One of my sons is currently taking a summer course through our county's e-high school program. From what I can see, since they've set it up with no class interaction, he may be learning facts but not necessarily grasping principles. This is always a danger when learning subjects alone and not as part of a group: You don't have to fully understand in order to make a good grade. For some things (such as math-related topics), it is important to learn by rote. For other topics, though, understanding principles would seem to be more important than simply learning facts. In a homeschooling situation, how best to ensure this?
In my house, we do not practice rote memorization for math at all. I don't believe in it. I would much rather my kids understand 100% why 3+3=6, not just be able to spit out "6" when I show them a card that says 3+3. I'm not sure how to help you with your issue, but just wanted to share my point of view.
At age 6 and in a traditional school in Britain, our class spent entire afternoons reciting tables up to 12. For the next 40+ years, though, I've been able to instantly multiply numbers together. So, for math, I don't mind my children learning some things by rote. On the whole, though, I agree with your comment about understanding 'why' more than 'what'. Doesn't this require some level of interaction, though, so the child can be challenged?
I have my 10 year old do all of my math at the grocery store... if I buy 3 of these boxes of mac and chees for 34 cents each how much do I need to add to our total (I have to keep a strict budget). He can spit the answer out in a second. Because I push him to use his math constantly in real life it just flows out of him. There have been times when we have used flash cards for math... but I have never pushed it as a timed kind of issue.. it was more of a "see the problem in your mind" kind of thing.
I think rote memorizaation is absolutely necessary with math. There is no going forward if the basics are not 100% mastered, it only leads to frustration. Just as you cannot learn to read or write without first memorizing the alphabet, you cannot move on to high math until the basics are so automatic that they require no thought process whatsoever. I don't think learning in a group is required or necessary, but it all depends on the student.
I agree. I think it has definately helped me to know my math facts. If you memorize them that doesn't mean you don't understand why. I think when it comes to math at a young age both concept and memorization needs to be taught.
I agree with Barbara you have to do both, know them by rote AND understand them or it wiill be constantly looking things up. I think they go hand n hand.
I agree - it is important, essential, to understand the *why* of things and not just the what, rote memorization. That doesn't make the rote memorization in itself a bad thing. It just should come *after* the mastery of the concept. The approach of each individual curriculum will determine this. The style of the teacher, if you will. If this program/class is teaching the rote memorization without ensuring that the student has first mastered the concept, I say it's a dud program and I'd find something else. And, I don't think being in a group has anything to do with either of the above processes.
I agree it doesn't matter when learning things by rote. For understanding 'why', though, I'd suggest a student needs to be challenged - either by us as parents or by peers. Why is it not this? Why do we believe that? What would happen if this was the case? Why is the other different? This is when principles become important so students can reach their own conclusions.
Public schools are a group setting. Yet many fail to convey the why, especially in math. Unfortunately they are great at handing out good grades when there is no sign of comprehension from the student as to how they came up with the answer in the first place. However, I do believe the parent, teacher, and curriculum should bring the point across so the student will learn how to grasp principles and not simply repeat facts.
I think that it makes much more sense that a child is likely to obtain a better grasp on concept in a smaller setting - such as the almost one on one ratio of being at home. In a large group setting, such as a traditional classroom, the teacher cannot be expected to make sure every individual student completely understands the concepts being presented. Tests don't necessarily convey this, as the aforementioned rote memorization would provide a crutch there. In addition, even if a student doesn't completely grasp a concept, large groups must continue on at a steady rate to stay with the average, median rate of all. So if a child is having a difficult time understanding, it matters not - what's next is next and it's time to move on. I don't need a group setting to challenge my dc. In fact, being near my child provides more opportunity to do so in real-life situations. Today, I took an Avon order from my aunt. My son added up her purchases and told her the total, and then counted her change. (He also let her know that only 4 candles on the cake was 28 short of what Dad really needs. LOL) I agree that a child needs a teacher. I just don't see the necessity of a group. If I did, I'd not have brought my child home for one-on-one instruction. Learning is very, very individualized. Everyone learns in different ways, at different rates, and any curriculum geared to a group has to take a generalized approach. I'm able to take a specialized approach with my own children, and what's good for the oldest might not work for the youngest. We do what works here, because the school system didn't.
But that assumes that homeschooling and group learning are mutually exclusive. The fact that you're using this online forum implies that you can be part of a group without having to attend one in person. Isn't that true for your homeschooled child too? They could be part of an online group, for example, just like you are.
The only thing best learned by rote in math is math facts. Everything else, you must learn the concepts. As far as group vs individual learning, I have found that individually, it is easier to teach concepts than in group situations. I have been tutoring math for a while and the 2 biggest problems are either not knowing math facts (rote learning) or not grasping any concepts at all. For example, this one person, she had no clue why she did fractions the way she did, she just kept trying to follow the steps. She got so confused and mixed up the steps as she had no clue why this step or that was applied. I had to back her up all the way to factoring to get her to where she could do it. She had spent years just learning a rote set of steps and it is nearly impossible to memorize things that way.
My 15 yo dd is struggling with her multiplication. She didn't do well in public school math, and I'm afraid to say I've not done a good job since she's been home (this will be our 5th year :roll. I've been trying to move on to pre-algebra and algebra even though she still is not "quick on the draw" with multiplication. The times tables weren't learned by rote at her school like I learned them when I was in school, and I haven't made it a priority so far. Any advice you can give me would be helpful. Thanks!
OH!< one mroe thing, I mentioend on the other thread but look at Math U see or Teaching Textbooks, they are both excellent! They are dvd or cd teachers and kids who did not get algebra ( my dd who is also 15) get Math with Mr Deme or the TT lessons, they both are really wonderful! I have a friend with a son who just didnt do great hated math, but he is using tt pre algebra andnow alg 1 and is getting it and really enjoying it to the point he is going over the lesson mroe than once just for fun! Check them both out!
For some children memorizing is a tedious waste of time. My son can't seem to memorize facts for the life of him but he doesn't see numbers like many children. He can add 3 and 4 digit numbers in his head but he doesn't work them in columns like many school children are stuck doing. He works them up (or down) more like counting change and somehow it doesn't exactly correlate with saying what 7+8 is. I don't know why the difference. It's almost like it is using a different part of the brain. He can work 7+8 in his head quickly but if he thinks he is supposed to answer as though he already knows it he blanks. He forgets that all he has to do is figure it out. He can do so fairly quickly most of the time if his brain doesn't shut off because he thinks he should know the answer already. He also doesn't memorize tricks. I tried to teach him the trick for multiplying 9's but he did not get it AT ALL. At a different time I heard him work a problem out loud for a game and he had figured out his own trick. He just multiplies by ten and subtracts the number he is multiplying by since multiplying by nine is always one less then multiplying by ten. It's hard to explain quickly on the computer so I hope that makes sense to everyone. The key with him is understanding. If he understands something he simply KNOWS it. There is no such thing as forgetting it like there is with memorization. I'm not trying to say memorization is a bad thing. For some kids it will be helpful but that doesn't mean it is essential for all children. This is simply for all those lurkers who have concept oriented children who would end up beating their head against a wall with all this rote memory stuff.
I guess it depends on her learning style and if it really is just a memorization thing. If you are only worried about memorizing and do not want to go back over concepts then a really good thing to do is to show her the patterns that multiples make. Going over a 100's number chart with a highlighter and highlighting multiplies of two or three or whatever number you are working for. She might find her own tricks as my son did. Skip counting is a useful tool also. If she has always had problems in math then it may not just be memorizing though so it would be helpful to narrow down the problems she might be having.
There is a big difference between memorizing and learning them. Learning is like what Froggers kid does with figuring it out in his head. Memorizing is just repeating facts, you don't even have to know after your done repeating them. We try to learn how to figure out a problem here, because if there is an 'easy way' to do something in your head, I think it must be done. My ds does addition to Multiplication in his head as well he has his own way of working it out, even writes numbers down the side of a page. He will write every number in conjunction to the number he is working .. if that makes sence. He writes lists of numbers.. from those lists he has his answers. He gets A's in Math almost constantly so I know he is doing it right. I teach him , or rather instruct him , in the correct way according to my math program, then allow him to mess with it in his own way and see if he can come up wiht the right answers. I tell him that there is a time to do it your own way and a time to come under the rules of math, like when there is a code, or such to follow in Geometry etc. That way he can learn math, really learn it. I love homeschool for that !
This is exactly why we don't do any rote memory practice in my home. Garrett is fast at math, but he works every problem in his head or on paper if its too hard.
