# How to teach math to a small child?

January 19, 2010 12:06 PM Subscribe

How do I teach math to a small child?

I read an article a while ago (before I had kids, so of course I didn't save it) about how traditional arithmetic teaching methods tend to decrease a child's ability to do algebra later on. (Something about how children are born thinking algebraically, but by constantly having them do 2+3=? equations they begin to think very linearly about numbers.)

Do you know of any books, websites, articles, etc., that would help in teaching math to small children according to these new pedagogical theories? I'm not looking to be a math drill sergeant, just to understand the theories and get some ideas how to incorporate solid math instruction into daily life. I feel confident in my ability to help them learn about reading, writing, social studies, basic science, etc., in daily at-home activities, but I'm a not-very-mathy person from a not-very-mathy family, so I want some better background on that!

I also had some trouble, personally, learning math in the ways its traditionally taught, and I thought at the time I read the article, "Hey, that would have made a lot more sense to me." So part of this is that I want to be sure I have to tools to help my kids if they turn out to have a math-mind like mine, since the schools here teach it the "traditional" way.

I read an article a while ago (before I had kids, so of course I didn't save it) about how traditional arithmetic teaching methods tend to decrease a child's ability to do algebra later on. (Something about how children are born thinking algebraically, but by constantly having them do 2+3=? equations they begin to think very linearly about numbers.)

Do you know of any books, websites, articles, etc., that would help in teaching math to small children according to these new pedagogical theories? I'm not looking to be a math drill sergeant, just to understand the theories and get some ideas how to incorporate solid math instruction into daily life. I feel confident in my ability to help them learn about reading, writing, social studies, basic science, etc., in daily at-home activities, but I'm a not-very-mathy person from a not-very-mathy family, so I want some better background on that!

I also had some trouble, personally, learning math in the ways its traditionally taught, and I thought at the time I read the article, "Hey, that would have made a lot more sense to me." So part of this is that I want to be sure I have to tools to help my kids if they turn out to have a math-mind like mine, since the schools here teach it the "traditional" way.

Couldn't you do algebra with little numbers and manipulatives?

i.e. 2 + heart = 5. What number should the heart be?

posted by debbie_ann at 12:30 PM on January 19, 2010

i.e. 2 + heart = 5. What number should the heart be?

posted by debbie_ann at 12:30 PM on January 19, 2010

You may want to do some research on the Montessori method of math - with young children it relies more on organic counting methods as they relate to things rather than rote memorization - it allows the kids to feel and see what math skills really are rather than just memorize 2+2=4.

It also allows the kids to think in algebraic terms - if only basically. You can set up any number of "solve for x" situations when you have the materials in front of you without ever referring to letter-for-number stand-ins. It is amazing how much young children can actually handle if presented properly.

And I love Debbie_Ann's idea! So many times we get wrapped up in the formality of how we learned algebra that we forget what the core of it is.

posted by Tchad at 12:53 PM on January 19, 2010

It also allows the kids to think in algebraic terms - if only basically. You can set up any number of "solve for x" situations when you have the materials in front of you without ever referring to letter-for-number stand-ins. It is amazing how much young children can actually handle if presented properly.

And I love Debbie_Ann's idea! So many times we get wrapped up in the formality of how we learned algebra that we forget what the core of it is.

posted by Tchad at 12:53 PM on January 19, 2010

I'm looking a little more for books (etc.) on theory and pedagogy for teaching to small children; we already do hands-on. What debbie_ann suggested was the sort of thing I remember from the article (and to make it hands on, one could do things like "you have two cheerios, and you want to have five, how many do you need?").

Child #1 is working on counting. Presumably more children to follow. So it's not immediately relevant but I am assuming there's reading involved for me, and I was thinking about it when playing some counting games. :)

(I have never heard of chisenbop but now I feel I must go learn it.)

posted by Eyebrows McGee at 12:53 PM on January 19, 2010

Child #1 is working on counting. Presumably more children to follow. So it's not immediately relevant but I am assuming there's reading involved for me, and I was thinking about it when playing some counting games. :)

(I have never heard of chisenbop but now I feel I must go learn it.)

posted by Eyebrows McGee at 12:53 PM on January 19, 2010

I'll ask again, since you missed anniecat's response:

How old is the "small child" in question?

posted by hal_c_on at 1:04 PM on January 19, 2010

How old is the "small child" in question?

posted by hal_c_on at 1:04 PM on January 19, 2010

In my household the Parker Bros board game Sorry was a fun way to introduce counting and numbers.

posted by Midnight Skulker at 1:19 PM on January 19, 2010

posted by Midnight Skulker at 1:19 PM on January 19, 2010

I thought "working on counting" was enough for age-wise, but if not ... yearish. :) As I said, it's not that it's important RIGHT NOW, it's that I want to understand the theory for when he's older.

posted by Eyebrows McGee at 1:22 PM on January 19, 2010

posted by Eyebrows McGee at 1:22 PM on January 19, 2010

I offer no help with ways to teach math, but the whole issue of how we learn math/numbers was recently covered in a Radiolab segment.

posted by Papa Mango at 1:26 PM on January 19, 2010 [2 favorites]

posted by Papa Mango at 1:26 PM on January 19, 2010 [2 favorites]

I have no concrete advice, as to the theory of it, but as far as putting it into practice, I would looks for toys and games that involve logic. (Age appropriate, of course.)

I was just over at a friend's house, and we were playing this game. It was sort of a kids bingo. Card with three shapes, and a little device that produced disks of five different shapes. You take turns drawing a disk and whoever matches wins. Easy to grasp, but works on the "which thing is missing" "what choices do I have" part of the kids brain. Sort of lays in a pathway for the higher learning.

I can only speak as a former kid, but I loved learning right up until what I was learning stopped being relevant to world around me. I would strive to point the concepts out as they come up in real life and to the extent the child can understand. Also the idea of symbols versus what they represent.

posted by gjc at 1:44 PM on January 19, 2010

I was just over at a friend's house, and we were playing this game. It was sort of a kids bingo. Card with three shapes, and a little device that produced disks of five different shapes. You take turns drawing a disk and whoever matches wins. Easy to grasp, but works on the "which thing is missing" "what choices do I have" part of the kids brain. Sort of lays in a pathway for the higher learning.

I can only speak as a former kid, but I loved learning right up until what I was learning stopped being relevant to world around me. I would strive to point the concepts out as they come up in real life and to the extent the child can understand. Also the idea of symbols versus what they represent.

posted by gjc at 1:44 PM on January 19, 2010

This is probably way overkill, but there are a number of homeschool curricula that take this approach. For instance, my five-year-old is working in the Math-U-See "Primer" level and right now he's learning to solve for unknowns in equations like ?+6=8.

Another curriculum that uses manipulatives of various kinds, and that some friends of mine really love, is RightStart Math. It uses a lot of math card games, and an abacus, and emphasizes kids learning to visualize numbers and problems in units of 5.

Miquon Math is very inexpensive, uses manipulatives, and maintains the approach that there is more than one way to solve a problem. My older son and I used it when he was quite young and it is good for giving kids a visual, concrete sense of the numbers and operations and their relationships as well as the idea that they themselves are creative problem-solvers.

You might find it interesting to browse some of the homeschool math curricula and see what they do.

That said, I second gjc about logic, number, and problem-solving games. I love Mindware and Fat Brain for those kinds of games and activities for my family.

posted by not that girl at 2:23 PM on January 19, 2010 [5 favorites]

Another curriculum that uses manipulatives of various kinds, and that some friends of mine really love, is RightStart Math. It uses a lot of math card games, and an abacus, and emphasizes kids learning to visualize numbers and problems in units of 5.

Miquon Math is very inexpensive, uses manipulatives, and maintains the approach that there is more than one way to solve a problem. My older son and I used it when he was quite young and it is good for giving kids a visual, concrete sense of the numbers and operations and their relationships as well as the idea that they themselves are creative problem-solvers.

You might find it interesting to browse some of the homeschool math curricula and see what they do.

That said, I second gjc about logic, number, and problem-solving games. I love Mindware and Fat Brain for those kinds of games and activities for my family.

posted by not that girl at 2:23 PM on January 19, 2010 [5 favorites]

The Radiolab segment above mentions children grasp numbers logarithmically, not algebraically. Did you perhaps mishear or misunderstand this?

posted by chairface at 2:33 PM on January 19, 2010

posted by chairface at 2:33 PM on January 19, 2010

With both of my kids, I have actually taught simple algebra to them along with simple addition and subtraction. It's not like it's much harder for them to answer the question, "2 + what = 5?" than "2 + 3 = what?" or "5 - 2 = what?" Same idea with multiplication and division.

If you do it like that, using a "what" in place of an "x" for a bit, I've found it's not hard at all for them.

Plus, you get the added bonus of saying, "Hey, cool, you're 5 years old and doing algebra. There are kids in 9th grade learning this right now." They love it, and I am betting that when they get to algebra class, it'll keep them from having the "this is a scary sounding class, it must be hard" attitude.

On a related note, there's no reason they can't grasp addition with negative numbers along about the same time they're learning subtraction.

posted by greenmagnet at 2:49 PM on January 19, 2010

If you do it like that, using a "what" in place of an "x" for a bit, I've found it's not hard at all for them.

Plus, you get the added bonus of saying, "Hey, cool, you're 5 years old and doing algebra. There are kids in 9th grade learning this right now." They love it, and I am betting that when they get to algebra class, it'll keep them from having the "this is a scary sounding class, it must be hard" attitude.

On a related note, there's no reason they can't grasp addition with negative numbers along about the same time they're learning subtraction.

posted by greenmagnet at 2:49 PM on January 19, 2010

I'm not an expert on this by any stretch, but I was thinking about my own math learning, and realized that one (maybe the) big difference between my experience in math, particularly in middle school, and the other kids was that I had zero problem translating the world around me to numbers. I had zero problem with word problems, in other words, while so many kids seemed to struggle with that in particular. It's more than word problems, though: algebra is trivial if you're used to thinking about numbers as representing "real" (whatever that means) "things".

If one of these methods mentioned above talks about spending a lot of time working with quantities of sand and/or water in differently sized containers, dividing the flow of things, maybe even looking at Legos and how you can build a good Lego bridge with one leg made up of X white bricks stacked with Y blue bricks, and the other leg made of X+Y red bricks -- but if they're not the same total number, the bridge won't balance -- I'd endorse that approach. Making numbers -- or rather quantities - _concrete_, so that one has an intuitive visual/weight understanding of the relationships between quantities and what that means, before you even get to the counting part, would be my vote.

posted by amtho at 6:40 PM on January 19, 2010

If one of these methods mentioned above talks about spending a lot of time working with quantities of sand and/or water in differently sized containers, dividing the flow of things, maybe even looking at Legos and how you can build a good Lego bridge with one leg made up of X white bricks stacked with Y blue bricks, and the other leg made of X+Y red bricks -- but if they're not the same total number, the bridge won't balance -- I'd endorse that approach. Making numbers -- or rather quantities - _concrete_, so that one has an intuitive visual/weight understanding of the relationships between quantities and what that means, before you even get to the counting part, would be my vote.

posted by amtho at 6:40 PM on January 19, 2010

Not sure if it's a pedogogical theory, but

I'd recommend Lockhart's _Mathematician's Lament_

for giving you a framework to work from.

"I'm not looking to be a math drill sergeant, just to understand the theories and get some ideas how to incorporate solid math instruction into daily life."

Daily life - that is key. Packing for a trip? Have them load the luggage, that's an application of combinatorics. Having pizza? Have them cut (or they direct and u cut) the pieces. What if another person shows up? How will u keep it fair? That's fractions and multiples. Ever see a dog catch a frisbee? What's a dog doing calculus! (predicting the rate of change - where the frisbee will be)

posted by at at 6:50 AM on January 22, 2010 [1 favorite]

I'd recommend Lockhart's _Mathematician's Lament_

for giving you a framework to work from.

"I'm not looking to be a math drill sergeant, just to understand the theories and get some ideas how to incorporate solid math instruction into daily life."

Daily life - that is key. Packing for a trip? Have them load the luggage, that's an application of combinatorics. Having pizza? Have them cut (or they direct and u cut) the pieces. What if another person shows up? How will u keep it fair? That's fractions and multiples. Ever see a dog catch a frisbee? What's a dog doing calculus! (predicting the rate of change - where the frisbee will be)

posted by at at 6:50 AM on January 22, 2010 [1 favorite]

This thread is closed to new comments.

meansomething to a mind not accustomed to thinking abstractly.posted by The Winsome Parker Lewis at 12:12 PM on January 19, 2010