Alright... I'm stumped. I need a way to teach my 8 year old math facts... problem is that he gets super frustrated the second he can't answer a question. Flash cards (that I hold) are boring. Left on his own, he "memorizes" them instantly and then is done with them - i challenge him to answer each one right before he's done, and he can but he has to think about each one. If I make into a timed game, he's not interested and won't do it... I tried xtramath.org and the one where you are a knight (xtramath is like computer flashcards, the knight one is more like a video game that throws out math problems you answer to advance) ... super frustrated there. He knows the concepts and can figure it out on his own, but we're starting to do more advanced stuff and him figuring it out every time is really slowing us down... plus, i really think kids SHOULD memorize the math facts... they're useful. Is there another way I'm missing? Should I just go through the stack once a day, as slow as he is at it until he picks up speed? WILL he ever pick up speed that way?
This gets into the whole philosophy of math education, but I have pretty strong feelings about not pushing the "rote memorization of math facts." Why? Well two main reasons.
First, ending up in a situation like your ds's, where this becomes a stressful, frustrating and/or endlessly tedious prerequisite for advancing to more interesting math, can taint a child's entire experience of math. The child begins to think of himself as "bad at math," and math as something difficult and hateful, when in fact arithmetic facts are the smallest part of math, bearing very little relationship to actual math aptitude.
Secondly, I think that there's a bonus that comes of not having the "facts" easily retrievable via rote memory while in the early years of math education, in that a child thus gets ongoing practice at deriving the solutions through mental math exercise. If "nine plus six" doesn't trigger the instantaneous delivery of a memorized response, your child will have to think through a process like "nine is one less than ten, so I can make ten by taking one from the six, so then I have five left to add, and ten and five is easy, that's fifteen, because fifteen means one ten and one five." He's just used the concepts of place value and regrouping. It might have taken him four or five seconds, but that's four or five seconds of exercise of his mathematical muscles. Done thousands of times over, that type of efficient use of mental math tricks and concepts will pay dividends later when he's trying to factor algebraic equations or convert something into scientific notation.
We are pretty much unschoolers, though my kids did enjoy using math curricula. All four of my kids were conceptually way beyond the 2nd or 3rd grade level in math before they got the arithmetic facts to an instant recall level. For fun they sometimes tested themselves for speed and accuracy, but we never did anything like drill. Because this made them a bit slower, the work they did with more advanced arithmetic was not high-volume repetitive work -- that would have been really hard for them. We used Singapore Math which was low on repetition, and I figured if they could show me perfect accuracy on two or three challenging problems they had the concept down and they didn't need to also do a dozen less complex practice problems. Gradually the rote recall just gelled, through naturally using the facts over and over again. In a school situation is might have been a problem, because they would have had to do pages and pages of practice, and wouldn't have been allowed to use a printed multiplication table to look up the facts when necessary. In our home, though, without large-group testing pressure, without endless pages of assigned practice, they were able to learn more advanced skills and many interesting things long before the rote recall was in place.
As a result my kids all really enjoy math, and I think that's the biggest indicator of success. We say this all the time with literacy ("what's important is to develop a love of reading") but I think it's just as true with math. Math is very cool! The inter-relationships and patterns are brilliant, the way it lets you solve problems in three different ways and end up with the same solution, that's exciting! You can build increasingly abstract layers atop each other by adhering to logical principles, and end up with solutions to incredibly complex problems, solutions that can't be intuited but are known to be correct: so amazing. There's no reason the world of joyful math discovery needs to be held hostage by "weak" rote memory skills.
At a 3rd grade level my kids were probably similar to your ds. By the time my were at a 5th or 6th grade level they were pretty fast at working out any necessary 'facts,' such that they could cope with school-like exercises without being unduly slowed down. By the time they were at a high school level they either had the facts memorized or were so fast at deriving them mentally that it amounted to the same thing. But the kicker is that they enjoyed math all the way through, advanced very quickly with their conceptual skills and have excelled (or are excelling) in accelerated advanced-stream math through to the senior level after entering the school system at a high school level.
All of which is to say that in your situation, having tried a few different strategies and seeing that rote memorization is not coming easily at this point, I would let it go for a while and move ahead conceptually, re-igniting some enjoyment of math.
Opinions may vary.
ETA: Oh, and lest it seem from what I wrote above that I was actively discouraging memorization with my kids, that isn't the case. I just encouraged what memorization they seemed ready and motivated to do, which in our case was a lot less than they would have been pushed to do by a traditional math curriculum. We had a table of the facts, laminated, and when one fact had become thoroughly memorized, we celebrated it by covering the answer up with a sticker. As the stickers gradually accrued, my kids would occasionally identify a particular fact or two that wasn't yet learned that they wanted to be able to remember, and I would help them focus on committing those to memory. "This week, I want to memorize 7x8 to fill in the gap on the multiplication table that's annoying me " was a far more effective strategy for my kids that going through a stack of flash cards.
Mountain mama to three great kids and one great grown-up
I agree that learning the facts first can make math dull, and possibly short circuit a real understanding of what the facts represent. I have nothing against times tables and that kind of thing, but I think they come at the wrong time. I think there should be a firm understanding of multiplication, and a chance for children to explore the concept for a long time before using the tables to help fill in the gaps and give them some short hand. And, not having to keep numbers in your head can allow to calculate amazingly large numbers that the brain can't truly comprehend. My daughter is learning multiple-digit addition with carrying, but she still wants to do it in her head and not do the shortcuts that allow her to add 14-digit numbers. She would be ready for the times tables about now, if she were interested. She might be a little behind in some ways than her schooled peers (she is bright, but not "gifted"), but the understanding she has runs deep, and she still enjoys math thoroughly, while her school peers are often dead tired of it. A good trade-off in my opinion.
"Let me see you stripped down to the bone. Let me hear you speaking just for me."
moominmama - I really appreciate your response. I have to get my mom out of my head sometimes (who is NOT a fan of homeschooling, and frequently bemoans the poor clerk who cannot make simple change of a 10.00 bill) ... and, there's another layer in that he'll be going to public school next year... So, he does need to get a bit more up to speed... but I don't think I'm going to push it as much... he's got the concepts down. We're starting a review with life of fred to make sure we're covering everything... and I think I'm just going to leave it at that... As long as he knows how/what/why to do.... I'm not going to worry about speed anymore... (if his teachers are unhappy -- I'll cross that bridge when I come to it).
lovemylab -- we cook together as often as he wants to, and thats how he learned fractions...(I am that bad mom that hides half the measuring spoons/cups on purpose) ... :)
No unschooler here, but happened across this thread searching for ideas for DS1 who is on Easter vacation and just eating up any math we can throw at him -
how about playing yatzee?
My dh never learned his times tables. His mother tried every which way she could come up with to get him to learn them and he just could not keep them in his head. He's terrible at doing simple arithmetic in his head too. When he went back to public school in 5th or 6th grade, they stuck him in a special needs class for math which was pretty humiliating as he was, in all other areas, neurotypical and bright. Then he got to middle school and they gave him a calculator to do the arithmetic stuff and taught him pre-algebra. He did fine from then on. He went through college level calculus and statistics classes for his degrees. He's still terrible at arithmetic, and remembering numbers in general (like, he can't remember my phone number!) but he's a gainfully employed functioning adult. Math facts aren't everything :)
Mommy to DS1 July '09 and DS2 Oct '12
OP, My children never wanted to practice math facts either.
In 2nd or 3rd grade they played Timez Attack and enjoyed it and learned some but didn't learn all their facts. (They were in school then so there was a bit of a push for fact knowledge; it was a Montessori school so not as much of a push as in PS.) At that time my children had no computer game or xbox experience so they were thrilled to be playing the game. My niece and nephew, who have played many electronic games, did not care for TimezAttack at all and said it was boring. We also played math games - like Check Math board game.
However, this year, we are HS'ing 4th grade and they wanted to learn multiplication facts but still didn't want to recite the facts or use flash cards. This fall they spent time playing Reflexmath.com (They loved it!). They now know their facts well and appreciate how easily they can solve other math problems. I think the combination of Reflexmath, mental math exercises and simple repetition through use helped them learn their multiplication facts.
I'm a big fan of using games to learn math facts. They're a lot more motivating than flashcards. Any game that uses two dice can be used to learn addition facts - you can play monopoly, chutes & ladders, etc. this way. There are also a wide variety of games that can be used to practice subtraction and multiplication facts. I use 10-sided & 12-sided dices to practice larger facts.
. and, there's another layer in that he'll be going to public school next year... So, he does need to get a bit more up to speed... but I don't think I'm going to push it as much... he's got the concepts down. We're starting a review with life of fred to make sure we're covering everything... and I think I'm just going to leave it at that... As long as he knows how/what/why to do.... I'm not going to worry about speed anymore... (if his teachers are unhappy -- I'll cross that bridge when I come to it).
Former homeschooler here. Not only did my kids end up going to school, now I work in one!
There were several things that my children were not at all motivated to work on when we were homeschooling that become important to them once they started school. Seeing that pretty much every one else your age can do something and you can't can be very motivating. Also, there are rewards for certain things. In the school where I work, passing a level of the timed math fact tests gets the student free ice cream and a ribbon.
Personally, I would call the school he will be attending and ask what their expectations are for the grade he is currently in. He might actually be doing just fine.
but everything has pros and cons
You might find this article interesting. It supports waiting to learn math facts and focusing on learning math concepts first.
@4evermom That link is terrific! I can't thank you enough as have been worrying about to start off teaching my Juni!
Happy to share:)
I never memorized math facts, either. I went to a Montessori school from 2nd grade through 5th grade that didn't focus on that. I feel like the only place where it's a problem is a timed test. And I just don't run into that situation as an adult.
I remember a math teacher expressing surprise at how well I did with word problems in 9th grade. Most of the other girls struggled to turn the sentences into mathematical equations on which they would then be able to apply their math facts. I was used to thinking about math in a more flexible way. Like Miranda's example, I change what I don't know into something I do know. And along the way, what I know naturally increases.
That was a great link! I love articles from "important" sources that have a wide viewership more than I enjoy similar articles from sources, like a HSing magazine or blog. It makes me happy to see these ideas become mainstream (though the Atlantic is still a long way from Cosmo or Family Circle).
I was one of those students who thrived on math rules and felt like I understood it, but never had an easy time with story problems. The words got in the way. Of course, it could have been more than a failure of math instruction. I do have difficulty visualizing--dimensions collapse, pieces of information get lost. Of course, get me in front of a knitting piece with a mistake and I can spot the mistake, know how it happened and how to fix it not because I have memorized the "fix" but because I can see the sequence of loops and how they form and where they need to go. The pattern of knitting has internalized and I don't have to think about it much anymore.
When I write instructions for other people, however, it is heavy with visuals but with very short descriptions. Not a story problem at all, with all those pesky complete sentences and punctuation. GAH! I think would have done better with "real-life" problems using the space I was in. That way, 3 (4) dimensions *stayed* 3 (4) dimensions. My rooms would not have collapsed and been twisted around like an Escher Sketch. Maybe lack of interest left me eternally at the "build it and see" phase! I would always prefer playing with dolls over blocks.
OK, now I'm rambling and my coffee is empty and it's a beautiful day.
"Let me see you stripped down to the bone. Let me hear you speaking just for me."
I haven't read the responses (it's late and I should be in bed.)
We are on the unschooling spectrum. Although we let math happen when it happens, I do think there comes a time when it's just easier to memorize the facts. So, our son is 8 and now is his time. 5 days a week he plays the games at www.mathreflex.com. He plays until the green light comes on (at this point that's about 15 minutes a day unless he is redeeming his points in their virtual store.) Right now he is working on addition and subtraction. When he started he could answer 11% of the 240 equations rapidly and correctly. After a month he is up to 64%. There is a 2 week free trial if you are interested.
We tried www.bigbrainz.com. It's a video game where you have to answer equations to move forward. However, it is a game where the characters are in mild peril and my son did not like that. They have free versions or you can pay for different games.
We are on the email list for www.bedtimemath.com (We also have their first book.) Every day we receive an email with a cute picture and a related story. Then there are three (or more) associated word problems ranging from simple to more complex. My son LOVES these.
Created an instant family (7/89 and 5/91) in 1997. Made a baby boy 12/05 adopted a baby girl 8/08. Ask me about tandem adoptive nursing. Now living as gluten, dairy, cane sugar, and tomato free vegetarians. Homeschooling and loving it.
I do think it's important to learn the basic math facts, but I try to make it happen in a relaxed sort of way. With my oldest, she was interested in learning them on her own, and asked for help. We went through a few flash card phases, but not too much; in the end, just by doing math on a regular basis, she ended up knowing them pretty well. Ds1 had to work a little harder; we did XtraMath to learn his addition and subtraction facts, which he hated but it did work. With multiplication, we got to a point where I felt he couldn't progress in math without knowing his facts well. I started giving him 20 single-digit multiplication questions everyday, printed off from free websites that generate math worksheets. I started off easy (with 1s and 2s) and gradually worked my way up. He didn't mind the process at all because I kept it easy, and within a few months he mastered the multiplication and division facts backwards and forwards without too much effort.
I went through multiplication facts with ds last year, and I am pretty sure that spending some time memorizing them is a good idea once they have the concept down, just to make more complex problems faster and less daunting.
Anyway, we use mnemonics, relaxation techniques, and cuddling.
Like OP's child, ds would get really upset about getting something wrong or not getting it fast enough. We did a lot of work on that issue. Deep breathing, etc.
I told him to try to say the answer as SLOWLY as possible, which was funny, and also made him go faster because he wasn't freaking out and getting all clenched.
For a while we'd do flashcards in bed instead of or before reading a story, which gave him that spoonful of sugar of getting to snuggle mama to help the medicine of multiplication go down. :)
ETA: ds and his mama are a lot a like when it comes to math, I have that to my advantage. I want to be clear that neither of us dislikes math, we love it, but memorizing does feel like a chore. I think the memorizing is so worth it, though, and so does ds.
We did *a lot* of concept before math facts-- the math facts were the *last* thing we learned before switching topics.
For instance, multiplication:
I had DS counting out multiplication for a long time, then he learned the multiplication tables, then long multiplication (definitely need some "rote memory" to be efficient at long multiplication).
We didn't treat division as a separate topic- I would often have DS check his multiplication work by using division and visa versa when we got to division.
We talked about fractions, percents, decimals (meanings and uses) for years before introducing a numerator or denominator- those discussions made topic so much easier and more meaningful when we had to sit down and write it out.
I do believe math facts are important, but introducing the method without a clear grounding in the concept just doesn't work for my kid.