This sounds EXACTLY like us. Every day I'm saying something like, "We don't quit in this family," or, "Remember, it's important to do hard things. That way you're actually learning something!" or, "Please give me 20 jumping jacks. We don't say, 'I can't.'" It's so easy to stick with the status quo - that's what I did my whole life - but I want better for my kids. I've talked to my oldest about how Beast Academy will be HARD. She's still very excited about it. I'm hoping she'll still be excited even while she's struggling to figure out the problems in the workbook. If this doesn't work out we'll just go back to Singapore, but I'm really hoping it works out because of the "fun" factor and the difficulty level.

Thinking about this some more: I do recall that page being difficult for my middle child (who actually is very "mathy" by the way) when we went through the Orange book. I think I just decided not to worry about it and figured she'd see more things like that in the future and would eventually "get it." That was an example from September. Have you not done any since then or was that just the easiest example to write out? Is she struggling with using the rods to add/subtract?

Hmmmm, that sounds frustrating. And it does make it especially difficult that she is one of the triplets. It seems like she needs a lot more practice with concrete materials. For instance, with the pattern problems, it sounds like she could have used some practice in making patterns with actual objects (pattern blocks, legos, beads, etc.) and counting backwards (maybe by having a row of items, taking one away and counting backwards while doing so). That particular sheet does not use concrete materials like most of the worksheets, but that doesn't mean you can't make it concrete. It really sounds like she's not quite ready yet for Miquon. (I know that makes it difficult since she's a triplet. Not sure how to advise you there.) RightStart A is a Kindergarten program, right? Could you do that with her and then move to Miquon? Or maybe keep her in RightStart and throw in some Miquon pages now and then as a supplement or to introduce topics (since it's a discovery program)? Just throwing out some ideas.... Oh, and I'd totally let her make a fairy with the rods! Nothing wrong with that. She'll still be internalizing the size difference and colors, etc. Would she be willing to play with the rods for 5 minutes (or 10 or whatever) per day as part of "school" as long as she could choose what to do with them?

No, of course children don't absolutely need to be in first grade to start Miquon. We start sometime in the 4 year range, in fact. But the OP's child is struggling so she should know that it's OK if her child isn't getting it quite yet. I just don't want her to give up the program because of that. I do want to add, though, that besides the early introduction of multiplication/division/fractions/exponents there is something else in the curriculum that I've noticed is "advanced" and could be a problem for some young kids - all the abstract symbols. With the introduction of other concepts comes the introduction of the symbols that go along with them. Usually kids in K/1st only have to deal with +, -, and maybe x and ÷. It can be hard enough to internalize the abstract symbols of the numbers themselves for some kids so I could see it being much more difficult when they are expected to remember what to do with parenthesis (or circles as Miquon uses at first) or arrows or all the other random and nontraditional ways Miquon represents certain operations. I absolutely LOVE Miquon and wish every child could use it, but I do see how this could be an issue for some....

My favorites are the MathGirl apps. They are supposed to be coming out with a multiplication one soon. I like them because they are all about visualizing numbers instead of just memorizing random facts. Definitely worth the money in my book! Other ones I or my kids really like: Match-Up Lite, Digitz, Name That Number (McGraw Hill), Rocket Math, Math Garden, Yukendo, Top-It (Addition and Subtraction), the McGraw Hill Baseball Multiplication apps I like the apps by Math Tappers, too, because they help in visualizing the numbers, but they're not as fun as many other apps. You'd probably have to actually assign them as part of school in order to get the kids to do them. Some other ones we have: AddBubbles, PopMath, MathMaster, Math Puppy, ArithmeTick, Math Pairs, Beat the Computer, Snake Puzzle

Can you give some examples/page numbers where she is not understanding? When you say you are teaching her "the procedure" what exactly does that mean? Are you showing her how to arrive at the answers with the Cuisenaire rods? Or are you showing her how to find the answer using procedures you learned in school? And is this "the baby" in your signature? If so, she may just be a little young. Miquon was written to be started in 1st grade....

My first suggestion would be to just go back and start at 2A with the whole program. You'll get the best results that way. Plus, if she is supposed to be in 2nd grade this year, then it won't seem as big of a deal to be working in a book that says 2. Singapore 2A and 2B really work on mental math a lot so if that's what you are wanting for your daughter then that is the level to start with. If you want to continue with TT and just add in SM but don't want to do all of it then I would suggest either the 2A textbook or the textbook and HIG. That is where the instruction is. The workbook alone will not guarantee understanding of the concepts. The HIG really does have a lot of good instructional and game ideas along with extra mental math lists that really help cement the concepts in their minds. Since you didn't use the HIG for your first go around, you may not have gotten everything out of the program that you could have. Another option would be to get some Math Mammoth books. You didn't say why you switched to TT but it seems like the reason most people switch is either because they don't think they're good at math or they don't have time to teach it so they want someone else to teach it for them. If that's the case in your situation then Math Mammoth would probably work better since it has no teachers' guide but teaches directly to the student. Another thing that stuck out to me in your post is the comment about your dd getting frustrated easily. My dds do this, mostly because they want everything to be easy and don't want to have to think hard. On the top of our white board is written, "Do Hard Things!" and, "Failure Precedes Success." I told them that my MAIN goal for them is to learn to work through frustration and not quit. I said that that's more important than any academic skill they could learn this year. So, to me their moments of frustration are a character building opportunity. We stop and I let them cry or have their tantrum (somewhere else if they're hurting my ears!) and then we cuddle and talk through it and, at some point, get back to work and finish the problem. This works for us because I try my hardest to make sure my kids are given work that is challenging but not beyond their abilities. If I sense that something is truly too hard for them then I have no problems putting it aside for a later date. I've also talked to them about that concept - easy, hard, and too hard. I've said that it would be pointless to give them work that was too easy - that would just be a waste of our time. And it would also be pointless to give them work that was too hard because they wouldn't be able to do it. But work that is simply at the level of HARD is GOOD for them. It makes them smarter and builds perseverance. Anyway, I've seen great improvement over the last year and a half that we have focused on this so much. Now if your situation has a different dynamic than mine, please feel free to ignore that last paragraph! I realize you weren't asking for advice on that topic, but I thought it just may be helpful. I hope something I've said is of some value to you. We've used Singapore through 2B, but not Math Mammoth so the advice I gave for that is just from researching online. HTH!

We had to stop at that same spot with both my girls. We did exclusively Miquon at that point along with lots of math games. I also bought the Al Abacus because it's a great manipulative to help teach the concept. (And, BTW, that concept is FOUNDATIONAL to mental math so it's really important to not rush through it but to thoroughly understand it.) Most likely the reason many kids get stuck at that point it because their digit span is not yet long enough. Digit span is the number of pieces of information you can hold in your head at one time. So if your daughter is trying to do 8 + 7 = ?, she has to think about the concept of 8, the concept of 7, the idea that 8 + 2 = 10 and then that 2 +5 = 7 and then manipulate that all in her head to make 8+7=10+5=15. That's just a whole lot to keep in mind at one time for a little kid! She'll do fine with it as long as you don't push it right now and just do something else while her brain matures!

http://www.artofproblemsolving.com/Videos/external.php?video_id=30

Thank you, Denise. I've gotten some helpful ideas from your blog before! I'll go check these links out!

I like your idea of using the balance. I was thinking of doing something like that. It does seem like you could easily replicate the HOE stuff, doesn't it? I need to look into it more....

If you can find the link, I'd love to hear/read it! Thank you!

Yes, I can see what you mean. And I always thought I was doing people a favor by teaching them that little trick! I'm starting to see that maybe all the things I learned in algebra actually have to do with each other. Am I right? I always saw it as all these separate pieces of information to be memorized that didn't really form any type of cohesive whole, but that's not how it is, is it?

I can see in arithmetic how my girls have been able to take the facts to 10 that they've memorized and used that to do EVERYTHING else in their heads - even multiplying and dividing some larger numbers. I like hearing that that's possible with algebra on up, too. I've been reading articles here and there by actual mathematicians and they seem to convey that idea, too - that you can take a very small body of knowledge and apply it to a wide range of problems without having to memorize hundreds of formulas. That is one of the things that draws me to AOPS and is part of the reason I'd love for my girls to go through at least a few of their books. I always thought I was so good at algebra because I had all the formulas memorized. I've tutored/taught math to so many people! And now I'm realizing that I really never knew what I was actually doing in the first place. But there's no reason I can't learn what I missed in high school level math! I'm doing it with elementary math. I guess I'll just keep going!

Beth, I just watched a few videos about this. I really don't like how they use a star to represent a negative number. I think my kids could handle negatives better than the whole star thing. You haven't found that to be a problem?

But when translating a problem into an equation I would just remember rules like "of means multiply" or "d=rt". I was still just applying rules without understanding... I think. Maybe I understand better than I think I do. I just don't know. I'm going to get an AoPS book to work through. Just trying to decide if I should start with the Pre-Algebra or Algebra one....

Yes, I mean, "Why do I write the equation to describe a certain problem the way I do?" I took Algebra I & II, Geometry, and Trig/Pre-calc and never even thought to ask WHY. How on earth did I get As in those classes without knowing why I was doing what I was doing? Something seems seriously wrong with that. There's a missing piece of the puzzle and I'm not sure what it is. Maybe that's why my question wasn't clear. I don't know what I don't know.

I've seen this mentioned a few times on the boards here. I'll look into it. Thank you!

Since finding Singapore and Miquon math (and reading Liping Ma's book among other things) I've found myself very concerned with whether or not my children have a conceptual understanding of what they're doing in mathematics. I do not want to teach procedure before the foundational understanding is there. We mostly use Base 10 blocks and Cuisenaire rods to demonstrate what we will eventually only be doing on paper with abstract symbols. This has worked out extremely well for us so far. I went through school with mostly a procedural understanding of the algorithms/formulas. I was very good at memorizing so I got good grades but I never really understood what I was actually doing. I didn't have a clear understanding of how place value and the base ten system had anything to do with addition/subtraction/multiplication/division and algebra was just playing around with letters and numbers to me. So now I'm learning along with my girls and seeing the "why" behind it all. I love it and I want them to continue to learn this way and not the way I was taught. With that being said, they are keen to learn a bit of algebra and I know some algebra will be introduced pretty soon in the Primary Challenge Math book which we are doing once per week. My concern is that they will be just memorizing steps (combine like terms, do the same operation to both sides of the equal sign, etc.) without understanding WHY. I don't understand why so how can I teach them what I don't know? I recently went through the Singapore CWP 3 and 4 books to prepare myself for what we're heading toward and I can see how the bar diagrams often give a visual for the algebra that you COULD do if you knew algebra. That was eye opening to me because, as I said, to me algebra was always just a bunch of numbers and letters that you have to move around in certain ways based on certain rules that had nothing to do with anything. Another eye opening moment for me was when I recently watched an AOPS Pre-Algebra video (Square of a Sum) and realized why I was taught the FOIL method for multiplying two binomials. There actually is a reason and it actually has to do with something in real life! Imagine that! I want my girls to always have those moments where they understand what it's really all about... So I guess my two questions are: Would it be a hindrance to them to learn some basic algebra rules right now to satisfy their curiosity? Can someone help me with the WHY of algebra?

I'm sorry if I made you worry! Totally not my intention. 5-6 is the AVERAGE age for learning to read, but just like there are kids who learn at 3 or 4, there are also kids who learn to read at 7-8 (or older!) and it is the perfect timing for them. No one worries if a child walks or talks a little later than average, but for some reason if a child hasn't learned to read by 6 in our culture, then everyone starts freaking out. I think it's because of how schools are set up with specific standards for specific grades. It makes everyone think that ALL 6 year olds should be developmentally at the same place and it's JUST NOT TRUE. Every child is unique. So aren't you glad you homeschool and don't have to worry about keeping your child right at grade level for every single thing? :) Really, your dd sounds like she's right on track and doing fine. Please don't worry!

Oh, also, I think the reason most kids read around age 5-6 is because that's when they hit a digit span of 5-6. My oldest started reading at 3 and her digit span at that time was 5. (That's how I started researching all of this.) My youngest is almost 4 right now and her digit span is somewhere around 4-5 and she is starting to read a bit but it is not fluent yet. I don't expect her to be reading actual books until her digit span increases a bit.

You've gotten some great advice and ideas here! I just wanted to add that part of the developmental readiness has to do with digit span. A person's digit span is the number of pieces of information they can hold in their mind at a time. It is part of working memory. There is auditory and visual digit span. Children usually have a digit span equal to their age until the age of 6-7. At that point it usually tapers off and stays in that range. Adults generally have a digit span of 6-9, but can be up to 12, I think (which would be really smart!). Anyway, I've read that a child needs a digit span of at least 5 to be able to read fluently. This makes sense because, like your son, if a child can't hold all of the pieces of info in his head through to the end of a sentence then he loses the meaning (usually of the middle because the beginning and end are easier to remember). So, to increase digit span, do things like the Simon game or Concentration/Memory game or anything else where the child has to hold info in mind while doing something else. Ask him to do 4 things for you (either small chores or make it a fun game) and see if he can do it. When he's ready, move up to 5 things. An easy way to test digit span is to slowly say numbers (or colors or items or letters) in a row, leaving 1-2 seconds between each word you say. Then have your child repeat what he heard. This tests auditory digit span. If he can repeat 4 things, then his digit span is 4. Make sure anything you do is fun, though! That should be top priority at this age! HTH! That was all from memory and it was several years ago that I learned about it so you might want to google more info!

Khan Academy. And it's free! If you REALLY want to be stretched, then try the Art of Problem Solving books.

Bravewriter Sonlight LA Bravewriter gives the philosophy and Sonlight gives specific assignments.

I can't even imagine how excited my girls would be about THAT! They are in love with the samples they've seen with the little beasts/monsters. I think they'd faint if they were princesses instead! I really don't like the beast theme, but we'll still be getting the books because the advantages should FAR outweigh my small annoyance in that area. The fact that it will be superior quality math teaching in a storybook form (plus a workbook!) is what has got me so excited about it!