teaching mathematical logic to children?
hello!
im doing volunteer work for a certain public school, with children aged 10-12. im was assigned to teach mathematical logic (finding patterns in a sequence of numbers, and answering "what number comes next?" kinds of things)
i've scoured the net, to find the most effective way of teaching this implicit subject. i have activity sheets, and i can demonstrate how to answer each one of them. But i want it to really be a learning experience, i want to have the children interact with the dizzying numbers on paper. is there an effective way to teach logic!? thanks!!!
i'm a college undergrad student. i'm familiar with logic, but never taught it in my life!
Mathematical logic is not about finding sequences and patterns... at least not intuitively.
Mathematical logic is based on principle and deduction... at least initially. And then applying that principle.
But math is a mental discipline. It's not only about getting answers. It teaches one to think abstractly, objectively, and logically. Not too many other subjects do that.
Looking at a sequence of numbers, it's not thinking, "Hmmm... that looks like a sequence... and the next number should be..." Please note: "It looks perpendicular" isn't accepted in a geometric proof. Logically, the first number is 1, the second number is 1, the third number is 2, the fourth number is 3, the fifth number is 5, the sixth is 8,the seventh is 13, the eighth is 21. Now, how we get the numbers in the sequence so far? (Principle). Now, there's not much chance, since they have no idea how to prove anything mathematically (deduction, induction, etc.)... you might teach them that too... based on what they know--but my guess is that most of their "proofs" will be examples. (Deduction) Now how do we get the next eight numbers? (Application).
Don't tell them the principle. Let them figure it out. Have them test their hypotheses. Give them paper, some kind of counters.
Give them a general, mathematically true statements... at least as general as you can get them to comprehend. . You don't need to blow them away with the mathematical terminology. Then apply that statement.
It's like blocks. Each block on the bottom represents the truth of a statement. Building on those statements you go up higher and higher. But take away one of those bottom blocks as untrue.. and the whole structure falls. THAT'S mathematical logic.
They need to know there's nothing magical about the characters "1," "2," "3," etc., and that they can be the same as the characters "a," "b," and "c."
They need to know that 0 added to any number gives you that number.
Then need to know that for any number they can give you, you can give them another number that when they add your number to theirs you get 0.
They need to know that 0 multiplied by any number is zero.
They need to know that 1 times any number is that number.
They need to know that for almost any number they give you, you can give them another number that when you multiply their number by yours the result will be 1.
They need to know that you can add numbers in any order.
They need to know that you can multiply numbers in any order.
There is one other property they will need to know, but you will need to be careful teaching it. I've never taught it to young kids, although they need it It's called the distributive property of multiplication over addition. a(b+c)=ab+ac for any numbers a,b, and c.
They need to know that if 5=2+3, then 2+3=5 (If a=b then b=a... the reflexive property of "=")
They need to know that if 2+3=5 and 5=1+4, then 2+3=1+4 (If a=b and b=c then a=c... the transitive property of "=")
Most of them probably know most of that anyway... but state them as principles upon which to do other stuff.
The way to make math stick is to keep using it.
They need to understand positional number notation. That way they'll understand "carrying" and "borrowing" better.
They need how to do stuff with pencil and paper. They can learn how to use a calculator and computer in another class. But they need too know that if an employer has a choice between one who can reason and think over one that relies on a calculator and computer all the time, the employer will hire the one who can reason and think... and maybe purchase the employee a computer.
Don't allow guesses. I had a mentor when I was 11 and 12. He would pose logic questions and would not allow guesses. Even if a guess was right, if I couldn't justify it, it was wrong--at least until I could prove it was right.
Kids aren't dumb. They're educational sponges. And they can soak up a lot. The problem is they traditionally don't have knowledgeable educators. To teach math one needs to KNOW math... not just a little more than the students... any more than a music teacher needs only to know what a piano looks like... or a history teacher needs only to know yesterday's date.
A "liberal arts" "education" is especially useless in math. For over 100 years teachers have been telling students, "You can't do that." In most instances, at least in my experience, what the teacher meant was, "I don't know how to do that," or "If you really want to know, see me after class (or after school) and I'll tell you. But we're not ready to discuss that in class just yet."
If they give a wrong answer, it's wrong... and you need to be able to show them why. "Nice try," doesn't cut it. It doesn't make any difference if the student is nice or or tries hard. In math "close enough" isn't.
I've taught in college, high school, and in elementary school. I was a mean old
It's neat to know that somebody really is interested in "doing it right." Thanks.
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