Math facts - can anyone suggest some reading on why they need to be thoroughly learnt

[IsabelC]

Ds is doing well with the understanding side of math. He totally 'gets' why sums are done they way they are, and he thinks it's fun to play around with adding up 10 digit numbers, etc. But he is struggling to remember his basic facts, 7+8=15, etc. I have been trying all kinds of ways to get him to learn addition facts "to automaticity" because I understood that this was absolutely necessary to progress.

 

Now today, I had the following convo with my dh. I'm venting my frustration about how ds can't seem to recall any but a few addition facts. Dh asks why I'm so stressed about this. When I explained how I thought it was crucial and that ds would struggle with everything else if he doesn't get this really well, dh pointed out that (a) I know math facts and can do lightning fast mental arithmatic, yet I failed math in senior school, and (b) he never got good at math facts, yet he did fine at university level math. He said that you don't need to do fast arithmetic do do higher math, and I should basically chill because it isn't that essential. :confused:

 

So for those who know about mathematics, teaching theory or are plain more experienced than me, what do you think? Does dh have a point? Are there any good articles you can point me to?

 

Thanks

[lllll]

..

Edited March 23, 2013 by 3kt68

[TravelingChris]

My kids never learned all their facts instantly. We tried for years. It has been fine. They compensate for it well and one does mental math faster than many kids who have memorized. My oldest got through calculus, and my middle is currently in Alg2/Trig.

 

Memorizing math facts has nothing to do with learning other non arithmetic math. My best math student was one who thought she hated math because what she really hated was arithmatic. She likes other, more complicated maths.

[Renee in NC]

Not knowing the math facts makes my 12yo much, much slower at math and he makes silly errors all the time. He's working on them, but they don't seem to stay in his head very easily.

[C_l_e_0..Q_c]

He said that you don't need to do fast arithmetic do do higher math, and I should basically chill because it isn't that essential. :confused:

 

I totally agree with your husband, and math facts are the main area where I disagree with the WTM approach to math. I have never mastered my math facts. I know quite a few of them, simply due to practise over the years. I am an engineer, I studied math all the way to the Masters level. I'm good at mental math, mainly because I don't know my math facts. Because I couldn't rely on the traditional ways of adding and substracting, I had to find other methods. The kids in my class who were good at math facts were not good at mental math. And the same can be said of my own DH, also an engineer, btw.

 

Knowing math facts down pat can actually hinder you in the long run. It's much easier to be able to play around with the numbers in your head, than to be able to do computational exercises like a machine.

 

No, I didn't force my kids to learn their math facts. My son did do stupid arithmetic mistakes, but I point them out, asking him to tell me why his answer doesn't make sense. Now, he's much better. He can *feel* when the answer he's got isn't logical. My daughter - doing MUS delta - is now the same and she's no math whiz, trust me. But she tells me right away "oh oh, this can't be right". She's doing the long divisions now (4 digits divided by 2 digits). Sometimes she has the math facts right, but didn't write the answer in the right place. But she's been trained to feel if the answer is logical or not. (it's basically a lot of evaluations in your head).

 

Math facts are just one tiny part of what math is all about.

[Mandamom]

In experience I've seen kids very tired and extremely frustrated after solving middle school math problems (fractions mostly) because they don't know their facts, particularly multiplication. These students know how to solve the problems but can't because they have to skip count each and every math problem (and problems within the larger problem they are working on -- adding fractions with unlike denominators or multiplying mixed numbers). I've seen them become very frustrated.

 

When I check students awareness of facts I'm not looking for the ability to do it quickly. I'm checking to make sure they don't have to skip county each and every problem. They should know it without having to count to the answer. So, those that process slowly can tell m the answer slowly as long as they aren't counting. Once they get the facts down their frustration level reduces.

[stripe]

How old is your son?

[Pixie]

Like CleoQc, I am also an engineer who has never really learned math facts for instant recall. I had to learn multiplication tables in elementary school but I never had to learn other facts. I learned them just by using them all the time, not by drilling. I am not stressing math drills with my kids. My 6th grader knows her facts pretty well just from using them all the time, my 3rd grader is working on learning her times table and I am helping her get better at figuring out the addition facts in her head faster. I am more stressing being able to manipulate numbers and how to figure out the facts fast than just being able to recall them.

[hsbaby]

I was never taught to memorize my basic facts. I was actually taught using touch points. I still rely on this method for basic addition/subtraction. I still visualize the dots in my head and have to count up or down. It definitely slows me down and, in school, often led to careless mistakes when I was trying to finish a math test in the allotted amount of time. I was able to get through college and pass all of the math classes so it wasn't debilitating, but I still would have preferred to have those basic facts memorized as I do with multiplication. So, I emphasize it with my kids for that reason.

[Nestof3]

I don't see how old your son is in your post, but memorization, in my opinion, helps out tremendously when doing long division and multiplying longer numbers. These problems become increasingly more difficult, and part of the frustration ends up being when the student has to keep stopping in order to add with his fingers or look at a multiplication chart. It distrupts the flow of the problem and results in more errors, in my opinion.

 

My boys are still in the process of memorizing, so I am speaking from current experience.

[Lolosoli]

I agree with the others. My daughter understood the concepts...but, had trouble with the basic facts and memorization. I didn't worry about it. I figured with enough practice it would become memorized. It didn't and now she struggles. It just makes math take soooo long.

 

I wish I had started her out with Math-U-See. We are switching her over to it now. It is what our younger boys started out using.

 

As for remembering the more difficult facts...such as 7+8. MUS teaches them to find the doubles. Most kids memorize the doubles facts easily. 7+7=14. Well, 7+8 is the same as 7+7+1....which equals 15. That made all the difference for my kids.

[Guest mrsjamiesouth]

I didn't make my ds 9 memorize the times table and last year we had the most difficulties in division. He still hates division and can take hours to complete his problems. I can see that it is all because he doesn't have his times table memorized. He didn't memorize the addition facts and just from use over and over he is fine on that end.

[C_l_e_0..Q_c]

He didn't memorize the addition facts and just from use over and over he is fine on that end.

The same thing will happen with multiplications. For some reason, most math programs I've seen do not provide enough repetitions with multiplications like they do with additions. Skip counting doesn't count btw... I despise skip counting.

 

I've provided my kids with a multiplication table that they can keep in their room. Since we do math at the dining table, at the other end of the house, they may get up, walk to their room, check the table, walk back while remembering the answer (they're not allowed to run in the house), and continue with their maths. After they get up 5 times for the same math fact, they choose to remember it ;-) I have never drilled my kids though.

[Guest]

My daughter learned her addition facts long AFTER she learned her multiplication tables and was well into percents and fractions. I think that one of the biggest myths about math is that you MUST memorize A before you can attempt B. As many people testified to in their responses, this is not always the case. I agree that being able to mentally manipulate numbers is much more useful in the long run. This happened to my daughter accidentally, not because I planned it; she had severe dysgraphia when she was young and could not do worksheet math for a number of years, and the vision difficulties behind her dysgraphia made flash cards not the best way forward either. So we did years of mental math, math "tricks," used manipulatives, made up word problems for one another, played math games.

 

And my husband, who is a chemist, uses the same kinds of mental manipulations and estimations as my daughter does. He says this is completely lacking in most graduate students, who can do any calculation by rote (or increasingly, on the graphing calculator), but not stop to think whether or not the answer they get makes sense.

[Teachin'Mine]

Understanding the concepts is great - and important. But so is knowing the facts. I don't know anything you can read to support this, but I think you're getting a lot of good feedback on what happens when they don't get them solidly. Just look at the frustration of a seventh grader doing fractions and decimals and having to use fingers to count everything. It sets them up for difficult years with math.

 

As far as how to have him learn them, other than repetition I really don't know. I'd make up my own flash cards with addition first, and start with the ones. Then just flip through them one by one and keep going repeating each time, until he absolutely knows one each and every time, and then just put that one aside. Go through the ones he knows maybe once or twice a week so he doesn't forget.

 

I had made a matching game for my daughter. I cut up index cards and put math facts on them. I'd write two facts which added up to the same each time I wrote new ones so I'd know there would be a good match for it. Then I'd play a game of concentration with them. She really enjoyed this, and it helped to solidify, if that's a word for this, the facts and she got to see that 4 +8 is the same as 9 + 3.

 

Your husband is right that you can be good in upper level math without knowing them, but it's so much easier throughout school if you do.

 

One of the things I loved about Saxon is that everyday they do a math facts sheet and have mental math too. We did the mental math verbally instead of her just reading the problems. It made it more fun too. :001_smile:

[joannqn]

I require that my kids know them well but not to the speed that many suggest. The reason is that I don't want to cause unnecessary frustration by continued practice, in part, because I know they will get continued practice with multiple digit multiplication (practices addition and multiplication) and long division (practices subtraction and division) and review pages in our curriculum. But I do want them to know them well enough so that each and every high level problem doesn't take half a day.

[2cents]

I had all of mine memorize the math facts. It was a huge part of our early math routine. I found that it was very helpful when they were doing their more advanced math processes. It makes homework and drill go faster and minimizes simple math errors. It gives them an edge on the annual SAT test because they do not have to stop and think as much. They are allowed to use a calculator on the SAT but I personally do not allow it, so knowing their math facts is essential.

[myfunnybunch]

In my experience, it depends so much on the individual child.

 

We do not do math fact drills to a particular fluency rate.

 

My oldest, despite her best efforts and tons of drill in her public elementary school, could NOT remember her math facts, to the point that she hated math because it was all drill drill drill. When she came home as a 6th grader, we let it go. She could use charts, count on her fingers, whatever she needed to do to get to the answer. I found that, for her, once she was allowed to let go of having to memorize facts, math became much more motivating for her. We discovered that she is genuinely gifted in mathematics conceptually, but she was getting so bogged down in the memorization struggle that she couldn't move on to the fun part. And she had naturally memorized most of her math facts by the end of 7th grade.

 

My first grader purposely memorized most of his addition facts on his own because he was tired of thinking them through.

 

My third-grader has just learned them through practice as he did his math. He uses a multiplication chart occasionally if he wants to go fast, but he's slowly weaning from it.

 

I anticipate with my youngest we'll be doing some fact drills because he seems to learn that way.

 

IMO, you and your dh are both kind of "right." Having math facts memorized is helpful, but it's not necessary. It's a bit like building a boat with an organized work bench versus a workbench that's scattered. The boat is the goal...do you take the time to clean the bench and organize the tools first (boring but makes things easier in the long run, my preference) or do you dive in to building the boat and figure out where the tools are as you need them? (You get to start on the actual project right away, but spend time searching for the tools, my dh's preference, as evidenced by his workbench. :D ) Either way the boat gets built.

 

Cat

[hornblower]

I recently read an interview with a brilliant PhD mathematics student, one of the top students in North America, major award winner etc etc etc & he admitted that he was terrible at arithmetic. It's not what mathematics is about when you get to a certain point.

 

There is a book I enjoyed called Math Power by Patricia Clark Kenschaft PhD in math, in which she talks about what she thinks it's necessary to know at certain ages. She's much more about understanding concepts than memorizing facts.

[Mejane]

I stressed about it, too. Now I wonder why. Son used Times Tales to learn the facts, but just doing his daily math problems is what really cemented them.

[cajunrose]

Great question! So, at what age do you think they should start memorizing them? How about addition? I have an almost 7 year old that is struggling at this. When should I expect her to know them?

 

Stephenie

[Karen in CO]

I think the addition and subtraction get easier with practice. I don't think they need to be drilled to death. The one think I do think is super important is knowing your multiplication tables before you get to long division. It is MUCH harder (if not near impossible) to do long division and fractions if you don't know your multiplication facts. Times Tales and lots of practice are a couple of ways to get there, but there are many others. Let your ds enjoy math. Relax and go about your life because there is a lot more to math than facts, BUT please keep in the back of your mind when you get to long division or when you start to struggle with LCDs, those multiplication facts are the keys to the kingdom.

[dirty ethel rackham]

I require that my kids know them well but not to the speed that many suggest. The reason is that I don't want to cause unnecessary frustration by continued practice, in part, because I know they will get continued practice with multiple digit multiplication (practices addition and multiplication) and long division (practices subtraction and division) and review pages in our curriculum. But I do want them to know them well enough so that each and every high level problem doesn't take half a day.

 

:iagree:

When my oldest was 8, we had this discussion. He could explain high level math concepts to me, but couldn't see a point to memorizing math facts. When 3 digit multiplication and long division problems took forever to complete, he decided that I was time to really get them down. I, too, don't really care if they can to x amount of problems in a minute - just fast enough that it doesn't slow them down doing complex calculations.

 

DD9 didn't have her facts down. She was muddling through on her Singapore Math until long division. After many tears, she decided to stop fighting on math facts. After many spits and starts, we found a method she likes. I write down the facts for a certain multiplier, then she practices with Learning wrap ups while saying the facts aloud - for a couple days in a row. Now she has them down well enough that she can do long division without effort.

[mcconnellboys]

Well, he can learn math basics either now or later. Learning now will prevent much frustration and possible failure when he's doing high school level math. Waiting to learn in college might be okay if he has good instructors there. Many larger schools have grad students who really often don't care much about teaching in the more basic math courses.

 

I used Math U See to emphasis drill work and memory for my younger son. I didn't use it as my primary program. I just let him do a page a day of it as drill work. I kept him a year behind where he was in math with it, too. I didn't feel he needed it for addition or subtraction, but I did feel he needed it for multiplication and division, so I started him in multiplication in fourth grade and division in fifth grade. He's doing algebra work this year and isn't have difficulties with all the multiplication/division that he has to do as part of those problems.

 

This year, first semester, I had him work through some of the Key to.... series of books on percents and decimals to give him extra practice with those subjects because I felt it needed that for algebra work, too. I think it has served him well.

[IsabelC]

How old is your son?

He is 6 and will turn 7 in June. He is working right at his grade 1 level, and we are trying to get addition, subtraction and multiplication to 4's finished by the time our school year ends in December. (Although, for some reason, he doesn't seem to find multiplication as difficult: he has already memorized bits of the tables and we haven't even done any practice on them yet, he just plays with the chart occasionally.)

 

 

As for remembering the more difficult facts...such as 7+8. MUS teaches them to find the doubles. Most kids memorize the doubles facts easily. 7+7=14. Well, 7+8 is the same as 7+7+1....which equals 15. That made all the difference for my kids.

My son does do this. He knows the doubles and a few other facts, and will use one as a crutch to get to another one rather than just counting on which he used to do all the time. But I'd be happier if he knew them all instantly because it's so much simpler and faster than reasoning "8+5, hmm, well I know 8+2 is a 10-bond, and I know 2+3=5, so therefore 8=2 plus the other 3 makes 13" when he's in the middle of a longer calculation later on.

 

 

My oldest, despite her best efforts and tons of drill in her public elementary school, could NOT remember her math facts, to the point that she hated math because it was all drill drill drill.

This is what we're worried about. Currently, ds likes playing with numbers and is happy when he learns something new about them. He loves the big stuff like googol and the idea of infinity, he likes the 'magic' numbers like pi, he likes to 'discover' the basic patterns that we take for granted, such as why an odd number plus another odd number always results in an even number. We're now at the point where we have to decide: do we hang back with formal instruction until he masters addition facts, or do we keep progressing and hope he'll pick them up through a combination of embedded practice and periodic bursts of drilling in fun ways. Is total mastery of facts worth the risk of putting him off the whole subject?

 

 

It's possible someone here could recommend another resource that may make it easier for you and your dc. What are you using now?

Our main resource is Mathspower http://www.mathspower.com.au/default.asp (it's an Aussie one, so many people wouldn't have heard of it). We love it for lots of reasons, but the main shortcoming is that it doesn't provide that much practice (possibly because it started out as an in-school or afterschooling resource rather than a complete homeschooling curriculum). They just assume that if your child doesn't 'pass' a lesson, you will repeat it and repeat it until he does. So we collect a variety of supplementary resources and add them in when we think he needs/wants more practice at something. We also work with the abacus and various other manipulatives when he wants something concrete to deal with.

 

 

Ps I should have also mentioned that he has Aspergers. This could have some bearing on the way he is learning. Also he falls to pieces under pressure, so I'd rather avoid timed testing.

Edited March 22, 2010 by Hotdrink

[myfunnybunch]

(Although, for some reason, he doesn't seem to find multiplication as difficult: he has already memorized bits of the tables and we haven't even done any practice on them yet, he just plays with the chart occasionally.)

 

This alone seems to indicate that he will probably do fine with some math drills to memorize his facts, especially if you keep it fun and make it more like a game. Try it and see how he does with it. He'll let you know if it's too much. :)

 

Where it gets to be a drag is when the student isn't allowed to move on to experience the fun of mathematics because they haven't learned the facts to a certain standard of fluency, or when they're drilled to the point of frustration. (That's what happened to my dd. Memorization of anything was a challenge for her.)

 

And read this: A Mathemetician's Lament

Someone from the board posted this a long time ago. It's not really about math drill, but I re-read it whenever I think about teaching math. It's inspiring.

 

Cat

[Hedgehogs4]

i personally always struggled with math facts. i've hated that i never had a successful feeling in math, made stupid mistakes, struggled with simple computation, so...

 

i insist that my kids be "fluent" in math, but here's the catch...i don't insist that they do it on my schedule. i simply keep working the facts in different ways until they have mastered them. they simply don't move on until it's learned. some creativity in drills is necessary, which means the onus is on me to be patient and come up with new ways to get it through to them. when they can do it at about 95% we move on, but still go back and practice the old stuff to keep it fresh and get it to 100% mastery.

 

we do use MUS, and are going to be supplementing with singapore math here, starting next week.

 

oh and guess what...my math computation is improving, right along with my kids.

[Guest]

My daughter, who also has Asperger's, memorized her times tables well ahead of her basic addition and subtraction facts. She was balancing equations while not being able to accurately count out the number of candles for her birthday cake on her ninth birthday, and she had trouble physically counting coins for a really long time. I'm sure this is not the case with all Asperger's kids, but I've known a number who show similar patterns of high level conceptual work mixed with difficulty in memorizing far easier, concrete arithmetic. (By the way, she's now doing regular textbook algebra with no trouble, at age 13.)

[Mejane]

Seriously. My husband works with million-dollar contracts on a daily basis and doesn't know his tables (or how to spell :).) Rote memorization does not equal success.

[Sara R]

Practice makes perfect--but only if you practice beyond the point of perfection, by Dan Willingham

 

All of us have a working memory and long-term memory. Working memory is very limited. You can only hold about 5-7 pieces of information in working memory at a time. Long-term memory, however, is unlimited. You get information from working memory into long-term memory through a lot of practice.

 

Math gets more complicated as it progresses. If you are using your limited working memory to simultaneously derive the multiplication fact and remember all of the steps for long division, chances are you are going to forget one of the steps of long division and make a mistake. However, if the multiplication fact is in long term memory, you will have more brain power to concentrate on long division, or whatever the new concept is.

 

Some people do fine in higher math without memorizing math facts. Usually these are bright people, with quick intellect, who can derive the answer very quickly. If it takes very long to derive the answer, the student is going to get lost.

[Sandra in FL]

math facts (especially the multiplication tables) automatically. It just makes math easier (and easy is important to me :-) Then we can concentrate on the tough concepts (Singapore) and not worry about computation.

 

My kids don't go on to multiplication until they have the +/- facts to 17 (Rod and Staff 1 & 2) down pat. Then I use Little Giant Steps' Skip Counting (not set to music) before each time table (recitation and Rod & Staff 3).

 

My middle ds (Asperger) took what seemed like forever to learn the +/- facts. I tried everything. The program that finally worked was Math Facts in a Flash which combined listening, seeing, speaking and writing.

 

Blessings,

Sandra

[Suzanne in ABQ]

In my experience, multiplication/division families are vital for long division, multi-digit multiplication, multiplication of fractions. There are many steps to these type problems. It's easy to get lost in the process, and forget what you're ultimately trying to do, if you're having to stop and skip count at every step.

 

Addition facts that make 10 are very important, but the others aren't. They can easily be figured if one knows how to make 10. All my kids learned, for addition, were the number bonds that make 10: (1 and 9, 2 and 8, 3 and 7, 4 and 6, 5 and 5). The rest, they figure quickly in their heads. For 8 + 5, for instance, my kids have learned to take 2 from the 5 and add it to the 8, to make 10. Then, add the 3 that were left over to the 10, to make 13. It looks complicated, but it only takes a second, less with practice.

 

So, I wouldn't use a bunch of time to teach all the addition facts. I'd use that time to teach concepts instead. Definitely take the time in 3rd-4th grade, though, to learn those multiplication/division families. They're fundamental to all sorts of higher level arithmetic.

[Teachin'Mine]

He's only six?! No problem!!! :001_smile:

 

If he was nine or so, then it would be time to buckle down and memorize. Give him time and he'll probably learn a lot of them just by doing the addition. Play games, let him be the scorekeeper so he can practice his addition. Make it fun! :001_smile:

[hornblower]

Someone just posted this to a hs list I'm on:

 

When Less is More: The Case for Teaching Less Math in Schools

 

It's from the Psychology Today blog of "Peter Gray, a research professor of psychology at Boston College, is a specialist in developmental and evolutionary psychology and author of an introductory textbook, Psychology."

[Guest]

 

When Less is More: The Case for Teaching Less Math in Schools

 

 

 

Thanks for pointing me to this; fascinating!!! A similar case has been made for not introducing reading at all until kids are seven or eight; they learn to read faster, less stressfully, and report liking reading more than kids who are put into formal learning at ages three or four. Again similarly, I've read that some European schools hold off on fractions until junior high; kids then learn them without the confusion and misery that many fourth and fifth graders experience. Older kids' minds are just more ready to think in the way that manipulating fractions requires.

 

Neil Summerhill, founder of the Summerhill alternative school, has also written that kids can learn all of K-12 math in something like 20 or 30 "contact hours," or direct teacher instruction, when they are ready.

Edited March 22, 2010 by Guest

[IsabelC]

Well we decided to try for a compromise. We'll still try to get him learning the facts, but we're putting much more emphasis on the fun aspect and the learning in context. He certainly doesn't lack the capacity to do sums, it's more that he can't take any pressure. Today he said "If I have two 20c coins, one 10c coin and one 50c coin, that would be a dollar." Now if I would have given him the sum

 

20+

20

10

50

__

 

he would have had a meltdown. So I hope we can get him practicing pretty much daily without feeling like he's being forced to practice ;)

[Haiku]

My oldest dd is a freshman in a public high school. She never learned her math facts (not for lack of trying on my part, but she also was adopted at an older age and had never been taught much math before she came to us). When she does a math problem, she has to skip-count every time she needs to use multiplication. Usually she has to write the skip-counting down. It's embarrassing for her, it slows her way down, and she doesn't really know whether she's made an error or not because she doesn't know what the correct fact "should" be. Even my first and second graders, working on addition and subtraction, can look at a problem they got wrong and spot their mistake. My freshman can't do this, so if she gets a problem wrong she has to re-do the entire problem.

 

I would definitely keep working on math facts.

 

Tara

[dirty ethel rackham]

Sounds like you found a good solution. I would never want to encourage a "drill and kill" mentality, but knowing them before getting to long division will be important. It sounds like you have time.

 

A couple things we tried - operational dice. In any game that used dice, we substituted operational dice for practice. It made a simple child's game more challenging and more fun. We have a "clever catch" ball basically a beach ball with math equations on it (some in word problems and some not). We play hot potato with it. If you are holding the ball when the timer goes off, you have to answer the problem that your left thumb is touching. We also played jumping math facts. I would place the facts on the floor and shout out answers. The child would have to jump to the card with a question.

[Marylou]

I wonder how/when

learned his math facts?!

[Marylou]

Someone just posted this to a hs list I'm on:

 

When Less is More: The Case for Teaching Less Math in Schools

 

It's from the Psychology Today blog of "Peter Gray, a research professor of psychology at Boston College, is a specialist in developmental and evolutionary psychology and author of an introductory textbook, Psychology."

 

Thanks for this article.