Today, I have decided to pass along some things I have learned in my eight year journey into homeschooling, in the hope that I might pass along some wisdom, and keep a few of you from wasting precious money and time.
It is truly amazing how much time, money and effort homeschooling families put into introductory math lessons. I have been in this category myself, so I know whereof I speak. After much consideration and on-the-job training, I have come to this conclusion: You do not need a math curriculum for your four- to eight-year-old child.
What follows is my own idea of an ideal math curriculum for your young student. Take it or leave it, as fits your family.
- Every day, count things around you. (How many apples do we need to buy? How many chairs do we need for the party? How many Legos did it take you to make that wall?)
- Make sure your child can recognize digits and number words. This is easily done by pointing them out in a magazine, newspaper, board book, or sign. All around us are numbers, if we take the time to notice them and share them with our children.
-Work on basic addition and subtraction facts with your young child. You can make flashcards with index cards and a marker for less than a dollar. My children used to enjoy making a game of it in the kitchen. For every correct answer, they advanced one floor tile. For an incorrect answer, they stepped back one tile. When they made it all the way to me, at the other side of the kitchen, we did a big 'high five'.
-Allow your children to play with measuring cups and spoons. This is a great introduction to fractions. To take this further for older children, have them help you double or halve a recipe.
-Make the calendar and the clock a part of every day. Have your child tell you when it is time for lunch or playtime. Practice writing today's date on his drawings. Memorize the days of the week and the months of the year by making a song of it. (How many days is it until Christmas? On which day of the week does Mommy's birthday fall? Can you tell me what is the eighth month of the year? What time is it? How long until playtime?)
-Our Store: Perhaps the single best learning opportunity there is, and a lot of fun to boot. Put some price tags on some of your pantry items, and then take turns with your children playing customer and shopkeeper. You will be amazed how far this pushes mental math. Use real money to "pay" and to make change.
-Math Manipulatives: a giant black hole to suck in your money. You may be tempted to purchase the big package of "manipulatives" that is suggested to complement your child's early math curriculum (which you probably don't need!). Here are my suggestions for a few common math manipulatives:
- Play money: Just use real money. Why pay for fakes? Just set aside a jar of actual money for your children to use for school. They will then get practice with the real thing they will need to use later in life. Pennies are highly useful as counters as well, and are surely cheaper.
- Blocks: besides being a lot of fun to stack and make towers, blocks are useful as counters, and can be expanded, if your child is ready, to model the concepts of perimeter, area, and volume.
- As previously mentioned, your measuring cups and spoons.
These are just a few ideas. I hope you can expand these with your own creativity. Each parent knows what will excite and motivate their children to learn.
Before closing, I would like to leave you with a couple of examples that I hope will encourage you (and if they don't, well, they are cute stories, nonetheless).
A Tale of Two Shopkeepers:
Eight-year-old J and six-year-old B , considering a play cash register: (This may not be verbatim, but I believe it is close.)
J: There are twelve keys here, you see? Four rows, three keys in each row.
J, looking to show off his new knowledge of multiplication: Can you add 3 plus 3 plus 3 plus 3?
B, after a moment of thinking: 3 plus 3 is six, right? so that's 6 plus 6. I think it's 12.
J (who lavishly praises the mental workings of his brother): YES! GOOD! You added it up.
Now look here: 3+3+3+3 is 12. You got it. That's the same as 6+6 is 12. You can also say that four groups of three equals twelve. Four groups of three is 3+3+3+3. You see? Multiplying is just like adding over and over. Three groups of four is twelve. Three times four is twelve.
B totally understood this coming from a peer, in this case, an older brother. He will have a firm base upon which to build his mathematical education. He gets it. No workbook or textbook involved. This information now belongs to him.
A Tale of Squares and Square Roots:
J and B had heard me talking with H (six years older) about squares and square roots. The blocks were out in a teasingly accessible area, and I began to stack them in ascending order, using only perfect squares. One block, four blocks, nine blocks, sixteen blocks...
I left to prepare supper.
Later that same evening B called me to look at his blocks. "Eighty-one," he declared, "makes a square of nine." Perhaps five minutes of further instruction later, my 6 year-old had total grasp of the concept of square numbers.
I'd like to leave you with one more math story, in the hopes that I am not rambling on and boring you.
How J "Did an Algebra":
Our wonderful local Unitarian Universalist Fellowship provides free math tutoring classes for middle and high school students, which my eldest, H, was keen to attend, perhaps not for acquiring knowledge, but for social reasons. Shall we leave that for another post and concentrate on the subject at hand?
J's piano lessons happened to occur just before these math sessions H wanted to attend. So we decided we would all go together to save time and gas. H would wait quietly while J had his piano lesson, then J in turn, would sit quietly during the "big kid" math class. We did this a few weeks in a row. I assumed J, as he was quiet and scribbling constantly, was drawing cartoons, as he does in free time at home. J liked to keep a notebook just like the big kids, and I did not bother him by looking at his papers.
After about four weeks of this, on our way home from the math class, J announced, "Today, I did an algebra."
"Great. Show it to me when we get home," was my response.
At home, a great surprise awaited me. Not only had J (8) made up an algebraic equation, he had solved for x, and ended up with the correct answer.
Yes, J, you did "do an algebra."
And you showed us how wonderfully open and intelligent a child can be if we simply refrain from holding him back.