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Teaching kids math

joesixpack

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I am the happy father of a 4 yo little boy who is, I think, exceptionally cute and a G.D. genius, too boot.

Well, he's not a genius, but I think he falls on the high side of average. At 4, he is able to read well enough to surprise all of his pre-school teachers and day-care providers. This has led many of them to believe that he falls into the "gifted" catagory. My wife and I feel it has more to do with the ammount of time we spent reading to him and teaching him his alphabet (he could identify all the letters at 2 and could even identify some words) My wife and I don't like to push the kid. When he starts to lose interest in something, we don't force him to continue.

Because he is at the point where he can almost read independently, I decided to start teaching him some basic arithmetic. I spread some pennies out on the table and we count them, then I divide them up into groups and we add them together (i.e., "here's two, and here's four, how many are there all together?). Not suprisingly, he counts them all up together and tells me the answer. Now if I take those same pennies and divide them into different groups (three and three, for instance) he still has to count them to give me an answer, even though, clearly, no pennies have been added to or taken from the table.

I can only assume this is normal for his age, but I don't really know. I do know that children below a certain age will think a tall skinny beaker contains more liquid than a short fat one, even after they have been shown otherwise ( I forget the developmental psychologist who discovered this, but I'm sure someone here can help me out. Piaget, maybe?)

My question is this; Am I wasting my sons time by playing the penny-counting game? When would he be ready to learn arithmetic and how will I know? Does it help him for me to spend time teaching him basic math if his brain isn't far enough along for him to get it all?
 
I have similar experiences with my kids (who are getting to be 8 and 14 now). When they were younger, my wife and I were always reading to them, playing math/counting games, and other activities. When asked a question about the world such as "What makes a Rainbow", I would give them answer as best as I could explain it, although it may take a bit. As a result, my kids have (so far) seemed to me to be above average in school (my son exceeds some of the "gifted" kids in things like math). I don't think we were pushy about it, just involved in their life. IMO, I think that staying the course of playing the penny game, reading to the kids, and being involved, your kids will amaze you and others.
 
joesixpack said:
My question is this; Am I wasting my sons time by playing the penny-counting game? When would he be ready to learn arithmetic and how will I know? Does it help him for me to spend time teaching him basic math if his brain isn't far enough along for him to get it all?
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Good question, and this relates to another thread in the forum on why, exactly, subjects are taught in stages. Children don't learn abstracts well when they're 4, and this kind of math has to wait a year or two. Operational numeretics can't be taught, it seems, they just have to grasp it.

Another interesting math-related stage is quantitative permanence. If you take one weiner and chop it up into ten pieces, until kids grasp quantitative permanence, they think the ten little pieces of weiner are 'more' than one whole one, even if they saw the whole cutting step.

Many experiments have been done, and the prevailing theory is that it's biological: that chidrens' brains actually physically need to mature to grasp these concepts.
 
You are not wasting his time any more than you were wasting his time reading to him before he could read himself. It's still important to do. At the very least, you are acclimating him to counting and adding games so that, when he has the ability to do it himself, he will already have seen it and think it's fun.
 
joesixpack said:
My question is this; Am I wasting my sons time by playing the penny-counting game? When would he be ready to learn arithmetic and how will I know? Does it help him for me to spend time teaching him basic math if his brain isn't far enough along for him to get it all?
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Even if he's not "getting" the math, he's enjoying time with dad, he's learning what you can do with things (count them, move them, talk about them), he's being listened to, and he's listening. And the exposure to the math concepts will probably help him put it all together when his brain is ready for it -- their minds are like steel traps at that age.

My kindergartener came home with a Saxon math activity for parents to do with their children. It involved putting "small objects, such as pennies or beans" into a cup, taking them out, counting them on the table, counting them back into the cup, etc. Sounds familiar?
 
Thanks for all the replies.

Does anyone here know a good place on the web to find some age appropriate math games for my 4-yo? I'll google it myself, but any input as to what's usefull and entertaining for a kid would be greatly appreciated.
 
My 4-year-old is almost 4 1/2, which makes some difference at that age. Most of the mathy games he likes are really pre-math (counting, sorting, matching, sequence, shapes).

I can't post links, but I'll try to give you an idea how to get to where my 4-year-old hangs out.

He enjoys several games at pbskids.org. He can even find the games he's looking for most of the time. One of his (and my) favorites is tangrams, which you can find by jumping to "Sagwa, the Chinese Siamese Cat", then selecting games. I had to show him how to complete a tangram the first time, but he picked it up quickly, and likes to go back and redo them all every few days.

BTW, a great resource for higher-level real math is Cyberchase (the show and the activities at PBSkids.org). Even the younger kids enjoy the adventure storyline, and some of the math soaks in. My now 6-year-old, at 4, showed me how to find the center of any regular shape by folding it exactly in half twice, after seeing it on Cyberchase. :)

The Starfall reading website at starfall.com has a few counting/sequence/calendar activities at the the top of the page, and my 4-year-old also likes to click through the stories.

We tend to use sites that work for a range of ages (my older son is 6). Which is nice, because the 4-year-old can manage quite a few of the activities, is challenged by many of them, and has some dangling just out of reach. The sites I found from a good google search (online math games preschool) weren't immediately impressive ... I'll have to see what the kids think.

Have fun!
 
joesixpack said:
Does anyone here know a good place on the web to find some age appropriate math games for my 4-yo? I'll google it myself, but any input as to what's usefull and entertaining for a kid would be greatly appreciated.
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One fun "mathy" thing you can do with a 4 year old is break out the legos/duplos. The concept that "3 2-block wide legos are the same as 1 6-block wide lego" is an excellent builder at abstract reasoning and something they can easily grasp. You can work it into building a lego house. If each wall is 8 bumps wide, how many 4-bump wide blocks do you need? Did building one wall reduce the width needed to complete another wall?

It's fun, you can do it together, and it's mathematics.

Something my two-year-old would do which amazed his pre-school teachers, claiming that his math skills were well beyond expected, was lining cars up, then put them individually in "parking spaces." Honestly I have no idea why this is a math concept, but hey, I didn't study early childhood education and they did.
 
joesixpack said:
Thanks for all the replies.

Does anyone here know a good place on the web to find some age appropriate math games for my 4-yo? I'll google it myself, but any input as to what's usefull and entertaining for a kid would be greatly appreciated.
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Hi Joe,

I don't know about links for games, etc, but I can recommend the whole "Jumpstart" series of computer software for kids. I think my daughter went through every one of them over and over again, from Jumpstart Preschool through Jumpstart 3rd Grade. She loved them, thought they were hilarious, and really learned alot.

I don't remember alot about the math games we played when she was that age, other than I do recall playing alot of "one of these things is not like the other" kind of stuff. Have a group of 5 pennys, 5 toothpicks, and 7 little rocks; see if she could count them up and figure out which was different. That sort of thing. "If I take away 3, will they be the same then, or different?"

We also played "store". Where she would set out a bunch of items, and I would come to buy them (usually with dominoes or poker chips or something like that). She would state the price, and I would look at my pile and say "Uh...How many is that?" and she would have to help me count them out. Then she'd have to help me figure out how many I had left, and whether the amount I had was enough to buy something else. "If I have seven, and that hat costs 4, do I have enough to buy it?"

Have fun!
Meg
 
When I was young and they were giving me the tests to determine mental development, I was sneaky. They said, which has more liquid in it? The tall one seemed to have more, and since it was seemed obvious, they wouldn't ask me if that were the answer. So I said "the same." Hehehe.

Edit: typo. I really gotta read this stuff over before I hit "Submit"
 
I'm fresh out of high school, and while I can't remember how I learned math, I've been turoring younger students regularly for years, including students in several grades.

Something I quickly discovered is that even math that seems obvious to adults may be completely incomprehensible to children. Your story about counting up pennies was a good example. It's not limited to math, either- when my younger sister was four, my parents were reading her a picture book and she continually tried to reach into the pictures to grab objects in them.

It's easy to forget that perception and cognition are very difficult processes, and that the early years of life are meant for practice with them. In other words, there's nothing to worry about.

As for good ways to teach children- as I said, I can't remember how I learned math, but what got me into science was the "Magic School Bus" books, Nova, and a fantastic computer game called "Gizmos and Gadgets" that focused on engineering.

IMHO, educational television is surprisingly effective- try to get him onto pretty much any show on PBS is good (I grew up on Bill Nye the Science Guy, but I think the show's gone now.) He'll have his whole teenage years to watch "The Simpsons"- try to get him to give "Scientific American" or "Nova" a chance.
 
joesixpack said:
I spread some pennies out on the table and we count them, then I divide them up into groups and we add them together (i.e., "here's two, and here's four, how many are there all together?). Not suprisingly, he counts them all up together and tells me the answer. Now if I take those same pennies and divide them into different groups (three and three, for instance) he still has to count them to give me an answer, even though, clearly, no pennies have been added to or taken from the table...
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My oldest is 11 and she'd still rather go outside and catch a mousie or two than play counting games with me, so I can't speak too directly from experience here, but it seems to me that what you are observing is actually a good thing.

As we grow older, we become able to take short cuts in our thinking: there were 6 pennies on the table before papa divided them into two groups, so even though they're now in two groups rather than one there are still a total of 6 pennies on the table. And short cuts are useful -- once we know what we are doing and are good at it.

What your son is doing is seeing for himself how many pennies there are. That's excellent training for a young skeptic. Even at an older age it's nice to remember how that's done, and the importance of doing it.

We often get in a rush, and don't want to take the time to verify something which we know must be so. That can be a useful time-saver, but it's nice to be in the habit of actually doing a careful count rather than assuming that things are as we think they are. If we start getting too careless and too hasty, we're going to be mistaken more often than we realize.

Let me increase the number of pennies from 6 to 60. A clever adult playing the penny game you describe reasons as follows: There were 60 pennies on the table to begin with, so even though they've been divided into two groups there are still 60 pennies. I don't need to actually count them to know that. That's a time-saving assumption -- but it is an assumption.

That's why, if we ask a truly clever adult how many pennies there are in the two groups, they would not respond, "Sixty". They would either count the pennies again, as your son is doing, or they would respond, "There were sixty pennies the last time I counted.

The problem is that many clever adults aren't quite clever enough to realize they've made an assumption, and so aren't quite clever enough to realize the assumption may not truly hold true. That's why magicians are able to fool clever adults more easily than young children.

So, yes, it will be exciting when your son learns to be able to take the short cuts that will enable him to know how many pennies there should be in the newly divided groups without painstakingly counting them all out. But what your son is learning and doing now is also cause for excitement and celebration.
 
Hi Joe,
I'd largely agree with what others have said here, but I'd add that if you're interested you should probably read "How Children Fail" and "How Children Learn" by John Holt. They were required reading on my teaching course, and they're really well written. They might give you more of an insight into what's going on in your son's head and how you can help him more.
 
I know my parents taught me a lot of math with card games. Counting the spots for points, symbology (face cards = 10, etc.), and just a little bit of probability (if you've already seen two fives, do you think another one will come up if I deal out ten cards?). Rummy always was big fun for me at an early age. It also led to the "hilarious" incident where my kindergarden teacher asken me to count, and my run finished with "eight, nine, ten, jack, queen, king."

I think there was a conference after that.

Dominoes worked well, too. They're easy to manipulate, the spots encourage counting, and many sets are color-coded for easy matching. Start with a double-six or double-nine set, and just play. Once the numbers are a little more familiar, a real game can be arranged.
 
"Math Is Fun"

It's a Brit site and I have used it in the past. You'll have to search it as I can't post URL. Isn't this supposed to be educational? Being able to post a link????

And Nova Land brings up something interesting - learning fundamentals and then applying shortcuts to learning.

Back to the Math is Fun site: There are games and manipulatives for kids of all ages. I do believe that with all there is to offer now from an educational perspective that it is staggering what young people will be able to learn and achieve through the use of technology and given the correct feedback. Mind you a four year is quite young and impressionable; however brain research shows that connections are made early on and the exposure to something educationally stimulating and enriching will can only benefit. Is anyone into discussing "learning styles"?

WD
 
Can kids that age do logic or is that part of the abstract bit?

Cause, I can't remember what I was doing at four, but I do remember being a bit older (7-ish?) and trying to do my mom's Dell Logic Puzzles. Then, when I saw pre-alegbra for the the first time, I made a connection between what I had been doing and what I was seeing.
 
LostAngeles said:
Can kids that age do logic or is that part of the abstract bit?
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I think that's where jokes and riddles come in. At a certain age, kids begin to be appreciate the humor that comes from the disconnect in logic that many jokes and riddles depend on. From there they move on to more compicated jokes and puzzles, such as the logic puzzles you mention.

I think puzzles (of which jokes and riddles are an early and easy variety) are a good way for people to learn mathematical thinking, as well as a good way to learn that math is useful and fun. Because of the way schools teach, too many people grow up thinking that math is just tedious arithmetic. Arithmetic is part of math, of course (and need not be tedious) but math is so much more and many people grow up without realizing that because of early negative experiences.
 
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I have a book called "Brain Teasers - Grade 1" which I use with my younger children. The simple rhymes are appropriate and fun for my 4 year-old twins (My First Grader actually finds them easy and dull so I have a more advanced book for him). I also recommend "Lollipop Logic" and a few other series.

Pictorial sudoku on 2x2 or 4x4 grids can be a fun challenge for a preschooler as well. You can make it a step easier by providing cutouts of the missing pictures that they can paste into the squares.

Some children work much better with hands on approaches. In this case, I would recommend fun manipulatives to make the child familiar and comfortable with numbers. Some children will not respond well to games because they get nervous or upset at the prospect of losing. My daughter gets terrible performance anxiety when faced with games, especially if there is a time limit involved.

I also think that cooking helps build early math skills. Have the child help to measure the ingredients. You can also have them determine how much/many each person will get. You can make cutting cakes, pies, pizza and even sandwiches into a lesson on fractions. Along this line, I had my son help with his birthday party plans. We discussed everything from how many plates and cups we would need (I told him that to be safe we should have 2 cups for each guest and let him figure it out) to the recipes for food and cake and what ingredients we would have to buy ahead of time.
 
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