Friday, July 25, 2008

Calendar for Children

Unlike adults, young children don't mind seeing time pass. Perhaps it is because they don't have much of a concept of life and death and ageing that they can get excited about marking a big red "X" across each day of the week on a calendar. At any rate, they like it, especially if they are counting down to something exciting like a birthday or other special event.

Children need to learn about the days of the weeks, and the months in a year, so it is a good idea to hang a yearly calendar where your child has access to it. It is a better idea to give your child a special calendar just for her.

This provides your child with a visual schedule of the days of the week, the months in a year, an understanding of when seasons occur, and the general passing of time.

You can use the calendar to mark special events, regular weekly events, and even keep a record of the weather. One way to do this is to use stickers or small stamps. I suppose some of you techy parents out there have ways to print stickers, but I like these Calendots from Organized Planet.

Give her the daily job of checking the calendar each morning to tell you what day it is and report any activities you may have planned. And, at the end of the day, have her put the big red "X" on the square. Remember, children love routine.

Buy a Scale and a Tape Measure

No, you're not fat. It's just a good way to help your child learn about measurement.

You can teach about measurement during the course of your days and have a lot of fun doing it. Your child may even think he is playing games with some cool toys.

Start by giving your child a set of measuring cups and spoons to play with. He can play at the sink measuring water into a dishpan. Put bubbles in and make it even more fun. You can give your child access to a sand or rice table, or sandbox or even the beach! Filling and dumping measuring cups and spoons is the beginning of learning about weight and volume.

When your is around three or four, or can recognize numbers, you can give him a ruler or tape measure to play with, supervised of course. Measure things together. Carrots, fingers, cloth, wood, fruit, toys, couches, name it.

With this you can introduce, as a matter of course during regular conversation, concepts such as big and little, short and long, near and far, few and many, empty and full, more and less.
Without even making a big deal about it, you will be using math terms every day.

When your child gets a little older, you can expand on volume and weight. Weigh yourselves at the grocery store, with and without groceries in hand. Find different scales at garage sales or on eBay, and set them up in an area of the house. Your child will spend more time than you would ever expect measuring things on a scale. Give her two items and tell her to tell you which one weighs more. Have her do it on a few different types of scales.

You can also ask her to measure things with a tape measure to see which are taller, or wider, or more. When she is old enough to count above ten, introduce inches, feet, yards, or metric measurements. Then you can ask her to measure the dimensions of a room or other objects on her own.

Enjoy these "games." You may be developing a future master carpenter, cabinet maker, chef, tailor, seamstress, or sail maker, not to mention accountant or astronomer!

Recognizing Numbers

Once children can count, a natural step is to learn to recognize numbers. Eventually they will connect that the symbol for the number three means "three things."
Here is how to help them make that connection:

Number recognition:
Point out and name numbers on everyday things, such as signs, receipts, houses, buses and anything else you can find that has numbers on it.

Play plenty of simple board games. Candyland can be played with children as young as three years old, and involves counting colored squares to moove a gamepiece. For variety, the game Trouble can be played by five year olds and involves recognizing the actual number and moving a game piece the number stated.

You can also play card games that require counting and recognizing numbers concurrently, such as Crazy Eights, Go Fish, Dominoes, and Uno.

Reading together can be one of the best ways to reinforce number recognition. Start, when your child is a baby, with simple cardboard counting books, and move on to more challenging books as your child matures. There are many number recognition books available at bookstores and libraries. Have your child casually count with you when you are reading. Say, "Let's count the baby chicks, " and take her little finger and touch it to each object while you are counting.

It is a painless way to teach and learn.

Classification Skills

Classification skills, or sorting skills, is another one of those cross-training skills that, when developed, help children in math, reading, and general logical thought process development.

It is one of the most important skills for creating a real thinker.
When children begin to classify objects (matchbox cars), sounds ( loud/soft, man-made/machine), flavors (salty, bitter, sweet) , or concepts ( real/make-believe) into categories according to traits they have in common, they begin to develop the ability to make connections. This is the precursor to logical thinking, and the ability to make predictions about the world around them.

You can help develop this skill.

First, help your child sort simple objects. Matchbox cars can go into a different pile than matchbox trucks, color laundry can go into a different pile than whites, plastic things can be differentiated from metal things, junk mail from regular mail, hard things from soft things, big things from little things. There is no end to simple object classification.

When the child is old enough to trust with nostril-sized things, have fun with M&Ms, raisins and grapes, buttons, nails and screws and bolts.

Then start asking your children some questions: Are these things alike or different? How are they alike? How are they different?

Play Uno with them when they are old enough. Uno matches wither by color or by number and is a wonderful game for teaching classification.

Take your child grocery shopping. Name the vegetables in the vegetable isle, then name the dairy foods in the dairy aisle. ON the ride home, ask your child to tell you names of different things you saw, and where they belong.

"We saw milk."
"Milk! Yes we did. Where was the milk?"
"In the berry aisle"
"No, in the dairy aisle. What else was in the dairy aisle?"

When you go to the fabric store (If you don't go, I would suggest a trip just for fun), take time to go through different fabrics, describing their texture, soft, smooth, rough, fluffy, itchy, see through, dark , light, solid, pattern. But a few remnants of fabric to take home and cut into squares for keeping in a "texture box."

Because the aim of this blog is to demonstrate ways to do "sneaky teaching" I suggest keeping things fun at all times in the early years. Direct lessons help, but informal opportunities for sorting and classification abound during the course of a typical day.


What is sequencing and why is it important to children?
Sequencing is the skill of arranging items or events in a particular order.

It is an important skill which has applications in reading, math, and telling time, all things we want our children to be able to do with ease.

How do you introduce your young child to this skill? It's not difficult, and it can be a lot of fun.
One way to do it is to play pattern games. Set up things that are long and short, dried spaghetti sticks, for example, and call them what they are. Point to each item and say,"Long, short, long, short, long...." and your child should pipe up with, "Short!" when you point to the next item.

Do this with colored things, such as red and green apples when you are putting away groceries.
Get some beads and string and make a simple two-color pattern, and have your child copy the pattern. When you are playing legos, have your child copy your color pattern, and then copy one that your child makes up.

If your child likes to do worksheets, print out some free pattern coloring worksheets from for him to color.

Or tell a simple a story, and have your child tell the story back using, "First, next, next, and last"

Good sequencing skills can greatly boost a child's reading and math abilities, and you can easily work on this at home during play. Your child need not ever know he is "working."

Learning to Count

Think of a chubby little two year old. What happens when you ask a two year old how old he is? He will often be able to say, "I'm two" while trying to make his sticky little fingers make the number two. Sometimes it's one finger, sometimes, it's three, or four. Sometimes it's actually two fingers.
No matter. This child who attempts to show any number when saying the word "two"is on his way to learning how to count and understand quantity.
This is the first important math concept young children learn: putting a name to "how many."

I'm going to explain the intricate teaching methods for helping a child learn to work on this important skill. Pay attention; it's complex.

You count. Count everything you come across. Count fingers, toes, knuckles,
Count socks in the laundry before they go in the machine, and when you are folding them. Count birds in the sky, peas on the plate, dishes in the sink, silverware at the place setting , sugar packets in the sugar holder, telephone poles, stop signs, number of hugs you get or give per day.

Play counting games. Tell your child to close her eyes and not open them until you count to five or ten or sixteen.
When you are hanging out playing with a game or toy, count the pieces before you put them away.

If your child is old enough not to stick things in her nose, spill out the coin jar and count them together on the floor. Don't worry about counting the value of the coins, just count the number.
Count beads, buttons from the button box, Legos, checkers, and Barbie shoes.
When she is a little older, start working on counting by ones, then twos, then fives, then tens. Group things together, and count by groups.

As always, don't push it. Keep it fun. Learning is a game. Learning is life.

Teaching Fractions

Fractions don't have to be painful. Teaching fractions is one of my favorite math subjects to teach, probably because it can be so hands on, it makes so much sense, and kids seem to get it rather easily.

You don't have to introduce the idea of fractions with numbers and lines. That is too abstract for "living math," and one of your goals in teaching math is to show them math that they will use every day.
My two favorite ways of introducing fractions are first through felt or paper cut outs, and then through cooking. I found that my children understood the measuring cup concept after they played with laying colored cut outs on top of each other, and learned to name the fractions.
For some kids, the pie fractions are easier than the measuring cup volume fractions.

Get some different colored felts from the craft store. Cut, out of the same sized but different colored circles: one whole, halves, thirds, quarters, sixths and eighths.

You can also do this with pieces of paper, which you can let your children color different ways -- blue for blueberry pie, red for cherry, or even pizza-colored!

Then, just play with the cut outs, naming the fractions. First, have your child identify the pieces. Say to her, " Show me one whole pie," Then take the two halves and say, "One pie cut in two parts for me and for you. Let's cut it in half," and pretend to cut it in half. Have the child serve you 1/2 of the pie. You play around with this a variety of ways, giving her fun quizzes, such as, "How many quarters can you fit into a half?"
You can also see which fractions don't fit. Ask her to show you how many thirds she can fit into a half and see what she does.
The goal here is to be casual, fun, and light-hearted.

You can also draw up several same-sized rectangles with lines for the half mark, quarter marks, third marks, sixth marks, and eighth marks. Let the child color, then cut the rectangles on the lines, and play that way.

If you order or make a pizza, have your child help you cut the pizza into halves, fourths, then quarters. Play games with this too, saying "I'm so hungry I could eat HALF of this pizza. Show me half of the pizza. Can you eat half of that pizza? Really?! Wow. I think I might only be able to eat a quarter of it..." and so on.

Cooking is another fun way to "play" with fractions. Simply include your child in baking and cooking projects, letting him wield the measuring cup. Help him measure the ingredients, naming the fractions when you come to them. Things WILL spill, so expect a mess and don't worry about it.
Take time to play with measuring cups at the sink, or with water in a bowl. Let your child explore the concepts through play.

Then later, when fractions turn into numbers and lines on paper, your child will already be able to visualize what 1/3, 1/4, or 3/4 looks like and will understand their values.

Thursday, July 17, 2008

What Do You Do If You Have a Math Freak?

If you find yourself with a child who is good at math and likes it, then you can have some real fun.

Do whatever you can to nurture this gift without burdening the child with forced advanced study. This could create a burned-out resentful child who closes his or her mind down to the fun of math.

Things you can do for your mathy kid:

Preschool -- count everything. Do counting songs, counting games, and make numbers and counting things be something you do all the time. Do quiz nights with addition, or months of the year or days in a week or year. Give her dominos or base ten cubes or tangrams to play with.

Elementary -- give your child a list of items when you go to the grocery store. Let him locate the items and add the total cost up, on paper or in his head. Work on estimation. Have him do the tax ( percentages) for the total bill. Have him figure out which items are the "best deal."
Get some math game books out of the library and play them. Do fun quizzes on math facts when you are stuck in traffic.

Middle school and high school -- if your child has a real love for math, have her join the math club at school. They often have competitions, and can take advanced classes. Try an online class or a math and science summer program. If your child is really advanced and self-driven, get some advanced math textbooks in the house for reference or working through. Encourage a community college class. Hobbies for mathy kids include astronomy, computer programming, orienteering, sailing, geocaching, and other GPS treasure hunting games. They might want to check out some of the archived college math department websites here.

Be proud of your math kid, even if you yourself don't speak "Math."

PS - If the opposite is true, check out these tips and help her overcome her "math anxiety".

An Interesting Viewpoint on Early Math Education

Part of being able to understand math comes form one's ability to explain it. Oral math is important.

An experiment from a New Hampshire public school , published in the Journal of the National Education Association, in -- get this-- 1935 -- rings so true for me that I keep coming back to it's concepts to explain how I think we should be teaching elementary math today, in this time of steriod-doped curriculum planners who start giving algebra to kindergartners.

This radical idea produced superior math performers, and readers, who went on to have an easier time learning higher mathematics when the time came. Here's the radical idea in a nutshell:

"The only arithmetic in the first six grades was practise in estimating heights, areas, and the like; formal arithmetic was not introduced until the seventh grade. In tests given to both the traditionally and experimentally taught groups, it was found that the latter had been able in one year to attain the level of accomplishment which the traditionally taught children had reached after three and one-half years of arithmetic drill. In addition, because the teachers in the experimental group had had time to concentrate on teaching the children to "read, reason, and recite," these children developed more interest in reading, a better vocabulary, and greater fluency in expression."

Read the article and tell me if you agree.

Monday, July 14, 2008


Yes, beans. Dried beans are wonderful little counters to use with children old enough to trust not to stuff them up their noses, yet young enough to still need help cementing the thought that the number "3" actually stands for "three things."

Here's a little dialog:

You: how old are you?
Child: Six
You: You've been alive for six years! Wow!Let's see what six looks like. Count out six beans.

Guided by you, the child counts out six dried beans from a small pile.

You: That's how many years you are. How many is that?

And so on.

You can have the child count them again, and then you can really start playing with the concept of six. Leave the fisrt six beans out of the big pile. Take combinations of beans that number to six out of the pile. Ask the child what 3 beans and 3 beans makes. Compare it to the six in the first pile. Do 5 beans and 1 bean. Do "7 beans take away 1 bean" and so on.

Short lessons like this will help children to keep in mind that math is real, not just a bunch of symbols on a page. You can do it with socks when sorting laundry, grapes at lunch, blades of grass at big sister's soccer game.

Keep it real. Keep it fun.

Wednesday, July 9, 2008

Math Out Loud

A nice way to help younger children to digest the meaning of numbers is through songs, rhyming games and poems.
Who doesn't remember "There Was an Old Lady Who Swallowed a Fly," "The Farmer in the Dell," "Over in the Meadow," or "A hundred Bottles of Beer on the Wall." These songs, likely to make grownups groan, help kids to cement a variety of early math skills.

Here are a few examples:

Counting Forward:

Over in the meadow,
In the sand in the sun
Lived an old mother turtle
And her little turtle one
"Dig!" said the mother;
"I dig!" said the one,
So they dug all day
In the sand in the sun.

Over in the meadow,
Where the stream runs blue
Lived an old mother fish
And her little fishes two
"Swim!" said the mother;
"We swim!" said the two,
So they swam all day
Where the stream runs blue

Counting backwards:

99 Bottles of beer on the wall
99 bottles of beer
you take one down, pass it around,
98 bottles of beer on the wall.

Size order: There was an old lady who swallowed a fly.
I dunno why she swallowed that fly,
Perhaps she'll die.

There was an old lady who swallowed a spider,
That wriggled and jiggled and wiggled inside her.
She swallowed the spider to catch the fly.
But I dunno why she swallowed that fly -
Perhaps she'll die.
There was an old lady who swallowed a bird.....(and so on)

"The Farmer in the Dell" also has size order in the song.

Young students don't have to slave over endless worksheets in order to learn math. We can keep it fun!

Tuesday, July 1, 2008

Math Drills -- Are They Really Useful?

One of the problems with elementary school math is the dreaded math drills. I believe you will find very few children who actually love math fact drills. I was one of them, but I believe I was in the minority -- preferring to repeat page after page of things I could do well, such as addition, subtraction and multiplication tables. I liked the self-competition. I liked scoring better than myself on the previous page. I liked striving for perfection, though I rarely achieved it.
This was a piece of cake compared to learning something new, which took more effort. I think math facts and drills are useful for reinforcement, but not for teaching the concept -- I believe that a set of flash cards take the skill out of context, and if the skill isn't mastered, then the drill will be pointless, frustrating hard work. I believe also, that drills help show the pattern of the fact, but that they should not be used to teach the pattern. Some kids just don't get it on their own and have to be "spoon-fed" the pattern, but really understanding the pattern is what makes them really know the concept. I would say that random drills, and mixed math facts should be used once the facts have been mastered, only for reinforcement, never for teaching.