Arithmetic is the simplest part of mathematics. A preschooler learns to count things. She eventually grasps the concept of "more," as in, "Which pile has more?" or "Would you like some more?" Kids have to understand that the squiggly lines called numerals have values we call numbers. The squiggly numeral 4 has a value that's one bigger than the squiggly numeral 3. 4>3 and so on. Once you understand the values, you manipulate them, with operations like addition, subtraction, multiplication, and division. Why?
Because manipulating the values represents higher level thinking. This is what education is about. You start at the basics and progress. You can't skip a step, not in math. What you learn is built upon what you already know.
What good is it to know it, if you can't do anything with it? So we memorize math facts. 1+1=2 and so on. Wait a minute - memorization is higher level thinking? Yes and no. You understand the concept of "mom gave me one, and then one more = now I have twice as many cookies to eat" before you start to memorize. You KNOW the concept. You MEMORIZE the facts.
Memorization is not "old school." It's tried & true. I hope that next time a surgeon operates on me, he has memorized every bone and muscle in the human body. That information will come in handy as he uses his higher learning knowledge to proceed with the surgery - I don't want him Googling locations of body parts on his iPhone while the scalpel is in his other hand.
Memorizing is simple and necessary, from toddler on up. For school age kids who need to learn facts such as the times tables, I recommend flash cards. Yes, flash cards. These wonderful little pieces of paper (homemade) or full-color card stock (store bought) should sit on the table closest to the tv. What? Yeah, bear with me...
Kids do not learn to speak by having formal 2-hour lessons thrice weekly. No. They picked up vocabulary a little at a time, in tiny daily doses. So don't make them sit through 2-hour sessions of math facts. Ugh. Put the flashcards next to the tv remote. When Junior is watching cartoons, and a commercial comes on, he picks up the remote, mutes the sound, and picks up the flashcards. How many can [he/you & he] go through during the commercial break? Show back on? Put the cards down and let him go back to the show.
You can do flashcards at breakfast, in between bites of oatmeal. You can go through them after school, or have him review them while he's in the car or bus on his way home from school. Review them during tv commercials, and again at bedtime. It will be a matter of mere weeks before he has them down pat. Seriously.
He'll build on what he knows about squiggly numerals when he learns about the values of coins and bills later on. And everyone needs to know that.
What old or new techniques are you trying today?