, helping your son use whatever math he does remember to figure out the problems he doesn't (at first) know how to do. (2) As I do for anyone whose student is struggling with math, I suggest you try a Buddy Math approach. By working together, you can support and encourage your son and keep him from feeling so overwhelmed by the page full of problems. Buddy math is not a curriculum itself, but a way to use whatever curriculum you have. It should work well with Saxon. And if at all possible, use a white board. Math is ever so much easier (or at least it feels that way) on a white board. (3) Set a timer for math, and make the time short enough that he feels the end is in sight. I suggest no more than 30 minutes a day, at least until you both adjust to homeschooling. And when the timer rings, STOP, even if you are in the middle of a problem. When I'm working with my daughter, we will stop at the end of any problem we finish in the last 5 minutes. Doing math in such short sessions has really helped us avoid the emotional melt-downs we used to have. Thinking is hard work, and she can only do it for a certain amount of time before she crashes. I much prefer to stop before the emotional crash rather than after it. And because I am sitting with her and working together every problem, I know exactly what she understands and when we can skip a problem (or even jump several lessons), which means that we manage to get through our textbook in about the same length of time as normal.

I used to say an hour a day from 6th grade on, but with youngest dd I'm finding that the Charlotte Mason concept of shorter lessons works much better. She can work for about 20 minutes, and then her brain is worn out. Thinking is hard work! And when we do Buddy Math and skip the busy-work and the stuff she already has mastered, we are finding that 20 minutes a day is enough so far (almost finished with AoPS Prealgebra). Most days, we do a second 20-minute session of enrichment math later in the day.

Are you actually getting out the MUS blocks and building the problem, or are you trying to do it as an abstract set of steps to follow? If you are using the blocks, you should be able to SEE each step and why it makes sense. Multiplication with blocks means making a rectangle (thus there's an obvious connection with the concept of area). The LENGTH of the rectangle is the number of blocks in each row (in your case, 21 blocks in each row). The WIDTH of the rectangle is the number of rows (in your case, 14 of them). Then the AREA of your rectangle will be the total number of blocks: 14 rows of 21 blocks per row. But the whole, big area can also be seen as four smaller sections, splitting the length and width along place value lines. That is, the length is split into the 20-block (2 tens) section and the additional 1-block section. And the width is split into the 10-block section and the additional 4-block section. So that means the big rectangular area splits into four smaller rectangles: 20x10 and 1x10 and 20x4 and 1x4. Basically, the blocks are showing a physical demonstration of what the steps of the standard multiplication method did. If you watch yourself go through the standard method, you should see each of these four smaller multiplications. But for many people, we learned to do the steps of the standard method without understanding what they meant. The block method, by breaking out the place value steps and showing how they each work individually, is supposed to build a firmer understanding. And this same block or box method (it's called the "box method" when you just draw the boxes on paper, rather than building the rectangle with blocks) will be super-useful in algebra, for multiplying polynomials and for factoring them, and even for learning to understand the quadratic formula. So it really is worth pulling out the blocks and figuring out what's going on.

If you want to practice basic adding and subtracting with negative numbers, here is a game my family and math club all enjoy: Hit Me! (A Math Game)

:iagree: We didn't use Math Mammoth at this level, but we found the same thing with Singapore Math: the books always start the year with the hardest stuff! For my kids, things like geometry and clocks and even fractions (at this stage) were much easier than the arithmetic at the beginning of the A-level books. So we used bookmarks and worked at several topics at once. A bookmark in geometry, and one in fractions, and one in the subtraction section -- but we spent the least time in that section, maybe only half a page per day. Also, for most elementary kids, working with abstract number calculations is very hard. Whenever my kids would get stuck, I would try to make up a little story problem to cover the same calculation. "You had 26 M&Ms, but you shared them with your friends. You gave away 17 of the candies. How many do you have left?" Somehow, having something solid to imagine helped my kids figure the math out. Another thing: when working with 3rd grade arithmetic, students should still be allowed to use manipulatives, if they want to. As I said, numbers are abstract, and that makes them difficult. Anything that lets your student wrap her brain around the problem is good! Finally, even though the book teaches a bunch of mental math techniques, your child does NOT have to learn them all, especially not all at once. If she has a mental math technique (ideally, something other than simply counting down) that works for her, she can do the problems her way. This is one advantage of doing our math buddy-style: I can model the book's technique on MY problems, but my daughter is free to use her own methods on HER turn. Over time, as we do many problems, she may decide that my way (that is, the book's method) is good after all, but she has plenty of freedom to "choose her weapon" of attacking any given problem. As others have said, switching curriculum may work for you. But you should keep in mind that the topic of subtraction is hard for ALL third-grade students. It's one of those plateau topics, where students tend to get stuck for a long time, and then suddenly it clicks and they start moving ahead again. If you like the MM books overall, then struggling with subtraction is not on its own enough reason to switch. Your daughter WILL reach the end of her plateau, even if you don't do any subtraction practice at all for awhile. Just take a couple of months off, if it's too much of a struggle, and play with other topics, and then come back and try subtraction again later. (I had to do that with two of my five kids.)

If your son likes NEM overall, you might encourage him that the first 4 chapters are by far and away the hardest. It gets easier once you are past the arithmetic "review" section.

I wrote up the lessons from my blogging class at our homeschool co-op. You might find some good tips there: Blogging 2 Learn. If she uses WordPress.com, she can set her blog to "private" and password-protect it. Or she can adopt a blogging persona (pen name) and still post photos and whatever (but make sure they don't have GPS data attached).

Puberty brain fog is real, and also the emotional mother-daughter conflicts that often come with puberty may be a contributing factor. Or maybe not --- you don't say how you and your daughter get along apart from school, but it's clear from the original post that you are both pretty worked up about math right now, and that high level of emotion makes it almost impossible to think clearly about anything. Something has to change. And you are right that taking two years off math is not a solution. But could you take 2-3 weeks? Not completely off, but doing something totally different that is still math, just not the type of math that she's been banging her head against. That way, the emotions would have time to cool down, and you will both have time to think about what to do next. Things you could try during your "textbook break": daily online logic puzzles: Daily Treasure, and the Set Daily Puzzle logic games like Mastermind, or logic puzzle apps on a smart phone or tablet the Dragonbox app coordinate graphing puzzle games taxicab geometry None of these are babyish. All of them are "real" math: logic, thinking skills, algebra, geometry --- stuff your daughter will need to learn, and stuff that shouldn't have all that emotional baggage attached. I would also suggest adding the Danica McKellar book Math Doesn't Suck. My daughter (now 14yo) has thoroughly enjoyed all the Danica math books, and they are a refreshing break from textbook work. When we had our seasons of mother-daughter emotional stress the last few years, it was nice to be able to step back and say, "Go do math with Danica." A reasonable daily schedule for your daughter might be (1) read her choice of sections in the Danica book, about 15-20 minutes' worth, (2) play 15-20 minutes worth of online logic puzzle or math games, and (3--optional!) no more than 10 minutes of practice on arithmetic facts. For practicing the math facts, again you want to try something totally unlike whatever you have done before. Here are some of my favorite ways to practice: KenKen puzzles Free Rice: multiplication or general math (pre-algebra) playing Contig (without a timer!) the Target Number game (without racing) And if you want more focused work on the times tables, I have on my blog a low-stress, conversational approach that focuses on building pre-algebra skills: Times Table SeriesWhile she is taking her break from the textbook, you should do some homework of your own: buy or borrow an old, used edition of Basic College Mathematics, as 8FillTheHeart suggested above. Sometimes you can get it through your library, or the older editions that the colleges aren't using any more will be really cheap to buy (just go down a few pages in the search results to find them), and the math is still the same. There are a variety of authors who do similar books, so if you can get more than one, that will let you compare to see if you prefer one author or another. Look at the book and consider whether it might be a good choice for your daughter, whenever she's ready to be brave and tackle arithmetic again. The fact that it's a college book should give her confidence that she's not as "behind" as you and she had thought. She CAN do this! Take it slowly, just a couple of pages a day. It is a college book, so it's okay to take longer than a year, if you need to. And then whether you use a college textbook, or go back to Math Mammoth, or use something else, I urge you to consider doing the math buddy-style. It has really, hugely helped my daughter's attitude about math that I'm not asking her to do it on her own, and that I give her the control of choosing which problems she does.

Contig can be played without a timer. We prefer that to the "official" timed version. And Times-Tac-Toe isn't timed either. In fact, most of the math games on my blog are either non-racing games or can be played in a non-racing manner, since none of my kids have ever enjoyed doing math under pressure.

I have a series of blog posts designed for older students to work on math facts and pre-algebra principles at the same time. You might find them useful: How to Conquer the Times Table

I once heard a math professor say, "The cool thing about math is that, even when there's only one right answer, there's never only one way to solve the problem." If her way is working for her, then I wouldn't fight it. I would make sure she also understood the book's way, but then let her work the problems however she likes. Especially if she's somewhat stubborn, like my daughter, she may come up with some really strange ways to work at times -- but at least she's learning!

I agree that much of what you describe is typical of his age. The early teen years are really rough on math. From what you said, it doesn't seem like he is having trouble with basic understanding, just with patience and careful work. But many kids find it even more difficult to be patient and pay attention to details when they feel like they are doing busywork---stuff they already understand. It's hard to put effort into something that feels pointless. Here's an idea: How about letting him work a couple of days a week on a free online algebra course like The Math Page Algebra or Texas A&M Beginning Algebra? Letting him "run ahead" like this will challenge him and stretch his ability, and also give him a foundation for whatever the public school has for him next year. And then on the other days he could continue using his regular textbook, and practice being careful with details.

Three things you might find helpful: (1) Don't expect your children to do math on their own. Most kids need one-on-one support and continual interaction, because they learn math through talking about it, explaining their reasoning, telling how they knew what to do---basically, the mathematical version of Charlotte-Mason-style narration. I really cannot stress enough how important this is! We do Buddy Math even in high school. (2) Word problems are much more important than straight-calculation problems. Make sure your kids do lots and lots and lots and lots and lots of word problems. Give them as much help as they truly need (i.e., read the problems aloud, do all the writing yourself from their dictation, ask questions as necessary), but try not to give more help than is needed. Often, just sitting next to the child patiently and giving them plenty of time to think it through is support enough. Oh, and a white board with colorful markers helps, too. It's amazing how much more fun math is on a white board. I have a blog post series on learning Singapore Math word problems: Elementary Word Problems Through Literature. (3) Games are a great way to earn and practice math! I have a lot of them on my blog, but Tens Concentration is probably the best to start with.

Long division is easier if you teach it with cookies. Cookies make everything better! The Cookie Factory Guide to Long Division

I don't even begin to push memorization until the very end of 3rd grade or sometime in 4th. At that point, my children will have spent plenty of time learning to recognize multiplication in a wide variety of situations, and they will be comfortable solving multi-step word problems that require multiplication or division. And they will have spent lots of time using mental math techniques (of which skip counting is a minor one) for figuring out lots and lots of multiplication problems. In the process, they will have naturally learned many of the multiplication facts. Our memory work is primarily a mop-up job, mastering the toughest facts that have resisted being pinned down---like 7x8. And we use our work with the multiplication facts to introduce and practice several important prealgebra concepts.

Be warned that most college textbooks give you many, many more homework problems than they expect any student to do. The teacher can select his or her favorite assortment of the problems, leaning toward the basic practice problems or the challenge problems, depending on the students' ability.

I think it depends on what you mean by "addition facts" and by "mastered." My kids hated timed worksheets full of abstract number problems (they much prefered story problems, which gave their imagination something to hang on), and I don't think they ever "mastered" the addition facts according to the definition of being able to finish a worksheet in a minute, or five minutes, or whatever timed drill you choose. BUT my children learned to be flexible in their understanding of numbers, their ability to manipulate quantities, and their methods for figuring out things they didn't remember. If THAT is what you want, then it's a continuing process that should be growing all through 1st and 2nd grade. By the end of 2nd grade, I expected my students to be able to mentally add or subtract numbers (with an emphasis on accuracy more than speed, and with the ability to identify whether to add or subtract when faced with a multi-step story problem) at least into the hundreds, using a variety of techniques---and one of those techniques would include applying whatever math facts they happened to remember.

Learning about numbers: How about number theory? (odds and evens, primes and composites, square numbers, triangular numbers, factors and multiples, etc.) hundred chart activities counting puzzles (how many ways can you do something?) negative numbers fractions (the entire fractions series--about 16 posts--is wonderful!) calendar puzzles money infinity "1+1=5?" Scavenger hunt "Would you rather have...?"

I have two blogs (see signature), both relatively silent over the summer but chock-full of great resources. The math blog has a lot of games and activity ideas for all ages. The other gives steps for setting up and growing a student blog, based on a class I used to teach at our homeschool co-op. This coming school year my youngest is entering high school and my third child will earn her BA. Our educational style has always been laid-back and eclectic, and I prefer to delay formal academics in the early elementary years. Actually, I've never done "formal" anything very well. :rolleyes:

:iagree: These two blogs are vitally important reading for anyone interested in a writing career.

A great supplement would be to use the AoPS online problems (Alcumus). She can set the server to give her specific topics, or just let it choose what it thinks she can handle (it's supposed to be responsive to what you get right or wrong). Lots of challenging puzzles there, to encourage her to think more deeply about the math topics. And if she gets stuck on something (in Alcumus or in her textbooks), the help forums there are very good.

Note: Some of the blogging lessons include a paperback book we were using in class for writing/editing practice. The book had some fun exercises, but it is definitely NOT required! I added it to our class to make it a more balanced language-arts class, just to entice parents to sign up.

I taught a blogging class at our homeschool co-op for several years, and I put all our lessons online here. I personally prefer the free WordPress.com (not wordpress.org, which is for the pro version) for its flexibility and features, but the same principles apply no matter what blogging system your student uses.

Yes, proofs are necessary. But they don't look like what you are thinking. A "proof" answers the question, "How do you know?" Therefore, when your student is working through a problem, periodically stop and ask about a step, or about the problem as a whole. "How do you know you can do that? How do you know that's what will happen? How do you know this is true?" When he answers (or at least, when he gives any answer other than "Because that's what the book says"), he is giving an informal proof. Informal proofs are the best kind. Trying to be too formal tends to bypass a student's common sense.

She's young. She has plenty of time. And math is MUCH more than just numbers. Therefore: Do something else---still math, but not numbers. Come back to numbers later, after the emotional baggage has had plenty of time to clear. Look at these three blogs for lots of creative suggestions: The Map Is Not the Territory Moebius Noodles (scroll down past the mpsMOOC13 summer course posts) Love 2 Learn 2day Or if you have trouble imagining how powerful math can be without numbers, get the Moebius Noodles book. The paperback price is very reasonable, or you can set your own price for the pdf.