Math is my son's weakest subject. I don't know if it's because he's not a math person, if I'm teaching it wrong, or if he's simply not "there" yet. Maybe all of the above. My question is ... When and/or How do kids transition from concrete math (2 apples plus 1 apple is 3 apples) to abstract math (2+1=3 on paper)? He's still in concrete mode, so he's very slow. Everything else he learns is done at lightning speed, so this puzzles me. Any "math people" out there care to share their thoughts on how they learned it? Or anyone HS'ing someone with a similar challenge, how did you get past it? OH! Not sure if this will help or if it will muddy the waters, but he learns great when he's doing something like ... I don't know ... times tables. (Not that he knows those yet. Just an example.) He knows 2+2=4 simply because it's an inside joke between him and his daddy. They've done it since he was a baby. He learns "facts" easily. It's the "why" behind math that he's not grasping, which is why addition/subtraction is so hard for him. I know times tables will be easy for him, because I just know how he picks up facts easily.
Many kids learn the order the numbers go in (counting) without having a concept of numbers being a value. Memorizing facts won't help if the child can't use multiplication to solve a problem, which ultimately is the goal of having people learn math in the first place. We use Math-U-See. There is a very good thread on MUS and Teaching Textbooks. I believe there were many people who advocated MUS as a good early elementary curriculum. It worked miracles for my son when he was young. He had gone to public school where they were expected to learn number order/families/etc.....lots of memory work, but no math. We had to start math from the ground up when we brought him home. MUS uses manipulatives as well as encouraging the child to use a multiple sensory approach. They learn to see it, say it, and build it. Ds is now 13 and hasn't used manipulatives for years, but it gave him a wonderful foundation when I thought all hope for math success was lost. He averages an A now.
What program are you using? We use Horizons and my son is actually "getting" the whys behind math and he is only 5. We tried MUS no success. I know I am not much help, sorry.
Different things are going to click for different kids, so MUS would work well for some and not at all for others, while Horizons is great for some, Saxon is great for some, CLE is great for some.... In general, I think math programs begin with concrete concepts (one block -- now add one more block and now we have two blocks, so one and one is two.), then to pictures (here's one picture of a block, then add a picture of another block, now there are two pictures of blocks, one and one is two), then in more general terms (here's a picture of a toy car, add a picture of a teddy, now there are two toys, one and one is two), then less specific representations (draw a stick, add another stick, now we have two sticks, one and one is two), then somewhere along the way showing the numeric way of expressing the concepts (1 + 1 = 2), then to leaving off the pictures/tallymarks altogether and just using the number sentences. Lots of steps. Some kids can just go from oral discussion of manipulatives to numeric representations, but others need all the steps from concrete to abstract, and some need that longer than others. But what a joy to see the lightbulb come on, right? A couple of weeks ago, our 6 year old first grader suddenly "saw" the concept of adding!
My son is in first grade and he still uses objects to do math problems, However we are currently working on memorizing math facts to help him do his problems faster. He understands "why" 1+1=2, but he's just not very fast with it yet...my middle child who is also doing mostly first grade work is much faster. I really think it's an individual thing for each child. We do use MUS and my boys LOVE it and math is so enjoyable for them.
We're using Abeka. I've seen MUS (because other people have it), and we've got the mathtastics DVD that he likes, but I really want to stick with Abeka, at least until the end of the year. I've changed SO many things this year, and I'm tired of spending money on things only to have it not work. A wise older woman once told me to buy whatever "I" like, and then make it work for each child's style. All of her kids were taught that way, and it worked well for them. We use manipulatives as well (although at first I was totally against them, because that's not how I was taught). I don't know. I'm just trying to re-think everything and don't want to start buying new things until I'm convinced it's the answer. Maybe he's just not as ready for math as he is everything else? Every kid is different. (He's on 4th grade reading, which is why math is so frustrating to us. Other subjects are average, but math is hard. I don't want him learning to hate it.)
I like manips at that age and Horizons is an awesome choice too! I think also that you need to keep with the m n m math. Hands on things work really they do! It is not something that you learn at once and da da! Math is an on going arning thing. You remind remind remind remind and keep going with it for 11 - 12 years of math stuff/. persistance presistance, it will come, hes only in first grade!
I would give him REAL things to count add, etc. if you are setting the table then add the forks in his hand to the ones on the table. Try to make the numbers relate to real things so he can recognize they have a value. I think real things are even better then fancy manipulatives that are sold with curriculum. I would say real things and then somewhat abstract blocks or beads and THEN move to the abstract. I have commonly read that manipulatives should be used until the third or fourth grade some people would say even higher.
When I did math with lil ones it was a lot of having pictures on one side of the plus sign & then some on the other. I found that if you do it easy like 1+1= , 2+1.... do all the ones for about a week. Then move on to the next. You may also want to google touch math. This might help as well. I know some who use touch math for only a couple number, some that really use it.
when I said manipulatives I mean M&Ms and legos that sort of manips, it I never used store bot offical manips loL! A manipulative is something you use your small motor skills on, finger play toys,
Added: if you make some number flash cards to put underneath your manipulatives, that might further help with the transition. Set out 5 M&Ms and 3 M&Ms, put the numbers underneath with a plus side between and an equals off to the side, then move them all to the other side with the answer.
