I am trying to figure out how best to support my ds7 in math. He is currently a 1st grader who is above grade level. His strength is verbal abilities. He is obviously not "bad" at math, but is quite insecure with his ability and knowledge level. Also, since he hates repetition, his fluency is definitely not where his ability is, but slowly improving.

He has recently discovered that he understands multiplication and can accurately solve problems. Yet, he surely has not memorized them. He now wants to move on to division. Shouldn't multiplication speed improve first?

He was given work from the gt teacher on ixl (which he hates). It's addition/ subtraction multi digit through 6th grade. (Does this mean kids are still doing +/- in 6th grade?) What I noticed when he worked on it is that he could easily do this math (somehow) in his head, but had trouble "showing his work". So, I've left it alone for now.

Last year, I bought MUrderous Maths. Unfortuneately, I thought it was more interesting than ds.

I just purchased LOF- just book 1. (Not sure if ds would like it.) It seems too easy. I'm wondering if I should try it (maybe with ds3.5 who is mathy)? If it would be better to start with a different LOF book? Does order matter for the story or the math?

Overall, I'm trying to support him. I want him to feel more confident in this area(s) while attempting to feed the need for new concepts. Thoughts? Thanks.

(Btw, this is never pushed on him. It is he who asks. Ex: His goal for 1st grade written on day1 of school was to learn division. I do think him seeing questions on MAP testing that he has no idea how to answer, cause great anxiety and determination to learn the concept to decrease the anxiety.)

When I was considering it I was advised to start with LoF Apples even if it was too easy - you can go fast, or read it to both kids together.

Puffin, thanks.

Melessa, I'm also trying to sort it all out as I go along so while I have no BTDT experiences to share, I have been thinking about this a lot.

If exposure to new concepts is your purpose, then I personally wouldn't worry about following an orthodox scope and sequence as long as your DS is enjoying the learning process.

If home ends up being his main place of math instruction because of homeschooling or afterschooling, then it becomes a whole different story but I'm not sure if you're heading down that road right now.

My plan for DD if we go homeschooling route is to get her through SM while supplementing it with both Montessori math materials and other "fun" resources like Beast Academy and iPad apps. I tend to lean towards unschooling side of things in general but when it comes to math, I like to know where we're going and how we're getting there.

I would have thought he would have started learning division in kindergarten? 6 piece of candy, 2 kids, how much does each one get? Are you (/he) thinking of long division?

Has he been shown multiplication tables like this 4 X 3 = 12 leads to 12 / 3 = 4 at school?

Expat Mama- I guess I do mean long division. (He does understand the above division- primitively- with pictures or word problems, not straight up facts.)

He has not been shown anything about multiplication or division. His exposure is via Compass Learning (time for learning for homeschoolers). Map scores somehow talk to Compass and give him activities that "he is ready to learn".

He has found a way to listen to the explanation once and fast forward to the quiz (if he gets it). It's an interesting concept, but bothers me that he's learning sololy from this program. I just try to provide support if the explanation seems wierd or he starts to get frustrated. It sort of works, but I would like another source in addition. I also know this program is on the edge of being not liked anymore.

Melessa,

I think the challenge with a "verby" kid is that verbal tasks come so easily to them, that math seems RELATIVELY difficult (and a DC's initial or eventual approach may be to want to avoid math altogether).

DD8, who is my extremely verbal DC, hit a "crisis" point with math in 2nd grade. Her school starts math differentiation in 2nd grade. DD was placed in the top group. DD's best friend seems to be HIGHLY gifted in math and would often finish math tasks more quickly. There were also some boys who were simply quicker at math facts than her at the beginning of the year. There was definitely an emphasis placed on speed in 2nd grade, as the teacher was striving for math fact automaticity. DD, who had for the past two years been used to having everything at school come so easily, now suddenly decided she was "stupid." (She has consistently scored 98-99% on math standardized tests, so it is a "relative" weak area - emphasis on relatively!). She routinely announced in 2nd grade that she "hated" math (DD tends to be a bit intense and dramatic, too)! I was horrified! 2nd grade is a bit young to start hating a subject!

We did offer her extra support and encouragement that year in math, and she seems to have gotten over it. She is still in the top math group, is doing great in it, and is making excellent progress. I think she has also gotten used to the differentiated math class. She still doesn't seem to love routine calculation and she is prone to silly mistakes because she tends to work quickly to "get through it." She recently started doing EPGY at home to "challenge herself," and had been progressing nicely. But I don't hear "I hate math" constantly now, either!

I do think kids that are very strong in one area tend to find that as their "comfort zone." DD needed a little push out of her comfort zone.

DD actually enjoyed several LOF books before loosing interest in them. Different DC may need different resources and approaches. My 2 DC differ from one another, so I try to offer different things up and we go with what they tend to like.

For instance, DS5, who seems to be more naturally "mathy," is doing Dreambox math at home. He's still in K, and we are pretty low-key about it. His strengths/weaknesses/preferences seem to be the absolute reverse of my DD. He has been able to read since he was 3, like his sister, but would prefer to do math. He also plays chess, and I do believe this builds spatial ability.

Dreambox seems geared towards the younger set. EPGY is drier, and probably works better for older children.

Melessa,dd4.5 loves math and is very mathy. She is not a fluent reader and does not enjoy reading. So kind of opposite but I have tried several math books with her including ixl, singapore math, and brainquest. he was finding 2nd grade math too easy and boring on all the three and I did not think she was ready for 3rd grade. So instead I got her this book.
http://www.amazon.com/Math-Gifted-Student-Challenging-Activities/dp/1411434331
Both of us love it. There is very little repetition and you actually have to think through the problems. I started her on first grade but planning to get the second grade soon. Barnes and Nobles has them, if you want to check them out at a store.
On another point in your post, DD can do multiplication and division even though she hasn't memorized any facts. She just uses various self-invented shortcuts. So I don't think you have to master the facts before moving on to advanced concepts with these kids. Once you give them a problem, they will use the tools they have or be motivated to learn the tools they need. I don't think learning the facts as an end goal would appeal to our kids. HTH

DS is the same age (first grade, just turned 7) and learned all of the multiplication facts last summer doing Big Brainz (or Timez Attack) online. There is a free version and a Deluxe version that's $20 for 3 months or something. He LOVED it because it was like a video game. I don't think he cared much about the math, he just loved the game. I know other kids who have tried it and were frustrated (because it is a fluency game and they need to put in correct answers within a few seconds), so it just depends on the kid. It starts out with a few facts and when a kid masters them it moves them on to a few more facts and reviews the facts later to make sure they are retained. They also have this for addition/subtraction facts.

DD is currently in third grade and the math curriculm teaches multplication and divison simultaneously. So you learn 5X4=20 and 20/4=5 at the same time. Not sure if that's a great idea or not. I just taught DS that division is the reverse of multiplication after he learned all of the mult. facts.

Thanks for all the thoughts!

blackcat- my ds did use timez attack a bit. However, it usually ends in frustration because of speed, finding the number, and typing it in. Since he feels he's bad at math, he assumed he wasn't ready/too hard until it profiled in his Compass Learning profile.

lovemydd- I really like all those flashkid books. I should look through what I have.

Loy58- How you describe your dd sounds very similar to my ds. I identified with much of what you wrote.

He doesn't want to "fail" by not knowing the answer.( Actually, his high math group is all girls and him.) he also rushes through his work and doesn't want to check for easy mistakes. Hopefully, we can help him feel more confident while still have fun learning:)

One thing I did at a certain stage was to sit with my DS and do the typing for him in these speed-based games. My fingers hovering over the numeric keypad (trying not to hover too obviously over the right answer, I remember!) and him shouting out the answer, with me keying it in immediately he did so. Helped a lot at a certain stage.

Yes, I have done this as well. You may also be able to change the settings so it gives them like 10 sec. per question.

I would not wait until your DS has mastered math facts before moving on. DS8 still does not have his times tables memorized, but we decided to move on and work on them over time.

You might also look at the Singapore Math Challenge Word Problems books. The actual arithmetic is straightforward, but the methods needed for solving the problems requires some thought.

For LoF, we started with Apples and tore through them quickly. Yes, all of the early books were too easy, but DS liked the story, and he learned stuff (e.g. sets) that was not covered in public school. We're on hiatus after Fractions, but we've got the books through Algebra. DS likes to read the physics, biology, and econ books on his own.

We also didn't force memorisation of facts before moving on. I feel like memorisation and rapid fire recall is a separate skill which is more age-based, and forcing it would have taken all the fun out of it. So for four years one of my kids progressed through math knowing how to multiply and divide but not knowing the times tables, then BAM, third grade hit and it was all memorising Pi and memorising this and that and everything else. Sure, my five year olds can do third grade math, but they're not third graders.

We used one of those grids for help, especially with division. Have you tried Kahn academy? It's pretty fun and they can follow their interest.

Thanks for the thoughts! I guess I am free to carry on as he is interested.

Read Chapter1 LOF yesterday, to both boys. It seems like that may work.

Knittingmom- I will check that book out.

Tallulah- I think I needed to hear that comment about age vs ability. I think I keep worrying that I'm going to not give him the right foundation which could negatively affect him later. I probably should just have more fun with it and follow his lead.

I think the point you made about the brain being ready for different aspects of mathematics at different ages is very important. It seems that a parent or teacher could waste months pushing the wrong topic, that could be covered in weeks later, simultaneously making math more of a chore than it should be.

To a large extent, the process of solving a new type of challenging math problem involves using a lot of math that a student already understands. For example, using a lot of arithmetic to solve simple algebra problems. If a child is unmotivated to practice arithmetic on its own, but is motivated to use arithmetic to solve algebra problems, it seems to me they are better off doing algebra.



My daughter is using the multiplication and division boards in her Montessori pre-school. I think they are a wonderful manipulative for tactile and visual learners. I'm formulating a plan to have her calculate some squares and square roots on it, too (which I doubt the teacher will present on her own.)

Wasn't there a thread on here recently about how strange it is that we treat math differently than reading? It was a great observation that we will let kids read or hear a wide range of stories without worrying so much that they get more out of one story than another, but with math we say, "you can't look at this until you learn that other thing." Khan academy and Math Mammoth have some great YouTube videos. And there's a video called "turtlehead multiplication".
One thing I learned was that "being ready to learn something" does not mean the same thing as "can do it by themselves already". It doesn't even always mean getting it right the first try. That should be obvious, but I only realized it when somebody said it. Now my kid learns what's called "separate strands" of math. That is, in one strand, he just wrapped up borrowing and carrying (and sometimes still counts on his fingers), another strand he's starting to study algebra, another strand he's doing Beast Academy, which teaches advanced concepts but is really about mastering the multiplication tables, another strand is elementary school problem solving, which is different than learning math and doing what you already know, it's about learning how to deal with problems you haven't been taught. I just really like what they said in that other thread that we limit exposure to math in a way we would never limit reading. We read widely and we can treat math the same way. Some blogs that support that idea are bedtime math, kitchen table math, and buddy math. We have a lot of separate math strands going, but we don't study math all day, just like we read a variety of stuff, but we don't spend all day reading either. Just sharing because it's one way my understanding has grown as a mom. Oh, there's so many things I'm learning about being a mom.

"Separate strands of math" - I love it! We are definitely doing this with DS8 (and now I have a name for it! Yay!) He loves watching Vi Hart and Numberphile videos, reading Pappas and Martin Gardner books, and learning about much more advanced mathematical concepts. All while working through early geometry, fractions, etc.

These "strands" should be placed in the following context:
http://en.wikipedia.org/wiki/Partial_order
http://en.wikipedia.org/wiki/Quasi_order

" for certain pairs of elements in the set, one of the elements precedes the other."
Yeah this and this
" In words, when a ≤ b, one may say that b covers a or that b precedes a, or that b reduces to a."
If that's what you mean, if not you lost me.

If Topic X is a prerequisite for Topic Y, then you should cover Topic X before Topic Y.

If Topic Y is a prerequisite for Topic X, then you should cover Topic Y before Topic X.

If neither topic is a prerequisite for the other then you may do the topics in either order, or do them at the same time.

But how much proficiency should be required in Topic X before moving to Topic Y? Understanding of the topic? Being able to do the arithmetic without using fingers/calculator?

It's a bit like that classic yes/no question: how long is a piece of string?

The second quote, from the quasiorder link, said a《b could sometimes mean a comes before b, sometimes a is part of b, and sometimes a is a smaller version of b. Since we're talking about early elementary here I would think that a is usually part of b and b covers it.

For example, the turtlehead multiplication video I mentioned could be used to practice multi-digit multiplication even if the youngster needs to count on his fingers or draw out and count the dots for some of the digits, as long as they understand what multiplication means and can work with numbers to that place value. If they understand numbers to that place value, then it's hardly different than doing page after page of single digit multiplication. Why would they have to have their times table completely memorized before they see something new they can do with multiplication, multidigit multiplying larger numbers.

I think it's the same for long division. If they can do all the steps, divide, multiply, subtract, then it should be okay for them to do a few problems while you tell them what the next step in the problem is. They won't want to do a lot of problems before they memorize the times tables, because it's tedious. And even then they'll probably only want to do a lot of them if it's word problems that require long division. But I don't think it hurts to let them do a few problems now and then.

That's an example of when b covers a. Subtraction, multiplication, and division are all part of long division, and long division covers it.

The first quote, from the partial order link, said some parts have one thing that preceeds the other (and some parts don't ). An example is that my kid has done the first few pages of an algebra book. He had to skip the problems that had fractions and decimals. He's barely worked with those. For those problems knowing fractions and decimals preceeded doing the math. For the other problems, it didn't.

I (think) it's okay to show kids things they're not going to "get" it all the first time. I think learning new things means looking at stuff that some of it you know and some of it you don't know.

On the subject of mastering arithmetic, , I waiting until DD completes her pre algebra class before I let her have a calculator because the AoPS class really emphasizes mastery of how to solve the problem first, I.e, get optimal algorithm for tackling the problem decided first before actually tackling the routine exercise of performing the calculations that I feel that if she demonstrates competence here that the mastery of arithmetic will thus be implicitly present.

A test. Even if it is just for fun.