This page is a permanent link to the reply below and its nested replies. See all post replies »
ArishMell · 70-79, M
How can you have "Pre-algebra"? That's like asking a book shop to obtain a copy of a treatise on mathematics, then saying you have "pre-ordered" it - impossible, except to Doctor Who, perhaps.
One useful definition of Algebra is that it encodes in an abbreviated, general form arithmetical rules or sets of instructions to carry out certain arithmetical steps, but is not arithmetic in a numerical sense. Neither is arithmetic, algebra.
So you won't learn Algebra (and indeed most of Maths) unless you understand Arithmetic first.
To show what I mean:
[2+4] X [2+4] = 6 X 6 = 36; alternatively {2^2 + 2X2X4 + 4^2] = 4+16+16 = 36.
That is pure arithmetic. I would not call it "maths" at all unless I was being rather Pseuds' Corner about it. But..... let's look at it algebraically:
(a+b)(a+b) = [a^2 + 2ab + b^2]. Oh that SW's text-editor would allow superscripts!
That is Algebra. It encodes exactly what the above arithmetic "sum" is doing with the values 2 and 4; but gives you a rule applicable to any pairs of values.
Is Algebra harder than Arithmetic then? It should not be.
It has foxed many generations of schoolchildren by its apparently abstract nature and saying things like a=b+t. How can a=b+t? After all, you don't spell the games implement "aaa". That mystique is wrong, but may reflect how Maths text-books and teachers, teach Maths.
So Algebra may be a lot easier if you bear in mind that definition above. You can extend it to, to consider that a Formula is a just shorthand instructions to work out Something Useful - like how much emulsion you need to paint the kitchen walls, or what value capacitor to use in an electronic filter circuit.
Also as my worked example shows, you can demonstrate to yourself how it works and that you are on the right track by substituting simple numbers for the letters.
.
Your question raises another point.
Algebra is not an academic subject on its own, any more than are trigonometry or matrices or geometry or logarithms. I've seen evidence suggesting that some people try to break Maths into hermetic, separate lines of academic study, but that seems a recipe for failure by losing the all-important connections between topics.
All these and more are topics within the academic subject or science that is Mathematics. Also, each can be studied to whatever level you like, but many are mutually dependent.
Algebra goes even further. It can be taken to its own extremes, but for all practical purposes it is the language of Mathematics generally, just as ordinary numbers and operators are the language of ordinary, value-manipulating Arithmetic.
One useful definition of Algebra is that it encodes in an abbreviated, general form arithmetical rules or sets of instructions to carry out certain arithmetical steps, but is not arithmetic in a numerical sense. Neither is arithmetic, algebra.
So you won't learn Algebra (and indeed most of Maths) unless you understand Arithmetic first.
To show what I mean:
[2+4] X [2+4] = 6 X 6 = 36; alternatively {2^2 + 2X2X4 + 4^2] = 4+16+16 = 36.
That is pure arithmetic. I would not call it "maths" at all unless I was being rather Pseuds' Corner about it. But..... let's look at it algebraically:
(a+b)(a+b) = [a^2 + 2ab + b^2]. Oh that SW's text-editor would allow superscripts!
That is Algebra. It encodes exactly what the above arithmetic "sum" is doing with the values 2 and 4; but gives you a rule applicable to any pairs of values.
Is Algebra harder than Arithmetic then? It should not be.
It has foxed many generations of schoolchildren by its apparently abstract nature and saying things like a=b+t. How can a=b+t? After all, you don't spell the games implement "aaa". That mystique is wrong, but may reflect how Maths text-books and teachers, teach Maths.
So Algebra may be a lot easier if you bear in mind that definition above. You can extend it to, to consider that a Formula is a just shorthand instructions to work out Something Useful - like how much emulsion you need to paint the kitchen walls, or what value capacitor to use in an electronic filter circuit.
Also as my worked example shows, you can demonstrate to yourself how it works and that you are on the right track by substituting simple numbers for the letters.
.
Your question raises another point.
Algebra is not an academic subject on its own, any more than are trigonometry or matrices or geometry or logarithms. I've seen evidence suggesting that some people try to break Maths into hermetic, separate lines of academic study, but that seems a recipe for failure by losing the all-important connections between topics.
All these and more are topics within the academic subject or science that is Mathematics. Also, each can be studied to whatever level you like, but many are mutually dependent.
Algebra goes even further. It can be taken to its own extremes, but for all practical purposes it is the language of Mathematics generally, just as ordinary numbers and operators are the language of ordinary, value-manipulating Arithmetic.