When it comes to multiplication, it is best to just memorize all the products of two single digit numbers.
A geometric interpretation of is that it is the area of the rectangle formed by two sides of length and , respectively. So, for example, if you want to teach your nephew how to find using coins, you would make a rectangle with rows of coins. Have him count the coins to get . Another way is to show that means you have with total values. Using and again, you would have .
Unfortunately, arithmetic is not the most intuitive thing. However, mastery of it is essential to understanding any higher level math. Eventually, he will just memorize the table like pretty much everyone else does. It helps though to use those visual aids and/or to break it down into simple addition to help him understand it better, rather than just memorize it and not know why those products are correct.
This takes me back to 5th grade. My teacher was fond of walking late into class and just startnig to shout out multiplication problems - dozens of them. Our task was to realize what was going on, grab a pencil and paper, and start writing answers. She didn't do this every day, but 1-3 times a week for the entire school year.
Moral? You can talk about patterns. You can discuss methods and tricks. There really is no substitute for drill and memorization of such fundamental concepts. Also, drill and memorization WILL NOT work in an atmosphere of fear, pain, or emotional distress.
Practical Example: Driving an automobile. If you had to RE-learn how to use the brakes, every time you used the vehicle, how safe a driver would you be? Some things are so fundamentally necessary that we MUST make them second nature. There really is no way to accomplish "second nature" except repetition. In some cases we call it "muscle memory" or maybe just "memory".
Do anything and everything.
Read license plates, decode the digits, and multiply them.
Open the phone book and do the same.
Count phone poles or mile markers while on a trip. If there are 12 phone poles in a mile, how many phone poles might there be all the way to his grandfather's house 10 miles away?
There are numbers everywhere. Use ALL of them to teach and to increase familiarity.
After you give him a problem, encourage him to give you one. Go ahead and get them right. There is no need to play dumb. Make it fun! You can say it's a hard one. You may wish to encourage him to have the answer in his head before you give your answer. This should keep him from asking you to multiply 3.845*1,305.
Sometimes, you may wish to tell him you have a hard multiplication problem for him. Give him one that isn't so hard and throw a fit when he gets it right. He'll love it.
Did I mention that you should use fun rather than fear? I think I did. If he's afraid, he has to figure out that he has friends and fear is not necessary.
My views. I welcome others'.
P.S. I managed a 100% on my multiplication marks in the 5th grade. Of course, this may have been a result of my being in love with the teacher. I probably saw her coming from farther away than the other students. Just for the record, I did get over it.
There are only a very few concrete ways to get people to do what you want:
1) Force, coercion, intimidation, and enslavement.
2) Love, patience, and consistency.
These apply to adults as well as children.
I hope it is obvious that #1 is generally considered inappropriate in virtually every phase of life or state of existence (excepting maybe a penetentiary). Unfortunately, this is the only tool of the public school system (excepting teachers who care - and there are fewer of these than there used to be).
#2 clearly is the way to go, but the laws of the land may think they do not have time for it. They want improvement NOW!! (q.v. NCLB in the U.S.)
If you, somehow, do not have any particulary time pressure, you are free to use #2, but do NOT overlook the "consistency" part. Set up a time when you WILL approach mathematics. Do it EVERY time. (EVERY day might be too often except for the more casual approach suggested in my first post.) Don't lose heart. It WILL make a difference. Do not at any time think, "Okay, I tried that." As soon as you are thinking past tense on your efforts, you are done. If he still doesn't get it, ever (he moves away from home and has a nice job at McDonalds), you still can have a clear conscience. I know; it's a very small victory compared to the one you seek.