kindergarten - do you teach math facts or just the concept?

[ChristusG]

I stink at math. Seriously. I want my kids to be better at math than I am. I was never taught the facts. You know, where I can just look at a problem and KNOW the answer without couting it in my head. Yeah, I can't do that.

 

My 5 year old is learning addition right now. She can do addition up to about 20 (where the sum is 20). She knows the concept. Should I incorporate the facts? Like print them on flash cards? If so, what's the best way to do that? Learn all the 0's first? Like 0+1, 0+2, etc. And so on? Only up to ten? Or higher?

 

I'd love some input. I can tell I'll be asking quetions here ALOT LOL. :D

[eight_gregorys]

I do teach the facts as they are introduced in our math program. (We are using Saxon Math 1.) I like to teach the how's and the why's and then will work on memorization. Typically I'm not one for rote learning, but when it comes to basic math facts like single digit addition and subtraction and multiplication facts, I do have the kids work on memorizing them. If they can't pull the answers out quickly, it makes upper level math VERY tedious.

[Alice]

With my just turned 6 yr old I have had him work on memorizing the facts but have also moved forward with concepts as he is able. So we don't stick with just memorizing facts until he knows them all cold because I think that would be really boring. I keep adding in new concepts and then also we work on the facts. On a typical day we'd do a lesson in the math book and then some problems in the workbook with that concept. Then we'll do a game or drill to review facts.

 

I use mostly games. Right Start Math games are very good, but expensive. It's $75 for the box which is really pricey. I went ahead and bought it and am pleased but realize it's icing on the cake. To me I thought it was a good investment as it has games for all levels and I figure I can use it with all the kids. I also like Peggy Kaye's Games for Math book. There are several games in there that we used to review math facts, they are easy to make yourself with posterboard or some are just with cards (Pyramid is a solitaire game that uses cards to review making 10.)

 

Some others he likes are Math War (like the regular war card game but you put down two cards and add them together, highest sum wins all the cards). Ds loves that one actually. I also just wrote all the math facts on index cards (no answers, just the problem like 4 + 5). Then I show him the cards and see how many he can get do in a minute. Ds is very competitive and loves the idea of beating his old record. I'll set a number that he has to get more than to win and then we'll play 2 or 3 times. This only takes 2 or 3 minutes but is a good fast review. For awhile we were doing it daily. I usually gave a prize for winnning (either beating the number I set or his record) but you wouldn't have to. Typically for us the prize was 15 minutes on the Lego website playing games, which is a treat for him.

 

As far as what facts to learn, the curriculum you are using might guide you. We use Singapore so I did all the facts up to 10 for addition, then added in the facts within 10 for subtraction, then the facts up to 20 for addition and so on. That fit with the order he was learning new concepts in the curriculum.

[ChristusG]

Yeah, I was wondering about just sticking with the addition facts because that could get boring. However, I dont really want to move into subtration until she learns all of her addition facts. I guess I could find other things to do. We're touching on the calendar right now so I could probably stick with that more while we do the facts.

[FO4UR]

Yeah, I was wondering about just sticking with the addition facts because that could get boring. However, I dont really want to move into subtration until she learns all of her addition facts. I guess I could find other things to do. We're touching on the calendar right now so I could probably stick with that more while we do the facts.

 

But subtraction is simply addition in reverse and so learning to subtract is a really good way to review addition facts.

 

MEP year 1 is great!!! If she understands the concepts, but you want her to practice - MEP will definitely get those facts ingrained (they spend a week on each fact family) AND it will stretch her understanding with the way it presents math.

 

ETA: Definitely teach until those facts are down COLD....BUT do it in a way that is enjoyable, challenging, even fun. games, choose a curric that re-teaches in a slightly different fashion than she had before (repeating the info), if she enjoys flashcards and timed tests - go for it....but do NOT equate math with drudgery at her age. You are building a foundation and not running a race. ;)

Edited November 12, 2009 by 3blessingmom
actually answering the question...LOL

[Spy Car]

Concepts. Deep and varied exposure to math concepts from as many angles as I can manage to teach.

 

Knowing "math facts" comes as part of the ends of the process, but it's certainly not the means.

 

Bill

[Spy Car]

But subtraction is simply addition in reverse and so learning to subtract is a really good way to review addition facts.

 

MEP year 1 is great!!! If she understands the concepts, but you want her to practice - MEP will definitely get those facts ingrained (they spend a week on each fact family) AND it will stretch her understanding with the way it presents math.

 

Agreed!

 

Singapore style "number bonds" are also quite helpful in realizing that subtraction and addition are related concepts. And we teach them together.

 

Of course, your children and mine also learned this from using Cuisenaire Rods.

 

Bill

[monalisa]

I contend that a person REALLY needs to know their math facts cold, and I think the earlier you start working on them the better. I worked with kids as a math tutor for a few years that did not know their facts in 8th and 9th grade -- its is really difficult to do algebra if you can't rattle off the facts from addition through division. Yes, flashcards are boring, but many things in life are boring. I agree with the suggestions about the games. Concepts ARE important, but the concepts for addition, subtraction, multiplication & division are very basic. The facts need to be embedded in the brain so that you can master the difficult concepts without thinking about adding/subtracting etc. (I have an MS in engineering so I took loads of math, which I wouldn't have been able to handle had I not known all my math facts by rote).

 

By the way, I came across something called Giggle Facts on Maria Miller's website (Math Mammoth author) that looks interesting for learning addition & subtraction facts with games. I think it was $40.

[Spy Car]

Some others he likes are Math War (like the regular war card game but you put down two cards and add them together, highest sum wins all the cards). Ds loves that one actually.

 

This is a fun (and useful) game. We call it "Addition War", and actually played it last night. It can be played with either Right Start cards, or with a standard deck with the face cards removed, and Aces as "ones".

 

We also play a version adding the two haves of domino tiles.

 

You can also do "Subtraction War" the same way.

 

But games are a fun way to solidify quick math fact recall.

 

Bill

[PeterPan]

What math curriculum are you using? Or are you just piecing things yourself? Many math curricula start in these early years building concepts that lay a foundation to understand place value, etc. later, so a good curriculum would be very valuable to you. It might be you didn't nail things because nobody ever explained them to you in a way that would stick. Head on over to http://www.alabacus.com and see if the way they explain things doesn't make it more clear for you. It balances conceptual understanding and fact drill through games and does addition first, as you say.

[stripe]

I don't think one needs to choose between facts and concepts. Have your cakes and eat them two!

[Lovedtodeath]

I think it is better to spend more time on concepts (two years) and do math facts later than most curricula introduce them. I really worry that memorizing the facts makes kids lose focus on the concepts too soon.

[LadyAberlin]

We use The mailbox mix and match games. My ds loves it and I just start off with a few facts and I slowly add in more as he masters the ones in the deck. if I were to do flash cards he probably wouldn't like it so much, but with the games he always wants to play at least 2 games in a row every day. He would play it more, but I don't want to. He has picked up the facts quickly that way. He understood the concept already he just needed help with quick fact recall.

[Dinsfamily]

I think it's better to make sure they have the concept down before memorizing facts. Otherwise, they could "cheat" instead of learning the concept.

 

My ds has understood addition for a couple of years and gets the connection between addition and subtraction so I've started "testing" him on his math facts with flashcards and it turns out that he has most of them down cold just from completing Horizons K. There are just a few that he was a little slow to answer.

 

He'll start learning about multiplication and division in a couple of weeks, but we won't start learning those facts until he completely understands that concept and all of his addition/subtraction facts down.

[Lovedtodeath]

I think it's better to make sure they have the concept down before memorizing facts. Otherwise, they could "cheat" instead of learning the concept.

 

My ds has understood addition for a couple of years and gets the connection between addition and subtraction so I've started "testing" him on his math facts with flashcards and it turns out that he has most of them down cold just from completing Horizons K. There are just a few that he was a little slow to answer.

 

He'll start learning about multiplication and division in a couple of weeks, but we won't start learning those facts until he completely understands that concept and all of his addition/subtraction facts down.

:iagree::)

[Emmy]

So far I've found with my kids that if we work with math and play math games enough, the fact come on their own. I would not "drill" a kindergartener but give her as much opportunity to use math as I can. I do have my kids drill when they are a bit older.

 

My 3rd son is K this year. I am mainly concerned with his understanding of the concepts (working with manipulatives) but as he's progressed we do math facts on paper - I started with +0 and+1. Then +2. Then doubles and facts that make 10. He probably could answer most of those on his own without building them.

[Spy Car]

I stink at math. Seriously. I want my kids to be better at math than I am. I was never taught the facts. You know, where I can just look at a problem and KNOW the answer without couting it in my head. Yeah, I can't do that.

 

My 5 year old is learning addition right now. She can do addition up to about 20 (where the sum is 20). She knows the concept. Should I incorporate the facts? Like print them on flash cards? If so, what's the best way to do that? Learn all the 0's first? Like 0+1, 0+2, etc. And so on? Only up to ten? Or higher?

 

I'd love some input. I can tell I'll be asking quetions here ALOT LOL. :D

 

Re-reading your original post, it strikes me that there is an important question of semantics with regard to your phrase: "She knows the concept."

 

In the light of day, I'm thinking you mean she knows how to apply the algorithm (how to work the equation) as opposed to having a deep conceptual understanding of the mathematics involved. These are two very different things.

 

When a young child has a firm grasp on how the base-10 system operates, how to decompose and regroup numbers, and understands concepts such as the "commutative law", then mathematics is akin to a native language.

 

Simply memorizing "math facts" or learning to apply an algorithm is a very limited form of math education. It not unlike "memorizing words", rather than learning phonics. It is important if you want to break the cycle of thinking yours is a family that's just "bad at math" you ought to question whether fault might lay in "the methods" with which you were taught, and which you in good faith are using with your daughter. Because that is very likely the case!

 

There is a book that I will strongly recommend you check out of your library called Knowing and Teaching Elementary Mathematics by Dr Liping Ma. She compares and contrasts the methods used in Asia, where math is taught with an eye towards deep mathematical understanding, versus the USA where we often use an "algorithm only" approach that teaches children "how" to solve an equation, but leaves out the "whys."

 

It is a very compelling book, and I suspect it would revolutionize the way you think about math and math education. It certainly made a huge impression on me. I'll link to the Amazon listing, and there in the "preview" you can read part of the opening chapter which give a good idea about where Dr Ma is going in the rest of the text.

 

Math can be fun, intellectually challenging, and a rich and rewarding experience for a 5 year old. I know, because I have a 5 year old who is getting a very different math education than the dreary one I received. What a difference!

 

There are ways to make the math journey fun and rewarding. You could end up discovering you like math (and are good at it). But now is the time for a quick reappraisal of the way you intend to teach this subject. If it is reduced to learning how to apply algorithms and drilling "math facts" with flashcards, you will IMO be missing out on the joys of math and limiting your daughter's education. It worth doing a reevaluation.

 

Here is the link for the book:

 

http://www.amazon.com/Knowing-Teaching-Elementary-Mathematics-Understanding/dp/0805829091

 

Best wishes.

 

Bill

Edited November 14, 2009 by Spy Car

[BikeBookBread]

Christus G, thank you SO MUCH for posting this question, and SpyCar thank you AGAIN for your insight. The Twirling Girlies are loving Miquon orange, although we are taking it VERY slowly, maybe too slowly. They love their rods, we've been playing lots of math games using dice, rods, pattern blocks and worksheets from the www.themathworksheetsite.com. Slow and steady wins the race in my mind.

 

To ditto you Christus G, I'm a math DUMMY, and I'm seeing lightbulbs coming on - concepts are now being understood that I was never taught in school - using Miquon. I had a "facts only" math education. I definitely think concepts first, facts will follow and the whys will be understood because of it.

[Spy Car]

Christus G, thank you SO MUCH for posting this question, and SpyCar thank you AGAIN for your insight. The Twirling Girlies are loving Miquon orange, although we are taking it VERY slowly, maybe too slowly. They love their rods, we've been playing lots of math games using dice, rods, pattern blocks and worksheets from the www.themathworksheetsite.com. Slow and steady wins the race in my mind.

 

To ditto you Christus G, I'm a math DUMMY, and I'm seeing lightbulbs coming on - concepts are now being understood that I was never taught in school - using Miquon. I had a "facts only" math education. I definitely think concepts first, facts will follow and the whys will be understood because of it.

 

Thank you Stephanie!

 

I'm with you, there is no need to "rush" thorough math at this stage. All the rod play the girls are doing will really pay-off. They will understand addition and subtraction inside and out.

 

One thing to consider adding (if you haven't) is Singapore-style "number bonds." Are you familiar with these? They look somewhat like this, although there are "usually" circles with spokes drawn around the quantities, while I will use "brackets"):

 

.......[8]

...^

[5] [3]

 

 

 

You can take some of the same "equations" in Miquon Orange (or make up some of your own) and have them express it as a "number bond." Usually "one" element of the number bond is the "unknown variable." This folds very well into Miquon-style rod play (and they can use the rods if need be to "solve" the number bond), but it adds another way of looking at numerical relationships. And it's a good way to test their understanding.

 

Bill

Edited November 13, 2009 by Spy Car

[Ellie]

If I were hsing littles again, my math curriculum would follow the recommendations in this article: The Story of an Experiment. It doesn't even mention kindergarten, as that has only become really popular in the last, oh, 40 years or so; arithmetic would be informal, just part of life, nothing specifically taught.

[Spy Car]

If I were hsing littles again, my math curriculum would follow the recommendations in this article: The Story of an Experiment. It doesn't even mention kindergarten, as that has only become really popular in the last, oh, 40 years or so; arithmetic would be informal, just part of life, nothing specifically taught.

 

Very interesting article. And one I need to return to re-read with greater care. I am impressed by the teaching style employed by Benezet in Part I. This shows brilliance! Concepts are made concrete, or if not concrete at least "pictorial", and the teaching is done in means children can comprehend. This is the thing of teaching I strive to achieve,

 

However, I feel the then throws the baby out with the bath-water. I don't think the answer is to delay formal education, rather it's to re-think what (and how) to teach young children. So he's right about not putting things in terms children will have a difficult time comprehending, or means that lead to superficial (and thoughtless) application of math formulas.

 

But there is a third way, beyond "delayed math." And the essence of this is in the first part of his essay. Programs like Miquon excel at giving children and their parent/teachers the means to build their skills with age appropriate means. Why miss these years of learning opportunity and the brain-building that comes with it?

 

Bill

[Caribbean Queen]

If she understand the concept of additon you won't need to memorize the +0 facts.

 

We got a CD called Songs that Teach Addtion that is cute.

 

We did oral drill.

 

We played homemade games with cards and dice.

 

We never did worksheets or flashcards in K, and he still learned the facts.

[Ellie]

Why miss these years of learning opportunity and the brain-building that comes with it?

 

Bill

But that's the point. Those years of learning opportunity and brain-building are NOT missed; they are spent in other areas. Notice that the author said that the dc whose formal math instruction was delayed excelled in reading and writing skills, and that they were able to pick up on one year the arithmetic that the other children had labored over for several years, to the detriment of their English skills.

[Spy Car]

But that's the point. Those years of learning opportunity and brain-building are NOT missed; they are spent in other areas. Notice that the author said that the dc whose formal math instruction was delayed excelled in reading and writing skills, and that they were able to pick up on one year the arithmetic that the other children had labored over for several years, to the detriment of their English skills.

 

I just don't buy the conclusion that developing math and critical thinking skills in creative and age-appropriate ways at an early age is in any way going to hamper the development of English language skills.

 

From the explanations given in the essay Benezet appears to be a gifted teacher. Variations on the sort of methods he uses can be used to great effect teaching math to young children. I'll grant that the methods most commonly used don't resemble what I'm talking about, and are what Benezet rightly criticizes.

 

But one either waits until a child reaches and age where they easily understands abstractions, or one changes the method of teaching to one that is age appropriate. I prefer the latter course.

 

Bill

[Ritsumei]

The curriculum we are using talks about "partners" in numbers - the 1 and 2 are partners in 3, for example. I don't know all the games they have in the book, as we're just starting out, but one thing I've seen done with this concept is "Math Mountains." You put the number at the top, and then the partners tumbled down the sides. We've experimented with doing this on our flannel board, but as I said, we're just starting out. It sets the kids up for both addition and subtraction, and helps them see the connections in a way that makes the algebra a bit more intuitive as they get bigger. Our curriculum actually introduces some algebraic concepts very early - in kindergarten - because the kids are solving for a partner some of the time, rather than just the answer: 3 = __ + 1. And partners make the forwards and backwards relationship of addition and subtraction make a lot of sense too.

 

I think that when we get to that point, I'll make some games for Monkey and we'll keep drilling those basic facts till he knows them in his sleep. Yeah, it's work, but some things in life just ARE work. However, it doesn't have to be unpleasant. Work doesn't need to be a drag.

[stripe]

Math is more than just arithmetic and measuring.

 

Couldn't one say that someone could learn all s/he needed to know about history, literature, and science in a short period of time by just waiting until age 15 to begin?

[Aloha2U]

I agree w/Spy Car's comments in post #17...

 

Re-reading your original post, it strikes me that there is an important question of semantics with regard to your phrase: "She knows the concept."

 

In the light of day, I'm thinking you mean she knows how to apply the algorithm (how to work the equation) as opposed to having a deep conceptual understanding of the mathematics involved. These are two very different things.

 

When a young child has a firm grasp on how the base-10 system operates, how to decompose and regroup numbers, and understands concepts such as the "commutative law", then mathematics is akin to a native language.

 

Simply memorizing "math facts" or learning to apply an algorithm is a very limited form of math education. It not unlike "memorizing words", rather than learning phonics. It is important if you want to break the cycle of thinking your a family that is just "bad at math" that you question whether fault might lay in "the methods" with which you were taught, and which you in good faith are using with your daughter. Because that is very likely the case!

 

I also completely agree w/stripe and OhElizabeth...

 

I don't think one needs to choose between facts and concepts. Have your cakes and eat them two!

 

Head on over to http://www.alabacus.com and see if the way they explain things doesn't make it more clear for you. It balances conceptual understanding and fact drill through games and does addition first, as you say.

 

We use RightStart (our math spine) for the very reasons OhElizabeth stated... and supplement with Singapore for drilling/practice through rote work.

 

Side Note: I purchased Audio Memory's addition/subtraction songs (2 CDs) and they really haven't moved from the shelf since their arrival last year. After reading this thread earlier today I attempted to give them another chance, but I've finally come to realize that we do not need them and will never use them - because of the way RS teaches my ds to understand concepts. I also own Math in a Flash addition/subtraction flash cards (new in the box), but I'm thinking that they'll probably never get used either.

 

RightStart's partitioning of numbers with part-whole circle sets is similar to the Singapore-style "number bonds" mentioned by Spy Car (post #19). So to piggyback on his comments...

 

 

One thing to consider adding (if you haven't) is Singapore-style "number bonds." Are you familiar with these? They look somewhat like this, although there are "usually" circles with spokes drawn around the quantities, while I will use "brackets"):

 

.......[8]

...^

[5] [3]

 

another thing to consider adding (that RS also does) is to have the child say all the ways to make/partition a particular number (for practice with the commutative property)...

 

10=9+1

10=8+2

10=7+3

10=6+4

10=5+5

10=4+6

10=3+7

10=2+8

10=1+9

10=0+10

 

9=8+1

9=7+2

9=6+3

9=5+4

etc.

 

 

HTH! :001_smile:

[stripe]

I also think if it were so incredibly common sense to learn math, then every adult would know basic math facts and have a good foundation.

 

Many American adults, at least, seem to NOT have this basic foundation. So, particularly if the parents are lacking that foundation, it would be hard to bring a rich understanding of mathematics to one's child's life in an "every day" sort of way without a curriculum. I think this is true for most things. If you are well-versed in a subject, you can whip knowledge out from under your hat, work it into everyday situations, answer all the questions your kids have easily, and come up with experiments on the fly. If you feel you are on more shaky ground, I think it would be wise to supplement one's own knowledge with books and planning of some sort. That doesn't mean it needs to be scary and unpleasant! I think kids naturally are curious and like to know things, and tend to enjoy feeling they are learning and growing.

[Ritsumei]

I also think if it were so incredibly common sense to learn math, then every adult would know basic math facts and have a good foundation.

 

Many American adults, at least, seem to NOT have this basic foundation. So, particularly if the parents are lacking that foundation, it would be hard to bring a rich understanding of mathematics to one's child's life in an "every day" sort of way without a curriculum. I think this is true for most things. If you are well-versed in a subject, you can whip knowledge out from under your hat, work it into everyday situations, answer all the questions your kids have easily, and come up with experiments on the fly. If you feel you are on more shaky ground, I think it would be wise to supplement one's own knowledge with books and planning of some sort. That doesn't mean it needs to be scary and unpleasant! I think kids naturally are curious and like to know things, and tend to enjoy feeling they are learning and growing.

 

:iagree:I do pretty well with math, though not outstanding, and I still prefer to have a curriculum to "hold my hand." Not that I do everything just exactly like the curriculum says; I didn't even buy the student book full of worksheets. We do it on our flannel board so that Monkey doesn't need to write because he's not ready for that yet. But it's really nice to have a book to help me make sure that we get it all, that we cover it in a sensible in kindergarten - like introducing graphing and measuring - I'm not at all confident that I would have thought to do. And I know that we wouldn't have had as much fun: Math Expressions has you do some fun activities! They're aimed at getting all different types of learners learning, but they're fun. Monkey's favorite is when he jumps in circles making animal noises. I have to keep track of the numbers on my fingers for him when he does that, cuz he gets so dizzy, LOL! But I figure that even with that it's still reinforcing, and he LOVES math.

[Spy Car]

:We do it on our flannel board so that Monkey doesn't need to write because he's not ready for that yet.

 

Have you considered Cuisenaire rods? Way before my son could write he loved doing math equations with his rods. It's another fun way to learn/play and especially favored by "monkeys". Don't ask me how I know :D

 

Bill

[Laura Corin]

I teach the concept at that age. There's lots of time to gain the maths facts by natural repetition over the subsequent years.

 

Laura

[Cera]

We just used flash cards (homemade) that we went through each night at dinner. She got a check mark on the back for each right answer (I give about 10 secs) and after 5 check marks I tossed them out of the pile. Occasionally I would add back the ones we removed for practice but it took less than a month for her to memorize all the addition facts from 0-9.

[Ritsumei]

I've been getting curious about them; they seem to be getting rave reviews here on the boards! I haven't gone and googled them yet though. Sounds like they're some of those great "toys" that the Monkey learns tons & never even knows it, which is right up our alley right now.